Foundational Metaphysics
Hello my fellow philosophers!
I have been meaning, for quite some time, to collect my thoughts on various topics into essays that can be readily deployed to others for critique (and otherwise discuss). Finally, I have produced the first of what will be many essays and would like to share it with any of you whom it may interest. I decided to begin with fundamentals and, consequently, my first essay is meant to be a discussion thereof.
First and foremost, I want to establish some ground rules for this discussion board--as my intention for this discussion is specific. Firstly, I urge respectfully that the sphere of discussion be constrained to the critique of the essay itself (which shall be provided at the end of this post); and anyone who would rather briefly discuss the broad topic without actually reading the essay (or simply doesn't contend with it) will be respectfully asked to either (1) terminate their discussion or (2) begin contending with the actual essay. Secondly, I think it is important to respect others and, therefore, this discussion board is meant as an open space to contend with the essay but while (1) respecting others and (2) genuinely attempting to iron man each other's views. Thirdly, I don't mind if people would like to converse with each other (without directly invoking me) as long as it contends with the essay in some manner.
If any of the aforementioned rules are deemed to be broken (by my discretion), then I will respectfully notify the offender and give them an opportunity to respond back.
With that being said, the last thing to note is that, for those who do invoke me, I would like to give your guys' views and critiques their respect that are due and, consequently, I may take some time before responding. Combine that with my busy schedule and slow thinking process and it could be a matter of days before I respond (or even more depending on the context of what was actually said). I just want to clarify that it is no way a reflection of "ghosting you": I will swiftly notify any offenders if I think they have violated any rules put forth hereon; so please do not take slow response times personally.
With no further ado, here is a link to the document (unfortunately I could not figure out how to attach it directly into the post):
https://doc.clickup.com/25785690/d/h/rjxau-165/bb1ef0d1c4b41c9
I hope you all enjoy!
Bob
I have been meaning, for quite some time, to collect my thoughts on various topics into essays that can be readily deployed to others for critique (and otherwise discuss). Finally, I have produced the first of what will be many essays and would like to share it with any of you whom it may interest. I decided to begin with fundamentals and, consequently, my first essay is meant to be a discussion thereof.
First and foremost, I want to establish some ground rules for this discussion board--as my intention for this discussion is specific. Firstly, I urge respectfully that the sphere of discussion be constrained to the critique of the essay itself (which shall be provided at the end of this post); and anyone who would rather briefly discuss the broad topic without actually reading the essay (or simply doesn't contend with it) will be respectfully asked to either (1) terminate their discussion or (2) begin contending with the actual essay. Secondly, I think it is important to respect others and, therefore, this discussion board is meant as an open space to contend with the essay but while (1) respecting others and (2) genuinely attempting to iron man each other's views. Thirdly, I don't mind if people would like to converse with each other (without directly invoking me) as long as it contends with the essay in some manner.
If any of the aforementioned rules are deemed to be broken (by my discretion), then I will respectfully notify the offender and give them an opportunity to respond back.
With that being said, the last thing to note is that, for those who do invoke me, I would like to give your guys' views and critiques their respect that are due and, consequently, I may take some time before responding. Combine that with my busy schedule and slow thinking process and it could be a matter of days before I respond (or even more depending on the context of what was actually said). I just want to clarify that it is no way a reflection of "ghosting you": I will swiftly notify any offenders if I think they have violated any rules put forth hereon; so please do not take slow response times personally.
With no further ado, here is a link to the document (unfortunately I could not figure out how to attach it directly into the post):
https://doc.clickup.com/25785690/d/h/rjxau-165/bb1ef0d1c4b41c9
I hope you all enjoy!
Bob
Comments (123)
Absolutely no problem! Take as much time as you want: I would imagine we both prefer substantive responses that take some time over swift, insubstantial ones. I have no doubt that you are an excellent, well-educated philosopher and, therefore, I am incredibly interested in what you make of the essay.
In terms of the question-begging, specifically as it relates to logic, I share with you in that concern and hopefully I can provide elaboration on why I don't think it is the case. For now, to keep it brief and allow you to navigate the discussion as you please, let me provide the following:
By a "logical language", I mean a formal logic (e.g., classical, intuitionist, paraconsistent, etc.) or an informal logic (which I am defining in its most general form: the attempt or practice at deriving logical thought and principles of logic outside of a formal setting). I am using "logical language" and "theory of logic" synonymously for the intents of the essay.
The proposition in the essay does not pertain to the logical axioms utilized in the examples (which would be what I was constituting as a consideration "of derivation" as opposed to the consideration of derivation of derivation--and its abstraction towards its recursive use). It is about the higher performance of derivation itself and, in the case of the essay, a proof of the principle of regulation as being a true sine qua non.
In other words, to keep this brief, the reader can most certainly reject and utilize whatever axioms they would like (or even attempt with none, at least prima facea), as the attempt to produce a logical language (i.e., formal or informal theory of logic) is only by means of the principle of regulation (as a sine qua non).
That is why I did not, to my self-assessment at least, invoke logical axioms as the grounds of any of the proof but, rather, only as an example derivation to demonstrate the proof of the sine qua non: I could have, for the sake of what I was trying to convey, utilized even the most irrational of premises (I just thought it would be harder for people to understand if I did). If there's anywhere that you deem question-begging in terms of logic, please let me know as I would love to reevaluate the essay if that is the case.
I look forward to hearing from you,
Bob
Nice to meet you my friend!
To be completely honest, I am not sure if your post was out of good faith or simply trolling. If the former, then I look forward to your assessment of the essay! If the latter, then I respectfully urge you to refrain from further trolling.
Thank you and have a great day,
Bob
Although I understand the point pertaining to the dispute amongst mathematicians over "potential" vs "actual" infinities, I am not sure how that objection relates to my essay. If you could please provide further elaboration, then that would be much appreciated.
Cheers,
Bob
But perhaps its my over powering ADHD that has me not holding my attention long enough to grasp the body of what you are building linguistically because I am confused about something,
You said "The primary purpose of this essay is a meticulous investigation of the foundation(s) of all derivation; that is, the consideration of the derivation of derivation and, subsequently, its abstraction towards a recursive utilization"
But then you go on to explain the perspective that we should have on several different semantic metaphysical concepts and tools yet not one time question if any of those tools should even be considered to actually be what they came to be?
You tell us how we should view and use and judge each of these semantic tools but once again not once question if they should be tools or if it's even possible to know if they actually are what they say they are before contemplating if they should be added into the tool belt or not
And as far as my understanding goes when you investigate something you investigate it is far down to the root core as you can which in my eyes means investigating if we should even consider it a tool if it's possible to call it a tool and if it could ever actually be what it says is before then learning how to utilize it
And lastly you touched on so many different tools and in such great depth on each one of those tools do you really expect people to do what you said? Or should I say do you think it's possible that a person can sat their tool belt down and pick up that one you just laid out in your essay? Do you think a person can remember that many new tools?, and utilize only those tools in the exact way you explained in your next essay that you write?
I'm not even sure if that's possible I don't know if anybody could remember that many methods of how to use that many tools and properly utilize them without their old habits kicking up causing them to judge things the way they're used to
Or am I just completely missing the entire boat on this one? Let me know please
Ninja'd. :cool:
There's no significant dispute that I know of. Most of us not in foundations or set theory are not concerned with "actual" infinity. I assume what you are talking about is moving backward through causation chains with no recognizable beginnings. Like backward iteration in which there is no end to the number of iterative steps, but the process is either bounded or unbounded.
Nice to meet you Cuthbert!
I have observed many discussion boards on this forum which do not exemplify what I am envisioning as a productive conversation and, therefore, I was merely, by established some rules, attempting to ensure some (what I would deem) methodological principles of discourse. My intention was not to make any commentary on the forum as a whole or to foreshadow a wave of bad actors.
I was incorrect in that judgment, although I think there are grounds to argue such (just given the one post), but that is why I simply responded to them stating that I wasnt sure what to make of it (and if it was trolling, then to stop or if it is of good faith, then I cannot wait to hear their feedback). I hope that my response was not taken with any offense: if so, then I apologize.
I am all for the idea of allowing the conversations to flow as long as they pertain to the essay (i.e., the OP). I do not see how the few rules I declared stunt any conversations, unless they are derailments. If you think that they are hindrances, then I would appreciate further elaboration on how. Nevertheless, I agree in that allowing a flow (as opposed to rigid, constant policing) is preferable and is my intention.
What exactly are you referring to by problem? A problem that majority constitute as such? What I constitute as such? The essay is meant as an articulation of the foundation(s) of my views and, hereafter, further essays will build off of it. I guess if one wanted to, they could view the problem as whether or not there are sine qua nons or not. The way I was positing the essay was more about a purpose rather than a problemand that purpose is clearly stated in the introduction. Someone can most certainly come along and hold no value in it (as I specified in the essay): I find nothing wrong with that, as this essay is for those who would like to discuss foundations in the sense that I described as a sine qua non. Is that what you are asking?
In other words, if one doesnt want to partake in such a purpose, they dont have to.
I have a couple in mind that were influential in my thinking, but they have no direct relevance to the essay: the essay is not meant to expound on the history of ideas (or the history of solutions to problems). If you have someone in mind (or some idea or solution) that you think contests with my views in the essay, then I would love to hear about them!
Bob
I apologize my friend! I honestly could not tell, but I see now that it was most certainly in good faith! With that being said, let me address your questions.
Before I can adequately respond, I would like to inquire exactly what you mean by semantic metaphysical concepts and tools? Are you saying that the essay defined terminology but yet didnt elaborate why they werent simply semantically defined differently?
If you could give me an example, then that would be appreciatedas I dont think I am quite following. Are inquiring why an in toto and in total were defined the way they were? As opposed to simply defining them differently?
The essay doesnt invoke the term tool: what exactly do you mean by that term? I am not attempting to ban its use but, rather, just wondering what exactly you are referring to?
The essay concedes that anyone can reject it; however, a sufficient proof has been established for it being true regardless of whether it is affirmed by any particular human being. Again, if you could elaborate, then that would be appreciated.
Prima facea, I think this is a different contention than the validity of the actual content of the essay. As far as I am understanding you (and correct me if I am wrong), it seems as though the entirety of the essay (and subsequent essays) could be true and yet there is still the contention that people may not be able to remember it. Is that correct?
I wouldnt say you are missing the boat, my friend! I am just not of yet completely understanding what you are conveying and thats on me.
I look forward to hearing from you,
Bob
I think there is a big enough recognition of it, for the sake of the essay, to clearly and concisely define the terminology. However, I agree that more than likely most people think of one infinity when they conceive of that concept.
In terms of infinities, heres what I mean:
infinite = limitless in content (with no specification, at this general level, of its form)
unbounded infinite = limitless in content (infinite) and unbounded in form.
bounded infinite = limitless in content (infinite) and bounded in form.
So an example of an unbounded infinite could be moving backward through causation chains with no recognizable beginnings; however, that is not the definition: it is an example of one specific defined infinite I discussed in the essay.
So, in the sense you put it here, a bounded backward iteration with no end to the number of iterative steps would be what is traditionally called an actual infinite and unbounded potentialwhich is what I was essentially noting in the essay (when defining). However, just to clarify, I am not defining an infinite nor bounded/unbounded infinities in that manner, but I could see them as less precise examples. Am I understanding you correctly?
Bob
It's simply a process that's unbounded. In math an actual infinite potential (I've never heard it called that - but I don't live in that mathematical world) is vague unless it corresponds to a cardinality. Tones-in-a-deep-freeze could go into this in a much more rigorous way.
Quoting Bob Ross
I would have guessed more precise. Give me an example from the real world of what you are talking about.
>>>I apologize my friend! I honestly could not tell, but I see now that it was most certainly in good faith! With that being said, let me address your questions.<<<
It's perfectly fine I can kind of see how it might have looked a little bit like some sarcastic narcissism so all in good faith no harm.
>>>Before I can adequately respond, I would like to inquire exactly what you mean by semantic metaphysical concepts and tools? Are you saying that the essay defined terminology but yet didnt elaborate why they werent simply semantically defined differently?<<<
I mean for example "Prima facea" would be one of them it would be a "tool" and by tool /semantic / metaphysical concept I'm just sticking labels on the same thing over and over again to try to make sure I cover the whole thing in stickers because I don't know exactly what the preferred thing to call it is but I'll call it a tool because it's something you utilize
>>>If you could give me an example, then that would be appreciatedas I dont think I am quite following. Are inquiring why an in toto and in total were defined the way they were? As opposed to simply defining them differently?<<<
Hmmm I'll try , so what I mean is that how do we know that the "tool" is even the very thing that it's name claims it to be
I realize you explain each one of them in great detail about how to use it specifically as well as its nature however we never question if that's a facade and we only think that that's its nature and we're not actually tackling the root of it because we're using fixed parameters by which we are allowed to examine it because we're allowed to examine it a certain way but what if it shouldn't exist in the first place because it's impossible for a human being to invoke that tool or even impossible for the human brain to know if something like that existed being the only one of its kind and things of that matter
An example being my personal view on time we use this concept called time or "tool" called time and according to the parameters we're told we're allowed to judge Time by it works and according to the parameters we're told to use time it works and usually we never question it because it works however I view time as just a concept that has been overlaid on an action that actually exists to make it look as if time is the thing that actually exists when it's not it's like a facade
I believe that there's change change happens to different things at different speeds and this happens in space so you could say SpaceTime but actual time linear the one that pseudoscience says eventually we'll be able to go back in time or hop to the Future in as if there's a version of us waiting somewhere in a filing cabinet to be messed with that concept called time does not exist yet it's easily usable and works in most scenarios and most people go their whole life without questioning it so that's the kind of situation I'm wondering could occur with these other tools.
>>>The essay doesnt invoke the term tool: what exactly do you mean by that term? I am not attempting to ban its use but, rather, just wondering what exactly you are referring to?<<<
Things like time is a tool the theory of gravity is a tool things of that nature the segments of your essay are discussing the mechanics of a tool I just don't have a better word to use so I'm confusing everybody using my weird bucket of random words LOL my apologies
>>>The essay concedes that anyone can reject it; however, a sufficient proof has been established for it being true regardless of whether it is affirmed by any particular human being. Again, if you could elaborate, then that would be appreciated.<<<
What I mean is there's so many steps in so many guidelines I think it's impossible for somebody to put down all their bad habits and all their good habits for that matter and use the format laid before us in this essay in its entirety I think there's too much to it too many steps I think that not only are people going to forget how to use the tool the way you said to use it but I think we're just going to revert back to our old habits when reading your next essay because your first one was so complex
I'm not even sure if that's possible I don't know if anybody could remember that many methods of how to use that many tools and properly utilize them without their old habits kicking in people just reverting back to their normal way of doing things and judging things
>>>Prima facea, I think this is a different contention than the validity of the actual content of the essay. As far as I am understanding you (and correct me if I am wrong), it seems as though the entirety of the essay (and subsequent essays) could be true and yet there is still the contention that people may not be able to remember it. Is that correct?<<<
Yes you are right they very well would be but I guess what I'm trying to say is that a person can make almost anything logically look true and be usable so long as you control what is considered to be true and how people use it
this is one of the fundamental building blocks of how cult leaders control their people is it might look illogical to everybody outside of the cult but to the people inside the cult they're only allowed to judge things a certain way and do things a certain way and as long as they stay within that framework things seem logical and they seem like they work but the moment you step out of that framework it crumbles
so in that same nature (although I don't think your essay is anything like a cult )but by in that same nature I mean that the same unrealization of something that might be there that we are not aware of
For instance the "tool" called "sine qua non"
It's easy to use and it works when used but are we actually using it properly? , Can we actually really know if a situation qualifies the use of the term "sine qua non"? How can re really know if there's no other option for a thing or situation I can we really know?
That's that kind of I'm talking about that I'm saying is not being done or at least I don't see it being done But I could be wrong
It depends entirely on what you are referring to as unbounded: content or form? For example, the set of all natural numbers is regarded as an actual infinite (what I deem in the essay a bounded infinite) because, although it is unbounded in content (i.e., theres a limitless amount of natural numbers), the form is of a set (which is a conception of natural numbers as a whole, in toto, which has bounds). I would say that an infinite is denoted by being limitless in content (with no immediate regard to its form), which I think is the only aspect that interests you (which is totally fine). If you are using infinite to denote something which is limitless in content (with no subsequent regard to its form, which would require a subdistinction of some kind), then as long as you are conceiving without which, not as an unbounded infinite negative (which you would term simply an infinite negative) that is fine. The subdistinction is still vital as the form of the infinite is important in the essay. For example, that is why it is without which, not and not without which, none. If you are able to discern that without postulating any subdistinctions of infinities, then I have no problem with that.
I have never heard of an actual infinite potential: the debate, philosophically and mathematically, is between actual and potential infinities. In other words, the valid form or forms of infinities is highly disputed, regardless of them all being limitless in content.
I think that, for you, going deeper than limitlessness is futile or maybe redundant (or extraneous maybe?). However, the distinction is prominent enough for me to deem it worthy of specification. If you are still able to understand how a sine qua non is not a bounded infinite negative (i.e., a proof of nothingness if without a conception) without positing a bounded infinite, then that is fine: I just dont see at this time how it would be beneficial to erode away that distinction.
I think we are both right in this regard, because we are anchoring precision on converse goals: I was using precision in the sense of the goal being to get to the most complete abstract of a concept (as opposed to particulars), whereas you seem to be (and correct me if I am wrong) utilizing precision in the sense of the goal being to get to the most particular of a concept (as opposed to abstract). Therefore, I meant it in the sense that my goal is not to define infinite in the sense of one particular example (of many); whereas, you seem to be thinking the converse.
The classic example is natural numbers: a full set of natural numbers is an actual infinite, whereas the continuation (in form) of natural numbers forever is a potential infinite. Another example is to take physical causation (as I believe you referenced earlier): the conception of the totality (what I would call in toto to be precise) of all physical causation is an actual infinite, whereas the conception of the continuation of some chain of physical causes/effects would be a potential infinite.
Bob
I still dont think I fully understand what you are meaning, but I think I have a better idea now: thank you for the elaboration! Let me try to clarify.
Firstly, the essay is not meant to be taken as a dogma: it is not positing sine qua nons as indubitable, irrefutable, or supreme. I dont find anything about it suggesting anything analogous to a cult, but I would be interested to hear what exactly you thought was meant dogmatically (if anything)?
Perhaps it would be beneficial if you specified one example within the essay that exemplified what you are trying to convey, as then I could do a better job at addressing your contentions.
So, for clarification, is everything constituted as a tool to you to some degree? Is that the idea?
By semantics, I usually am referring to argumentation pertaining to what underlying meanings should be attached to what words to optimize the expression of the view at hand. Are you defining it differently?
By metaphysical concept, are you referring to something that is not merely a concept?
I am not entirely following: maybe a specific example would help. All areas of inquiring must start with definitions, whether they be implicitly or explicitly defined. My essay is merely explicating those definitions to provide the utmost amount of clarity possible. If there is a definition of a term you dont think is correct, then I would be more than happy to engage in semantics about it: I just, as of yet, dont really know what terms you are contending with my essay.
A facade is when something is not of the nature one supposed it was. What about my terminology is a facade? I think they are clearly defined and justified. One can most certainly contend with those definition if they would like: maybe in toto isnt the best word for conceiving a conception as a whole? Theres nothing dogmatic about that definition: it is just for means of conveying my main message and that term was just the most suiting.
This essay is to be considered prior to ontology and epistemology. Therefore, it is not a discussion of knowledge (i.e., of whether a human brain knows X). Likewise, there isnt an assertion that there is a brain or that it is ontologically what exists as a material substance: none of which, for or against, is addressed in the essay.
Time may very well exist, ontologically, or maybe it doesnt. If the former, then it isnt necessarily a consideration of a tool, as it is possible, prima facea, that what a human utilizes as time isnt how time actually exists. I would agree though that a lot of our ever day-to-day ideas of time are typically socially constructed; but, that doesnt mean that time doesnt exist at all nor that it is completely socially constructed. I could, for example, measure only by the hour; or only by the day; or never at all; or only by means of a generic change; all of which does not prove time is holistically a facade.
Are you referring to Special Relativity vs the colloquial use of time? I dont think are should be disbanded of: theres not much use for special relativity in the laymen lives. Its contextual.
I am just not sure what about the tools of my essay are a facade or even suggest it: could you provide an example?
No worries my friend! I am trying to understand your view; however, I am just not quite following as of yet.
Firstly, I think this objection is irrelevant to whether the essay is true or not.
Secondly, this could be said of anything that surpasses any given individual in terms of their potential (or faculties of reason). Most people cant fully grasp many academic concepts, even basic math. Are they all in vain in virtue of that? I personally dont think so.
Again, my definition of true, in the essay, is not dogmatic. Within all fields of study, and even colloquially, some definition of true must be formulated. This is why I gave a very precise definition of true and false in the essay.
I think I should clarify that the principle of regulation is not by any means something enforced upon people: it is being argued as something that is always occurring. Its not that being need to be consciously aware of such a principle: it is being argued as always there.
Also, many principles are utilized all the time in the field of logic (e.g., law of noncontradiction) which are by no means dogmatic in virtue of being a law or principle.
So using it properly I would deem apart of the sphere of the next essay, which will depict the consequences of its affirmation. The purpose of the essay put forth here is a proof that it is true that it is being used as a sine qua non.
The essays purpose is to (1) endeavor exactly on that journey and (2), thereafter, prove that the principle of regulation is qualified as a sine qua non. Do you think that it isnt true?
Firstly, again, the essay is prior to knowledge in a formative, epistemic sense: so a sine qua non is not being postulated as known in any manner.
Secondly, When you ask if you could ever rule out an unknown extra option: nothing about a sine qua non determines that, in your derivation, that you could not arrive at that conclusion.
Thirdly, a proof of the principle of regulation being without which, not (i.e., an unbounded infinite negative) lies in the essay: I am not sure what about it you are specifically contending with? Is the proof invalid?
Bob
SUBTOPIC: Fundamental Issue
?? Bob Ross, et al,
Please forgive old man.
By its very nature, "Metaphysics" is a type of "thinking outside the box." The entire concept of "infinity" [(positive or negative)(bounded or unbounded)] is alien to Metaphysics. In each study, inquiry or, investigation, of that which is determined to be a Metaphysical event is explained in the portion of the outcome or product that deals with methodology.
Just my thought.
Most Respectfully,
R
Tuesday, July 12, 2022 (1)
Nice to meet you Rocco!
I apologize: I am having a hard time understanding this question. Could you please reformulate the question? What exactly are you asking (what is "the first question")?
The essay depicts one sine qua non, which is the principle of regulation; that is, as defined in the essay, "the subordinate rules cannot be affirmed and denied in accordance to the superordinate rules within the given operation of derivation". This principle is not argued, in the essay, as "unchallengeable", indisputable, irrefutable, or indubitable: it is considered, on the contrary, a sine qua non.
Sort of. Again, it is not argued in the essay as "unchallengable". Moreover, in the essay, it is directionally related in the converse manner to what you seem to be conceptualizing it as: a sine qua non is what is being related to the law/principle. The essay is not arguing for an "unchallengeable law" which, thereafter, is related to a sine qua non: the law is determined to be a sine qua non, and that is all the essay covers. Likewise, it is not argued as absolute nor necessary (although I understand one's urge to commit to that idea, it is strictly separated from the specific, narrow sphere of argumentation that the essay is supposed to cover).
We may be utilizing the term "metaphysics" differently (and that is fine!). For me, I am using in the sense of "a study of what is outside objective experience" and "a division of philosophy that is concerned with the fundamental nature of reality and being and that includes ontology, cosmology, and often epistemology". The reason I termed it "foundational metaphysics" is because the foundations are what I deemed not a matter of objective or subjective experience: it is the pinpoint, so to speak of all derivation (however, it is specifically "all" in the sense of an unbounded infinite negative as opposed to a bounded infinite void). With that being said, I am completely open to the idea that "metaphysics" is not the best term, so please correct me if you think I am wrong!
I am not sure how you derived this conclusion? Many metaphysical discussions pertain to eternity, for example, which is a infinite of some sort. I don't see how metaphysics is alienated from the discussion of infinities. Of course, I understand that certain specific infinities are out of the discussion, such as physical causation chains.
I am not entirely sure what you mean here: could you please elaborate further? I've tended to see metaphysics pertaining to the logical explanation of the overlying instantiation of the physical world. For example, platonic idealism would postulate that Universals explain the phenomena of particulars in the physical world: that is an explanation, regardless of its validity, of the overlying instantiation of the physical, particulars of the world. Is that what you understand metaphysics to be as well? Please correct me if I am wrong.
Thank you,
Bob
An example is Aristotles unmoved mover as the cause of all motion.
A close second to my principle interpretation of your essay says>analysis & derivation share important common ground to the effect that derivation is a type of analysis.
Let me assert a premise All origins are paradoxes.
Your narrative ventures into paradox.
[i]1 and 1 are identical but not indiscernible. This implies that 1 simultaneously
is/is-not itself, a paradox.[/i]
You support the above with,
It must also be regarded, briefly, that law of noncontradiction can possibly be negated by the individual at hand by means of this principle of regulation and, therefore, the principle of regulation can be regarded as the most abstract form of the law of noncontradiction.
At this point, principle of regulation has expanded its scope to encompass the super-position of QM (in cognitive mode). Importantly, in so doing, it contradicts itself super-positionally.
Now your essay seems poised to utilize higher-order logic henceforth. However, instead of this, its progress appears to snag on some basic questions.
{Infinity} bound/unbound/indeterminate are solely objects of a priori cognition. As such, they exemplify ideals along the lines of Platos Ideal Forms. I question placement of ideal objects at the foundation of metaphysics as it is supposed to examine the real, not the ideal.
Maybe you can refute some implications of my following questions.
Whats the difference between a bounded finite & a bounded infinity? I ask this question because, at one point, you say,
the content of an indefinite could possibly have bounds (thereby be finite)
This statement declares that bounding entails being finite, so how bounded infinity?
You also say,
Now, the bounded infinite noted before should be clarified as not pertaining to the content of the infinite but, rather, its form and, therefore, does not constitute as indefinite.
Is content sans form intelligible? Is there a type of form that has no boundaries? Whats an example of boundaryless form? If there can a content without boundaries, how is it differentiable from other contents? How is a set composed of boundaryless contents intelligible as a set of discrete things?
The existence of a thing = all attributes of a thing, including its content & form. In separation from each other, content & form are unintelligible.
Can you visualize content that is discrete & perceivable and without form?
Can you visualize form that is composed of nothing?
Any intelligible description of infinite volume i.e., set of infinite volume>bounded infinity is merely reification to (asymptotic) sample as infinite is a cognitive abstraction that, when paired with a boundary, signifies a paradox> the limited limitless.
Consider the set of all natural numbers. Imagine the set is a bag & the natural numbers are colored balls being thrown into the bag. This can be but an asymptotic approach to bounded infinity, as any specifiable boundary cannot hold or bind an unspecifiably large volume.
First causes, I assert, possess transcendent boundaries, which is to say, non-local boundaries. As such, these boundaries of first causes require examination by higher-order analysis.
Metaphysics necessarily concerns itself with examination of the paradoxes of non-local boundaries.
If its true that all origins have paradoxical boundaries, which is to say, all origins have non-local boundaries, then derivation from origins (sin qua nons) is trans-logical, and thus epistemic, logical & ontological disciplines are only axiomatically justified by local origins (sin qua nons).
There is a gap separating local origins from analysis_derivation to phenomena. Theories that support analysis_derivation to phenomena must rest upon unanalyzable axioms.
Axioms are the metaphysical boundaries of 3-space phenomena.
If the above is true, then analysis, in the instance of derivation from non-local origins, must be higher-order analysis, which means a multi-dimensional matrix above our 3-space matrix. This higher-order matrix is the tesseract, a 4-space matrix + time.
SUBTOPIC: Fundamental Issue
?? Bob Ross, et al,
Well, evidently I have no idea what I am doing.
[QUOTE="Bob Ross;718036"]
I apologize: I am having a hard time understanding this question. Could you please reformulate the question? What exactly are you asking (what is "the first question")?[/quote]
(COMMENT)
I thought you were opening a discussion on a focused topic. Please disregard my previous comment.
Most Respectfully,
R
Tuesday, July 12, 2022 (2)
Quoting Bob Ross
"Highly disputed" within a certain, relatively small, subset of mathematicians.
Dispute Over Infinity Divides Mathematicians
Sorry to have gotten off on this tangent. I guess I don't understand your philosophical argument. To me "derivation" means putting together certain things, and this can involve the passage of time. Hence, a kind of reverse iteration of causations.
Let me see if I can sum up your argument. sine qua non means "without which, not". Which means, "If this does not exist, this derivation cannot follow"?
As an example, A -> B. But also, C -> B. If we removed A from the derivation, we would still have C. So neither A, nor C, are a sqn. If however we had A -> D, and in the removal of A, it is no longer possible to ever derive D, we have a sqn. Does this approximate the idea fairly?
If so, this is similar to a contrapositive of derivation. Perhaps a way to view it is a bachelor is an unmarried man. The term bachelor is derived from the "unmarried man". Without an unmarried man, there can be no bachelor. A man is a bachelor if and only if he is unmarried. Being an unmarried man is the foundation of a being a bachelor. In this case, we could call "unmarried man" to be a superordinate rule. The subordinate rule would be the creation of the term "bachelor".
I think what you also wanted to note was that a superordinate rule can be a subordinate rule in relation to its previous derivation as well. So, I could look at the term "man", and note (as an example, not denoting the correctness) that some creature with an 46 chromosomes in an XY structure exist, and from there, we derive the word "man". In this case, the chromosomes would be the superordinate, while the term "man" would be the subordinate.
That being the case, we can create superordinate clauses that work, but do not negate the subordinate when removed. It is not necessary that I know of chromosomes to derive the word "man". I could note its a "human with particular reproductive anatomy". Thus while the chromosomes can be a superoridinate to man, it is not a sqn. This is simply a bounded capture of a man, but in tota, not in total.
Let me know if I'm on the right track or it needs some correction Bob!
Quoting Philosophim
Nice :smile:
I am trying to suppose that derivation has no foundation and no derivation; or that derivation cannot be abstracted; or, if it can be abstracted, it cannot be abstracted towards a utilization; or, if it can be abstracted towards a utilization, it cannot be abstracted to a specifically recursive utilization; and it may be that, even if all that can be settled, the recursive utilization may be unbounded but not infinite (like the surface of sphere) or it may be infinite but not unbounded (like the sum of a convergent series) or it may be neither infinite nor unbounded or it may not even be the kind of thing that could described as either.
I should add that whilst I'm attempting to make these suppositions, I am not succeeding well. I can't get much sense out of any of them - either supposing their truth or their falsity. So I wonder: what problems or questions are you addressing? How have other people addressed them? What difference would it make if you changed your mind and decided to deny everything that you wrote in the essay - say, there is no principle of regulation, never was and never needed to be - what difficulties would that cause for us?
Hello ucarr! I appreciate your analysis and response: let me try to respond adequately.
I would say that it depends on how you are defining first cause whether my essay is participating in that kind of business. Although it may merely be semantics, I personally dont think that a sine qua non is a first cause. To me, a or the first cause implies an arbitrary discontinuation of a chain of causation (whether that be mental or physical or what have you) at a supreme or ultimate element. This utlimate element is usually eternal, which is usually meant in an actual infinite sense (that is, a bounded infinite which has been proven in toto to exist).
For example, lets take your example:
I wouldnt constitute an unmoved mover as a sine qua non. It requires a specific derivation (with certain presumed axioms) which can be possibly omitted.
By derivation, I mean the procedure of producing conclusions. So I would agree that analysis is being utilized pretty synonymously with derivation (if I am understanding you correctly). By of derivation of derivation, I mean the analysis of derivation itself (i.e., analyzing the procedure of producing conclusions if you will).
I would like to clarify, briefly, bound vs unbounded infinities, as you seemed to a bit confused on what I meant:
So, first, I am making the distinction based off of the grounds of form vs content. Form is the boundaries of the concept. Content is what is contained in the form. Therefore, a bounded infinite is conceived in toto by means of a form with boundaries, whereas an unbounded infinite is only conceivable in total by means of a form with no boundaries. Now, you brought up a keen insight:
It depends, first and foremost, what you mean by intelligible: my immediate reaction is to say that a content sans form is not conceivable in toto, but conceivable in total. I think the issue you were running into is that you were trying conceive of an unbounded infinite implicitly in toto and, thereafter, rightfully determining that it is a contradiction in terms (which is what I also noted in the essay)(i.e., limited limitless). Therefore, I think, and correct me if I am wrong, you may be thinking only of content and form as inseparable and, to a certain extent, I would agree; however, I dont think that that negates what I am saying either (but correct me if I am wrong).
Form is like the shape, if you will, of something, whereas the content is what is actually contained therein.
So an unbounded form is not not form or sans form: it is a form that cant be conceived in toto. If a conception is of without a conception (i.e., not-A is without A), then the form of without A is nothing (0) because its content is nothing (0). The form requires some sort of content to be conceivable (other than 0, lets say) (in toto or in totalor potentially, if you will, conceived of as 0 in toto or 0 in total would suffice for all intents right now). The visualization, thus, of something composed of nothing is nothing. I dont see anything paradoxical nor contradictory about this: am I wrong?
Let me take your example to try and clarify:
In set theory, they quite literally postulate the set (i.e., {N}) of natural numbers as an actual infinite, which is considered a complete set of infinite elements (i.e., a set, formally speaking at least, is a bounded form).
Think of it this way, if one accepts the intermediate value theorem, then there is exists an actual infinite of points between two points on a graph. Therefore, the line that can be drawn by connecting those two points is said to have an actual infinite of points that compose it; however, the interesting thing is that the conception of the line itself is as a bounded form (i.e., a line which begins at one point and ends at another) but yet is said to have content (that is, is composed of) an infinite amount of points. This would be what is traditionally called an actual infinite (of which I term a bounded infinite).
The problem with your example, I think, is that we dont, unlike a line, conceive of a bag as holding, prima facea at least, an infinite amount of balls: we assume it can hold a finite amount. However, we could say that a given ball is constituted by an infinite amount of points (which would be a better example of a bounded infinite).
With that being said, let me go back to your paradoxes:
Firstly, you could, for the intents of the essay, postulate all origins are paradoxes as a superordinate rule, within the context of your derivation, and continue down that derivation to determine the exact conclusion you made: this entire process (that is, derivation itself) is still abiding by the principle of regulation and that is the main focus of the essay. My premise that 1 and 1 are identical but not indiscernible was apart of my example of derivation (which I was defining the law of identity) which a critique of that premise has no bearing (I would say) on the principle of regulation. Even if it is the case that my premise implies that 1 simultaneously is and is-not itself is a paradox, that whole procedure abided by the principle of regulation. The principle of regulation doesnt dictate what I or you think is rational but, rather, what is possible (including the very concept of possibility).
I was not meaning here to postulate a logical axiom that the principle of regulation is the law of noncontradiction, just that, abstractly, it could be regarded as similar since it disallows affirmation and denial within an incredibly specific sense. That sense is so specific that I dont honestly think it is synonymous at all with the law of noncontradiction but, to be fair, I mentioned it. If it helps you understand, then please regard the principle of regulation as completely separate from the law of noncontradiction.
I dont see how this is the case, but if you elaborate further then I can more adequately respond.
Could you please define higher-order logic? You may be right: I am just not sure specifically what you mean by it.
If you could elaborate, then that would be appreciated. At first glance, I dont think my essay is dealing with first causes nor transcendent boundaries, but it depends on how you are defining them if I would agree or disagree definitively.
Firstly, my essay is not grounding itself in objective nor subjective reality (therefore, not a consideration of 4 or 3 dimensional space). Secondly, as a side note, I dont think anything transcends human reason (not even the very concept of transcending human reason).
I look forward to hearing from you,
Bob
Absolutely no worries my friend! I think we are mutually just as confused as each other with respect to conversation. Perhaps I can clarify the purpose of this discussion board: it is to discuss the essay linked in the OP. If you would like to contend with it or give comments, then please feel free!
Bob
Not all my friend! I am just not entirely sure the relevance to the essay itself: are you contending that I ought to remove the unbounded vs bounded distinction because it is not highly disputed amongst mathematicians? Even in that case, I think they are necessary (and I elaborate further if you would like).
By derivation, I simply mean the procedure of producing conclusions. I wouldnt, for the intents of the essay, pose it as involving time (although I think a good argument can be made for it). The consideration is very narrowly scoped for the essayand purposely so. It is a consideration of foundations, and I do not consider time to be a foundation in the sense of a sine qua non. I can elaborate further if you would like. But I understand what you mean and, in terms of practicality, I would presume that kind of conception of it works very well.
Bob
Hello Philosophim! I am glad to see you again!
So without which, not is meant as an unbounded infinite negative (i.e., if not A, then an unbounded infinite of negative judgments). It is not meant to negate only one particular derivation.
A sine qua non is not denoted by being the anchor of a biconditional statement (such as D IFF A); for that could entail that it is only valid within one or a finite set of contexts. For example, its possible that A IFF D is true of context C1 but not true of context C2. That would not be a sine qua non.
It is not the contextual superordinate and subordinate relationship (of the principle of regulation) that is meant as a sine qua non: it is the principle itself. Therefore, an unmarried man would be, given your definition, a superordinate rule in that context but it would not be a sine qua non (the more abstract principle of regulation is). I am not sure if that is what you are implying there (in that case I would say it is incorrect) or if you were merely giving an example of a superordinate/subordinate context (in that case, I think it is correct).
However, to clarify, a sine qua non is not in itself a contrapositive conditional, but superordinate rules can regulate the derivation to have such (if that makes any sense).
Yes! And the very derivation of the process you just described (i.e., the defining of a word, the definitions of those words, the definition of defining, the regressive pattern, the cyclical pattern, patterns themselves, etc. can be abstracted to superordinate rules that govern the ones within the context of your example). Does that make sense?
I am not sure what you mean here: maybe I am misunderstanding you. The process of derivation is simply the production of affirmations or denials in relation to the implicit or explicit superordinate rules.
Even if chromosomes were considered essential to the given definition of man, it would not be a sine qua non: is that what you are stating here? Within the context of the given definition of man (lets say that an essential property is having chromosomes), it would follow that a man without chromosomes is a contradiction in terms. When I derived that just now (that it is a contradiction in terms) I also, subsequently, utilized superordinate rules to assert it (and that can be continually abstracted towards higher superordinate rules). I could posit that man is not defined by chromosomes or what have you, but that would be a different context. The main point here would be that chromosomes is not persisting across an unbounded infinite of contexts, even if it is essential to one. I think you may be thinking that sine qua nons are when the superordinate is in a contrapositive kind of conditional, but the sine qua non proposed is the process of all the possible contexts of superordinate and subordinate relationships.
I look forward to hearing from you,
Bob
At the beginning of the endeavor of writing the essay, that is exactly what I was wondering as well. Thats why I kind of postulate it as a purpose rather than a formal problem: nothing about the essay states that there must be sine qua nons but, rather, only that there is one that is provable. If I went into the essay trying to prove there were any, then I would be just fulfilling a bias.
I realized, to keep it brief, that even if I concluded that there was no foundation to derivation, or no derivation, it is all by means of the principle of regulation (or whatever one wants to call it).
Well, let me see if I provide my thoughts (although I may be misunderstanding you):
Not a recursive utilization: I think that the principle of regulation proves that it is. By recursion, I mean that it utilizes itself and thats as far as I can seem to go. Every step I take, every definition I utilize, every connection I make, and every conclusion I perform is inevitably regulated by superordinate and subordinate rules.
It may be unbounded but not infinite: I may just be misunderstanding you, but an unbounded finite seems like a contradiction in terms to me. Finite content entails finite form. In terms of a sphere, it depends on how you are specifically using that analogy if I would agree or disagree. For example, if I continually walk around a sphere endlessly, then that action is an unbounded infinite. The content of the sphere itself, on the other hand, is finite and therefore the bounds of the sphere is finite (it has a finite form). What exactly were you trying to explain with it? I dont see as of yet how it would be ever an unbounded finite.
Infinite but not unbounded: Things like the sums of convergent series is what I was describing in the essay as in total (as opposed to in toto) and are what I would consider the summation of an unbounded infinite. I do not think that the limit of X approaching infinity is a bounded infinite nor the summation of infinite parts. A bounded infinite would be if one were to posit, I would say, that there are an infinite amount of points in a line that connects two dots and yet the line itself is bounded in form.
Oh I see. I understand that, but the problem I am addressing is exactly that: the consideration you yourself just claimed you could suppose their truth or falsity. The question of derivation of derivation (and its abstraction towards recursive usemeaning of derivation of derivation of derivation of ): are there any sine qua nons? That is the question. Otherwise, there is simply the arbitrary.
It is really a question of whether derivation is arbitrary (i.e., axiomatic) or grounded in a sine qua non. I wasnt stipulating one as supreme over the other: I simply wanted to derive if there is. If not, then my subsequent essays would have been derived from axiomatic principles for foundations. Is that what you are asking?
Bob
Not at all. I just pop in now and then whenever math is mentioned and provide my perspective. Most in my profession are not in foundations. In the most recent 24 hour period only 1 in 58 papers submitted to ArXiv.org were in that subject (logic, set theory, etc.).
I appreciate your friendly attitude! :cool:
I asked what difficulties would be caused by denying everything you wrote - for example, supposing there never is such a thing as a principle of regulation, never has been and never need be. Does that cause a problem in any way? The answer to that might give me an idea about the value of the theory - that is, why it might be needed.
With a view towards answering the above question, I'm making an attempt to get my general bearings within your project by elaborating the overview below. Let me know if it's sufficiently accurate to be helpful.
Schematic of Foundational Metaphysics of Derivation
A scheme to establish an algorithm for expressing & establishing a causal chain of derivatives culminating in a conclusion. This algorithm will be expressed in terms of the widest generality.
Some key elements that hold priority within the scheme:
The principle of regulation
The sine qua non
Superordinate rules
Subordinate rules
{Infinite Series} bound, unbound, indeterminate
{Ground} not subjective, not objective
By convention, the derivatives are configured in accordance with the established rules of inference.
The upshot of the scheme is elaboration of a plan applicable to the entire edifice of derivation to a conclusion.
Successful execution of the scheme will, by design, entail the establishment of a foundational metaphysics of derivation to a conclusion.
This foundational algorithm will embody a logical imperative for all derivations to conclusion.
Could you clarify with an example here? When you mean infinite, do you mean "All possible derivations in total/tota"? To compare again to the bachelor, we could derive another term called a bachelum, which is an unmarried man that is about to be married. Again, we could not derive the term bachelum without the superodinate "unmarried man". As such, there are an infinite derivations we could not create without the concept of "unmarried man", many which we do not directly know or have been invented yet.
Quoting Bob Ross
Could you give an example of what you mean by context here? If it is unbounded context, I cannot see a sqn forming simply by the fact language and thinking can change. Lets look at the principle of regulation. A fine principle, but can it be proven that its a sqn in unbounded context? What if something does not think in a derivative manner? This may be due to low intellect, or simply a brain that does not process in such a way. Does a plant think in terms of the principle of regulation for example?
The problem with an unbounded infinite is we can always come up with a situation that negates another.
To your end, I believe you are implying a bounded context. For example, in individuals who have the capacity to only think in superordinate and subordinate manners, we could say the principle of regulation holds. Because people in this context have no other way of possibly thinking, it is impossible to think differently. Among creatures that had alternative thinking processes, the principle of regulation does not apply to them.
Again, please correct me where I am incorrect Bob.
Oh, I see! I would love to have a conversation about infinities (e.g., set theory) if you are interested: my knowledge of it is by no means expert level and would love to hear what you think of it. However, for this discussion board, if the discussion of infinities doesnt pertain to the essay in the OP, then I would like to respectfully ask if we could shift that discussion to occur somewhere else (that is, if you would like to continue that discussion). Feel free to DM me on this forum whenever you would like! Or maybe you would like to open up a discussion board specifically pertaining to infinities (or maybe there already is one that I am not aware of)? Otherwise, no worries.
Same to you my friend! (;
Bob
I think I understand what you are asking (but correct me if I am wrong), and, unfortunately, I anticipate that my answer will not be satisfactory. You see, for me, I consider an axiological evaluation outside the scope of the essay itself. If I were to respond with any given problem, then it would necessarily presuppose some set of values (which I am not attempting to argue for nor against in the essay): that is kind of my dilemma. In other words, a problem, to me, entails necessarily an underpinning value (e.g., if I value being well fed, then something which contradicts that, at least prima facea, may be a problem for mebut it is no problem if I reject the underpinning valuation).
It is simply an inquiry into how the process of derivation operates as opposed to critique of a derivation itself. I think it is and will be useful for my subsequent essays, but I am not arguing for its value in the essay.
With that being said, I feel like I didnt really answer your question. I think that its usefulness is found in after it is found to be true (regardless of the value of endeavoring on a such a journey in the first place). For example, albeit outside the scope of the essay, I think that the principle of derivation (being a higher order, so to speak, than derivation itselfor at least, for all intents and purposes, can be visualized that way), once it is affirmed, proves the relativist nature of any particular derivation. That will play a significant role in my epistemology, for example, which will not assert its construction as built on any absolute conclusion from my derivation (assuming I am not persuaded to change my mind by the time I start writing that essay). Maybe that will help you understand its value to some degree (or maybe not).
If that wasnt a satisfactory answer, I apologize and please feel free to grill me harder on it and I will do my best to provide something which I think isnt extending into the sphere of speculation (on my end).
Bob
Sounds good my friend: hopefully I can provide a substantive and helpful response here.
If I am understanding this title correctly, then I actually think it is a really good title! It could be thought of as a scheme of the foundations of the metaphysics of derivation (kind of a bit wordy, but I think is true nevertheless).
I wouldnt use this terminology, but I think it suffices. My concern is that it isnt quite narrow (or precise) enough; but for intents and purposes that is fine. I would say to keep the concepts very the most generic senses of the terms. For example, causal chain would be incorrect if it were to assert for or against it being physical, mental, or where this causal chain is originating from. But in the sense that there are a series, if one wills, of connectives: thats basically derivation.
If you would like to use that kind of terminology, then I think that is fine (for all intents and purposes): I will do my best to interject when I think your use deviates from what is meant by a sine qua non.
If by key elements you mean key terms being used in the essay, then I think that most of your list is fine. Except:
There is no indeterminate category proposed for infinities: it is indefinitenesswhich I wouldnt hold means the exact same thing (but if you just mean that in the sense that the bounds in undetermined, as opposed to indeterminate, then I think that is fine). For me, I am defining indeterminate as not able to be determined, whereas undetermined simply means it hasnt yet been determined.
Since you included this as an element in the list but not others (like how it is not indubitable), I feel inclined to ask if there is some sort of significance you are extrapolating from this particular claim that isnt found in the other (such as the aforementioned example)? By Ground, I am thinking of an ontic claim: is that what you mean? In that case, I am not saying it is or is not grounded in the subject or an object (or objects or what have you): I am claiming it is simply not addressed, purposely, in the essay. Attempting to argue for any sort of ontic claim, even its own ontic grounding, is beyond the scope of the essay.
By established, I would like to clarify that they can be either implicit or explicit.
By derivatives, I am thinking of conclusions produced via the process of derivation. Please correct me if that is not what you meant.
By rules of inference, I would agree if you mean the relation between superordinate and subordinate rules. They can be, for intents and purposes, thought of as inferred in the sense that they are intuited, which I mean in the sense that we dont necessary explicate them.
If I am understanding correctly: exactly!
If I am understanding correctly: yes! I would slightly refurbish to be establisment of a foundational metaphysics of derivation itself or of derivation to any given conclusion: just to clarify that it is not just a particular conclusion. That might just be knit picky though (:
I would have a problem with the use of the term, semantically speaking, logic. However, I see this as one of the potential weaknesses of the essay; that is, it could be considered a logic, but as the nth-order logic where n is actually an unbounded infinite series. You see, in that sense, it could be considered a higher-order logic (maybe thats what you meant in your previous post?), but I dont think it is constituted as a second-order or third-order logic (as it is an actually abstraction to an unbounded infinite use). If you have any ideas on this, then I would love to hear them!
Other than that, yes it is an imperative (the principle of regulation) of all derivations to a conclusion. Well said ucarr!
Bob
I want to clarify that I think you are thinking of it conversely to what I was proposing. When you say:
That proves that unmarried man is not a sine qua non, which I believe (and correct me if I am wrong) you are thinking it would prove it if theres an infinite amount of things that could be postulated without unmarried man. It isnt that if without A, theres an infinite of other things we could postulate, therefore A is a sine qua non: it is if without A, we are met with an infinite amount of negations (nots) (e.g., without A, not this, without A, not that, etc. until we realize by proof that it can be abstracted to infinity as without A, not ... if you will).
One of the reasons I made the distinction between bounded and unbounded infinities is because one (not necessarily you) may be incentivized otherwise (that is, if it is just postulated as infinity) to counter the validity of the idea of a sine qua non by means of asserting that they can conceive of and derive infinities of negations (as a concept) as without another concept. For example, one may be inclined to determine that they can categorically define that Y is without X and Y is an infinite of negations. That can most certainly postulate it, but I wanted to clarify that that is by no means a counter to the validity of a sine qua non (as an idea). You see, as I would argue, that concept of Y, valid as it is by means of derivation, is a bounded infinite because I can abstract further by questioning the grounds of that very concept of Y, thereby invalidating it as an unbounded infinite.
By context, I just loosely meant an idea that is sandboxed. So it is perfectly possible that A IFF D is only true within a sandbox, so to speak, and not true universally.
I am not entirely sure if I am understanding, but by unbounded context I am envisioning a sandbox which has no bounds in form. That seems kind of like a contradiction in terms to me: a context, by definition, has a limited form, otherwise it is not a context.
If you are trying to inquire how it can be proven sans context (i.e., unbounded context), then I can provide further detail: I continually performed abstraction to its highest point, whereat I could not longer abstract higher and, thereafter, determine what (if anything) produces the negation of those abstractions if removed (or it could be thought of as the negation of particulars too, if you will). The principle of regulation was the only thing that remained. Now, at this point in my thinking, it was not so discernible whether it was (1) an unbounded infinite, (2) a bounded infinite, or (3) indefinite.
To keep it brief, I determined it not to be #2 by virtue of the proposed definition of sine qua non the negations cannot be conceived in toto and, therefore, it is not possible to prove a in toto conception without the utilization of the principle of regulation in the first place (as a separate, out of scope of the essay, derivation). I determined it not to be #3 because the derivation of without the principle of regulation was recursive (thereby solidifying its infinite nature as opposed to be undetermined bounds in content).
Firstly, I would say that the essay is meant only to prove in relation to the subject at hand (or more modestly, me as the subject). I by no means disproved or even mentioned solipsism. However, with that being said, I think it is easily arguable that this principle extends to the vast majority of non-brain-dead human beings: the principle is observable without postulating an actual subject as the originator. In terms of low intellect, I think they still exhibit the principle, just not as rationally as we do. Even the most primitive use still counts to me.
In terms of animals, I think most would fit the bill and maybe plants. To be honest, I havent contemplated that aspect enough to give a substantive response. However, I do think, off the top of my head, plants, for example, exhibit the abidence of such a regulatory principle (e.g., a plant does make binary decisions, which does require superordinate/subordinate rules, albeit it primitive).
Maybe if you provide an example I could respond better: what about the principle of regulation do you think doesnt hold for a plant that demonstrates it reacts to its environment (which, I would argue, pretty much happens in virtue of them being aliveno?). I certainly dont think a plant would be able to affirm the principle of regulation, but I think I can affirm that they use it (which is a different claim, I would argue).
I look forward to hearing from you,
Bob
No, that wasn't my intention. What I was trying to note was there are an infinite number of things I could postulate with "unmarried man", that I could not postulate without "unmarried man". If unmarried man did not exist, then the defintions of bachelor and bachelum would not exist. Perhaps the words could still exist, but their meaning could never be "unmarried man", because "unmarried man" does not exist. If we disregard all possible synonyms for "unmarried man" in all possible contexts, would this be a sqn?
Quoting Bob Ross
I think I understand this. Words like bachelor and bachelum all rely on the concept of "unmarried man". Again, it is not the words we are really referencing, but their meaning. Without "unmarried man", any derivations from the concept of "unmarried man" cannot exist. Of course, there are a potentially infinite number of derivations we can establish from "unmarried man" that we could not without the concept of "unmarried man". From the finite springs the infinite, though this infinite is bounded by the finite superordinate.
Quoting Bob Ross
The problem I see you running into is when you note a "universal" infinite. Having worked with infinite before, its very easy to lose the real consequences of true infinity. Real infinity has no limit. Which means practically any formation within that infinite can also be negated.
Think of numbers for example. Numbers are bounded limitations within true infinity. One such measurement is discrete data versus continuous data. Continuous data is a bounded infinite, such as "height". In theory, there is no limit to how high we can measure. A discrete data point would be 5 feet high.
As noted, continuous data is still a bounded infinite. Without the context of dimension, height just dissolves into the true infinite. There are an infinite amount of potential dimensions that we can create within that true infinite. To your point, I'm noting that the rule of regulation too would dissolve into the true infinite without certain bounded contexts. If a sqn must be true universally, then it must be true in the unbounded infinite.
Quoting Bob Ross
This is still within your own bounded context. I take no objection to there existing a sqn within a bounded context. It is completely true that you thought everything you did, and could only come to one conclusion. But is that true of all contexts, of the true infinity? That has not been proven. Let me give you an example. There are some people who cannot visualize in their mind. As in, they cannot think of images like most people can. They close their eyes, and the world is completely dark for them. Think of the host of conclusions and thinking you've done with your ability to visualize in your head, and then try to imagine the conclusions one can or cannot make if they cannot visualize.
In the same manner, a personal conclusion of thought within your own bounded context does not prove a universal context. In the same manner, we can imagine a creature that can think without the rule of regulation. Its difficult for those of us who use the rule of regulation on a daily basis to imagine this, but we already know that some things think differently from ourselves. This is what I was noting earlier. If you personally think using the rule of regulation, and nothing else, then yes, its a sqn for you. But that doesn't mean its a sqn for something that does not think like you do.
Quoting Bob Ross
First, there's the idea that we're assuming our own basis of thought applies to all other thinking things. We cannot conclude that just because you and I think in the terms of the principle of regulation, that every other thinking thing does as well. All it takes is one thinking thing that does not, and then we don't have a universal sqn anymore. I'm not saying you can't come up with a universal sqn, but it must be provably true within the true infinite. I don't see the PoR doing that currently.
Second, we can speculate that a plant, or any other creature thinks with the PoR, but we have to prove that. The burden of proof is not on me within the true infinite, the burden of proof is on yourself. And even if we prove that, we must prove it for all plants of that type, then all plants, all creatures, etc. The PoR is not something provable, because it is a bounded idea that relies on certain bounded infinites thinking in a particular manner.
Now, if we have a bounded sqn, we avoid the problems noted above. That of course, brings about new problems. If sqns are bounded to contexts, which context should we choose? I think you know this, which is why you wanted to note a sqn is universal. The ultimate problem is that I believe you have not shown that the PoR is something true universally. As noted above, I'm not sure its something you can either.
That being said, it may be that there are things I still don't understand, so please correct me if I'm in error. I also think the PoR is a fine principle within bounded contexts, and see nothing overtly wrong with it within these bounded contexts. I just don't think at this time that you've provided what is needed to show it is true universally, and not just within the contexts you've been thinking in.
I differentiate indefinite from indeterminate thus, the former means not specified whereas the latter means cannot be specified.
It may lie outside the scope of your project, but I want to broach the topic of infinity as it is conceptualized by you vis-a-vis how it is conceptualized by me.
I define infinite as volume unspecifiable. This is a way of saying infinities cannot be made explicit. I believe this truth persists even in the instance of hierarchies of infinities.
If {x_?} = infinity and P = {x_?} and IFF_not = if and only if negated and if {x} = bounded set, then P ? IFF_not for {x}.
The above argument is predicated upon boundary = territorial limit.
Positing an infinite value (unspecifiable volume) within bounds is tricky because, in my opinion, territorial limit takes on a special meaning such that limit transforms into asymptote.
Perhaps curiously, an infinite value "warps" a (conceptual) boundary into a "curved space" that functions as an unspecified boundary in that it is a boundary that is never reached.
Is an unreachable boundary really a boundary?
In the instance of a bounded infinity, whose unspecifiable volume is quite free to expand forever, can we truthfully claim that it is contained?
It occurs to my visualization that a bounded infinity is a configuration wherein an unspecifiable volume has PoR as a neighbor who speaks another language and thus, there is no dialogue between the two. In this situation, can we truthfully say PoR acts as modulator of unspecifiable volume?
Quoting Philosophim
Quoting Philosophim
Quoting Philosophim
To far greater extent than Philosophim, there's much I neither know nor understand, thus I might be egregiously wrong when I use my argument above to expand Philosophim's doubt to include bounded contexts.
Having said that, I admit I do, now, have the audacity to entertain nascent doubt about the PoR's ability to modulate a bounded infinity.
Note The core logic of my argument is the following premise,
Premise the inherent unspecifiability of an infinite volume implies its expansion towards a boundary is necessarily asymptotic.
In your reply to Cuthbert's germane remarks you seem to me to have replied, (and pardon my extraction thereof what might appeal to me)
Quoting Bob Ross
My impression is that by reducing the process to what is 'true' you have already relinquished your quest in favor of strictly realist binary meta-possibilities. For example, there is no truth in science! In science true is replaced by correct or more likely or most likely the case. In most aspects of personal life the only truth is death (and not even life according to our faithful judges). If this is so given that the process is not the same as its derivations, then you might limit yourself to closed objective identity and the PNC everywhere. Since I am a radical metaphysical pluralist I hope I am wrong in this.
You are correct and this is why the form, as opposed to mere content, of an infinite is incredibly important. Lets take my Y example again: without Y, theres an infinite of postulations that cannot be proposed anymore (lets call that infinite X).
Theres two ways (pertinent to this conversation, that is) we could conceive of this X: in toto or in total. In terms of the former, it is conceived of as bounded in form (i.e., complete in form). In this case, if Y can be omitted and there are still concepts which remain intact, then Y is not a sine qua non (although without it there is X). In terms of the latter, it is conceived as without bounds in form (i.e., never complete in form) and, in this case, there must be no exception to the negations (that is, every concept is being negated).
Therefore:
It would not, because fundamentally we would have a situation where we are positing without Y, theres a bounded infinite of negative judgments. That claim is not coherent if posited as an unbounded infinite because the omission of unmarried man leaves many concepts intact.
Exactly! It is still an infinite negative judgment, and valid at that, to assert the withouts of unmarried man, but it is bounded and not unbounded. Same is true of chains of infinities, cyclical infinities, etc.: they are only conceivable by means of eroding the infinite to a bounded one (that is, by means of conceiving it in toto: complete). Its subtle, but an incredibly vital distinction (I think at least).
As you noted, continuous data (and height) is a bounded infinite; that is, must be conceived as in toto, which is not a sine qua non. I dont have any contention with the idea that, in content, we can measure height infinitely. Maybe I am misunderstanding you, as I see nothing wrong with this.
However, I want to clarify that I do not use the language of true infinite (although you certainly can), and so I am interpreting that as an infinite (which is simply defined, generically, as limitless in content, which no specification of its form). Correct me if I am misunderstanding you here.
That is what my essay is arguing for: by being a sine qua non, it is an unbounded infinite.
Whenever I even attempt to derive other contexts sans my own, it is contingent on my own. I never once escape out of my context, not even in terms of conceiving of escaping my own context. This is why the principle of regulation is an unbounded infinite (more precisely, sine qua non).
The best I can do is postulate that, via my own derivation contingent on me, that if there were a duplicate reason out there of mine (to any degree in its manifestation), then this principle would apply. But that will always be inevitably self-referencing.
If they react to their environment to any degree other than 0, then I think it is provable that it applies to them. By conclude, I mean it in the most affirmative & negative sense (affirmation and denials). Its not that they have to explicate this process of the principle of regulation or that they have the exact same faculties of consciousness as me: its that their conclusions are regulated by this very principle.
I cannot think of a creature that can think without utilizing (implictly at least) superordinate and subordinate rules. I can conceptually the omission of the concept of principle of regulation from my mind and attempting, thereafter, to derive what is left, but that inevitably utilizes it. If you can conceive of such a thing without its utilization, then I would be genuinely interested to hear more! How are you able to do that?
I will say that my approach, or argument, is that it regulates me and all human beings (and most likely creatures) that exhibit any form of life. Prima facea, I can trick myself into thinking sans my context to see what someone who wasnt constrained to PoR would exist as, but that inevitably utilizes it as well! If there is a way to break the cycle, I would love to hear about it!
So, I guess, it depends on what you mean by universal. I cannot constitute it as not universal (in virtue of being my context) because sans my context is still contingent on PoR for me. Furthermore, I could postulate an if conditional of how it would be for an individual who didnt have such a regulatory principle guiding their derivation, but that, again, is contingent on it.
Perhaps you have found the root dilemma of my essay!
I do want to clarify that I am able to derive other contexts sans me, but what do I mean by me? Can I posit a context sans PoR? No, and that is my point.
I would ask, in light of what I previously stated, for you elaborate on how you are able to omit the PoR when deriving conclusions of its omission. I would like to know how it is not recursively utilized therein. If you can demonstrate that, then that would be really helpful for me!
All derivation is subsumed under this principle for me, as a subject, and thus nothing escapes it (not even that idea of escaping). Therefore, it really is an unbounded infinite, universal if you will, but maybe I am missing something. Maybe it is possible to conceive of its omission without recursively utilize the principle itself: but, yet again, I just used it to postulate that possibility. Maybe you mean something entirely different than me by universal?
If this is the case, I would love to know how. I wouldnt say I am in agreement with you: I think it is proven to be universal, but I could be wrong as always!
Bob
I think I understand. Basically (and correct me if I am wrong), an infinite within bounds actually simply approaches the limit as opposed to actually reaching it. So, for you, I would image that the contents of a line connecting two dots does not actually reach the two endpoints: it approaches them infinitely. Is that correct?
I think, if that is what you are saying, then this objection makes sense (in those terms as you proposed):
To me, this still produces the same in toto claim (that is, a complete infinity): even if it asymptotes, every single point within the infinite of points of the finite line exists. For every possible point, it exists between the two dots on the line and the two endpoint dots exist for the line: therefore, the concept can be thought of as in toto (that is, complete, which is an encapsulation within a finite).
To be honest, I actually think that you are right, as you are discussing the rightful method of conceiving of a bounded infinite (I would say): the infinite content quite literally does approach as opposed to arrive at the ends. If it reached the endpoints of the line, then it wouldnt have an infinite content.
Assuming I am not misrepresenting your view (which please correct me if I am), I would like to clarify that a bounded infinite is just like that line connecting two dots: theres a form that is conceivable in a finite concept (i.e., the line from point X to point Y), but the content quite literally is infinite and, therefore, the points approach the endpoints which actually achieves a complete concept when combined with the endpoints themselves (i.e., an infinite approaching, asymptoting at by endpoints + the endpoints themselves is conceivable as a complete concept).
By unbounded, I meant that it cannot be conceived of as this sort of complete, in toto, concept: try to imagine a line that just continued forever and, with respects to its ends, never ended a particular point. For all intents and purposes, that would be unbounded in form and that cannot be conceived of as in toto. The best I can do is formulate its in total by means of a summation of its parts (potentially, that is, depending on what the parts are).
I am sorry, I dont quite follow what you are asking here: could you please elaborate further? What do you mean by neighbor? PoR, as I was postulating it, is, as opposed to a kin to, a unbounded infinite (or unspecificable volume that cannot be conceived in toto).
I honestly have no problem with this premise: I think you are misled to a wrong conclusion by it though. A infinite volume that asymptotes as two finite endpoints is a bounded infinite, as it can be conceived in toto. I might just be misunderstanding you thought, so please correct me where I am wrong!
In terms of Philosophims argument, I think it reveals a more fundamental dispute I will have to contend with: is it possible to extend this beyond the sphere of my individual context. I think it has been proven to be true, but theres much to discuss (so I could be wrong). The problem, I think, is that one is perfectly capable of omitting themselves (i.e., their context) to see what remains and, thereby, if it is constrained to my context then that is self-defeating. However, I think it is a facade of sorts: one cannot actually conceive of sans themselves (in sense of derivation). When someone validly conceives of someone elses context sans their own, this is all contingent on their derivation and does not transcend themselves whatsoever (I would argue). If you would like to discuss Philosophims objection as well, I would be more than happy too! I will leave it there for now and let you navigate where you would like to go from here.
Bob
Nice to meet you magritte!
For clarification, are you saying that defining what true I have thereby restricted myself to some set of realist binary (so true or false) meta-possibilities? By binary meta-possibilities, do you mean that I am rejecting non-binary ones (e.g., like fuzzy logic)? By meta-possibility, what exactly are you referring to?
I have no problem with using cogency as opposed to an absolute truth in relation to derivation and the conclusion produced therefrom (if that is what you are getting at: I am not too sure yet). But then we need to define what you mean by true? I do not mean it in an absolute sense at all.
Can you define truth for me (in terms of what you mean)? I was anticipating you would have claimed the opposite, as death is an induction and thusly more likely the case.
The principle of regulation by no means necessitates the principle of noncontradiction. Furthermore, I would argue that process of the performance of derivation abides by the principle of regulation but, more importantly, not that the performance of derivation is always exactly the same. One person could use PNC, another could not. Nothing about my essay favors either one (at least that I am aware of).
I may just be misunderstanding you, so please feel free to correct me!
I am by no means an expert on metaphysical pluralism, so if you could elaborate a bit on what you mean that would be much appreciated!
Bob
Tones-in-a-deep-freeze is more an expert in this area. I'm from the generation of naive set theory. Your use of infinite is a philosophical excursion beyond my experience.
Quoting ucarr
The set [0,1] is uncountably infinite with no asymptotes. Clueless what you mean.
Quoting ucarr
Give an example, please.
I fail to see where any of this is going. I got lost somewhere around a principle of regulation. Some time back Philosophim gave a short but clear example of where he thought this was going. Bob, I recommend you do the same.
Oh I see: no worries my friend!
There is an example in the essay which I think explains it well: did you find it to be confusing as well?
Bob
Sorry, Bob. See if you can parallel what he did in a short paragraph. A clear example with less abstraction. Give a clear example of the principle of regulation as well. Or just ignore me and continue on - I would not take offense. :smile:
That said, such risky ventures are not without precedent - Gödel used a spin-off of the liar sentence to torpedo Whithead & Russel (vide Gödel's incompleteness theorems).
Nevertheless, from the posts I read, the OP gets points for being systematic, a quality that I respect (a lot). Bonam Fortunam OP.
P.S. A quick question: Why, o why [math]\infty[/math]?
Thank you for your reply Bob, I believe I'm beginning to see what you're going for more clearly. First, lets cover what I mean by the true infinite versus the bounded infinite. Lets look at the true infinite as all possible numbers. Within that infinite, you can have bounded infinites. For example, all numbers that end on the tenth's place is a bounded infinite within the true infinite. A bind is a limit. To speak of an unbounded infinite, is to speak to something without limits.
Within the infinite, I can create many bound ways of comparing numbers. I can create bounded ways of adding, substracting, etc. But does the negation of one of these comparisons negate the true infinity of numbers? No. But if we think about numbers for a second, we realize they are bounds as well. Each "number" is a bounded concept. So we get rid of numbers as well, and we are finally left with true infinity.
When you say a sqn is needed, because without it an unbounded infinity is negated, I'm not sure that's possible. The unbounded infinite is a total, and we can only represent it with a toto, or a bounds of some kind. For the most basic of bounds, we create a number, 1. To your principle of regulation, we can then create the number 2 as a subordinate to the idea that its a 1 and a 1 together. Is there a superordinate to 1? I'm not sure.
The point though, is that all ideas are bounded within unbounded infinity. Unbounded infinity is the stream from which all identities and relations are pulled from. Unbounded infinity is where all bounded infinities are created. An unbounded infinity is something we can never understand in total, but only in toto as well.
So when you declare a sqn is that without it, unbounded infinity cannot exist, it something that I'm not sure can ever be proven. The best you can do is use bounded infinity. But at that point, that seems to defeat the purpose of the sqn. The best we can do is re-create our "bachelor" example repeated among several different contexts. The PoR is no exception.
Quoting Bob Ross
Being in bounded infinites is not a bad thing however, as I believe its the only way we can have concepts. Perhaps we can simply reform your idea into, "A sqn is what is needed for concepts to exist." Basically try to find what is logically necessary for concepts to occur.
The PoR is a logical way of relating concepts. But can a being have a concept without conceiving of superordinate and subordinate concepts? Yes, we can prove this. To have a subordinate or superordinate concept, one must have two concepts. By the nature of a concept being a derivation, one must be formed before the other. If one cannot conceive of a single concept without the PoR, how does one conceive of the first concept?
One must conceive of that first concept prior to the second according to the PoR. That means one must be able to conceive of a concept without the PoR, because prior to the first concept, one has no concepts. If one can conceive of a concept prior to the PoR, than the PoR is not necessary to conceive of concepts. If this is the case, one could also conceive of a second concept that had no relation to the first concept. The ability to create concepts does not necessarily mean one will create derivated concepts, or use the PoR.
Thus we've shown that while the PoR is a way to view derivation itself, it is not necessary to hold or create concepts. Meaning that the PoR cannot be a sqn as the idea of "concepts" itself can still be conceived without it.
Overall, I think the true problem is trying to include unbounded infinity. Perhaps there is a sqn for unbounded infinity, but I don't think the PoR is it.
SUBTOPIC: Fundamental Issue
?? Agent Smith, et al,
(COMMENT)
The concept of that which is boundless, with no beginning and no end, that which is beyond the termination of any set, or larger than anything imaginable (?) is not all that controversial.
If one either argues for the belief in a deity or against a deity, one must have some idea as to what "infinity" means. The degree of that understanding is altogether different.
(COMMENT)
Acknowledging a presentation that is assembled as a coherent body of ideas or principles ? even that which is considered a balanced equation, is what it is... Once you grasp that a "Fibonacci Sequence" has the same number of elements in its set as does the "Set of All Numbers" THEN you begin to understand "infinity."
(COMMENT)
Certainly, both the set of all physical laws of the universe ? and the set of all that is beyond the limits in the physical laws of the universe ? are the same in size and magnitude.
Most Respectfully,
R
Saturday, July 16, 2022
Felicitations Rocco Rosano. Great to see you're still alive & well!
To get straight to the point, I'd like to bring up for discussion two kinds/types/varieties/strains of ideas (using an entomological analogy):
1. Instar ideas (immature/half-formed): Infinity is one such; we have a very rudimentary understanding of what it is despite the fanfare and celebrations of the early 1900s. I wouldn't recommend it as a foundation for any thesis.
2. Imago ideas (mature/fully-formed): Think of one and post it. One example is the concept of numbers as abstractions of "similar" sets.
This seems arguably non-mathematical. "all numbers that end . . ." is still unbounded in the traditional sense. If, on the other hand, you mean positive numbers less than or equal to 1, this set contains 10 elements. I think the real problem here is in not using existing math concepts for infinities, boundedness and unboundedness The notions of things being derived from preceding things and participating in further derivations, some of those preceding things being essential and others not, is pretty simple.
I admit, I did not read the entire essay. :sad:
Note: had to correct myself. Easy to put foot in mouth.
Regarding {0,1} graph {x = 0.1 + 0.01 + 0.001 + 0.0001 + 0 nth.1 < 1}.
Above is my attempt to show a counting series from 0 towards 1 for values of x that graphs as an asymptotic progression.
The gravitational force of an infinite volume curves its own graphic progression to such an extreme it never achieves escape velocity to the next whole integer.
An asymptotic relationship requires a function g(x) where Lim f(x)/g(x) =1 as x becomes infinite. Or something similar.
Quoting ucarr
A reference for this would help an awful lot. :roll:
I must concede that, at this time, I do not have readily available a short and simple explanation for the principle of regulation (that doesnt erode some of the meaning thereby). However, with that being said, let me attempt to give you a brief, overly-simplified example.
Imagine I were to postulate that A is true wherein A is a statement (whatever you would like it to be, lets say). A is true is the affirmation that A is true. This affirmation abides inevitably by superordinate rules (that is, it could not have been affirmed otherwise by the utilization of other implicit, in this case, principles that are affirmed). Lets say, for example, I were to postulate that my affirmation of A is true (i.e., A being true) by means of mere whim (i.e., completely arbitrary and baselessjust a random thought that manifested in my mind). Now, that justification can be the shifted focus: I affirmed that the affirmation of A is true is by means of mere whim. This postulation, likewise, inevitably abides by superordinate rules, of which I can explicate (or simply move on and thereby they remain implicit). I can do this forever.
I want to emphasize that the above example is incredibly over-simplified, but let me know if that at least partially helps you understand. If not, I can try again.
Bob
Nice to meet you Agent Smith!
I understand that many fields of study are still of yet formulating the behavior and kinds of infinite (e.g., mathematics), but I dont see its controversy with respect to the essay: could you please elaborate specifically on what within the essay is controversial (with respect to its use of infinities)?
I appreciate that my friend! If you could please elaborate on your contention with its grounding in an unbounded infinite, then I would love to explore that issue.
Bob
Although that is fine if you would like to use that kind of distinction, I would like to note that that is not what a bounded infinite is defined as in the essay. All possible numbers would be, with respect to the essay, a bounded infinite. I can abstract, for example, its contingency on distinction which thereby erodes it to a bounded infinite (i.e., conceived in toto); for I cannot posit the omission of that hypothetically unbounded infinite of possible numbers without conceiving it as in toto, of which its omission is entirely possible if everything was oneness. Thats just one example of many principles that it presupposes. Perhaps my essay, on that section, was misleadingas I did mention that the regards of postulating natural numbers can be possibly either unbounded or bounded, but what I was meaning to say is that it has no direct relevance to the point I was making therein (i.e., in toto vs in total). Maybe I should refurbish that paragraph if you think it was misleading.
Again, I would argue that the concept of all possible numbers as an unbounded infinite can only occur by means of the misapprehension of thinking it is such while actually conceiving it in toto. The idea of an unbounded infinite of possible numbers is contingent on many principles and faculties of reason (e.g., possibility, necessity, spatiotemporality, etc.).
Now, to your point I think, it is entirely possible to posit hierarchical structured infinities. For example, you and I can most certainly posit a bounded infinite wherein each element contains a bounded infinite and so on. I could postulate that there is a contingency structure (wherein the lower is contingent on the higher) that looks like so:
{All possible numbers}
{n + 1, } {n + 2, } {n + 3, } etc.
The infinite sets of the iteration over each possible number + 1, + 2, +3, etc. is, as you said, contingent on the concept of there being an infinite set of possible numbers; however, this is a bounded infinite of bounded infinities: any permutation you choose, I would argue, is boundedwhich I dont think we are agreeing on as of yet.
By true infinite, I think you are talking about something entirely different than me, but I could be wrong.
This is where it gets incredibly subtle, but equally incredibly vital: it is not without it an unbounded infinity is negated but, rather, without it there are an unbounded infinite of negations. Sounds kind of like the same thing, doesnt it? I agree, but yet they are entirely different ideas.
In terms of the former (your version), I would have no choice but to concede that a sine qua non is simply a misapprehension; that is, not an unbounded infinite is to necessary conceive of it in toto to thereby flip its affirmation into a denial (i.e., negation): therefore, it would be nothing more than the masking of a bounded infinite under the name of an unbounded infinite. However, in terms of the latter (my version), it is simply the negation, sequentially, of everything (i.e., not , not not { }). I think this is potentially where you may be misstepping (or I may be simply incorrect).
It is entirely possible to declare a particular derivation complete; that is, that it has been sufficiently justified and, therefore, can be put to rest. This doesnt negate the principle of regulations truth: that assertion (i.e., that it has been sufficiently justified) is yet another conclusion which utilized the principle of regulation. This then can be further abstract to question its validity, which inevitably utilizes PoR. Likewise, it is entirely possible for it to remain implicit, which still utilizes PoR.
So, whether 1 has a superordinate or not, in the sense that you are asking, I think has not relevance PoR directly: you can posit whatever you want, which will be via PoR.
Although I think this may be just that we are defining the terms differently, I want to clarify that the essay proposes the converse: a unbounded infinite is never understood in toto, but can be in total.
This is not, if I am understanding you correctly, what the essay defines as a sine qua non. To omit something is to thereby conceive of it in toto (as opposed to in total). So if you try to omit an unbounded infinity by any means it is thereby eroded to in toto. One cannot without a unbounded infinite, I dont think at least.
Unfortunately, that would defeat the point of the essay, as that is not a foundation (unless we speaking of contextual foundations). Likewise, a sine qua non is not deriving what is necessary for concept to occur, as that is within the sphere of critique of derivation (as opposed to its higher form of performance of derivation). Also, existence, to me, oversteps the bounds of the essay, as I am not trying to get into ontology therein.
This would be true if the principle of regulation pertained soley to explicated superordinate and subordinate rules. Its quite literally being postulated as an unbounded infinite of such. One can most certainly conclude something without explicating or even understanding how they were able to do so. Furthermore, all concepts are derived (that is, produced from the process of derivation): I am not positing that one can only formulate derivated concepts.
It cannot be conceived without its implicit use. However, it can most certainly be something the individual at hand has no clue about; nevertheless, concepts cannot be conceived without the principle of regulation.
Bob
There's no reference for my line above. It was produced by my act of imagination that attempts to parallel your elaboration of asymptotic relationship in line one above with Einstein's General Relativity. I'm trying to say that infinite volume, like infinite gravitational field, warps neighboring spacetime (in this metaphor spacetime = the number line) into a field so curved neighboring objects cannot achieve escape velocity from its grasp. "Material" evidence of this warpage herein is the asymptotic graph of numerical progression rendered as "curved numbers."
Re: g(x) where Lim f(x)/g(x) =1 as x becomes infinite. Let's suppose this to be numerical time dilation, with the progression of the value towards infinity being "time." This numerical dilation grounds an intentional maneuver that makes an equation start rendering an infinite value. We might think of this maneuver as the act of dropping a graviton into an equation in order to intentionally make it go infinite.
Foraging around for an application of the numerical graviton maneuver, I come up with using the graviton maneuver to effect a numerical time dilation that facilitates topological examination of boundary equations for First Causes.
Note -- Curved numbers have some type of relationship to imaginary numbers. I sense this because imaginary numbers, being displaced from the set of real numbers, exhibit something in common with curved numbers, extreme warpage.
If someone can further distill this relationship into clarity, I trust it will prove to be mathematically lucrative.
Being new to the game of philosophy, I could, of course, be way off the mark.
Muchas gracias señor!
@Bob Ross [math]\uparrow[/math]
Same question: Why does metaphysics tend to have foundations that use [math]\infty[/math]?
Thanks. It's a matter of chains of encompassing superordinate categories with possible overlaps, I suppose. If so, I can see where you deal with infinities.
superordinate category
Thanks.
To be honest, I think this is an entirely separate question from the essay, as you are questioning the entirety of the branch of metaphysics: which is not addressed therein. Honestly, I cannot authoritatively assert why, in a generic sense, philosophers have posited countless formulations of limitless foundations for their views; but I can state that any other form of "foundation", with regards specifically to the provided essay, would simply not be a foundation. A limited foundation, to me, begs the question of its further, higher abstraction--unless, that is, it is posited as axiomatic or arbitrary (or something similar), which, in that case, it simply is conceded as not foundational in the sense the essay is contending with.
With respect to your other post:
I don't honestly think that the proposed sense of an unbounded infinite in the essay is a grounding in ignorance. If you could specify exactly what about a sine qua non is problematic to you, then I would be able to respond more adequately.
Also, I would like to note that nothing within the essay is based on knowledge (and, moreover, the essay explicitly states that): it is ascertainment, which is defined very precisely therein. There's no epistemic consideration, in a formative sense, as the essay's sphere of discourse is meant of that which precedes the formulation thereof.
Bob
If I am understanding you correctly, then, as a simplification, yes. With respect to the image you linked, the all encompassing circle would be the superordinate and the smaller ones within would be subordinate. Now, imagine that contextual relation continued forever.
Bob
And complicated by the fact that different contexts could mean different superordinate circles.
If by "complicated" you merely mean that it is more complex than the provided illustration, then I agree.
Bob
Ok so you have all of these things tools whatever you want to call them for simplistic speediness of referencing sake that way I don't have to elaborate on each individual one let's just call a tool like for instance your wrench is a "sine qua non"
Or any one of the other things you pointed out and explained
So with that said everybody's got their tool belt on that you laid out in detail ready for the next essay to arrive for us to then use our tool belt on to work out whatever that essay is talking about
But my question is even though we can use these tools do they actually exist in the sense that it's possible to even have a tool that is what it says it is?
The one that's on the top of my head is the tool called "sine qua non" is it even possible to know a sine qua non? I know it's easy to say that something could be a sine qua non but are we even capable of knowing something like that can even exist there's so many variables in the world so many possibilities for things so much information that one person cannot know so then to say something like something is a
sine qua non seems to be stating something that is impossible to actually know if it really is a sine qua non or not
So my question is why don't we question if these tools can actually truly exist or if we're just pretending that they exist
By tool I am understanding you to mean a means to an end. Correct me if I am wrong, but, for the intents of my response here, I will be assuming that definition.
If by this you mean that the subsequent essay(s) will utilize the concepts explained in the antecedent essay(s), then I agree.
Can you please elaborate on what you mean by actually exist? For example, if you mean to question whether there is a sine qua non that exists outside of my body (or what have you), then I would say that the essay doesnt argue for or against it: theres no objective vs subjective consideration as such is only via the principle of regulation and, therefore, it holds its rightful place in a subsequent essay.
Likewise, can you please elaborate on what you are referring to by have a tool that is what it says it is? The concepts within the essay are defined concisely and precisely, so I am imagining you are more contending with where (if anywhere) they exist (in an ontic sense). Is that correct?
To be incredibly precise with my terminology, as it relates to specifically the essay put forth, it was proven to be ascertained but purposely and explicitly not known (in an epistemic sense); that is, epistemology is not something which is constructed within the essay as that is out of the sphere of that essays jurisdiction, so to speak.
Whether a sine qua non can be known depends entirely on its reevaluation via the individuals accepted epistemology, which has no bearing on what was being proved in the essay.
Again, I would need further, more precise elaboration on what you mean here. Are you questioning whether there is a sine qua non in the outer world? What exactly do you mean? A sine qua non is defined precisely and the principle of regulation is proven to be true in the essay. In another essay, I will demonstrate, given more than likely a set of axioms, that the principle of regulation resides within reason of a given subject, contrary to being grounded in an object, but that is beyond the scope of the current essay in the OP. Is that the realm of discourse in which you are contending?
The essay is meant to prove its truth, not prove that we ought to pretend it is true. If you dont think that was adequately proven, please elaborate further on what exactly was inadequate about it. Furthermore, existence (in an ontic sense) is out of the scope of the essay; however, feel free to continue to utilize it to convey your contentions and I will do my best to respond.
Bob
I can't speak for Mayael but I can say how I understood his questions. By 'tools that actually exist' I understood the question to mean the same as I asked. Let's suppose that everything you wrote is the exact opposite of the truth. Let every sentence be negated. Let the principle of regulation be rejected and let sine qua nons go back to being what they were before. If we do that, what has been lost? What problems would that create for us? Is the whole thing a chimera, an airy nothing - a non-existent - a pretence? I am putting the matter more starkly - rudely - than Mayael - who in any case may not have had quite that in mind. So, for what it's worth.
By "a tool that is what it says it is" I understood to mean use of language with clear sense and purpose and without equivocation or confusion. For example:
Quoting Bob Ross
'Ontic' means 'related to existence' and there is no special ontic sense of the word 'existence'. Ontic existence is a kind of existence only in the way that canine dogs are a variety of dog. It's about not chucking in technical terms that lack technique - tools that don't work - or don't exist. Again, I'm not speaking for Mayael but it's my interpretation.
With my scant knowledge of philosophy (or metaphysics) I can't tell whether Bob is out on the cutting edge or is being cleverly deceptive, ala Sokal affair. Has he taken simple ideas of generational derivations and convoluted them on purpose, or am I just failing to appreciate his insight?
Whatever. He has stirred up a conversation. :cool:
I can see how your contention is similar to Mayaels; however, I have not understood, as of yet, Mayael to be making your contention (but I could be wrong). Thus far, I need further clarification from Mayael to help me understand what they are precisely trying to convey.
In terms of your contention, if you could please review my response here, then that would be much appreciated. Perhaps you did respond and I simply missed it?
Please feel free to refer me to your response if that is the case; otherwise, I would love to continue our conversation if you could provide a response to mine.
As far as I have comprehended, Mayael is speaking much more broadly than use of language as a tool: it seems as though, although again I could be wrong, they are speaking in terms of a means to an end. However, Mayael can most certainly provide an alternative definition if I am misunderstanding here.
Let me clarify what I meant by ontic.
Language is utilized most definitely not used in one universal contextual sense and the most generic subdivision is colloquial vs formative usages of languages: by the former I mean a looser, but adequate for everyday life, use of a term, whereas the latter is a highly specialized and precise definition for the branch of study (or even particularized further if you will) meant for the formation of new ideas (or critiques or what have you of existing ideas within that given field). A word can quite literally be the exact same and be posited in an utterly different manners depending on the context (and each within their own rights and proper justifications).
By ontic, I do not merely mean related to existence, I mean something related to ontology--which is a branch of study pertaining to what really exists. It is, as I was utilizing it, quite literally a contextual usage that is not within the realm of colloquial use (i.e., it is within a formative sense). For example, I may proclaim to my friends, at a casual gathering, that this cup I am holding exists and everyone , unless it is a highly philosophical moment, will know exactly what I am referring toas I am merely deploying the term exists in a loose, colloquial sense (and that is totally fine). However, that was not an ontic claim, whereas if I were to claim that noumenon, one substance, one will, etc., then that would be. Ontology is about what really exists as opposed to a looser, colloquial use of the term (which usually is deployed to merely depict something resides outside of imagination or what have you). Therefore, that is why I was asking for clarification and I can assure you it is no pointless, superfluous invocation of fancy terminology.
Bob
Although I may be misunderstanding, I am slowly extrapolating that you may be refraining from voicing your full concerns (pertaining to the essay) because you are not vastly knowledgeable in metaphysics: my friend, I want to clarify that I would nevertheless love to hear your contentionsregardless of your knowledge on the subject at hand. If you dont want to, then that is completely fine as well though.
On a separate note, I can assure you that my intention is not even in the slightest to convolute a simple idea; however, if you think that is the case, then I would love to hear why! I think, with respect to the essay, it is incredibly easy to deviate from the intentions of it and, therefore, I am doing my best to be as precise as I possibly can. I think for some it is being interpreted as mere whimsical, superfluous verbiage that means arguably less than nothing, but I can assure that that is not my intention and, consequently, I am genuinely interested to hear everyones contentions.
Bob
So your cup exists but it does not really exist. It exists in a colloquial sense but not in an ontic sense.
The ontic sense is clarified by adding italicised 'really' to 'exists'. But this does not seem to add anything to the sense. I'm writing this post. Am I really writing this post? If I'm writing it, then I'm really writing it. If I'm really writing it, then I'm writing it. 'Really' is an intensifier, adding to emphasis, but not to sense.
Quoting Bob Ross
Thank you, I did see your response to my questions. At the risk of summarising inadequately, you seem to be saying 'wait and see how I use these concepts to make an argument in a future essay.' Fair enough. You have laid out the tools. Are they useful tools? What did you create them in order to achieve? Are they valid - do they exist? What questions or problems are you trying to address - what task did you create the tools for? You seem to be looking for validation that they are good, useful tools. I am sorry that I can get little sense out of the one you emphasise most. The principle of regulation as formulated seems not to have a clear meaning.
I asked whether this principle can be denied or asserted with equal consequence. Suppose I say - hang on, the opposite is the case - what difficulties would that create for me, what absurdities or contradictions would it land me in? In short, what problem does the principle of regulation solve?
You said it more precise than I'm capable of formulating
Like you were saying this entire essay in subsequent essays might work under the rules established in the original essay and everything might function perfectly fine but like you said how do we know that it's real beyond the confinements of the essay itself like you said if we take the essay and throw it away what are we left with how does it affect other things because although it might function the way it says it will function within the essay does it actually function that way in the real world or is it just a mirage
And kudos to Bob for being so patient with us he truly has a virtuous personality LOL it's like a single daycare worker working overtime by themself with a room full of 3-year-old brats that their parents forgot to pick up from school and somehow in the midst of this he remains calm if that ain't zin then I don't know what is LOL
Let's say there are two kids playing with their bicycles one kid does this cool stunt going really really fast totally impresses the other kid so when they go to school the other kid is bragging about his friend and how fast he was and says he's the fastest bicycle rider in the world now when other kids hear this they want to test him so they go out and have a little competition and he beats all of them
now does that mean he's the fastest bicycle in the world?
No not hardly however saying he's the fastest bicycle in the world is an easy thing to say and testing it it seems to be proven to be true according to their limited understanding and resources however fundamentally speaking or from a big picture standpoint it's not in the slightest bit
and accurate statement to make despite the fact it very well could be true it's most likely not for many reasons but that doesn't matter because to those kids the phrase is easy to say and the tests prove it to be true according to their limited perspective
Likewise why aren't we questioning if that is in fact what is happening with the things presented in your original essay?
I believe you answered this and you replied to me saying that that was beyond the scope of this essay which is fine if that's the case but my question is why?
Me personally I tend not to waste my time with things that aren't as true as possibly can be and I don't find interest in exercising my brain with exercises that don't actually reflect a bigger picture usability and only work within the scope of their intended use because I feel like that can create bad habits and or give a person a false sense of reality kind of like playing video games too much makes you less sociable with people because it's not a good representation of actual reality likewise I only entertain things that are as real as can be
I'm not saying I'm judging your essay by any means in a negative way I understand people like to do mental exercises for various reasons and that's totally cool I was just stating my personal preference
I wasnt claiming the cup does or does not exist in an ontic sense but, rather, the meaningful distinction I find between different usages of the term existence. Let me try to clarify with an example: lets borrow a couple different philosophers to demonstrate what I am attempting to convey (that is, by means of my interpretations of them).
Lets say I am holding a cup in my hand.
From my interpretation of Spinoza, he would not deny the existence of the cup in my hand as it appears, but would deny it in an ontic senseas he would claim that the cup actually exists, in an ontic sense, as apart of one absolutely infinite substance (i.e., God).
From my interpretation of Kant, he would not deny the existence of the cup in my hand as a phenomena, but would deny it in an ontic senseas he would claim that what exists is actually noumena, of which we can only ever know it by means of negative judgments. In other words, he would claim, in a nutshell, that the noumena conforms to the mind a priori (most notably time and space).
From my interpretation of Schopenhauer, he would deny that there is a valid separation between phenomena and noumena, and, thusly, would posit that they are the same thing; furthermore, he would posit that what actually exists, in an ontic sense, is an infinite will. In other words, the cup exists as an object (phenoma are noumena), but what really exists is an infinite, blind will.
My point here is that, to my comprehension, theres a meaningful distinction between objects put forth in front of me and what lies at the bottom of existence (or what actually is existence); that is essentially what I am trying to convey. It is most certainly possible to assert that what actually exists is the same as what exists (which would be essentially claiming that whatever is deemed existent must be also in an ontic sense), but my point here is that that is not necessitous at all (personally I would find it problematic).
useful is relative to the individual at hand. I can attest that I find it useful to understand, metaphysically, how derivation works, but that doesnt necessitate that others find that useful.
I created sine qua non (the term) and discovered whether there are any true sine qua nons: I would clarify that I didnt simply create the principle of regulation.
I wanted to discover whether such foundations exist, or whether it is essentially arbitrary (or contextual).
This is where, I would argue, it becomes necessary to be precise: validity is not necessarily linked to existence. One can most certainly package them together, but that is not necessary. That is why the essay proves that the principle of regulation is true (being defined precisely in the essay, which would be constituted as valid) and not what exists. So, I would answer two-fold: yes the principle of regulation is valid, and the essay doesnt state yes or no to its existence (in an ontic sense specifically).
The task, or purpose, is to derive if there are any sine qua nons, of which one is determined to be true (i.e., principle of regulation). Given the definition of sine qua non, it essentially is meant to derive whether there are actual foundations to derivation or not. I think that is a pretty fair and important purpose, but please correct me if you think otherwise.
Not quite, I would say. Again, the essay explicitly states that value is of no consideration therein (i.e., usefulness I would attribute to that area of discourse) and by good, I am not sure what you mean: can you please define it?
On the other hand, I am looking for critique of the essay, so in a way anything that remotely critiques it is fair game (so if you think the essay should address its usefulness or unusefulness, then that would be a fair critique to explore!).
But the essay proves, as it has been written as of yet, that the principle of regulation is true. Not that it is useful.
By the one you emphasise most, I am starting to suspect that you may be under the impression that the essay proves multiple sine qua nons: it only proves one (i.e., principle of regulation). So I just wanted to clarify that that is the only one proven.
In terms of not having a clear meaning: how so?
The absurdity would be that the denial of the principle of regulation thereby utilizes it. However, it is still, nevertheless, possible for someone to simply reject it (as anyone can reject anything). I am not positing that the principle of regulation is something which can be separated from the subject at hand. For example, if we were to debate about whether redness is an inherent property of the cup I am holding, then we could, upon ending our discussion, continue our lives without such a considerationas many concepts are completely independent of whether redness is an inherent property of a cup. This is not the case with the principle of regulation: if I reject, then I used it (and vice versa)--but that doesnt negate the possibility of someone simply living their life ignorant (willfully or not) of their utilization thereof. Maybe that clarification will help resolve some of the confusion; otherwise, feel free to hammer me harder.
Bob
Within the essay, it is proven to be true. I am arguing for its proof as utilized as an unbounded infinite, which quite literally means that someone cannot even posit what is real without its underlying (or overlying) utilization. Even if someone were to negate the entire thing, then I would argue they still utilized it. Does that sort of answer your question?
I appreciate the compliment, but I wouldnt regard anyone in this discussion board (thus far) as a brat: I think that some of my contenders are conceptualization the essay in a different light than I am, which more conversations will help each of us understand each other better.
The claim that this kid is the fastest bicycle rider in the world is false, because we can prove it. For example, lets say we are constituting the fastest by means of the current record holder. If that is the case, then we can prove, deductively, that he is not when we time him and find out it is nowhere near the world record.
Likewise, lets take this more literally: lets say, by fastest bicycle rider in the world, we mean that literally out of every single person on the planet they are the fastest. Now, the world record is usually recorded in a manner that requires a hierarchical competitive structure, which usually omits people who didnt have the opportunity to race. There are many factors that go into bicycle races, which I will spare you the boredom of meticulously exposing. My point here would be that we deductively know that the claim, as posited now, is an induction; that is, the premises do not necessitate the conclusion and, therefore, we cannot know that anyone is the fastest bicycle rider in the world right now.
This is not the case whatsoever with the essay (I would argue) that I wrote. It is proved deductively (which rules out the idea of my second aforementioned example of an inductive argument) by means of proving it to be true and, therefore, it is not open ended like the bicycle example.
Questioning anything within the essay to be true or false is perfectly within the scope of the essay, and, furthermore, I would love if you did!
However, right now, I dont think you have contended with the actual proof in the essay, which is meant to prove it is true. If you think that the essay is not, in fact, proving that it is true, then I would love to hear why!
So, what I meant is that epistemology and ontology are out of the bounds of the essay (i.e., is it known?, does it exist?). However, questioning its truth (as in, whether it is true) is perfectly within the scope of the essay. Although I may be misremembering, I dont think you have actually, as of yet, argued why it is false (or, at least, if not false, why it isnt proven to be true).
The essay is most certainly meant to prove that the principle of regulation is true.
So, you seem to be using as true as possibly can be and real as can be synonymously; however, I am merely clarifying that (1) the principle of regulation is argued as true, and (2) epistemic and ontic claims are beyond the scope of the essay. Let me know if I need to clarify further on this, as I may still just be misunderstanding you.
I totally understand! I think the more we discuss, the better we will be able to narrow down our differences and potentially come to an agreement!
Bob
I would also like to clarify that, despite ontology and epistemology being considered out of bounds of the essay, I don't want you to feel like you cannot argue for why it should be a consideration (if that is something either of you wish to do). As of now, they are considered beyond the scope, which I can elaborate further if either of you would like, but I am completely open to any counter arguments you may feel inclined to provide.
Bob
And with my bicycle analogy I totally agree with your reply on it and how we would conclude that he is nowhere near the fastest bicycle rider in the world that's the same way I would have come the same conclusion I agree with you on that however my point to that was that based on their limited abilities being young kids let's assume this was before cell phones in the internet being the people that they are (adolescents) they do not have all the same tools at their fingertips that adults and modern times have and so their perspective and their way of testing the hypothesis is a very limited small barbaric kids version
and that was the point that I was trying to use to compare is that you're giving parameters and limitations and within those parameters and limitations the tools appear to be real and do work in the manner that they need to because when we question them we're questioning them within the parameters you've set and when we do that they are rendered as real and usable and good but is that only because we're stuck within that narrow parameter? If we were to expand further past would we find something else? That was the point in my analogy of that
Now I'm by no means calling your essay limited stupid youthful barbaric or any of those other things by any means it's actually way more complex than my brain is used to dealing with but I was simply using the analogy in comparison of limitations not of complexity by any means.
But regardless you're still not getting the point that I'm trying to convey and I'm having hard time trying to figure out how to convey it so bear with me while I try to gather my thoughts
The reason that the consideration of what exists and what is known (or lack thereof) is outside the scope of the essay is because to conclude anything with respect to either is to import an epistemology and/or ontology, which the essay is not aimed to lock anyone into or against any given epistemology or ontology; for the essay pertains not to derivation (which is what would be utilized to construct any resemblance of either) but, rather, the process of derivation itself and, therefore, the essay is true regardless of what one posits for either. Derive that this particular epistemology is most suiting to you and it will have no direct relevance to the principle of regulation; derive that this particular epistemology is not suiting, downright false, absurd, etc. and, likewise, it will have no effect on the principle of regulation (nor sine qua nons). Same goes for ontology, logical languages (i.e., theories of logic), etc.
In attempt to resolve some of the confusion, let me try to explain what I think you are asking and, thereafter, you correct me where I am wrong. Moreover, let me, for the sake of the conversation, step past the bounds of the essay to hopefully help guide the discussion.
I think that you are essentially inquiring how one can truly deem any given proposition true given the fact that they are limited in their faculties of reason and, therefore, it could be entirely possible that one is really analogous to a child who is right given the context of their limited faculty, but, on the contrary, wrong in relation to an adult (who is typically capable of much more sophisticated reasoning).
If I am understanding you correctly, then here is my response:
Firstly, this can be posited for any given theory, statement, assertion, etc. For example, one can most certainly question whether humanity can deem something true of anything: is Special Relativity true or are we simply like children that think they are the best bicycle rider? How can we be certain, in other words, that some of the top discoveries, the top minds, arent just ignorant of their child like boasting?
Secondly, I think this is, abstractly, really an issue pertaining to the postulation of something outside, or completely transcendent, of oneself: truth, knowledge, existence, etc. For the sake of conversation, let me step outside of the bounds of the essay and acknowledge that any of the aforementioned (i.e., truth, knowledge, existence, etc.) can be viewed, prima facea, as transcendent of oneself. If one does that, then they are faced with this dilemma I believe you are voicing: how do we ever know, prove to be true, or claim existence to anything when we cannot be certain that what we deem so truly coincides with that transcendent truth, knowledge, existence, etc. The problem here, I would say, is that, in a deeper sense (i.e., not prima facea), nothing transcends reason (in relation to the subject at hand): not even the very concept of nothingness. There is no transcendent truth, knowledge, existence, etc. It is a contradiction in terms to hypothesize about something sans reason when reason was what derived sans itself.
So, when I claim that the principle of regulation is true, I do not mean truth in the sense of something which transcends, in relation to me, myself, nor, in relation to you, yourself. To be honest, its not that I would deem it a figment of the imagination but, rather, simply a contradiction in terms.
I can only ever provide what I deem worthy as true, which could be false (I dont consider myself God (; ). Furthermore, I cannot prove it aligns with some sort of transcendent of myself truth, if that is what you are asking. In terms of the simple child analogy, I can deem it to be proven to consume all derivation, which removes the possibility for its exclusion; however, I could be wrong (as always).
Theres two ways I am interpreting this: (1) expansion in the sense of allowing other considerations (e.g., importing a wide range of other held view, beliefs, etc.) and (2) the expansion of the understanding (i.e., reevaluation in hindsight).
In terms of #1, I think it is proved in the essay that expanding into other considerations is all in vainfor all of those importations would be via derivation, which the process of which is performed via the PoR. If theres anything you would like to introduce into the mix in terms of consideration that you think would potentially invalidate my essay, then please do!
In terms of #2, I cannot, in all honesty, ever solidify any of my views as 100% guaranteed to be right, in the sense that I could guarantee that I will never be able to negate my current views. So, in this regard, I dont really see it as an issue as this can be posited for anything.
The hidden #3 would be, I would say, the idea of expansion into what transcends the subject at handsuch as a truth which is sans subject. I think I already addressed this: theres no such thing. However, I want to clear that, in some of this, I am overstepping the bounds of what is required to prove PoR: one can hold there are truly transcendent truth via PoR.
No worries! I completely understand!
Let me know if I did a more adequate job at addressing your contentions. If I am still completely missing the mark, then please correct me as you deem fit.
Bob
So now hmmmmm... So then whats the next essay? I'm dying to see how this all ties into the next part not that I'm smart enough to know how to do anything with it LOL but nonetheless I'll pretend like I am lol
True. The dark side of the moon exists and it is not an object put forth in front of you.
On this view, from the proposition that X exists we may not infer that X actually exists - it is not 'necessitous.' That's awkward. If you have a theory that your cup may not actually exist (having proposed it yourself as a straighforward example of something that uncontroversially does exist) then you've made a muddle. To ask "What does it mean for something to exist?" is sensible enough. To give an answer that denies actual existence to the very thing you have chosen as an example of something that exists is confused. The theory is invoked to elucidate a given fact - if it turns out that the fact is inconsistent with the theory then I think it's the theory that has to give way.
It may be that your cup exists but that your cup is not the thing that I think it is. Just as, for example, stars exist but stars are not the things that the ancients thought they were. They may not even be the things that we think they are.
Quoting Bob Ross
You think it's clear but I say needs an example or two. E.g. a 'subordinate rule' is 'Don't walk on the grass' and a 'superordinate rule' is 'Notices in this park are posted with authority of the Town Council'. 'Derivation' is 'If p, then q. p. Therefore q.' 'Derivation of derivation' is 'If 'if p, then q. p. Therefore q', then 'If p, then q. Not-q. Therefore not p'. 'Recursive' means, well, I don't have an example. A 'sine qua non' is for example. Examples are the baby-walkers of the mind.
You do give an example of a superordinate rule:
What makes this a rule? What makes it superordinate?
It looks like a proposition. I have say it also looks false. I take 'indiscernible' to mean 'impossible to tell the difference between'. I have never been able to tell the difference between "1" and "1" or between 1 and 1. I can tell the difference between several instances of mentioning the number 1. I would happily buy the proposition that 1 is identical with 1 and that to mention "1" at the start of a sentence is different from mentioning it at the end. Is that what you mean? If so, that seems OK, but it does not look like a rule. It looks like an observation helping to distinguish an entity from the mention of an entity.
I entertain hope that your above claim expresses a/the crux of your essay's purpose. In line with this assessment, your premise says,
PoR can never be excluded from context. Proving this logically renders PoR as sine qua non WRT context.
Does this imply the concomitant> Derivation can never be excluded from context.
Does this lead us to> Context contains at least (2) sine qua nons: PoR & Derivation
Does this lead us to> Context contains at least (3) sine qua nons: PoR, Derivation & Time
If you can prove this, do you have a set foundational to logic?
Since these questions are whoppers, let's focus on PoR.
Please elaborate how regulate & modulate compare.
Please elaborate how PoR & PoM compare.
I am glad I finally was able to understand and address your contentions properly!
The next essay will pertain to the investigation of the obligation to affirm PoR (or lack thereof) and the consequences of affirming PoR. However, I do not want to actually spend the time writing it until I think that all the contentions with this essay are resolved (someone may convince me that I am partially or holistically wrong, which would render any further essay that builds off of it useless to me).
Bob
I would say not quite. existence is indexical: is it awkward that I can refer to different people with the same word he? I personally dont think so. I can posit, without contradiction, that the cup in my hand exists (by constituting, for example, its existence as phenomenal) while denying it as existing in an ontic sense. I gave a couple examples, such as Spinoza to illustrate this clear distinction: do you disagree with that distinction as demonstrated in the examples? If I were to posit, for example, that the cup in my hand exists (contextually to phenomena), but really exists as one infinite substance, then, regardless to its truth, there is a distinction being made there within the concept of existence. Another example is that a cup may exist in the sense that I can interact with it, yet not exist sans my consciousness. Again, just an example of how there is a distinction here to be made.
It is confusing if and only if one is conceptualizing existence as one universal context (as opposed to separate contexts). Again, I can say this thing exists as a phenomena and not as a noumena.
I think that if one is to accept that something may not exist as they deem it, then theres necessarily a split between existence which I constitute of things and existence as things-in-themselves (or potentially things from someone elses perspective or what have you). If you are, on the other hand, uniting existence under one context, then I dont see how you can state this star exists as X, but its actual existence could be completely unrelated to my conjecture: theres an implicit separation into two contexts there.
There is an example in the essay (as you note later on), but I suspect you found it unsatisfactory (which is totally fine).
An example of a subordinate rule can most certainly be Dont walk on the grass and a superordinate rule, contextually to that subordinate rule, could be because notices in this park are posted with authority of the Town Council. I dont see anything wrong with this example if it makes more sense to you (its perfectly fine). I would note that this can be continued further (if one wants) to question the authority of the sign, etc. and through the whole process, continually, one is performing it via PoR.
By derivation of derivation, I mean to derive derivation itself. So, instead of discussing whether a particular set of premises and conclusions are true, it is a consideration of the process of derivation itself (i.e., how is derivation itself possible?). If conceptualizing that as specifically if p, then q. p therefore q for derivation and if if p then q. p therefore q, then p. p therefore q as second order derivation (i.e., derivation of derivation) then that is fine: that would be an example within the realm of logic, which is a form of derivation.
By recursive utilization, I mean that the idea is to abstract up to higher orders of derivation until (if at all) we reach a recursive use forever. By recursion, I mean, like a program, the utilization of itself by itself. This is most common in software engineering, wherein programmers will code functions that invoke themselves some finite set of times. However, within the essay, it would be a recursive use for an unbounded infinite (that is, to be more precise, an unbounded infinite of negations). A sine qua non is not an example, I would say, of a recursive principle, as it is merely a definition: without which, not. If some principle were to exhibit that sort of concept (i.e., sine qua non), then it would be an example of a recursive principle that is unbounded infinite of negations. It is entirely possible to have finite set of recursions, like in programming, which is not the focus of a sine qua non.
The reason it was a superordinate rule was because it was, within the context of the example, a regulating principle (rule) having greater importance or rank as another. In other words, it was meant as an example of an explication of the implicit overlying guiding affirmations of the subordinate rule (in this case: 1 = 1 was the subordinate rule, which can be also simply noted as an conclusion).
As noted explicitly in the essay, the focus of the example is not the truth or falsity of the derivation, it was about the higher principles involved: it is about what is occurring for the derivation to occur:
However, before the demonstration, a couple clarifications must be noted. Firstly, the proof of the principle of regulation has no bearing on the derivation demonstrated in the example but, rather, on the higher form of derivation itself; that is, the higher procedure, as abstracted, utilized to perform derivation itself. Therefore, the reader is urged to focus heavily on the higher principle(s) engaged in the derivation of derivation as opposed to focusing on the derivation.
You can most certainly negate my example derivation (for example, that 1 and 1 are actually indiscernable as opposed to what I claimed) by means of deriving that conclusion which, in turn, inevitably is by means of the PoR. The point is the overarching process in play, not the specific conclusions themselves. With that being said, let me address your contentions with the derivation:
I mean more of what you said at the end there: the law of identity. That is, we use 1 and 1 interchangeably for most situations but understand that they are discernible. As you noted, location and time are arguably the two biggest factors that make 1 and 1 most definitely not equivocal. Nevertheless, I am still able to postulate, assert, command, state, etc. that 1 = 1.
By rule, I mean a regulating principle. Within the context of my derivation in the example, 1 and 1 being identical but not indiscernible was the superordinate rule guiding my conclusion that 1 = 1 (in part); in other words, a regulative principle determining the course of my derivation. Does that make more sense? If not, let me know!
Bob
I think that the two biggest cruces are (1) whether the individual at hand can transcend their own context (which is what you and Philosophim brought up, I would say) and (2) whether the idea of the essay preceding logical languages (or theories of logic) is question begging. Those, I would say, are the most concerning aspects, fundamentally, of the essay. So I would agree with you on that.
I agree, but I want to clarify that, more abstractly, it is PoR can never be excluded--it isnt just contexts. For example:
I am not sure what WRT stands for, but a sine qua non has no prepositions (as noted in the essay), so it is not sine qua non of WRT context. This may be me just splitting hairs though, because a context that is universal I really wouldnt constitute as a context, but if that is what you mean, then I would agree in saying that PoR is a sine qua non (without a preposition).
Although I completely understand why you were inclined to conclude this, I dont think it is correct. Firstly, a sine qua non is without which, not (where not is an unbounded infinite negative) and, therefore, the possibility of without PoR, not derivation invalidates derivation as being a sine qua non. Secondly, this is exactly why, derivation not being a sine qua non, produces the possibility that someone can completely remove it within their derivation (no matter how irrational it may be, as someone else could easily mention that I just literally said someone can remove derivation from their derivation), whereas they cannot remove PoR without utilizing it. Let me know if I need to explain more, as this is definitely where it starts becoming necessary to be precise with my terminology.
Likewise, time is by no means something one can posit as sine qua non, as without PoR, not time and, honestly, there are many principles that are required for it to be affirmed in the first place (i.e., faculties of reason which allow one to determine that time is enveloping of oneself, or that there is a non-temporal true claim, or neither true nor false, etc.).
I think where you may be misstepping (or I may just be wrong) is that the essay does not utilize a logical language and, therefore, many axioms that most people are more than comfortable swiftly deploying is beyond my reach in the essay. All that is utilized is the use of PoR to derive if there are any sine qua nons and, thereafter, the proof of one.
Likewise, you may have also noticed that it isnt logically (meaning from a constructed logical language) coherent (at least on most logical theories) to claim multiple sine qua nons as truefor if there existed two then they are thereby not sine qua nons (thats a contradiction). In other words, if a sine qua non is without which not, if we allow ourselves the importation of useful logical axioms, then only one can be true by definition (otherwise we have a situation where two principles are supposed to be negatable in relation to one another, but yet the source of an unbounded infinite of negations respectively). However, this is not argued for in the essay because it is, albeit enticing, something which would require the use of logical axioms and, therefore, I dont think, as of yet, it can be argued for.
By modulate, what are you referring to? I am not completely following.
Bob
I think that the two biggest cruces are (1) whether the individual at hand can transcend their own context
Context ? Environment. In my thinking, environment suggests state of affairs, which suggests reality.
In your usage here, is individual can transcend their own context an action symbolic or literal?
(2) whether the idea of the essay preceding logical languages (or theories of logic)
My thinking proceeds from foundational assumptions that bump up against some foundational assumptions employed herein by you.
An essay is, at bottom, the logical language of argumentation
The stuff of logic is a continuum of conditionals that unfold sequentially, thus implying a temporal process
Although logical expressions can be conceptualized as atemporal mental objects, continuity is always empirical & temporal
[i] a sine qua non has no prepositions
a context that is universal I really wouldnt constitute as a context [/i]
If, as I interpret you to be saying with the above two claims, sine qua non is not of anything, and, moreover, is not at all contextual, then I get the impression the whereness of sine qua non is more mysterious than the position of an orbiting electron at any given moment. Is that the case?
Firstly, a sine qua non is without which, not (where not is an unbounded infinite negative) and, therefore, the possibility of without PoR, not derivation invalidates derivation as being a sine qua non. Secondly, this is exactly why, derivation not being a sine qua non, produces the possibility that someone can completely remove it within their derivation (no matter how irrational it may be, as someone else could easily mention that I just literally said someone can remove derivation from their derivation), whereas they cannot remove PoR without utilizing it.
The above section of paragraph is wonderfully clear and thus it makes me hope Im beginning to get some real grounding within your essay.
I now have an impression of your essays essence via use of a helpful metaphor wherein your sine qua non holds status akin to the singularity that precedes the Big Bang.
If theres even a particle of truth in application of my pre-Big Bang metaphor to your metaphysical claim, then hopefully I can proceed to an understanding youre wrestling with the boundary ontology of origin.
Boundary Ontology of Origin continuity via hyper-logic across the super-position of a non-localized QM event.
The above definition is my best-to-date exposition of a hairy beast of a concept that is one of my works-in-progress. I wont elaborate its possible pertinence to your essay because that would entail an inappropriate digression from your work. I will say I expect it to inform some of my commentary upon your work henceforth.
Likewise, time is by no means something one can posit as sine qua non, as without PoR, not time and, honestly, there are many principles that are required for it to be affirmed in the first place (i.e., faculties of reason which allow one to determine that time is enveloping of oneself, or that there is a non-temporal true claim, or neither true nor false, etc.).
Since you reject time_sine qua non, I think it imperative you state (If you have not done so) whether PoR_sine qua non is temporal, or atemporal.
Ive been understanding regulation in the everyday sense of a transitive verb that controls & shapes an object under its influence. I dont presently see this function as being atemporal.
Answering the question of sine qua nons relationship to time entails whether or not your universe is static or dynamic. Does a universe without motion make any sense?
Likewise, you may have also noticed that it isnt logically coherent to claim multiple sine qua nons as truefor if there existed two then they are thereby not sine qua nons (thats a contradiction). In other words, if a sine qua non is without which not, if we allow ourselves the importation of useful logical axioms, then only one can be true by definition (otherwise we have a situation where two principles are supposed to be negatable in relation to one another, but yet the source of an unbounded infinite of negations respectively).
Your above statement, speaking potentially, has a lot to say to the project to bring the rules of inference into congruence with QM.
Please elaborate how regulate & modulate compare.
By modulate, what are you referring to? I am not completely following.
My Apple Dictionary tells me regulate & modulate are synonyms. Ill buy that. However, I sense that modulate, more so than regulate, gets into the deep interior of language.
Language -- a collective, or gestalt of the systematic boundary permutations of a context or medium; a record of the systematic boundary permutations of a narrative medium.
If the above claim contains a particle of truth, then your sine qua non, as presently perceived by me, embodies something akin to the Original Utterance, itself, in turn, akin to the pre-Big Bang Singularity, itself, in turn, akin to Gods Let there be light!
I hope youll forgive the tincture of theism_Jungian psychology pooling into my assessment of your essay.
Might sine qua non, per your essay, be your Logos?
Indexical means 'relative to context of utterance' - like 'he' or 'here', as you say. The term 'existence' does not seem relative to context in that way. You go on to say that it has different senses, which is different from indexicality. You may well be right. Hamlet exists as a character in a play and does not exist as a flesh and blood human being. So sure, there are different kinds of existence in that way. But to say for example that Hamlet exists but does not [open italics]actually[close italics] exist is confused and confusing. To choose Hamlet as an example of some entity which uncontroversially exists is equally confusing. You chose the cup in your hand as a straightforward example of something which exists, distinguishing it perhaps from the tiger in your hallway which (ex hypothesi) does not. That's a much better example. But it does not allow for the kind of apparent equivocation that Hamlet does. It's a useful example specifically because it won't let us wriggle away from its existence.
Quoting Bob Ross
The problem is that your cup doesn't exist sans your consciousness and the cup in your dreams also does not exist sans your consciousness. We are left with the problem of distinguishing a cup in the hand from a dreamed cup. That is, a real cup from an imagined cup. Or, in other words, a cup that exists from one which does not. Similarly, the cup in your dreams also exists contextually to phenomena and for all I know it may exist as one infinite substance as well. But at some time, possibly outside the philosophy laboratory, we are going to have to distinguish the cup of our dreams from the cup in our hands, the car that hit ours from the car that did not, the positive bank balance from the negative. I mean, while we enjoy this delicious atmosphere of confusion we must still keep a concept of 'existence' tucked in our back pockets for use when we actually need it and not just for when we are playing at metaphysics. And that, I submit - the concepts tucked away for use when we are serious - is our metaphysics.
If the terms mean something like the interpretation I gave them, then I can get little sense out of this - except perhaps that if we fail to follow rules of logical inference, then we will fail to make logical inferences.
It is true that 1=1 in the world defined by the definitions and rules of mathematics. The rest of us just accept this truth on blind faith based on the accomplishments and power of mathematics to be useful in the sciences.
I have brought up the pitfalls of 'true' in metaphysical reasoning. For metaphysics akin to mathematical reasoning, True is a binary value for evaluating dichotomies, any other use of truth is common but can be shown to be invalid or unsound. Since '1' is just like any other concept, it can not be true that '1' and '1' is anything other than '1'. Just as 'orange' and 'orange' are 'orange' and nothing else. However, instantiations of 'orange' are countable. 1 orange +1 orange = 2 oranges. And 1 apple +1 orange = 2 fruit.
* I have edited this comment *
Quoting Bob Ross
We're in agreement then Bob! That's what I was trying to point out.
Quoting Bob Ross
I don't think so here. I was regressing through all numbers, and noted that all numbers themselves are a bounded infinite as well. I was trying to lead to the point that an unbounded infinite cannot be quantified or limited.
Quoting Bob Ross
If we are in agreement that numbers are bounded infinites, then whenever we come up with an identity, we are creating some type of bounded infinite. If we use the word "negations" were are implicitly talking about bounds then. I don't think we can say an "unbounded infinite of negations". That's really, a "bounded infinite of negations". I can see an unbounded infinite negated, because an unbounded infinite is the base from which all bounded infinites are formed. But if we say that all possible bounded infinites are negated, isn't that the same as stating an unbounded infinite is negated? Can you give an example showing how they're entirely different ideas?
Quoting Bob Ross
Thank you, I re-read and realized you had covered that part. Also, you have not had the chance to show how sufficient justification works under your system, so I accept this for now.
Quoting Bob Ross
For myself, I think this is a crux of your argument that needs better explication. You are as usual, brilliant Bob, but I'm having a difficult time conceptualizing the latter as something real. In trying, the best I can come up with is that it is some conceptualization that is necessary for an unbounded infinite to be. The best I can think of is that we must be able to make conceptualizations out of/within the unbounded infinite. Because if something could not, then nothing could create any sort of differentiation between bounded, and unbounded. Does this somehow fit within your PoR?
Quoting Bob Ross
This again is where I have a hard time. Without a sqn, nothing can be. Which means without a sqn, concepts cannot be either. The way I read the essay and your explanation, it seems to imply without a sqn, the infinite, bounded or unbounded could not be.
Quoting Bob Ross
Again, I think this is really where my issue resides. The unbounded infinite is the source of all explicated infinites. Negating the unbounded infinite, negates all explicated infinites as well. Without a sqn, the unbounded infinite would be negated. And I think we agree there is only 1 unbounded infinite, as more than one would be by definition, two bounded infinites. All explicated infinites are within the unbounded infinite. Which means a sqn is necessary for all explicated infinites to occur as well. If this is the case, then a sqn must stand without contradiction in all explicated infinites. Meaning that if it does not stand within even one explicated infinite, it cannot be a sqn.
As I noted earlier, the burden of demonstrating this is nigh impossible to meet. But this again, is through my interpretation so far that the sqn is a misapprehension. If you can demonstrate your version " it is simply the negation, sequentially, of everything (i.e., not , not not { })." somehow is not logically equivalent to my version, then there may be something to explore.
This essay might get a larger following if all this infinite stuff were in mathematically acceptable nomenclature. Just a thought.
I apologize for the belated response ucarr! I had a hefty week or so. With that being said, let me dive into your post.
Thank you for the clarification: I was not familiar with that acronym.
I wouldnt quite go as far as to claim context is synonymous to environment (maybe thats why you used a tilde equal sign?--to suggest an approximate equivalence). I would be hesitant to confine context to reality (which I would agree is implied with environment, at least to some degree). Therefore:
In terms of object relations, I would say that I can meaningfully produce contexts sans-my-body (e.g., I can see red, but they cannot).
In terms of consciousness, it is much harder to produce anything (or at least anything rational) without admitting the contingency of other objects on the sensations and perceptions of my object (i.e., the body). However, it is possible for a subject to posit things without their bodies (no matter how irrational/rational it may be), as it is possible to deny the contingency of something on such and, not only that, but people can produce meaningful predictions that involve positing their non-existence. So I wouldnt holistically grant that I cannot posit sans-my-consciousness.
In terms of reason, I think that, although an individual can still assert its omission, the most rudimentary thereof is without omission (in possibility). This is the area of discourse which I am attempting to convey with the principle of regulation.
Now whether that is literal or symbolic, as I do not entirely know how you are utilizing those terms, I will leave up to you.
I think, in the sense you are positing it, I would agree. However, I would distinguish logical language (in the sense of a formal or informal theory of logic) from hyper-logic (maybe meta-logic?--I am not too sure as of yet). If you mean it in terms of the latter, then I agree. If in terms of the former, I disagree.
Within the scope of the essay, I would disagree (albeit incredibly reasonable to assume). Yes, it is reasonable to infer that the procedure and proof of the essay is necessarily that of temporal relations (sequences in succession of one another). The important thing is that, as of now, I find such a conclusion (i.e., derivation or the principle of regulation is temporal) to only be found by importation of other axioms (or, in my terms, superordinate principles which are not apart of the standard terminology nor proof explicated in the essay. My point here is not to completely discourage your conclusion here, but only to expose that it is by means of other superordinate rules other than what is required (I would argue) to prove PoR to be true. In other words, it is entirely possible for one to accept PoR as true and immediately thereafter assert PoR is in time, is time, is sans time, neither in or outside of time, etc.
I would personally agree that derivation is always empirical and temporal; however, I dont find, as of yet, that that is necessary to hold to prove PoR. Please let me know if you think I am wrong here.
I am not entirely certain that a stable methodological approach can be establish to examine the properties or existence of PoR, but that is something I am currently contemplating. I find compelling arguments to assert it is aspatio-temporal (because there is no where which would reasonably pertain specifically to PoR and any derivation of its temporal sequences of derivation are simply via it), but, in contradistinction, I find it compelling to argue for its spatio-temporality (because being sans time & space seems merely to be a conceptualization under space and with time); however, I think both arguments are within the real of critique of derivation (as they are both inheriting from this PoR meta-derivation if you will) and, therefore, I think that, with respect to PoR itself, the best way to conceive of it for the essay is neither true nor false of the former nor the latter. It just simply seems inapplicable, but correct me if I am wrong.
If I am understanding the analogy correctly, then I think I would more or less agree. PoR is simply what (I think) can be proven to be a sine qua non, which essentially means that it is the meta-derivation (so to speak). Although I think theres a strong case to make that I am acting as if PoR is what ontologically exists, I cant say I am able to place that within the essay itself (for the same reason as my previous elaboration on spatio-temporality).
One could, I suppose, think of PoR as a spark of derivations. Is that what you mean?
I would emphasize that the essay is not making reference to reality though, so it is not entirely analogous to the Big Bang.
By QM, do you mean Quantum Mechanics? If so, the essay is not meant as an exposition of any quantum mechanical principles (nor is it meant to assert for or against any given scientific principle). Again, the essay is meant to be a inquiry into higher reasoning (or lower depending on how one wants to visualize it).
In terms of superpositioning, do you mean to reference its use from quantum mechanics? If so, I would say the same thing as previously, but please correct me if I am misunderstanding you.
I appreciate and respect your effort to keep our conversation pertinent to my essay, but if it helps you elaborate on your views (in contrast to mine), then please feel free to discuss them!
I dont find time to be a consideration necessary to prove PoR as a sine qua non and, furthermore, any assertion of atemporality, temporality, spatial references, etc. is via PoR (thereby dependent on it). As I alluded to earlier, I think for the sake of the essay it may be best to conceive of a sine qua non as neither in time nor not in time.
I agree, but by regulation I was meaning to govern or direct according to rule, which (I think) coincides with my construction of superordinate and subordinate rules. I am honestly not sure what modulation would entail beyond regulation, but if you think it is a better term for what I am trying to convey then please feel free to critique me!
If I am understanding correctly, I dont think our ideas are perfectly aligning, but are similar. Maybe in due time we will determine them to, indeed, be equivalent.
Although I dont mind you invoking theology, I dont think PoR is synonymous with the vast majority of conceptions of God, Logos, or the Original Utterance. The essay isnt positing it as what created the universe, it is simply where I hit bedrock: it is the most rudimentary aspect of me (that is, me as reason: the subject).
If you think it is more alike to theological conceptions than I would grant, then I would love to hear why!
Bob
Upon further contemplation, I agree with you that he, as an indexical use of language, is not analogous to my use of different senses. However, what I was really trying to convey in terms of indexical is of or relating to an index, which I do still think applies (although my example of he was fallacious).
I still think that there is a meaningful distinction to be made the sense of existence of a thing and there are different terms for such. For example, ontic (e.g., noumena and phenomena) usually refers to the being of things and ontological is the discussion of being of being (e.g., dasein). In terms of ontical consideration, I would simply dividing it up further:
There is a colloquial sense of existence wherein laymen tend to denote an objects tangibility.
There is a phenomenological sense of existence wherein in a person denotes that an object exists as an appearance, with no immediate classification of what it may exist as otherwise.
And so forth
Now, to be honest, I slightly blundered in my use of ontic, in hindsight, as what I really was trying to convey was what sense they were meaning the term more generically than that.
When you say it is a confused outlook, I would agree if what you mean is that it would be a contradiction to assert that, for example, something exists phenomenologically and does not exist phenomenologically. However, I would be hesitant to concede that making such contextual sense of existence are unwarranted or that they are confusing.
A cup does not uncontroversially exist, unless you are referencing a colloquial use of the term (e.g., it is tangible). Many philosophers, some of which I already mentioned, would not state a cup exists ontologically (or they may have other distinctions such as a cup as a noumena verses a phenomena).
If by tiger in your hallway, you mean an imaginary tiger, then I would say an imaginary tiger exists in the imagination: thats still qualified as existing. Again, if you are thinking of colloquial to be, then, yes, an imaginary tiger is not tangible, therefore it does not exist (and that is a meaningful distinction in its own right).
This is true, and the subject can do so however they so please. In a colloquial setting, I typically denote a tangible cup (i.e., non-imaginary) as a real cup because I know most situations that is how everyone is thinking about it (they arent philosophers); however, I can easily and reasonably (I would say) assert that both the imaginary and non-imaginary exist in their own respects. Therefore, an imaginary cup is not the same as a non-imaginary cup, but nevertheless they both certainly exist.
I think you are committing an equivocation: just because two things are phenomena doesnt mean they are equivalent. Just because I conceive of a chair and a table under the concept of object does not mean I can thereby assert them equal to one another. An imaginary and non-imaginary cup are both phenomena, but are nevertheless distinguishable in many meaningful ways. Likewise, one can most certainly reject the phenomena vs noumena distinction, as my main point pertained to possibility and not favoring one over the other.
Practicality is a worthy consideration, but I genuinely dont see, as of yet, how one cannot pursue such within what I have posited hitherto. Nothing about what I stated necessarily determines imagination and non-imagination indistinguishable, an inability to distinguish different cars, nor an inability to discern bank balances.
I understand: it seems as though you are arguing for the practical over what you would deem the philosophical; however, I think the deeper issue is that they arent incompatible with one another whatsoever.
If theres any way you think I can provide better clarification on the essay, then please let me know! What I can say is that it is not about failing to make logical inferences, as that is a contemplation of logic, which is not determined nor argued for in the essay.
Bob
I would like to clarify that the essay pertains to the higher principles involved in the example given therein, as opposed to a critique of the derivation itself (i.e., of the example derivation of 1=1). Therefore, within the scope of the essay, nothing about it is meant to prove that you must accept 1 = 1 as true. This seems to be what you are contending with: am I correct? If not, please correct me where I am wrong.
Since this seems to lie at the foundations of your paper it would be good to make it a bit clearer what you are talking about. I'll ignore the infinity stuff, that itself is puzzling from a mathematical perspective.
Another member of TPF has in the past submitted a lengthy and sophisticated essay on a theory of everything (or roughly that), starting with an assumption every fact in the universe can be encoded for use in Turing machines. But doesn't explain how.
When one doesn't explain clearly at the outset what the fundamentals are or how they can be attained, readers may not be enticed to go further.
But that's just how I see it. Others here may differ. OK :cool:
In isolation, I agree that your quote of mine makes little sense; however, in the context of the entirety of the response where it is contained I think it makes sense. I would suggest reading this post in its entirety (if you haven't already) and then feel free to ask specific questions about it.
If I had to extract certain parts of the linked response, then I would provide further context:
Nothing about it has to do with the fundamentals being proven in the essay (i.e., that the principle of regulation is a sine qua non--being a true statement) I would say. If it is still confusing, then please let me know and I can elaborate further.
I am not familiar with the essay you are referring to, but it seems disanalogous to mine. It seems as though the point of their proof was to show that their claim is true, yet their proof was vague: I don't find that my proof is vague, but correct me if I am wrong.
In terms of your other post:
What exactly would you suggest in terms of mathematically acceptable nomenclature? What about our discussion of infinities is confusing within the apperception of mathematics?
Bob
Quoting Bob Ross
I asked my questions about time vis-a-vis PoR because I want to know who does PoR as sine qua non have as his neighbors? I was conjecturing that time is one of PoR's neighbors. As such, time does not prove PoR as sine qua non. Instead, time is one of PoR's neighbors, which is to say time & PoR are a matched set. One always implies the other.
I haven't forgotten your explanation to the effect that, by definition, two sine qua nons are mutually exclusive and thus cannot both belong to one set.
Some other candidates for neighbors of PoR might be superordinate & subordinate rules? This would mean PoR's neighborhood is divided by class, with the superordinates as elites & the subordinates as commoners? PoR, totally aloof, sits on high & reigns over both? Even if this is the case, the lowliest subordinate rule nonetheless stands a comrade alongside PoR. This is so because, by force of the premise> universe is the limit of system, without which, not is, in fact, bi-directional. In other words, no object inhabits absolute isolation. Therefore, speaking extremely broadly, all things are equal.
With the following, I will try to show why I suspect sine qua nons cannot be mutually exclusive.
If PoR has no neighbors, then for me a fundamental question arises pertaining to relationship. Derivation & meta-derivation, as I presently understand them, imply inter-relatedness i.e. relationship.
If PoR has no neighbors, how can it fulfill the role of sine qua non in total isolation?
Moreover, if PoR has no peers, that is, no other sine qua nons as neighbors, how can he be an unbounded infinite? Haven't you established a causal agent confined to a single set as a bounded infinity?
Quoting Bob Ross
I'm wondering if the above assertion (that sine qua non WRT temporality is undecidable) raises a question of foundational metaphysics> When the temporality of an object is undecidable, is not the location of said object also undecidable?
If the answer is yes, then how can sine qua non fill the role of foundational cause of derivation?
My underlying premise here is that even a purely cognitive "object," holding a priori status, by force of causality (inter-relatedness) obtains location. In this example, location of sine qua non is first member of a sequence.
I'm starting to suspect that sine qua non, as absolute solitary, without neighbors covering peers & subordinates alike, in parallel to the singularity of the Big Bang, cries out for conceptual revamping that addresses the deeply problematical boundary ontology of origins.
Hello Philosophim,
Wonderful points as usual! Let me try to respond adequately.
By negation, to be more precise, I mean a complete negation; that is, that the entirety of what is negated is completely obliterated (so to speak). Therefore, I do not mean a partial negation. Consequently, I am in agreement with you that not X necessarily entails that X is bounded (which is what I noted as being conceived in toto) because to negate it I must implicitly treat it as completely not (as opposed to partially not).
However, as far as I am understanding you, you seem to be asserting that an unbounded infinite of negations (which, we are in agreement, is an unbounded infinite of nots of bounded concepts) is somehow entailed to be equivalent to a bounded infinite of nots of bounded concepts. In other words, it seems as though, from my point of view, you are rightly identifying the bounded nature of the contents of the unbounded infinity and, in virtue of that, extending it (or maybe misassigning it) to its form.
Categorically, I think it would be a contradiction in terms to posit the negation of an unbounded infinite: that is actually a bounded infinite. Let me try to explain:
I dont think these are the same concepts that you just described and I think it is the root of our dispute. Firstly, it is important to note that I am not, at this point, attempting to prove that there is an unbounded infinite but, rather, I am merely trying to prove there is a valid concept of such that is at your disposalfor, as of now, it seems as though your contention lies in the denial of an unbounded infinite as a valid concept (i.e., it is really a bounded infinite assigned a new name).
To simplify it down for all intents and purposed for now, it seems as though, to me, you are essentially stating: an unbounded infinite of nots = not an unbounded infinite.
I would describe it as a difference between conceiving in toto and in total. Bundling up all those negations found within the unbounded infinite into a complete concept is to necessarily contradict the very concept (that is, attempt some operation which necessitates it to be conceived in toto). By concepts I am not entailing that it have a bounded form, which is what I suspect you are at least partially committing yourself to.
You are conceptually performing a different task to completely negate an unbounded infinite. What you seem to have done is analyzed the content of an unbounded infinite in terms of the sum of its parts to derive what it approaches (i.e., in total) and, thereafter, conflated that with in toto--thereby considering not an unbounded infinite valid; However, nothing about the sum of the parts of a concept entails that it can be conceived as a whole (that is, nothing about being conceivable in total entails that it is conceivable in toto).
This is the exact issue that required of me to explicate that, in the essay, a sine qua non is without which, not not without which, none; that is, the natural and swift leap from the sum of the parts of the content of a concept cannot entail its form in any way whatsoever (and nothingness is a great example of that). The unbounded infinite of nots does not necessitate nor prove a complete concept of nothingness (i.e., in the essay: none). The essay itself, consequently, does not even attempt to prove that without the principle of regulation, there is nothingness, because the PoR is also valid of the statement without PoR, not nothingness and without PoR, not everythingness (and so on): there is nothing which escapes it, so to speak.
The issue you may be having conceptualizing it is quite understandable, as with everything else we tend to swiftly conceive of finites and bounded infinites in toto based off of in total: but I have separated the two modes of thinking. For example, if one were to postulate what an infinite of empty sets would exist as in space, then they are more than likely going to quickly derive the summation of the parts to conclude that it would be nothing. This, however, in the sense of separating the two modes of thinking, is only valid by positing the form of the infinite as bounded. Therefore, I am noting the two different modes of thinking involved in the assessment:
First, the individual determined in total the infinite of empty sets, which is 0. This mode of thinking requires simply the ability to conceive what a sequence approaches (e.g., I cannot actually perform 0 + 0 forever, but I can nevertheless reasonably conclude it results in 0).
Second, the individual implicitly shifts their mode of thinking to in toto to package and bundle their conclusion into a wholly conceivable concept (e.g., 0 in space is nothing); that is, they assume that their evaluation in total of the infinite of empty sets warrants the ability to substitute the infinite for a bounded counterpart equal it in total (e.g., the total of the infinite is 0, therefore where ever I utilize the infinite I can substitute 0 for it). But, there is a distinction here, I think, in that they are not necessarily equivalent and, thusly, they are not always guaranteed to be valid of substitution: performing substitution of a bounded for an unbounded necessarily means that the form of the concept has been reshaped (by means, I would say, of utilizing a different mode of thinking). This substitution is only valid if the intents have no bearing on the form of the infinite: if the form matters, then 0 cannot be a valid substitution for an infinite of empty sets. Admittedly, a vast vast majority of the time I think the form is dismissable; however, my essay (I would argue) is an example where the distinction is vital.
I may be misunderstanding you here, but PoR can be utilized to make distinctions, but the very concept of PoR is also via itself. Therefore, the indifferentiation or differentiation of PoR from other things is via PoR. In that sense, PoR cannot be separated from anything, including nothing.
Another great point Philosophim! This, I would say, is your other major contention with my work (which is not the same as what was previously mentioned). Let me explain it back to you (to ensure that I am understanding correctly) and then I will attempt to adequately address it. Heres what I think you are essentially saying:
#1
p1. A sine qua non is without which, not
p2. Therefore, by definition of #1p1, a sine qua non contains without which, not concepts
#2
p1. A unbounded infinite is a concept
p2. By substitution property and #1p2, a sine qua non contains without which, not unbounded infinite
p3. By #2p2, it is a contradiction in terms to assert an unbounded infinite as a sine qua non.
p4. Therefore, an unbounded infinite cannot be a sine qua non.
The issue I would have is:
1. #1p2 is only partially true: I am allowing a concept to be incomplete in form and, therefore, a sine qua non only contains without which, not concepts with a complete form. The mode of thinking matters to me.
2. Therefore, a sine qua non cannot contain a concept with an incomplete form.
Note: by incomplete form, I do not mean a concept merely conceived as incomplete in content (e.g., an incomplete apple) as that is complete in form (e.g., a complete concept of an incomplete apple).
Now, at face value, my response seems to be a contradiction: if a sine qua non is an unbounded infinite of negations, then it seems as though I ought to be able to negate it within itself, otherwise it cannot be deemed true. The answer is that one can subvert a sine qua non through itself; however, that is to necessarily erode its form to that of being bounded (i.e., to shift my mode of thinking to in toto), which is not really a sine qua non: I am thereafter dealing with an imposture so to speak and not the real thing.
Likewise, if only complete forms are allowed, then it seems as though there is something which persists with the negation of a sine qua non: concepts with incomplete forms, which contradicts the idea of it being a sine qua non in the first place. However, again, an incomplete form is an unbounded infinite or a contradiction in terms (e.g., either unbounded with infinite content or a contradiction wherein it is unbounded with finite content). In terms of the latter, it is invalid. In terms of the former, we must contend with it: does an unbounded infinite persist, as a concept with incomplete form, without a sine qua non? The answer is no, because, again, to posit an unbounded infinite as without a concept necessarily shifts the mode of thinking in toto, which contradicts the term itself. If this operation is permitted, then the unbounded infinite simply (1) is not an unbounded infinite and (2) does not persist without a sine qua non because its eroded bounded conception is wholly within the jurisdiction of a sine qua non (without which, not). Therefore, I submit to you that an unbounded infinite is not out of nor within wholly and, therefore, it stands not outside (without) a sine qua non and, in turn, it does not pose a threat to the concept thereof.
Again, I think that our dispute first lies in whether an unbounded infinite is valid as a concept, which hopefully I have proved herein, and, after that we can then discuss whether there is such a concept. As always, I could merely be wrong about the concept itself.
Bob
Yes, I think this is really the issue. Lets see if we can put this in terms of math.
You already mentioned that the infinite X is bounded if we use actual numbers. The only way to really capture an unbounded infinite is not to use numbers at all, but the relation itself, where is is not limited by any number or dimension. I have no problem with this. What I will attempt to demonstrate is that there is only one unbounded infinite, and the X "without numbers" is it.
Your original bounded infinite could be represented as
X = Y with limit 5. Here we have X is fine as long as it doesn't equal 5. But if X is bounded as soon as numbers are used, then as soon as a number is used in the equation, it is also bounded. So X = Y with a limit of 5 is a bounded infinite by the limit.
But lets go further. X = Y is really a limit of "Whatever Y is, X is. We can say we won't assign actual numbers to X, but there is a number, a bound within the formula itself that acts exactly on a limit. That limit is that Y will always be X, and Y cannot be anything but X.
The above may be confusing, so let me add another detail. 2X = Y. Now we explicitly have a number in which Y will always be double X. Even if we don't use actual numbers in X or Y, this double explicitness is a limit, or a bound. Referencing the previous X = Y, lets change it to 1X = 1Y, which is equivalent.
Ok, if X, unnumbered is an unbounded infinity, while all the rest are bounded, can we have multiple unbounded infinities. Can I just say Y without using actual numbers and have that different from saying X without actual numbers? Besides the symbol itself, they are both identical. X is unbounded, and Y is unbounded. They are not bounded in relation to one another. If they are not bounded in relation to one another, they are not different from one another. Neither has any limits, so they are both the same.
Lets now translate that to words, context, and meaning. As soon as you put a limit in words, context, or meaning, you are no longer talking about an unbounded infinite. You are talking about a bounded infinite.
Now, this still doesn't convey the whole idea fully. We now have to change it to words, meaning, and context. To represent X, we need unstated words, unstated meaning, and unstated context. The moment we state anything, any "number", we are now within a bounded infinite limited by the expression of that word, meaning, and/or context.
Can we have a sine qua nons for an unbounded infinite. Yes, but there is only one. That would be "not X". If not X were true, then X would not follow. Anything more specific may be a sqn for a bounded infinite, but it cannot be a sqn for an unbounded infinite.
The same applies to the principle of regulation. Within X words, Y meaning, and Z contexts we are still bound by words, meaning, and context. Let simplify this further. W = { X, Y, and Z } all without "numbers" or explicit individual representations. W is still bound by X, Y, and Z. The only way for W to be unbounded is just "W".
So I do not think it can be shown the Principle of Regulation is a sqn. There are specific words, such as principle, regulation, of, that are understood within a particular bounded infinite meaning, and in particular bounded infinite contexts. Can thinking things within this limit form and use conclude the logic of the principle of regulation is necessary. Absolutely. But can this be concluded from "W" alone? No, I don't believe it can.
To clarify onQuoting Bob Ross
No, I'm not stating this. I'm stating an unbounded infinite is not a concept. The moment we create a concept within it, we are now within a bounded infinite. As such, there is only one unbounded infinite. Anytime any explicit infinite is proposed, it is by nature bounded.
That being said, this does not mean you should give up on the principle of regulation as a basis for a theory. I think it is a fine starting point, and I know I, and probably many in this discussion would love to see where your mind takes this. I would hate it to be stopped by something as trivial as a debate over infinity.
You shouldn't need sqn's to prove the principle of regulation to logically thinking minds. And even if you do, perhaps its something you could come back and show later? Is the concept of a SQN within an unbounded infinite absolutely needed to continue your line of thought from the PoR proposal? If you just started the sentence with, "If we have the ability to derive, the principle of regulation logically arrives," would that hamper what you want to do? I feel you have so much more to say, and possibly introduce greater thoughts that I would hate to see stopped over focusing on what may be a technical, and perhaps unnecessary detail to show us what you have planned.
In my experience in philosophy, it is easy to get stuck on approaches that seem necessary to us when first formulating the idea, but as we evolve the idea, were perhaps not as necessary or important as we thought to those who are reading our papers. Consider your readers so far. Very few have argued against the PoR, but almost everyone has a problem with your views of infinity. Now we may all be wrong, and you may be correct. But is it necessary at this time to focus on the infinite as such, or can this be shelved or stated another way that allows your readers to focus on the first premise they can readily accept?
Quoting Bob Ross
This right here is where I think you should go into detail. Prove not only to yourself, but that none of us can conclude anything differently. If you do this, I don't think anyone is going to need the infinite. How in the absence of derivation must we all necessarily have the principle of regulation? If I am not a being able to derivate, could I conclude I could not derivate?'
I look forward to your work Bob.
:up:
If I am understanding you correctly, then I would say that there is no neighbor to PoR. I think, and correct me if I am wrong, you are essentially arguing that time and PoR are biconditionally related. However, an argument for time (and, I would say, space) encompassing all ones cognitive faculty requires the use of axioms which do not lie within the essay. The axiom, so to speak, for the essay is two-fold: (1) an engagement in the attempt to derive a sine qua non and (2) implicitly the use of the definitions without contradiction.
With that being said, I agree that derivation implies time (and space): it is just that that would require axioms not granted nor required to accept PoR.
I think that, upon further contemplation, I can prove, without the importation of other axioms, that two or more sine qua nons cannot be true. For example, if there were two true sine qua nons, then they would, by definition, have to independent, but, also by definition, they would be, as independent without which, not, biconditionally dependent on one another. In other words, for one to be a sine qua non, the other would have to be dependent on it; but, since likewise for the other, they would really be two biconditionally dependent concepts, which would not be sine qua nons by definition. Therefore, there can only be one true sine qua non. I think I will interpolate that into the essay here shortly.
PoR is the principle that the subordinate rules cannot be affirmed and denied in accordance to the superordinate rules within the given operation of derivation (as a recursive principle). The terminology of superordinate rule, subordinate rule, rule, in toto, in total, etc. are merely a means of describing PoR itself and, therefore, I, as of now, do not see them as neighbors of PoR but, rather, more like a means of explication.
I apologize: I may have lead you astray by not acknowledging that only one sine qua non can be true. A sine qua non is not isolated but, on the contrary, it is that which everything in total (as opposed to in toto) is contingent upon (including contingency as a primitive faculty of reason). Therefore, it is ever present (in total that is, not in toto).
PoR is what we utilize to determine what time, undeterminancy, location, etc. is. It is what we utilize to determine what is is, etc. It doesnt have a location like a physical object in space (I would argue).
I dont think it is a priori or a posteriori because both require PoR to classify anything therein or to even construct the terms themselves. I dont think it would make sense to classify it as a priori, for example, because that is merely something else we derive, given a set of implicit or explicit superordinate rules.
Although I may just be merely misunderstanding you, I do not view a sine qua non as isolated whatsoever.
Bob
My issue would be that not X is a bounded infinite and so is without numbers: they both must conceive of the concept in toto to negate it. Therefore, without numbers really is an assertion that negates itself: for I am forced to conceive of numbers in toto, which is a complete whole (i.e., a traditional numeric one) which entails I have not, in fact, omitted numbers thereby.
In saying this, I think (although correct me if I am wrong) I am, at prima facie, not only agreeing with your examples but also supplementing them here.
That is why a sine qua non is not one in a traditional, numeric sense: it is an infinite in total as opposed to in toto. I can posit as many in toto conceptions I want, systematically, (i.e., numerical wholesone) within a sine qua non (as being negated) without contradiction.
Likewise, I also agree that two unbounded infinites is a contradiction in terms and, therefore, I will interpolate that into the essay (as I believe I can prove it without further axiomatic importations).
In other words, one sine qua non is not one in the sense of a numerical whole but, rather, in total; that is, the analysis of what it approaches without the ability to encapsulate it. Perhaps a distinction of a numerical one (i.e., in toto one) and a in total one would be useful in the essay?
Again, I would say that all of this, including any conceptions without numbers, for all intents and purposes, is being conceived numerically (that is, in toto). just w could very well, depending on how one is noting its form, be one (in toto) or one (in total)--I am unable to discern given the context thus far.
In terms of the arguments for our contingency on words (as an example), that argument is ultimately contingent on PoR. A set of implicit or explicit superordinate rules were utilized to derive the conclusion (reasonable and rational conclusion I must add) that a human being is contingent on words to explicate their messages (or at least, heavily contingent, as body language is a thing technically). However, the argument from the essay is that without PoR not a human being is contingent on words.
I am not quite following what you mean by W alone: could you please elaborate a bit? The point of noting the form of an infinite is for the expression that one cannot omit it without absurdity in relation to the definitions provided: it, simply put, cannot be bounded. I feel like we are more in agreement then we may have realized.
I view this as you defining concept as having an essential property of bounded form; however, it is possible to define it as bounded or unbounded in form and I do not see, as of yet, why this would be a contradiction or an absurdity. Therefore, I think, so far, we are merely semantically disagreeing. If by concept you mean something with necessarily bounded form, then I simply would have to come up with a different term. I think what you are trying to convey is that that term I create, whatever it may be, is necessarily bounded in form: but why? At the bare minimum, I can conceive of a concept which prohibits boundaries as a continual process (therefore, not merely within a context of space or time or what have you).
I agree! I think that I am going to begin building off of the essay and, once I am done, I will post them all together (as I think doing it in segments has only produced more confusion). I think that this essay will be readily available to reference if a conversation requires it, but theres no need to squander time on it right now. With that being said, I still would love to hear what everyone thinks, so continuing to contend with infinities is totally fine with me: I will just be allowing myself to continue my adventure whilst that is occurring.
Regardless of how one puts it, whatever they derive utilized the principle that the subordinate rule(s) could not contradict the superordinate ones. However, the tricky and slightly confusing aspect is that, they can most definitely utilize PoR in a manner where they are convinced that it is not true or the case.
For example, if I were to postulate a concept of a being that cannot derivate, then I am doing so by means of deriving something which cannot derive. Consequently, whatever concept I derive for non-derivation is contingent on derivation to have been manifested.
As another example, if I were to postulate a concept of a derivation that is not the use of subordinate rules not being able to contradict the superordinate rules, then I can readily identify the superordinate rules I utilized to even derive that very concept itself. As a particular example:
I concluded X.
Y was the sole superordinate rule within the derivation of X (i.e., I determined it solely off of X, lets say).
X is and is not true of Y.
Therefore, PoR is not applicable to this derivation.
Therefore, PoR is not true.
If I take it as granted that each is true (e.g., Y actually was the sole producer of X), then I can dissect this further to realize it is being derived by PoR (as it is a mere facade that it is not applicable by means of the possibility of negating it). For example, for me to have concluded X, I abided by the rule that the following could not be true and false within the derivation: X can be true and false of Y and Y can still determine X, but thereof cannot be true and false lest I concluded X is indeterminate as is. Likewise, to determine something as the sole contributor requires its own set of derivation with this same exact relation (and PoR being not applicable by some deductive or inductive argument, and PoR not being true by some deductive or inductive argument, etc.). Likewise, my argument that it is required requires one, and so forth. I can quite literally keep abstracting, particularlizing, and more generally deriving this infinite nest whereof it never rests upon an absolute foundation, so to speak.
This even functions for irrational or absurd derivations, such as:
I think 1 = 2 is true and 1 = 1 is true
We can perform analysis on this in any direction, with any goal, in mindbut one of particular interest is that they seem to be committing to the idea that 1 is and is not 1 (i.e., the absence of the law of noncontradiction): that would be an implicit superordinate rule.
In explicating that to them, they may reject that notion as well:
I accept the law of noncontradiction and 1 = 2 and 1 = 1 is still true.
Assuming, for all intents and purposes, that they arent merely conceptualizing things differently or semantically refurbishing well known concepts, they are still abiding by some set of superordinate rules to be able to possibly derive it in the first place. It could be that they hold the law of noncontradiction as exempt from itself or some other goal motivating their derivation, but the point is that we never get to a point where we can rest metaphorically upon absolute grounds, so to speak. Even if I conclude that they simply derived it arbitrarily, then the rule of arbitrary randomness governed their derivation. And my conclusion thereof and its justification will be by superordinate rules as well.
Bob
Or be revealed as poetry that can't be combed into a formal system ?
I may have been focusing too much on bounded vs unbounded when I think toto and total are really the focus in your essay. I think what I'm trying to note is that no matter how you shake it, toto and total are both bounded infinities. But I honestly don't think that's important to your overall concepts and where you want to take the essay.
So with this, let me make sure I understand your definitions of toto and total without the use of bounded and unbounded infinities, but just infinities. Instead, let me relate it to concepts if I could.
Lets look at the concept of "trees". A tree can be imagined an infinite number of ways. In toto seems to be close to "realized".
"In toto, on the contrary, cannot be conceived for a given concept without admitting of that concept bounds (in form). " - Foundational Metaphysics
So if I were relate this to trees, perhaps we could say its the realized number of trees for just one person. But, just because we have a realized a limited number of trees, it does not negate the fact we could keep realizing more. In fact, an infinite amount of trees if we so desired.
To my mind, the words total and toto is more like potential vs. actual. If I imagine the total amount of trees I can conceive of, its infinite. But if I imagine the tota number of trees I can conceive of, this seems to require a form of some sort, like trees. But, when speaking in total, I require some word like "trees" as well. There's no real difference in this instance, because both are still the unrealized concepts of trees themselves.
Instead of using both tota and total as representatives of infinity, perhaps one should represent infinity, while the other represents what is realized within the potential infinite. Infinity after all, can never be fully realized by any being. It is a concept of an unending pattern. I think this is also where you're implicitly intending to go, but feel free to correct me if I'm wrong.
So for example
1. The total number of trees I can realize is the unformed potential of all possible trees. As they are unformed, we cannot establish them all. It is an unending pattern.
2. The toto number of trees I can realize is the actual number of trees I realize (perhaps through my life? Or X time?). Perhaps in your original conception we could say if you lived an infinite time, the toto number of trees would be all the trees you actually conceived of during your infinite life.
The point that I want to note is that there is no actual infinity, only a potential infinity. As we are limited beings, the actual of what we are cannot be noted in terms of infinity.
I also don't think this hurts your essay. If we go to the principal of regulation, we can then apply the concept similarly. The total number of derivations I'm able to make is infinite. The tota number of derivations I have made are X. We can derive from concepts in two ways. I can derive a concept post, or subordinate, that follows from my current concept. Or, I can also derive a concept pre, or superordinate, that creates a concept that one could use to lead to the original concept.
As an example I could create the concept of a man on a moon. Then I could create the subordinate concept that, "The man traveled there from Earth". Taken without the consideration of derivation, one could say, "Ah, the man traveled to the moon from Earth, that's why they're on the moon." While the order of time or logical consequence might indicate it as the "beginning", in order of derivation, it is actually the second concept conceived of.
As such, we could say the toto number of concepts would be the derivation chains I've conceived of, but in total, there are an unrealized infinite I could conceive of. Is this along the lines of your thinking, or am I still missing or confusing something?
This leaves the sqn. What I feel you are trying to imply is that a sqn is what is required for the potential of derivations to exist at all. Because the total number of derivations I can make is unrealized, we're not going through and cancelling a "set" of all unrealized concepts I would actually make, but the total potential of what I could make. Because this is unrealized infinity, there are no "numbers" or actuals to negate, only the potential itself. Does this work?
If this is the case, you're noting that the principle of regulation is a sqn, because without the principle of regulation, there can be no derivation in potential. If derivation could only be done with subordinates, it would miss the picture of the superordinate. If derivation could only be done with superordinates, it would miss the picture of the subordinate. And if a being did not consider anything subordinate or superordinate, there would be no derivation at all.
For me, this is where I think the essay runs into problems. Noting that derivation has both superordinate and subordinate concepts is fine. But those are simply definitions we can realize. What is to prevent a person from defining derivation as something that is only subordinate? What if they made a different word for constructing a superordinate, and did not find that was a derivation at all? What if something has a completely different thought process than ourselves?
Quoting Bob Ross
Yes, you are doing so, but you didn't negate the fact that the being could not derivate. And this being may be a highly intelligent being, even another human. Such a human could not use the the PoR. But this is basically because we have defined it as such right? If something cannot conceive of both superordinate and subordinate ideas, by definition, it cannot derivate. The PoR is not a universal concept that can be used or understood by all thinking things. It is a descriptor of certain logical processes of some beings.
But here is where I don't see a problem. The PoR is a concept that can be used and understood by many thinking things. I don't think you need a sqn to assert the PoR as a concept to derive other concepts. I think its a fine proposal that can be demonstrated, used effectively, and agreed upon by most people. Is it a necessary concept to thought itself? No. But is it a fine concept that I believe you will use to derive and explore other interesting and possibly useful concepts? Yes! So please continue Bob.
Here are commonly accepted concepts and notations:
[math]S=\left\{ {{s}_{n}}:{{s}_{n+1}}={{s}_{n}}+\frac{1}{n},\text{ }{{s}_{1}}=1,\text{ }n=1,2,3,4,... \right\}[/math]
[math]T=\left\{ {{t}_{n}}:{{t}_{n+1}}={{t}_{n}}+\frac{1}{{{n}^{2}}},\text{ }{{\text{t}}_{1}}=1,\text{ }n=1,2,3,4,... \right\}[/math]
[math]I=\left\{ r\in R:0\le r<1 \right\}[/math]
[math]Y=\left\{ q\in Q:0\le q \right\}[/math]
[math]X=\left\{ 1,2,3 \right\}[/math]
S is countable, infinite, unbounded above but bounded below.
T is countable, infinite, bounded above and below.
I is uncountable, infinite, bounded below by its greatest lower bound, which it includes, and above by its least upper bound, which it does not include.
Y is countable, infinite, bounded below by its GLB, which it includes, but unbounded above.
X is finite and bounded above and below.
I suggest either using "bounded" and "unbounded" in their proper sense or defining other words to express what you mean. For example, S and T could be called something like scripted infinities, whereas I and Y would be unscripted infinities. But other mathematicians might disagree. If one has any math training it is disconcerting to read your definitions.
Nice to meet you Pie!
Could you please elaborate on what you mean by this? At prima facea, I dont see how the essay would be poetry, as I am thinking of writing that uses rhythm, vivid language, and often rhyme to provoke an emotional response . In the essay, I am attempting at defining, clearly, a sine qua non and, thereafter, that the principle of regulation can be regarded as a such: I am not sure what emotional response can be derived therefrom, but I would be interested to hear what you think!
Bob
Wonderful analysis as always Philosophim: let me try to adequately respond.
For clarification, in toto and in total are meant to describe totality in relation to forms vs. contents of concepts (as a distinction between them) and are not infinites themselves. In other words, I would like to clarify that neither in toto nor in total are concepts that directly entail an infinite: the former is a conception which is conceived (i.e., defined) as holistic, whereas in total is the conception of the summation of its parts (i.e., in content).
Therefore, one can have a conception, A, of which they conceive in toto (i.e., as complete in form) and be able to formulate a conception, B, that is the summation of the parts of A (which would be in total). For example, I can manifest a conception of a set of integers {1, 2, 3} and determine that the summation of the parts as 6: the former is a conception in toto, and the latter is a conception of that conception in total. Firstly, I would like to clarify that by summation of parts, I am purposely leaving it vague, like that of a protocol, which is merely meant as any sort of combination of entities (e.g., {1, 2, 3} could be concatenated or mathematically summed for all intents and purposes or even a limit: 123 or 6 or what have you).
Secondly, it is important, as you probably immediately noticed, to note that my previous example is of a concept of finite form and content: now, we must properly determine the possible permutations of both to provide further exposition into such a distinction. For both, I think it is reasonable to conclude that there are three options for each:
1. Indefinite
2. Infinite
3. Finite
And, thusly, we can analyze each permutation of such, like so (briefly speaking):
Indefinite form and indefinite content
Indefinite in content dictates we cannot determine it in total but, rather, only the scope which we currently have.
Indefinite in form is a bit trickier to imagine, but it is something which the individual at hand has neither asserted its finitude nor its infinitude. Arguably, this is simply a state of confusion; that is, I am fairly confident, given a confused example, that I could expose whether it is finite or infinite.
An example of this would be if I were to know that there is a function, f(x), which has a point (3.3, 4.27) and I were to conceive of its form as simply undetermined in bounds (i.e., I am simply confused or, at least, refraining from judgment). The knowledge of the point is a scope, so to speak, of which I know of the content of f(x) and my undetermined boundaries of the concept of f(x) is form. In terms of the former, I cannot determine in total, but I can meaningfully assert that whatever it is it must involve that point. In terms of the latter, regardless of how mislead I may be, I simply have not asserted a form (even though, as I stated previously, I think both of us would probably be able to tell which one it really is).
In terms of the essay, this kind of conception (in form and content) is simply a state of confusion or ignorance and, therefore, is not relevant to the principle of regulation.
Indefinite form and infinite content
An infinite content can be determined in total.
An indefinite form, as per the last example, is simply a state of ignorance, so I wont linger on it any further.
An example would be a function, f(x), where I know its absolute minimum is y = 2 and that the limit as x approaches infinity from the right side is infinity (no rhyme or reason to those numbers, I just made them up). I can conclude, in total, that the sum of its parts (i.e., y values, lets say) is infinity: for an absolute minimum at y = 2 indicates that f(x) is never negative ys and the limit from the right being infinity tells me that even if the limit to the left is a finite number that the summation of the ys will be infinity.
Again, I would say the concept is finite (that is, bounded), but technically I could be in a state of ignorance or confusion, thusly determining it as indefinite.
Indefinite form and finite content
This is really just ditto but with finite set of numbers (for example), so I wont linger on this either.
Infinite form and indefinite content
So this is interesting, because it is incoherent: if I assert that a concept is infinite in form, then its content must be infinite. If I assert the content is finite, then I must, conceptually, either implicitly or explicitly, fill the remaining parts with voids (or a filler of some sort). Otherwise I am admitting the concept to be unable to be negated, for example, yet have a totally negatable finite content, which isnt coherent. The only way to repair this conception is to admit of it void filler parts.
Infinite form and infinite content
This is the realm of sine qua nons (and, in virtue, the principle of regulation): a concept which is repetitive affirmation of negations would be an example of it. This kind of form entails, I must add, only one of its kind as a conception (and not just merely in existence).
Infinite form and finite content
Same situation as infinite form and indefinite content: I must either (1) fill with voids to ensure the form is coherent with the content or (2) strip the form to a finite.
Finite form and indefinite content
This would be a concept which we have limited scope of its content, but we do conceive of it in toto; that is, as a finite form. This is perfectly coherent in itself.
Finite form and finite content
There are ample examples of this one that I feel you are well aware of, so I will not linger.
Finite form and infinite content
This would be like the whole set of natural numbers.
Besides providing the aforementioned as hopefully a means of better explication on my end, the other main point here is that nothing about knowing in total grants anything in toto, and vice-versa.
So, let me finally address your trees analogy:
The concept of trees is a bounded concept because it is conceived in toto (that is, a holistic concept) and I can determine in total the summation of its parts. In other words, for example, I can negate your entire concept of the toto number of trees ... just as much as I can for your total number of trees ... because I can bundle them up into a holistic concept (i.e., both are actually in toto). Likewise, I would like to stress that nothing about me asserting it as conceivable in toto entails what the state of in total is (other than what one could infer from my explication of the permutations of form and content).
Arguably, I would say there is one which could be valid but if it is then there cannot be more.
If I am understanding you correctly, then I would say that you are noting something distinctly different from in toto vs in total; they refer to the same conception and, therefore, to convert your idea here, it would be more like: the number of concepts that you have conceived of would be finite in content and bound in form; or, if you wanted to attempt it, infinite in content and bounded in form; or, infinite in content and unbounded in form; etc.
I believe so: a sine qua non (specifically denoted as the principle of regulation) is what is required for the potential of derivations to occur. A sine qua non is sort of like a procedure wherein one negates all concepts in total, but obviously by means of strategic elimination and not brute force (as that is impossible).
Thinkers can most certainly (and arguably will) construct their own derivations that omit, in definition, the concept of superordinates, subordinates, PoR, sine qua nons, etc. To me, this is not a problem: I am not attempting to argue that it is impossible for one to miss this principle. By means of it, it is entirely possible to never realize it. In your philosophy, I would view this as analogous to discrete experiencers, which do not, for your argument to work, have to ever realize they are discretely experiencing. Nothing about this, to me at least, is wrong nor a contention with the essay. But please correct me if I am wrong!
I guess I am a bit confused here: what, in terms of mere possibility, could be defined as a thinking being which necessarily does not derivate? I would argue, upon further reflection, that all life can be classified as using PoR. PoR itself holds no inherent necessity of the degree by which it can produce superordinate/subordinate rules: a plant grows towards light, a bee operates by means of calculated movements (albeit not necessarily self-aware), etc. By my lights, I am having a hard time thinking of anything that would be constituted as thinking yet cannot derivate (to any degree, more specifically).
I look forward to hearing from you,
Bob
Thank you jgill for the elaboration! I am most definitely not an expert mathematician and I most certainly do not want to come across as disconcerting. Let me attempt to adequately respond to your post and you correct me where you deem fit.
Unfortunately, I do not know how to properly format mathematical equations on this discussion forum, so for now I will have to write it in less pretty formatting (dearest apologies in advance).
I think that I understand: there is a set, S, where S is the outputs of the function equal to:
f(n) = n + 1 / n
Where n is constrained to be positive integers (i.e., natural numbers).
It is infinite because the limit as n approaches infinity is infinity, i.e.:
limit n + 1 / n = ?
n ? ?
Because 1 / ? is equal to 0 and thus we have ? + 0 = ?
This one is confusing me a bit, as I dont see how it is bounded above. By my lights, since we are speaking of natural numbers, then the negative n values do not exist and, therefore, are omitted from our consideration. Therefore, although taking the limit of n ? - ? is - ?, it holds no relevance if we are speaking of only positive integers for n. Therefore, the limit one really ought to care about is n ? 0:
limit n + 1 / n^2 = ?
n ? 0 +
limit n + 1 / n^2 = ?
n ? 0 -
They equal each other, therefore:
limit n + 1 / n^2 = ?
n ? 0
And, also, it is important that as n approaches infinity it also equals positive infinity:
limit n + 1 / n^2 = ?
n ? ?
Both, in quadrant one, approach infinity and, consequently, I do not understand why the related function, f(x), that is the values contained in set T, would be bounded above and below: are you referring to the x = 0 asymptote (i.e., that it is constrained to natural numbers)?
Makes sense.
I think that bounds in mathematics is simply asymptotes, limits, restraints to X or Y, and any finite segments (e.g., T would be bounded on the left and restrained to natural numberscontrary to my previous contention--, and a line segment from the interval [0, 3] inclusive would be a bounded finite).
To explain my form vs content, take set T that you defined and, more specifically, take note of my previous contention/confusion (i.e., the limit exists for 0 even though 0 is an asymptote because the left and right converge to the same value, which is valid technically). The content of f(n) would be the y outputs and the form would be, with respect to the left in quadrant one, its bounds to the asymptote x = 0.
At a deeper level, though, the problem would be that any unbounded f(n) one could provide is bounded to the, in toto, concept of that two-dimensional spatial graph. Nothing about it is an unbounded infinite; although I understand the confusion now, as I am not refer to a contextual usage of the term unbounded as in n ? ? = ?.
Bob
Alas, for reasons good or bad I have no clue, you've compromised on what Robert M. Pirsig calls quality! No matter, I understand!
Hi ! I sometimes talk with people on forums who have various intuitions and suggestions about infinity and other mathematical concepts. Often enough they've had no experience writing mathematical proofs, which is like not knowing quite what math is, at least to a mathematician (even if, in fact, one can go a long way in applications without ever learning proofs.) 'Poetry' is a just a metaphor for these ideas that are not yet in mathematical shape. It's fair to expect some mastery of real analysis from an innovator. (Algebra and topology are natural mentions, but real analysis is the serious theory of the numbers we all are somewhat familiar with.)
Bob, when one expands the sequence:
[math]{{t}_{2}}=1+\frac{1}{{{1}^{2}}},\text{ }{{t}_{3}}={{t}_{2}}+\frac{1}{{{2}^{2}}}=1+\frac{1}{{{1}^{2}}}+\frac{1}{{{2}^{2}}},\text{ }{{t}_{4}}=1+\frac{1}{{{1}^{2}}}+\frac{1}{{{2}^{2}}}+\frac{1}{{{3}^{2}}},\cdots ,\text{ }{{t}_{n}}=1+\sum\limits_{k=1}^{n-1}{\frac{1}{{{k}^{2}}}}<\infty [/math]
Quoting Bob Ross
The real numbers constituting [0,3] are uncountably infinite, but the set of these numbers is obviously bounded above and below. This would of course be a finite line segment.
Quoting Bob Ross
No. S is unbounded above, and if one plots a graph of the terms of S (vertical axis) vs n (horizontal axis) one would need a piece of paper having infinite dimensions. However, the sum of that series diverges so slowly that the sum of the first 6,000,000 terms is less than 21 !
I appreciate the elaboration: thank you! I understand what you are conveying and I think it is perfectly fair and reasonable. However, I would like to note that my essay is not within the actual sphere of mathematical discourse (in other words, it is not a paper intended within the context of formal mathematics): it is a philosophical work pertaining to metaphysics (which I am understanding your metaphorical use of 'poetry' to be synonymous with 'non-formal-math' so to speak). Although there is always much to read, I can say that the vast majority of philosophical works pertaining to metaphysics that I have read do not provide formal mathematical proofs because, quite frankly, it isn't meant to do so. With that being said, if you think I ought to provide a formal mathematical proof of something within the essay, then please feel free to let me know! I would love to hear your critiques.
Bob
Awe, I see! I thought you were outlining a set because T was encapsulated in brackets, which I thought meant 'a set'. Correct me where I am wrong, but T = { } seems to be a set and not a summation (?). To me, nothing about the notation of T = { ... } entailed that one is summing each t of n. My question to you would be, assuming I am simply misapprehending, what about your previous notation entailed (symbolically) the summation of T's elements? I understand that your use ? in your most recent post does, but I am failing to see how the T = {} does.
In terms of summing t of n, I totally agree and understand that starting at 1 will result in the limit approaching infinity to equate to 1.
Agreed.
That is true; however, the entirety of mathematics is bounded philosophically speaking. For example, S is unbounded above because it approaches infinity, but S is a bounded concept of which I can negate: not S. This is where we start the philosophical inquiry which has no bearing on formal mathematics. If S were philosophically "unbounded" as a concept, then it would bleed into everything, so to speak: S would also encompass a jurisdiction over my apple I am eating right now, which we both completely understand this is by no means the purpose of formal mathematics whatsoever.
I think, and correct me if I am wrong, we are simply contextually utilizing the term differently for different contexts of inquiry (one of philosophy and the other of formal mathematics). For example, in mathematics, a line segment is bounded and yet has an infinite amount of points in between (due to intermediate value theorem), while a line that approaches negative infinite and positive infinity that is constrained to asymptotes x = 1 and x = 5 is also bounded with an infinite amount of points in between those asymptotes; for math, there's is a meaningful distinction between the two, but, in terms of what I am noting, they are both bounded infinites.
If you believe this to be a confusing conflation of mathematical terminology, then I am more than willingly to consider what you think would be better terms!
Bob
Perhaps you might just stick with the archaic terminologies of infinity (potential & actual) and avoid "bounded".
This is an essay in philosophy, not mathematics. Don't worry about it. It's your project. I'm still unsure of what PoR is, other than a sort of linear process that goes from previous to following. I'm not your target readership. I have enough trouble trying to keep up with a very minor PoR in a certain low interest math topic. :cool:
Likewise Bob! Despite my points against your essay, I am always impressed by your creativity, open mind, and thought process. Lets dive in again.
Quoting Bob Ross
For me, the confusion about toto came because your previous paragraph talks about infinity. You then mention toto is a concept without bounds, which implies infinity. But if I'm understanding correctly, we're really talking about form, vs what makes up that form. So for example, a tree is a form. All the indeterminate encompassing (possibilities?) which can make up the form of a tree are toto, where as if we could know all the possibilities, we could summate those in total.
But then there seems to be a contradiction here:
Quoting Bob Ross
If a set of integers is 1,2, and 3, aren't the total number of integers 3? If we're listing the set, then we can say the collection is made up of 1,2, and 3, and we don't need the word toto.
Quoting Bob Ross
Here is where I also think there is a conflation of words. Bounded does not mean finite. You can have an infinity for example that is bounded by whole integers. All meaningful infinities are bounded. An unbounded infinity, is everything without any defined concept. In the past I've called it "the sea of existence".
Bounded can also refer to the finite. So I could have a set of integers bounded between 1 and 4. Those integers would be 2 and 3. My point in the earlier post was to note that when we speak of meaningful infinity, it is always bounded. It may be bounded by the idea of, "All integers". So that would be an infinite set of numbers that precluded any fractions. This is the same as stating, "All integers less than y=2".
Thus if the following is true:
Quoting Bob Ross
then all meaningful infinities can be determined in total. This again leaves me wondering where toto falls. Again, the overall feeling I get from your essay is more that toto describes the indefinite, or the unknown. The toto number of trees a person can conceive of is an indefinite concept, but one we can conceive of with some type of limit. It is not infinite due to a person's limited life span, but one cannot actually count the number of possibilities.
We can also imagine the idea of an infinite amount of possibilities one person could potentially imagine, even though in reality there are only a limited amount they actually imagine. I could see this as the infinite version of toto that expresses indefinite form. The problem is provability, which of course one can never do with the indefinite.
But again, I'm still not sure we have a clearly defined and applied term of "toto". I think it loses its use in your paper because I believe there is a misunderstanding of infinity and the term bounded. With the idea that all meaningful infinities are bounded, and that we can also bind finite sets, how can toto be used clearly without any ambiguity?
Quoting Bob Ross
So back to this then, infinite form and content would be all possible forms one could give within all of infinity. This again is the unbounded infinite, or all of existence that one person could form. If you remember our conversation, a form as I'm seeing it would be a "discrete experience". I have largely avoided referencing the terms in my previous paper, as I do not want to distract from yours. But I feel this accurately communicates my intentions easiest, so I will do so here. This is the form within the infinite. So all possible forms would be all possible discrete experiences.
So within all possible forms, you propose a concept that if this concept does not exist, neither can any other concept. Without this discrete experience, no other discrete experience can exist for example. While I am ok with the idea of this, I still am having difficulties seeing how the principle of regulation is this sqn.
Only repeating myself once, you still have the problem of a thinking thing that does not derive. I've mentioned before that you would have to analyze other thinking things besides humans to show that all thinking things derive. At best, you can claim that all humans of a certain intellect derive. I have no problem with this.
At a conceptual level beyond all of this, I would still assert that one must come up with a concept first before one can derive from the concept. The sqn to me would be that one must be able to conceive some form within the unbounded infinite. Without this, no other form can exist within the infinite. From there you could derive the principle of regulation, but I do not see it as a sqn itself. So if you are to assert that the PoR is a sqn, how do you deal with the above concept? Is it not true that the real fundamental is the ability to first conceive of a concept, before one can derive from that concept?
Great work again Bob, I look forward to hearing from you!
The use of numbers and infinities seems to create confusion. Even the use of the word "derive" is a bit problematic. Are you speaking of the derivation of concepts or of physical processes that demonstrate cause/effect, or both?
Hello Philosophim,
As we already discussed, I apologize for the late and overdue response: I have been preoccupied with other things lately and, thusly, have not had the time to adequately respond.
Moreover, since it has been so long (which is entirely my fault), I have developed my view quite significantly since then; so much in fact, that I think a bit more elaboration on my end will suffice to relinquish all the confusion that has sprung thus far (as they are squarely, in my opinion, due to the vagueness and prematurity of my original essay).
Firstly, I would like to note which terminology (of which I used in the essay) that I find to be of no use anymore: pretty much all of it other than PoR itself. Sine qua nons are, in hindsight to me now, just an obscurity conceptually that need not be invoked to convey my view that pertains to the essay. Honestly, I should probably just re-write it. Likewise, infinites do not need to be invoked (or at least I dont think) to portray the real, true underlying meaning I was so inadequately trying to express.
Consequently, I think it is better if I elaborate on what PoR really is instead of focusing on deconstructing my own essay (because it is too inadequate and confused to me now). PoR is really what I would consider the fundamental logic of reason (as the faculty of the mind) in a transcendental sense (i.e., the necessary preconditions for the possibility of being a mind). It is that which is implicitly required to be a mind, as opposed to something one is or is capable of fixating upon as a mind; so, to address your contention about provability, there is no requirement for a being to be capable of thinking rationally in sense of fixating upon formal logic or what have you to nevertheless fundamentally be governed by PoR; and there is no need for a being to derive in the sense of what the average human being doesas by derive I mean it in a more general, mere sense: an implicit conclusion. A plant doesnt decide nor is it aware of its conclusions but it regardless derives to grow towards the light.
Which leads me to a giant cause of a lot of ambiguity in my essay: the incredibly blurry line between concepts and objects. I made it sound, with the use of infinites, like a sine qua non would be essentially a pure infinite object, which would just equate to an unterminating, absolute infinite of existencewhich is not what I was trying to convey (but I inadequately described it). What really should have been described is that which a mind is contingent on in order to even be such (i.e., transcendental aspects of a mind) and that would have segued into PoR as an example of it.
To give you a bit deeper insight into my position now, I hold that all life is fundamentally will, and will and mind are inextricably linkedas to be a will is to choose one motive over another at any given point in time (which I would consider a process of a mind). Therefore, I view a plant just as much as a human as a will and, subsequently, as a mind where mind is meant to be interpreted in its most rudimentary sense (as obviously there is much difference in terms of a human mind vs a plant mind). I dont think a plant is thinking in the sense that it is leveraging words and concepts to derive its next move but, nevertheless, it does fundamentally choose a motive over another (e.g., it grows towards the light). PoR is a guiding, necessary principle of being a mind (and a will): there are superordinate rules (i.e., subjectively affirmed guiding principles) which derive the conclusions (i.e., subordinate rules) which, in turn, guide the actions of the will. There is no person alive which can be without with principle (implicitly): no matter how disabled they may be, they are fundamentally a will and a mind which, in turn, entails that they performs actions (no matter how basic or ill-executed) based off of intentions which, in turn, are motives which were determined by obligations to rules (i.e., superordinate rules). To me, to posit hypothetically a being which has not PoR is to posit an unalive being (i.e., a being with no will: a corpse with no life).
Hopefully that helped clear up the confusion and if it didnt them please let me know! Again, I apologize for the belated response and for the fact that my ideas have evolved since our last encounter but, nevertheless, I hope I adequately addressed your contentions (otherwise, please point out where I failed to do so).
I look forward to hearing from you,
Bob
Hello jgill,
I apologize for the belated response my friend! I have been, unfortunately, very busy and havent had the time to look at the forum.
Now that I have been thinking about it more, I think you are right with respect to many regards: I do think that, in hindsight, I wrote the essay too vaguely and inadequately; so I totally understand your confusion.
To answer your question, what I was talking about was, in hindsight, transcendental logic (i.e., the study of the necessary preconditions, sometimes called a priori conditions, for the faculty known as reason); and so by derive I was referring to reason with no direct connection (or disconnection) to causality. Personally, I dont think reasoning is a process which can be reduced to physical causality, but I dont think it matters which stance one takes on that issue to accept PoR.
I want to apologize again and thank you for your responses!
Bob