Infinite Regress & the perennial first cause
You could simply start off with asking whats the problem with infinite regression anyway?
Yet this never satisfied the philosopher, namely Aristotle. Hence the proposal of first cause or the uncaused cause.
I find his dissatisfaction with infinite regression unsatisfactory for if infinite causes are the chain of sequences ad infinitum does such a chain not imply a closed loop, like that primordial snake ouroboros eating its own tail.
As far as I see it neither a first cause nor infinite causes solve the problem of infinite causality, but visual aids help to a certain extent, in the end were left with a circle asking where the circle came from is a valid question and its representation of circular logic in a way answers it.
The circle drew itself, this is the conclusion I draw from it, meaning it was self caused.
But hang on a second, if it was self caused then there cant be an infinite regression of causes.
Anyone wanna trash this theory?
Yet this never satisfied the philosopher, namely Aristotle. Hence the proposal of first cause or the uncaused cause.
I find his dissatisfaction with infinite regression unsatisfactory for if infinite causes are the chain of sequences ad infinitum does such a chain not imply a closed loop, like that primordial snake ouroboros eating its own tail.
As far as I see it neither a first cause nor infinite causes solve the problem of infinite causality, but visual aids help to a certain extent, in the end were left with a circle asking where the circle came from is a valid question and its representation of circular logic in a way answers it.
The circle drew itself, this is the conclusion I draw from it, meaning it was self caused.
But hang on a second, if it was self caused then there cant be an infinite regression of causes.
Anyone wanna trash this theory?
Comments (142)
Bravo invicta! I applaud you for this determination.
Infinity and finitude are two sides of the same dynamic. They require one another as mutual existants.
The circle is the perfect elementary geometric example of the relationship between infinite irrationality and A-B linear or finite rationality.
A circle has 3 features. The circumference, The radius and the focus/central point.
The relationship between these 3 things represents the whole spectrum, the relationship or "triad" between infinity and finitude (the two poles at either extreme).
The central axis is static. Unmoving. Unchanging. A single point. A singularity. It is finite, fixed. It is highly rational. Located. Consistent. Constant. Objective.
The radius is a midway between the circumference and the central axis. It is the link between them and thus shares both properties, it exemplifies balance: half fixed, half dynamic/changing: in the sense a radius is fixed in length, but dynamic in angle of relationship to the center. The radius can assume any projection/vector or rotation in 360 degrees of the central focus. So it represents the interim relationship between the other one 2.
Finally we have the circumference. Purely irrational in vector/direction and length. Never is it moving in the same direction to the previous point along it's course.
The angle or relationship with the center is constantly changing, a state of pure flux, as it revolves around it. It's length is also arbitrary in that it flows directly into itself endlessly. Arbitrarily, we can assign a start point and an end point such that we could make the circumference linear (to unravel it/straighten it up) and assign it a finite length in relationship to the length of the radius from the center, but in doing so we violate it's circumferential nature. We disengage it from the central focus when we examine it's arbitrary finite length.
Ultimately the beginning and end are the same point on any circumference.
Pi determines the relationship (thus naturally using the radius or diameter - double radius) between the center and circumference. It is irrational and endless. But can be made finite to any decimal place for convenience, at the disposal of accuracy.
When this comes to linear vs circular arguments. They are inseparable from one another, and biased in their individual favouring of either infinity or the finite as a satisfactory explanation. But in either case they're both equally correct and incorrect. Neither can be taken in isolation, as an absolute and final account. The only truth in linear vs circular argument lies in understanding their relationship to one another. And their innate non-rectifiability. The relationship itself is the real unifying factor.
The "infinite regress" is the circumference. As it tracks into itself or infinitely regresses into itself ie "loops" or "revolves".
Everything "infinite" revolves around something "finite". Just as everything that is in a permanent state of change (falsity, transformation or flux) revolves around something permanently unchanging (fundamental truth/constancy/law/rule).
My advice in your quest for answers, is to read into/research the significance, symbolism or role of the circle, cycle, wheel, revolution, circumpunct, sphere, dome, etc as well as triads, trinities, triangles and pyramids in ancient texts, religions, spiritual teachings/mysticisms, philosophies and science (biology, chemistry and physics especially) through the ages and make links between them as geometry demonstrates fundamental relationships and truths about the universe through all ages (because they are the innate structural and relative/relationship basis for all existants).
For Aristotle, the problem with infinite regression is that we would not be able to learn anything theoretical in such a universe:
I'm with you. It ties in with the question of whether or not something can come out of nothing for which I have two possible answers, depending on my mood - 1) Of course 2) It depends on what you mean by "nothing."
I could understand up to this point, after that I seem to have got lost in translation.
But back to the circle, this self-drawing circle. How could a circle draw itself ? This doesnt make sense when looking at it from this line of reasoning as its metaphorical at best. If it did indeed cause itself then why not a straight line ? Simpler, easier.
This is a non-issue because as you will see the circle answers the question more succinctly then a straight line as logical explanation, its our best understanding of infinity as a circle does not have a starting point. Yet when we do draw circles we have a starting point or two starting points to be precise if we wish to draw a near perfect circle the centre and circumference.
there could be more esoteric explanations as to infinity but theyre beyond my understanding.
Yet the simple yet complex circle which in itself contains Pi (itself an infinite) points us in such a direction in our inquiry. An irrational number that stretches forever, a hint there of the nature of infinity.
This apparently random number that has conjured the circle stretching forever yet producing the most simple of shapes, a circle ??
If I elaborate further it will sound like bullshit so I must stop here.
I applaud your perspicacity. There are mathematical ways of avoiding circles, but not now, I think. :chin:
I only say that because if I was to carry on Id be going in circles
Closed deductive loops are quite valid.
They just do not get you very far - no further than where you started.
Here, though, you seem to be claiming that a "sequences ad infinitum" implies a closed loop. It doesn't.
The trouble with making use of "first cause" is that the notion of causation is problematic.
Quoting SEP: The Metaphysics of Causation
At the very least, causation causes more philosophical problems than it solves.
Quoting jgill
Just so.
Funnily enough I was aware of the same objection upon writing, well spotted Banno. Still it might be defensible, and quite possible, so, but If it isnt I will concede.
Here we go. And please bear with me here.
Ad Infinitum of course latin for infinity. The circle of course being dictated by the circumference/diameter produces Pi. Now assume you only know Pi
Lets simplify
X/y = Pi.
If you only knew Pi, which you obviously cant as its irrational and infinite could you draw a circle?
Of course not.
Thus, infinity, taking Pi as a currently known example is non-repeating and unpredictable
Pi, draws a straight line in a circle, and since no we cant square a circle the implication of this is that not only is PI not self-recurring (non-repeating pattern) but that the relations of circumference/radius can never be calculated.
Of course we can know Pi: it's the ratio of circumference to diameter. I can draw a reasonable circle of any diameter up to a 20cm or so; after that the paper is too small.
I don't see that your argument works.
Its an example of circular logic in Action. The full Pi is non-repeating and goes on forever. You will draw a very good circle but it wont be a perfect circle sorry, because you cant determine Pi
No it isn't. The methods used to calculate Pi are iterative, not circular.
The implication being of course that a perfect circle is not physically possible only in the realms of mathematics.
I dont blame you Banno, where did this infinite irrational Pi come from, its definitely not something physical as a how could a perfect circle exist in the physical world when it cant be drawn, a perfect circle is only abstract and unable to be represented or drawn because Pi is non-repeating and goes on forever
Is it not purely abstract?
No. A closed loop does not answer Aristotle's quest for an explanation of Causation itself. Note that in the Ouroboros symbol, the snake that seems to be recreating itself, actually has a head and tail, a beginning and end. A true infinite loop would have no head or tail. :smile:
Youre saying im being irrational just like Pi. If pi was rational and predictable yet infinate would it not make a linear straight line rather than a circle ?
Point being, even Isolating Pi to 3 decimal places could you draw a non-perfect circle ?
That's actually a good point I have sometimes mused over. Perhaps the symbol is eternity as devourer of itself.
Hmm. Well, it seems you both go on forever.
I don't think Aristotle would have described his work that way. He was surrounded by those who rejected the idea of an intelligible whole. He fought them tooth and nail.
Not quite unpredictable, as the first 100 trillion digits in its expansion are now known. Why on Earth someone would make that their life's work is beyond me.
Quoting Banno
I suppose so. But when context is specified it's not so problematic. I put a kettle on the stove and turn on the burner. The kettle boils over. Because I turned on the burner - just don't go down the rabbithole. I can set up a causal chain in math using iterations or compositions of functions, basic in dynamical systems.
A circle is a very close approximation of Pi which is infinity itself.
It doesnt exist in the real world by the fact that in its close approximation it comes in on itself demonstrates the circularity of such an infinity.
In a sense, whilst Pi was known to the Greeks, it is actually a Greek letter in their alphabet, they never truly realised the implications of such a number, even Archimedean approaches never went more than two decimal places, so its real infinite nature was not readily apparent.
Though PI itself remaining an abstract with imperfect manifestation of itself in the form of a circle perhaps only comes to our understanding by fact of producing the approximation of such a shape.
PI even has a starting value. 3.14 somewhat implying that if it does have a starting value does infinity too?
I believe, again, that this line of reasoning is incorrect, even though by granting it such a concrete starting value (which is always an approximation), by the fact that this value itself never finishes, lets it remain in the realm of the abstract and pure mathematics.
That sentence is nonsense. A circle is not Pi. Pi is not infinity.
Of course its a circle, even though the approximate value is derived from circumference/diameter
You are far too casual with your terms. Pi is exactly the ratio of circumference to diameter. It is not infinite. It cannot be express with a finite number of digits in decimal notation.
Pi is not a circle.
Ok then mister, please give me the exact value of Pi :rofl:
Of course its a circle what is the value of the line when youve performed the calculation circumference/diameter its Pi of course.
On the other hand, extensional interpretations of a convention refer to worldly observations to which a mathematics convention is applied, such declaring a visible circle to represent or "approximate" Pi. Here the word "approximate" is misleading, for the visible circle isn't part of the convention but an imprecise application of it. (Any application of a convention is invariably imprecisely applied)
You persist with this crap, thats a formula of Pi.
Please paste below the infinite non-repeating sequence of Pi
But that does not make it infinite.
It is expressed exactly by
Surely youre winding me up, but Im not laughing Pi is serious business
The supposed issues that trouble you arise from your own lack of clarity.
Pi is clear as day to me, let the below image remind you again. Read @simes post
Theyre one and the same, or at least our closest understanding and interpretation of infinity. Neatly summed up and expressed by
So I'll leave you to it.
Well thank you for that :rofl: pi is not infinite apparently according to Banno, geez!
They're not, the sign expressed for infinity is simply ?
Further, you have different levels of infinity labeled ? (aleph)
Expressed as an infinite step, aleph-null, aleph-one, aleph-two, and so on.
Pi is not infinity, it is an irrational number that has its most common use in the measurement of circles, but it's much broader than that, featuring areas like trigonometry, probability, gaussian function, equation for the wave function etc.
Secondly do you deny that Pi goes on forever ? If you deny such a fact and dont believe that Pi goes on forever then youre as badly mistaken as Banno Im afraid.
@Christoffer
Doesn't matter how you twist it, these symbols are established mathematical symbols and terms that have a specific use. ? and ? are used for infinity in mathematics, while ? is not.
This is what Banno is saying. The fact that the decimals goes on in infinity does not make ? infinity. A property of a function or thing is not the thing itself. Your hand is not you, it's a part of you. If you say that Pi's decimals goes on in infinity, then you are basically saying ? goes on for ? in level ??.
Basically: ? ? ?
There's nothing to really dispute in this, you're talking about mathematics, and in mathematics there are no real grey areas, it is what it is.
It's not belief, mathematics is mathematics, so you either learn it and understand it or you don't.
Quoting invicta
What does this have to do with confusing infinity with pi?
Quoting invicta
So?
Quoting invicta
Does not change the terms and numbers used in mathematics.
Quoting invicta
Pi's decimals are infinite, it is not a term for infinity. I don't know why you persist in talking about beliefs like that, you just sound deeply confused.
Where's your argument? What's your argument and what's the conclusion you're trying to convey? I've read a lot of posts by you since you joined but there's very little philosophical scrutiny and practice in your arguments, you simply tell others to believe what they believe and that you are correct anyway. It mostly seems like you're just bombarding the forum with posts everywhere but have little interest in actual philosophical discussion or accepting established facts. In here you're actually trying to establish your own interpretation of something that has no interpretative angle, the terms and mathematics are as objective as anything comes. Their use is established and there's no post-modern deconstruct of any of it because it's based on pure mathematical logic.
? is not the term for infinity.
? and ? is the terms used for infinity.
If you profess some knowledge of Mathematics then youre clearly unaware of this.
https://en.m.wikipedia.org/wiki/Uncountable_set
Still, ? ? ?
An infinite set is not infinity itself. You are confusing ? with ? having an infinite set.
I don't know how to describe the simplest of logic here. I'm far from being a mathematician or anywhere good at it, but you don't have to be in order to understand basic logic. As an analogy, this is basically as logical as 2 + 2 = 4, but you are claiming that 4 is 2 because there are two 2s creating a sum of 4. All of this is basic mathematical logic and proper use of the terms. To say that ? is ?, is simply just wrong. That ? possesses ?? of its decimals, is correct, which is just what you linked to as a description. ?? is an infinite set, the decimals of ? is an infinite set... but ? itself is not infinity.
If you're gonna use mathematical terms in your argument (whatever that is), then you need to use them correctly in order for the argument to make sense, otherwise you will get into back and forths like this because no one understands your argument when you are confusing everything together and don't seem to understand the basic terms you use.
I still dont see how or even why youd object to that.
@Banno
Whats your problem ?
You declaring something does not make it true. That's a sign of pure delusion and in terms of discussing philosophy, you've reached a dead end since there are no axioms surrounding any argument you discuss, your own opinions, or your interpretation of other's arguments. It's a dead end.
Quoting invicta
Object to you declaring new meanings of established mathematical terms, or object to Pi having an infinite set of decimals? The former, yes, the latter no.
Quoting invicta
Correct
I take this as an admission then that pi goes on forever. Finally
Pi decimals goes on forever, it is an infinite set. However, that is not what you said:
Quoting invicta
That you cannot see the difference between "decimals go on forever" and Pi is infinity, is what makes you confused and unable to understand what everyone is saying. You simply seem unable to understand the difference, either due to a language barrier or simply a lack of knowledge, but you simply can't seem to accept that you are wrong in what you conclude here.
Quoting invicta
...but you just keep on going in some delusion that you still know more than the others even to the point where no one can take you seriously when you keep on trying to win an argument that is so globally and logically defined and accepted by everyone except yourself.
Why do you persist with this low-quality level of philosophical engagement? You need to up your quality.
I'm not an Aristotle scholar, so that comment was just my general impression. But here's a quote*1 that seems to have it both ways : Causal Monism (general causality) and Causal Pluralism (sequential causes). I suspect that Plato might be more inclined to view the First & Final Cause as a Holistic, Ultimate, Ideal entity or concept. In any case, only an Eternal (timeless) Cause would put an end to the infinite regress (space/time) of causation. Perhaps Einstein's Block Time*2 would qualify as Causal Monism, since there is no cyclic time for sequential causes to do their thing. :smile:
*1. [i]Causality is at the heart of Aristotles scientific and philosophical enterprise.
. . . Aristotle is committed to a form of causal pluralism . . .[/i]
https://plato.stanford.edu/entries/aristotle-causality/
*2. Block Time? : "Everything everywhere all at once"
Those like Aristotle and Leibniz, who think that time is not independent of the events that occur in time, deny the existence of absolute time, ..
https://plato.stanford.edu/entries/time/
During a discussion of his predecessors, Aristotle said Plato included two of the four Aristote worked with and why it was not enough:
The addition of the fourth cause (efficient) comes from not being able to treat the eternal beings and what comes to be and passes away the same way. A step toward that method was to get past the monism of Parmenides:
In this respect, the Prime Mover is the beginning of the series of causes but not the 'first' of that series because its principle is not the same species as the "moved." I would not call that a denial of the 'existence of absolute time' but a limit to what we can be thought about it.
Sorry, arguing with bear-trap is pointless. Each of you is looking at the question from a different perspective, so your views will never meet, unless at Infinity. :joke:
Pi is infinite :
"Pi is magic. It is a number that is infinite, universal, transcendental, and irrational. It appears everywhere, and my mathematician friends tell me that Pi is as close to religion as you can get in math."
https://press.princeton.edu/ideas/pi-is-magic
Quoting invicta
This is gobbledygook. But I would not be surprised were you unable to see that.
As usual, we have here a vocabulary conflict between people with opposing points of view. Such disagreements are not resolved by disparagement. The word "infinity" has several definitions, depending on context*1.
I suspect that is using the term "Infinity" to mean simply a never-ending series of numbers*2. Perhaps a better word would be "indefinite". His colloquial usage is different from your technical version, but not meaningless "gobbledygook"*3. My tongue-in-cheek "Pi is infinite" link may be somewhat "gobbledy", but it expressed a notion that may be closer to Invicta's usage regarding "infinite regress". The number PI is a never-ending series, but in practice it has a finite value*4. PI as a concept is irrational, and in a general sense unbounded or infinite*5. :wink:
*1. What is Infinity?
[i]Infinity is an idea of something that has no end. In general, it is something without any bound. It is a state of endlessness or having no limits in terms of time, space, or other quantity.
In Mathematics, infinity is the concept describing something which is larger than the natural number.[/i]
*2. Infinity : a number greater than any assignable quantity or countable number (symbol ?).
*3. Gobbledygook : language that is meaningless or is made unintelligible by excessive use of abstruse technical terms; nonsense.
*4. PI infinite :
How is pi infinite? Its not infinite in value. Its more than 3 and less than 4, so its numerical value is certainly finite. Whats infinite about it is the amount of time, or more precisely the amount of calculation, that it would take to express its exact value.
https://www.quora.com/How-is-%CF%80-infinite-if-a-circle-has-finite-area
*5. PI is irrational :
Hence, pi is a real number, but since it is irrational, its decimal representation is endless, so we call it infinite.
https://www.scienceabc.com/pure-sciences/do-we-have-any-mathematical-proof-that-pi-is-infinite.html
?2 and e are other examples of irrational real numbers, not ? either.
? or 1/3 is a rational number that can't be expressed by a finite string in ordinary decimal notation.
If we suppose there are no circles (in nature), then there are some other shapes instead.
What shapes are possible (in nature) anyway? Are straight lines?
The concept of self-organization might interest you. In this book, a theoretical physicist looks into the cosmology of Jacob Boehme. He makes the argument that Jacob Boehme's conception of a self-organizing world might end up being more important in the long run than his contemporary Galileo.
Or for something a bit more down to earth there is Erich Jantsch's "The Self Organizing Universe," which I have heard good things about, although it is a bit dated.
Melanie Mitchell's Complexity: A Guided Tour is very good to, but isn't trying to look at any sort of big picture. But, it provides a look at how "a circle can draw itself," in a systems perspective.
Huh?
Quoting invicta
You would deny Invicta the privilege of meaning what he says?
Then you are harder on him than even I.
The tools of philosophy are the words they use, so it is best we use them with due diligence.
The account in the OP is as follows:
Quoting invicta
And the clear answer is no, it doesn't. There is a difference between an infinite progression and a loop.
When this was pointed out, Invicta doubled down:
Quoting invicta
Of course, we do know pi. A formula for it was given above, and the definition is the subject of primary school mathematics. The discussion continued with Invicta playing on the two meanings of "irrational", only to arrive at
Quoting invicta
...which as i said, is gobbledegook. A circle is no more an approximation to pi than a fish is an approximation to a democracy; And Pi is not infinity itself.
Philosophy is about getting the words right. you, @Invicta and have yet to understand this.
And isn't far ahead of you.
That is not the sum total of the subject although it's an important part.
Aristotle's argument for a first cause is based on the observation that motion and change are fundamental features of the natural world and are characteristic of everything that we observe. He believed that motion and change cannot occur without some cause or explanation, and that this cause must itself be unmoved and unchanging. Aristotle argued that if there were no such first cause, then motion and change would be infinite and eternal, without any ultimate explanation or source.
I think part of the reason for his insistence that the first mover must itself be unmoving is derived from the Phaedo. In that, Socrates suggests that in order to explain a particular phenomenon, one must have knowledge of a more general principle or cause that underlies it. Socrates refers to this more general principle as the "cause" or "explanans," and the particular phenomenon as the "effect" or "explanandum."
Socrates asserts that the explanans must be of a higher order than the explanandum, because it is the more general principle that explains why the particular phenomenon occurs. By this logic, if the unmoved mover itself was subject to motion and change, then it would provide no explanation for these, as it would itself be part of what we are required to explain.
So in answer to the question, I don't think Aristotle's principle of the first cause can be equated with the uroboros, and the idea of 'self-causation' in respect to such an analogy is muddled.
Quoting Wayfarer
Yep.
Sorry, I forgot to provide a link. That quote came from a math website. I didn't make it up. :smile:
[i]Infinity is not a real number, it is an idea. An idea of something without an end. . . .
{1, 2, 3, ...} The sequence of natural numbers never ends, and is infinite.[/i]
https://www.mathsisfun.com/numbers/infinity.html
No. As I pointed out above, the meaning of "infinite" varies depending on context and intent. So, I'm merely allowing to use the word in a way that suits his context. I don't necessarily agree with his conclusions, but I want to hear his argument -- in his own words -- not necessarily in my personal vocabulary. :smile:
[i]Infinity is not a real number, it is an idea. An idea of something without an end. . . .
{1, 2, 3, ...} The sequence of natural numbers never ends, and is infinite.[/i]
https://www.mathsisfun.com/numbers/infinity.html
INFINITE:
Df. x is finite if and only if x is 1-1 with a natural number
Df. x is infinite if and only x is not finite
Df. x is countable if and only if (x is finite or x is 1-1 with the set of natural numbers)
Df. x is denumerable if and only if (x is infinite and x is countable)
Df. +inf is an element in the extended real system such that for any real number x we have x < +inf. Note that for any specification of 'the extended real system', +inf can be any object other than a real number or -inf (see below), and +inf does not have to be infinite (in the sense of 'is infinite' defined above).
Df. -inf is an element in the extended real system such that for any real number x we have x > -inf. Note that for any specification of the 'the extended real system', -inf can be any object other than a real number or +inf (see above), and -inf does not have to be an "infinitesimal" (and 'infinitesimal' is not defined anyway, except in non-standard analysis, which is different from the extended real system).
CIRCLE:
Df. L is a circle if and only there exists a plane and member x of that plane such that L is the set of points all equidistant from x
Df. if L is a circle, then x = G(L) ('the origin of L') if and only if all members of L are equidistant from x
Df. if L is a circle, then x = C(L) ('the circumference of L') if and only if there is an increasing sequence of lengths of perimeters of inscribed polygons such that x is the limit of the sequence
Df. If L is a circle, then x = D(L) ('the diameter of L') if and only if x a line through G(L) such that x ends on both ends on members of L
PI:
Df. x is a real number if and only if x is an equivalence class of Cauchy sequences of rational numbers
Th: if x is a real number, then x is infinite
Note: The above theorem is an artifact of the construction of the reals as equivalence classes. The theorem only says that the CARDINALITY of x is infinite; it does NOT say that any real number has infinite MAGNITUDE. Cardinality and magnitude are DIFFERENT. No real number has infinite magnitude.
Df. if x is a member of the extended reals, then x has finite magnitude if and only x is a real number
Df. if x is a member of the extended reals, then x has infinite magnitude if and only if (x = +inf or x = -inf)
Th. if x is a member of the extended reals, then x has finite magnitude if and only if x is a real number
Th. if x is a member of the extended reals, then x has infinite magnitude if and only if (x = +inf or x = -inf)
Df. x = pi if and only if for any circle L, x = C(L)/length(D(L))
Th: pi is infinite
Note: The above theorem is an artifact of the construction of the reals as equivalence classes. The theorem only says that the CARDINALITY of pi is infinite; it does NOT say that pi has infinite MAGNITUDE. Cardinality and magnitude are DIFFERENT. pi does not have infinite magnitude.
Th: pi has finite magnitude
Df. if x is a real number, then s = the decimal expansion of x if and only if [fill in the definiens here of the well known notion of a certain denumerable sequence]
Th: The decimal expansion of pi has no terminal repeating subsequence
Nice, Tones. I'll go along with that. Thanks.
I added this:
Df. if x is a member of the extended reals, then x has finite magnitude if and only x is a real number
Df. if x is a member of the extended reals, then x has infinite magnitude if and only if (x = +inf or x = -inf)
Th: pi has finite magnitude
Math definitions will not resolve the terminology disputes in this thread because is not making a mathematical proposition. "Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics : the abstract science of number, quantity, and space. That may be why such open-ended (infinite???) concepts are annoying to some posters, since it can't be ruled True or False by numerical authority. Satisfactory (not true or false) answers will depend as much on intuition as on logic.
As evidenced by never-ending dialogues on this forum, some philosophical questions, including definitions, are often as clear as mud. If metaphysical meanings were as "clear" as math, we wouldn't have forums for extended argumentation. Instead, we could just "shut up and calculate". For those who prefer the clarity of Math, here's a nice online discussion forum : :smile:
Wolfram Community :
https://community.wolfram.com/content?curTag=mathematics
The Metaphysics of Stephen Wolfram :
https://www.youtube.com/watch?v=-jNMh8uuqQY
Or will you claim anything in order to defend your account?
The gravamens may not be mathematical, but certain mathematical points have entered in. As to the mathematical points themselves, agreed upon definitions are crucial. If some of the same terminology is used in philosophical senses different from the mathematical senses, then each time it should be made explicit which sense is active.
Pi is mathematical. And 'is infinite' has both a mathematical sense and philosophical senses. Whatever else one may wish to say philosophically about Pi and the notion of infinity it is at least a good starting place to reference the mathematical definitions. And by doing that, I cleared up a common confusions about mathematics:
(1) There is a distinction between the adjective 'infinite' and the noun 'infinity'.
For the adjective, we define:
S is infinite if and only if S is not finite.
For the noun, we define by choosing objects to serve as +inf and -inf in the extended reals.
The adjective and the noun should not be conflated. In particular, other than the extended reals, in ordinary mathematics, there is no object named "infinity". An such infinite sets such as the set of natural numbers is not named "infinity".
(2) There is a distinction between cardinality and magnitude.
Pi has finite magnitude.
Pi has an equivalence class of Cauchy sequences of rationals is infinite (has infinite cardinality).
(3) The decimal expansion that represents Pi (as Pi is the limit of the sequence) is infinite and has no finite initial subsequence that converges to Pi.
One can say whatever philosophy about the notion of infinity, but when it's mixed with mathematics, such as Pi, Circles, sequences, etc., the one should at least get the mathematics right before invoke it in one's philosophizing.
Quoting invicta
"Pi is a circle" is a mathematical claim, not a philosophical claim.
Mathematical definitions of 'Pi' and 'is a circle' are crucial for settling a dispute about the claim "Pi is a circle".
As previously noted, I interpret his use of "infinity" as a philosophical postulation, not a mathematical proposition. Apparently, your more restrictive*1 vocabulary (your account) does not allow that distinction. :smile:
*1. Two-Valued Logic is Not Sufficient to Model Human Reasoning
https://ceur-ws.org/Vol-1651/12340059.pdf
If you would like to make some point about what is written in a paper, then you can say what that point is, rather than just have me scurry and sidetrack to read something that you haven't said what about it you think is important to consider relative to what I've said.
What could that mean? Pseudo-scientific garbage? New age postulating?
Certainly that's not philosophy, in anything more than a "pop" sense; though it is apparent from your odd threads and faux footnotes¹ that you do not understand.
Philosophy is not "making shit up", as so many here seem to think.
1. What was the remainder of the name of that article, the bit you intentionally left out? What was the topic of that article? What point did you think you were making by the pretentious footnote?
He then equate pi with circles and with infinity. Both of these are at best misleading.
Philosophy is not about misusing terms, as seems to think.
Wrong. I and others have studied infinite regress in detail, as infinite compositions or iterations.
Quoting Gnomon
What is "the natural number" ?
Dedekind's definition of infinite:
a set is infinite if and only if there is a bijection between the set and a proper subset of the set
|S| = ? ? ? (bijection): S ? T ? S
The even numbers is a proper subset of the naturals, and there's a one-to-one mapping between them, hence the naturals is infinite. Might also be what you wrote, . Also related to equinumerosity.
Tarski came up with another concise definition that can be shown identical to Dedekind's.
I didn't mention Dedekind infinitude, only because I had too much to cover already.
x is infinite <-> x is 1-1 with a natural number. [call this 'Tarski infinite']
x is Dedekind infinite <-> x is 1-1 with a proper subset of x
I don't like the use of the lemniscate as you do, because it invites conflating the point of infinity in the extended reals with a cardinal. Also, we don't write 'card(S) = leminscate' to say that S is infinite. As you mention, there are infinite sets of different cardinalities, so it can't be the case that there is just one object (named by the lemniscate) that all infinite cardinalities are equal to.
Quoting jorndoe
Tarski's definition and Dedekind's definition are not equivalent in ZF but they are equivalent in ZFC.
S is a set
?(S) is the set of all subsets of S including ? and S itself
- the power set, Weierstraß, Cantor
F ? ?(S) is a family of subsets of S
m ? F is a minimal element of F ? ? x ? F [ x ? m ]
- no smaller subset
M(F) = { m ? F | x ? F ? x ? m }
- the set of minimal elements
S is finite ? ? F ? ?(S) [ F ? ? ? M(F) ? ? ]
- a set is finite if and only if every non-empty family of its subsets has a minimal element, Tarski
S is infinite ? S is not finite
I'm guessing that's what you had in mind also. (?)
Anyway, didn't mean to distract the regress, ouroboros, etc discussion.
All I had to say is in the title. :smile:
*1. Two-Valued Logic is Not Sufficient to Model Human Reasoning
https://ceur-ws.org/Vol-1651/12340059.pdf
Irrelevant ! I didn't intend to defend 's conclusions, but just to defend his right to use a colloquial meaning of "infinite" in a philosophical proposition, without being challenged to present a mathematical or scientific justification. The OP presents metaphors of snake-circles, not mathematical proofs. Is "self-caused" a mathematical concept?
Obviously, what has incensed some posters in this thread is the supernatural implications of the OP. Which they hope to demolish by turning a broad philosophical question into a narrow technical definition. Even though the universe is now known to have a finite beginning in spacetime, some thinkers like to think of it as infinite/eternal, so they don't have to deal with open-ended questions such as the OP. :smile:
PS___I usually find you to be more open-minded than the True/False debunkers. In a different thread, one poster asserted that "the opposite of science is pseudoscience". Which is indicative of either/or ; two-value reasoning. In that case, Philosophy must either present empirical evidence, or be rejected as Pseudoscience. Personally, I view Philosophy as complementary to Science, using different methods.
Colloquial : (of language) used in ordinary or familiar conversation; not formal or literary. ___Oxford
STUDENTS COLLOQUIAL AND MATHEMATICAL DISCOURSES ON INFINITY AND LIMIT
https://files.eric.ed.gov/fulltext/ED496910.pdf
Quoting jgill
I'm not a mathematician, so I don't discriminate between Natural and Super-natural numbers. Is Infinity literally supernatural? :smile:
In mathematics, the natural numbers are the numbers 1, 2, 3, etc., possibly including 0 as well. Some definitions, including the standard ISO 80000-2, begin the natural numbers with 0, corresponding to ... ___Wikipedia
Usually when someone posts a link, it is taken as a suggestion to visit that link. So, without you saying what specifically you wanted me to take from the article, I would have detoured to read and study an article of which all you mean to say is what you posted anyway.
And nothing I've said depends on claiming that two-valued logic is sufficient for modeling human reasoning.
Quoting Gnomon
It wasn't just philosophical. There is a mathematical context also, whether primary or secondary. Especially the assertion that Pi is a circle is mathematical.
Quoting Gnomon
I don't know who you think was incensed.
In your definition of the set of minimal elements, you mistakenly left out a quantifier over 'x'.
The formula should be:
M(F) = {m e F | Ax(x e F -> ~ x proper subset of m)}
Then the rest of the definition of 'is finite' is good.
Yes, as you might know, in a 1924 paper, Tarski stated the definition and proved its equivalence with other definitions, as discussed in Suppes's great intro text book 'Axiomatic Set Theory'.
It also turns out that Tarski's definition is equivalent to:
S is finite <-> S is 1-1 with a natural number.
That is not my intention for using links. Instead, I try to say what I have to say in the post, and then add the links "for further reading"--- if someone is interested in more detail. In contentious threads like this though, where my limited knowledge will be challenged & dismissed, another function of links is to let the experts speak on the same topic, with the kind of authority I lack. :smile:
Good to know that I don't have to scramble to read an entire article you've linked to just to know what you're claiming.
Anyway, again, nothing I've said depends on claiming that two-valued logic is sufficient to model human reasoning. So I don't know the relevance of your comment to me that two-valued logic is not sufficient.
Here's what jgill responded to and his response:
Quoting jgill
His response is quite relevant to your claim that infinite regress is not addressed in mathematics.
Quoting Gnomon
I don't know who you claim are the "some posters", but at least I have not "hoped to demolish" the poster's notions about "supernatural implications". If the poster thinks it is supernaturally implied that Pi is a circle, then I don't have much to say about that except that it is worthwhile to mention that P is not a circle, from which one can take whatever supernatural implications one thinks there are to take.
And as to "demolishing", the poster himself invited:
Quoting invicta
Tones, apparently you didn't read the OP, and responded only to some abbreviated second & third replies to assertions about Pi & circles & infinity. I would have to be an idiot to make the "claim" you pin on me above. Perhaps that prejudicial misunderstanding is why some posters are treating as an idiot, or worse a woo-monger. I am not arguing with your mathematical acumen, just with your mis-interpretation of what is being said.
What I actually said was that his OP was not a scientific or mathematical assertion, but a philosophical "theory" for discussion. He was disagreeing with Aristotle's use of "infinite regression" as a reason for proposing a First Cause. Then, he offered an alternative metaphor of a snake eating its tail, raising the issue of whether a circle is an example of infinite regress, due to its association with the irrational never-ending number PI. He even asked if "anyone wanna trash this theory?". Would anyone in his right mind ask that of a mathematical fact?
I actually disagreed with his use of the Ouroboros metaphor. But when others began to make an issue of the PI/infinity concept, I simply pointed out that it was used in a metaphorical context, not as mathematical fact. So, get off his back. If you want to get technical, PI is indeed an infinite series of numbers*1, and a circle -- no beginning or end -- is sometimes used symbolically as a metaphor for infinity*2. Unfortunately, he continues to argue with Banno about interminable terms that have no bearing on the original post -- just digging himself deeper into the shallow end of philosophical debate. :smile:
*1. The approximate value of pi is calculated to be 3.14159265 . and is an infinite decimal number. Therefore, it can be concluded from the above explanation that pi is an irrational number.
https://unacademy.com/content/question-answer/mathematics/is-pi-a-rational-or-irrational-number/
*2. Why is infinity not represented by a circle?
Why is the infinity symbol not a circle? Because it was already being used by the number zero, the letter 'O,' the composition operation for functions, and the degree symbol, among other things.
https://www.quora.com/Why-is-the-infinity-logo-shaped-like-an-8-and-not-like-a-circle
Pi, spiral, symbol, math, infinity, irrational number :
An infinite causal chain does not imply a causal loop. Not even metaphorically.
It's not apparent, because it's false.
Quoting Gnomon
I can't help you there. You made the claim:
Quoting Gnomon
jgill replied:
Quoting jgill
You replied:
Quoting Gnomon
But jgill's reply is relevant, by saying that there is mathematical study that addresses infinite regress.
Quoting Gnomon
For the record, whether or not other posters have done that, I am not one of them.
Quoting Gnomon
But you also said, "Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics". Then, when jgill mentioned that there is mathematics that addresses infinite regress, you declared that to be irrelevant. Obviously, it is relevant to reply to "X is not addressed by Y" by saying that one has specifically studied Y addressing X.
Quoting Gnomon
You wrote:
Quoting Gnomon
invicta starts with some non-mathematical musings but then also connects that with mathematical subject matter.
(1) I asked before, who do you claim is incensed?
(2) Whatever may nor may not be the case with other posters, I have no interest in demolishing his non-mathematical musings.
(3) invicta himself invited his post to be "trashed". I mentioned that in connection with your protest that posters are hoping to demolish the "supernatural implications" of his post.
(4) When a poster connects non-mathematical musings with mathematical subject matter, it is reasonable to point out where the poster is seriously confused about that mathematics.
(5) It is a not mere a "narrow technica[lity]" to mention that, for example Pi is not a circle.
Quoting Gnomon
For the record, whatever may or may not be the case about other posters, I made no comment on the acceptability of invicta's notion of Pi vis-a-vis the notion of infinity. Instead, I just gave the relevant mathematical definitions if anyone might care about the mathematics, and a suggestion that, as far as the mathematical aspects of the conversation, disagreements about definitions are not necessary.
As to metaphorical couching, invicta moves between non-mathematical musing and mathematics. At any given point it may be difficult to know whether he's being merely metaphorical or intending to be mathematical. But at certain points, he is explicitly mathematical, as he even challenges ANOTHER post to raise HIS game to mathematical precision:
Quoting invicta
Quoting invicta
It is just not the case that one has to accept everything invicta says as merely metaphorical when he himself presses others to be mathematically exact.
Quoting Gnomon
Most technically that is not the case. Depending on the approach, Pi is an equivalence class of Cauchy sequences of rationals, or Pi is a Dedekind cut. Perhaps one may also attempt to define 'is a real' as reals being denumerable sequences, but that is not common. (2) Pi also is the sum of an infinite summation. That is, Pi is the limit of a sequence.
Quoting Gnomon
Of course. And a symbolic metaphor for a thing is not that thing. When invicta says that Pi is a circle, and even presses others to be mathematically exact in disputing that claim, it is unreasonable to disallow that he is himself speaking about mathematics not merely his non-mathematical musings.
/
That graphic of digits of pi arranged in a circle is probably lovely, but I don't know what one is supposed to infer from it.
One can arrange digits of any number on any figure you please. One could arrange digits of Euler's constant on a triangle. That doesn't make Euler's constant a triangle. Not even a metaphor for a triangle. One can arrange digits of Pi along a hexagon. So Pi is no less a hexagon than it is a circle. And if one says, as does invicta, that Pi IS a circle, then a circle is a hexagon.
Again, I did not say what you attribute to me. The "not addressed" is your imaginary addition to what I said. Such irrelevant insinuations often diverge mundane philosophical threads off-topic into long sub-threads on peripheral technical or emotional issues. The open-ended OP --- an essay question, not true/false --- regarding opinions about "First Cause", was of mild interest to me, but not the nitty-gritty facts of mathematical infinities.
This whole off-topic series of accusations & counter-accusations is what I was referring to as "the shallow end of philosophical debate". I hope to have a more productive discussion with you on a different topic, where polarizing hot buttons have not been pushed --- accidentally or deliberately. Let's get back to sharing opinions on general philosophical questions, not specific mathematical technicalities. :smile:
Referring to as "he" :
"Unfortunately, he continues to argue with Banno about interminable terms that have no bearing on the original post -- just digging himself deeper into the shallow end of philosophical debate."
That is nothing less than bizarre for you to say.
You wrote:
Quoting Gnomon
And I said that you wrote: "Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics".
Then you say that you did not say it and that it is an imaginary addition to what you wrote.
You did write it; it's not an imaginary addition:
Quoting Gnomon
/
Quoting Gnomon
You said that jgill's comment was irrelevant. I pointed out that it is relevant. And then you rejected that, on the bizarre basis that you didn't write ""Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics".
Shallowness is not preferred, but neither is incoherence. jgill's comment was not shallow and it is preferred that it be defended against your exclamation "Irrelevant!", and it is preferred that a thread not be so incoherent that a poster claims that another poster fabricated a quote that was not fabricated.
There is no "addition" to my quote of you. On the other hand, a few times you've added bold to quotes by me, without indicating that the bold was not original. That's not a huge deal, but it is inaccurate and it's apropos to mention it in contrast to your bizarre claim that I added to a quote of you.
Quoting TonesInDeepFreeze
As to accusations, I haven't made any. On the other hand:
Quoting Gnomon
False accusation.
Quoting Gnomon
That's not an accusation, but putting a pejorative moniker on an interlocuter is less than high minded. I don't mind that kind of thing, but pointing it out goes to highlighting that you are mentioning shallowness while you also contribute to it.
Quoting Gnomon
That is tantamount to an accusation that other posters have posted in anger. I said I don't which posters you claim to be incensed; but you still don't say.
Quoting Gnomon
That is an accusation. And it's not clear that it's true. I'm not convinced that anyone has acted as if philosophic claims must be reduced to technical claims. But when philosophical claims do invoke technical matters, then it is wholly legit to talk about how those technicals are being treated.
/
Quoting Gnomon
In other words, I am being asked not to post on an aspect of the conversation that interests me. Yet, I have explained quite well why that aspect is important. Invoking mathematics into a philosophical argument deserves not mangling that mathematics. Posting incoherently about the mathematics is a set up for degraded discourse from the start.
At best, the poster should say from the start: "I use a lot of mathematical terminology. It is not to be construed that it has anything to do with the ordinary mathematical meanings. Rather, it's just my own personal use of technical language. And while I don't stay with ordinary meanings found in mathematics, or even in everyday use, I don't define my personal use either. I expect that readers put aside their own understanding of the terminology, but still see what I personally mean though undefined. Any confusions therefore are not my fault but the readers' fault."
So, yeah, anyone is free not to comply with your suggestion that we stick only to the aspects of the subject you want us to stick to. Again, when philosophical questions or arguments are couched with mathematical claims, then it is not just appropriate, but it is very helpful, to discuss whether the mathematical aspect is being well treated.
Quoting Gnomon
And other people are interested in the mathematical aspects that were mentioned. In particular, I contributed a table of definitions so that, at least, discussants don't need to get bogged down in disagreements about mathematical senses.
Surely, you don't think a discussion should be limited to only the aspects that interest you?
Quoting Gnomon
Let's stick with the philosophy and not get bogged down in the nitty-gritty facts about ancient symbols and illustrations. [sarcasm, of course] Oh, but wait, maybe posters should not talk about the mathematics mentioned in relation to philosophy, but, on the other hand, there should be no preference that Gnomen not talk about ancient illustrations mentioned in relation to philosophy. [more sarcasm, of course]
/
Quoting Gnomon
Just to be clear, you are quoting yourself, not me.
I'm not sure what your point about the pronoun is*. Just to be clear, you first used male pronouns for invicta.
* Though I would agree, especially since 'invicta' is feminine, without knowing the poster's gender, that it is presumptuous to use male pronouns. But one, such as yourself (and me and others, later), might be forgiven for that lapse.
Quoting TonesInDeepFreeze
Quoting TonesInDeepFreeze
/
Quoting TonesInDeepFreeze
:up: :clap:
I owe you an apology. I assumed the subject of the sentence was obvious. But, in retrospect, apparently not. Mea culpa.
Therefore, to avoid contributing to the ongoing confusion, I should have emphasized that it's the "philosophical concepts" that are not addressed by mathematics. "Infinity" is a legitimate mathematical topic, but "Infinite Regression" is an ancient philosophical conundrum. Hence, to get into mathematical technicalities is irrelevant to questions about a world-creating act of Causation. An Uncaused Cause or Prime Mover is a Platonic/Aristotelian notion of Metaphysics, not Physics, nor Math. Does that make sense to you? Or do you think philosophical questions can be solved mathematically?
In the OP, A self-drawn circle is the theory to be "trashed", not the definition of Infinity. Since the topic is hypothetical/metaphysical (an idea, not an object), Plato used creation myths, not math, to illustrate his concept of a First Cause. Likewise, Invicta was using symbols & metaphors to make his point. Unfortunately, by introducing PI into the discussion, he opened himself to mathematical criticism. But I still maintain that the discussion veered off-topic into irrelevant technicalities. Apparently, in the face of such sniping, Invicta bailed on his own thread. :smile:
For those interested in the actual topic of this thread :
From OP : "But hang on a second, if it was self caused then there cant be an infinite regression of causes. Anyone wanna trash this theory?"
That's a big "IF", but IMHO he's correct that a self-existing First Cause*1, would be the initiator/creator of causation in our contingent world*2. Hence, by positing a First Cause, the Greeks were avoiding the absurdity of infinite regression*3 . If we can all agree with that interpretation, maybe Invicta will get back in the game.
*1. first cause, sustaining cause, unmoved mover, necessary being :
On the one hand, the argument arises from human curiosity as to why there is something rather than nothing or than something else. It invokes a concern for some full, complete, ultimate, or best explanation of what exists contingently. On the other hand, it raises intrinsically important philosophical questions about contingency and necessity, causation and explanation, part/whole relationships (mereology), possible worlds, infinity, sets, the nature of time, and the nature and origin of the universe.
https://plato.stanford.edu/entries/cosmological-argument/
Note -- Do the general questions listed above have mathematical solutions?
*2. First Cause : Though they often disagreed, one principle of philosophy on which Plato and Aristotle agreed was that existence and the universe required a First Cause or Prime Mover - a god of some kind. Their argument was basically as follows. Every finite and dependent being has a cause.
Note -- Therefore the regression of finite causation ends at the beginning.
*3. Infinite Regress Arguments attempt to refute a position by showing that the position leads to an absurd infinite sequence. This argument strategy is used in collaborative reasoning in everyday life, in science and in philosophy.
https://www.nottingham.ac.uk/humanities/departments/philosophy/research/research-projects/infinite-regress.aspx
Note -- Maybe Invicta will add to his theory an explanation for why Infinite Regress of Causation is deemed Absurd by some thinkers, even though that's exactly what the Multiverse theory postulates.
Apparently he/she has just been released from suspension.
Not necessarily implied that lines makes circles but that a line with irrational extension would snake its way when drawn.
But the diameter is a straight line
https://en.m.wikipedia.org/wiki/Diameter
And the importance of this obvious fact is . . . . ? :roll:
Mathematically speaking ?
Let C = 1.
Pi = C/D.
So 1/Pi = D
Toward a contradiction, suppose D is rational.
So there are integers n and m (m not equal to 0) such that D = n/m.
So Pi = m/n.
So Pi is rational.
But P is not rational.
So a contradiction.
So it is not the case that D = 1/Pi is rational.
Quoting invicta
As opposed to what? Philosophically speaking, artistically speaking, athletically speaking?
/
Anyway, your claim that Pi is a circle is false.
/
Quoting invicta
I don't know what you mean by 'irrational extension' or 'snake its way when drawn'. But this is the case:
The decimal expansion of any real number is denumerable. The set of points on a circle is uncountable. So there is an embedding of the decimal expansion into the circle (with points in the circle ordered in the obvious way of "left to right" from highest point to lowest point and "right to left" from lowest point to highest point).
But there is an embedding of the decimal expansion into lots of kinds of geometric figures. There is an embedding of the decimal expansion of Pi into a triangle, into a hexagon, into a line... And there's nothing special about Pi in that regard. The decimal expansion of any real number can be embedded ("arranged") into a circle, or triangle, or hexagon, or line...
Pi is not a circle. But the decimal expansion of Pi can be embedded into a circle. If you find philosophical significance in that, then okay. But then why not find philosophical significance also in the fact that the decimal expansion of Euler's constant can be embedded into a triangle? Or what greater philosophical significance with one over the other?
Never, as it turns out.
It's hard to know if he was putting me on. has a great deal of patience dealing with these things. Thanks, Tones. :cool:
The bolding is not mine. You've quoted me a few times as you've added bolding. I already asked you to note that the bold or emphasis is added. Are you not familiar with that convention?
Quoting Gnomon
Yes, the subject is:
"Infinite Regress" and "First Cause"
The predicate is:
are philosophical concepts that are not addressed by Mathematics
That is a claim that "Infinite Regress and "First Cause" are (1) philosophical concepts and (2) they are not addressed by mathematics.
jgill mentioned his own studies in which mathematics do address those concepts.
Interesting that you immediately pounced to declare "Irrelevant!" when jgill shared his knowledge that there is mathematics concerning the subject of your sentence.
Quoting Gnomon
That is dogmatic. It is not precluded that mathematics may inform philosophy. It is not precluded that different areas of study may illuminate one another.
Moreover, separating out my earlier part in this discussion, the mathematics I mentioned was not meant to confirm or dispute any philosophy, but rather to offer standard definitions to the extent that the discussion did go into mathematics. But then also to flag the blatantly false claim that Pi is a circle.
Indeed, invicta has gone on to challenge other posters in explicit mathematical terms. I pointed this out to you twice, but you SKIP it, I surmise because for you to recognize it would be to recognize that your claim is false: It is false that it was only other posters who wanted to follow up on the mathematical aspects of invicta's postings while invicta merely wished to use mathematical terminology in a metaphorical way.
Here is is yet again; this time explicitly challenging in a mathematical context:
Quoting invicta [bold added]
invicta has been mixing mathematical terminology and mathematics subjects with his personal philosophical musings. It is quite appropriate for people to check the mathematical usage and mathematical claims. It is not incumbent on anyone to limit discussion to your own judgements as to what is and what is not relevant, especially when the original poster has explicitly challenged other posters as to mathematics qua mathematics.
And you don't need to say 'technicalities' over and over, as if the fact that mathematics is technical disqualifies it here. It's mathematics, which, of course is a technical subject.
Quoting Gnomon
I hope you don't propose that as a dichotomy.
Of course, one may propose that mathematics may inform the metaphysical questions while not claiming that mathematics solves the questions.
Quoting Gnomon
Then it would be a good idea for anyone who wants to divorce that subject from math to not bring math into it.
Moreover, again, different fields of study may illuminate one another. Much of philosophy has been informed by mathematics and by science.
Anyway, again, it was invicta who invoked mathematics, so naturally people will comment on it.
Quoting Gnomon
Whatever other posters have in mind, I haven't said anything about 'self-drawn circle'.
And, at this point it is egregious that you keep SKIPPING the point I have made a few times already:
I posted the mathematical definitions of the terminology 'is infinite' and 'points of infinity' so that, to the extent when 'infinity' is mentioned in a mathematical context or context that mixes mathematics with philosophy, we may avoid pointless terminological contestation. Moreover, to highlight the crucial distinction between the adjective concept 'is infinite' and the noun concept 'infinity'.
Quoting Gnomon
You don't have a basis to infer the reasons for invicta's posting frequency.
Quoting Gnomon
Of course, one may be interested in invicta's philosophical gravamen while also being interested in the mathematical notions he mentions.
Quoting Gnomon
Of course those are informed by mathematics and science.
contingency and necessity. That is informed by modal logic, which is a study in formal logic very closely related to mathematical logic.
mereology. Also studied in formal logic.
possible worlds. Again, informed by modal logic. Also, analogous to semantics for intuitionistic logic for intuitionistic mathematics.
infinity. The notions 'is infinite' and 'points of infinity' are informed by mathematics.
sets. Informed by set theory and class theory, which are mathematics and are themselves foundations for mathematics.
the nature of time. I don't know about 'the nature of', but the subject of time is, of course, informed by mathematics and physics.
the nature and origin of the universe. questions about the universe are of course addressed by cosmology, which is informed by mathematics.
It is curious, at best, to me that a person would want to dogmatically declare that philosophy should not be discussed in cross-context with other subjects. Especially when the original poster her(or him)self introduced mathematical aspects and not merely metaphorically. On the contrary, intellectual curiosity, intellectual creativity and open mindedness invite cross-study/conversation, not shutting it down.
Again, that is not my claim. It's your erroneous interpretation, but not my intention. "Infinite Regress" and "First Cause" are examples of the subject content, acted upon by the predicate. Instead, it is "philosophical concepts" that the predicate modifies with "not addressed". And it's the "Infinite Regression"*1 argument, not the definition of "Infinity", that is in question.
However, I admitted above that the sentence construction could be misconstrued --- by someone with a pre-conception. Especially after the impassioned mathematical side-track had been going on for a while. That's why I added the bold, to indicate the subject of my sentence.
I suspect that we are actually in agreement about the math of PI & Infinity, but perhaps not about the philosophical concept of a pre-big-bang First Cause. Unfortunately, seems to be insisting on a colloquial usage of "infinity", while you are insisting on technical definitions. Therefore, on the side issue of Number Theory, the post is at an impasse. But the philosophical notion of a causal-regression-halting First Cause (or Prime Mover) has not been addressed & resolved in this thread, so is still an open question.
Consequently, the Pre-Big-Bang state of being (Ontology) remains a contentious issue among philosophers. Yet I maintain that it is a valid enigma, that serious scientists have attempted to resolve, not with math, but with the endless regression of a god-like eternal Multiverse*2 (Many Worlds), without beginning or end. :smile:
*1. Infinite Regress Arguments :
An infinite regress is a series of appropriately related elements with a first member but no last member, where each element leads to or generates the next in some sense.
https://plato.stanford.edu/entries/infinite-regress/
Note -- The relationship between elements is Causation, not mathematical value. The "first" member is the element in question.
*2. Why the Multiverse is a God-of-the-gaps theory :
"Gods existence is not provable by observations. The Multiverse is not provable by observations. God explains the Universe. The Multiverse explains the Universe. The Multiverse, then, is a lot like God. Weird, right?" ___by astrophysicist Marcelo Gleiser
https://bigthink.com/13-8/multiverse-religion/
Note -- You don't have to "waste time" by clicking on the link. I included a summation in the quote.
I have asked you at least three times not to do that, but instead to indicate that the bolding was added.
Clearly, by this point you are egregious.
One more time: If you add bold in a quote of mine, then note that the bold was added.
Quoting Gnomon
It's literally what you wrote. So, what you wrote is not what you meant. Of course, one may always correct what one wrote to align with what one meant. But it's not jgill's fault nor my fault to have replied to exactly what you literally wrote.
Quoting Gnomon
Wrong. The word 'are' begins the predicate.
Subject:
"Infinite Regress" and "First Cause"
Predicate:
are philosophical concepts that are not addressed by Mathematics
This could not be more clear as basic English. 'are' begins the predicate.
The sentence says that "Infinite Regress" and "First Cause" ARE (1) philosophical concepts and (2) not addressed by mathematics.
Jack and Jill are happy kids who like to play.
The subject is Jack and Jill. The predicate begins with 'are' and the predicate is 'are happy kids who like to play'.
I hope you understand by now.
Quoting Gnomon
Blame the reader for a "pre-conception". No, the two readers here read your sentence at face value, literally what you wrote.
And even IF you had written the sentence so that 'philosophical concepts' were part of the subject:
"Infinite Regress", "First Cause", and philosophical concepts are not addressed by mathematics
then still, it is the case that mathematics (and science) may be used, and is (are) used, to inform philosophy.
It is only dogma that mathematics should not be discussed in this thread and that, even more generally, mathematics should not be discussed in addressing certain philosophical questions. Not only is that arbitrary self-serving dogma, but it is deleterious to the benefits of cross-study and an expansive discussion about various subjects.
And your would be controlling dogma is untenable anyway as to this discussion, since the original poster first brought mathematics into the discussion (and not just "metaphorically", and indeed the original poster did not qualify that the mathematics she or he invoked was merely metaphorical) and later the poster explicitly challenged ANOTHER poster to be mathematically "exact" on a point of mathematics and then explicitly challenged another poster to provide a "mathematical" answer on a point of mathematics.
You have SKIPPED my adducing that fact at least two times now.
Quoting Gnomon
I never said that the definition of 'infinity' is in question with that particular comment of yours. Whatever you meant by "Infinite Regress" and "First Cause" is up to you. But they are the subject of the sentence you wrote, not 'philosophical concepts'.
Quoting Gnomon
That you go, argument by mere characterization.
I haven't been impassioned, nor was jgill impassioned.
And to say it's a 'side-track' is question begging, since whether mathematics is apropros to the subject is what we've been disagreeing about.
Your position is blatantly untenable:
It is invicta who first introduced mathematics into the discussion. And then invicta later even challenged another poster to justify a point mathematically. And then invicta explicity challenged for "mathematical" response.
And you SKIPPED the points I made about mathematics and philosophy interacting.
Quoting Gnomon
I haven't stated any opinion on first cause. And, by the way, 'big bang' is ordinarily understood to be a subject of physics and cosmology, a scientific notion, so it too is informed by mathematics.
Quoting Gnomon
Please quote what you regard as invicta saying that she or he means only a colloquial sense.
Quoting Gnomon
That is a major STRAWMAN.
(1) I have not insisted that usage be confined to only the technical definitions. I offered the technical definitions so that there would not be pointless disputation in regards the mathematical aspects of the conversation.
(2) I did not address invicta's notion of infinity. Rather, I addressed his claim that Pi is a circle. And later his arguments about inscribing the expansion of Pi in a circle.
You have imposed on me things I did not say. Perhaps due to YOUR preconception. Philosopher, heal thyself.
Quoting TonesInDeepFreeze
And, of course, the Greeks never said that Pi is a circle.
Seems that I didn't include my reply to that.
It is not clamed that mathematics solves those philosophical problems. It is only claimed that mathematics may inform solving the problems.
Anyway, again (because this fact keeps getting SKIPPED by you) in context of this thread, it was invicta who invoked mathematics to defend her(or his) argument, and not with a proviso that that was merely metaphorical, and later explicitly challenged for "exact" mathematics on a mathematical point and then explicitly for a "mathematical" reply on a mathematical point.
Yes. I emphasized the subject of the sentence, to show where you missed the point of the original statement. Apparently, that didn't have the desired effect. But I'll continue to do it again, if you continue to misinterpret my meaning. In the words of Paul McCartney, "let it be". :smile:
You say you'll do it again. And you did just do it again. The bolding you put in was not mine.
And you did it just to prove that you can - a childish, petulant act.
You are wrong.
(1) Even people who radically disagree at least respect the honesty of not misrepresenting a quote to make it appear the quoted person emphasized words that he did not emphasize. That is just BASIC common sense and intellectual honesty. I have seen even the worst Internet creeps - demagogic, specious opinion writers, bloggers, and forum posters who at least indicate where they have added emphases in quotes. But you insist on putting yourself beneath even that minimal convention of honesty.
(2) I didn't misinterpret anything. I took your statement literally as you wrote it. A school kid could diagram the sentence to show its subject and predicate. As I said, if you meant something different, then that's not my fault. And I have not insisted that you did NOT mean something different - only that it's a plain fact that it's not what you literally wrote, therefore jgill and I were not incorrect to respond as we did to what you literally wrote.
(3) Even IF (which is not the case) I misinterpreted you, there is a distinct difference between even willful misinterpretation and misrepresenation (which are not acceptable) and willfully fabricating emphases in quotes. The latter is just pure blatant dishonesty above even arguable disingenuousness.
(4) As to misunderstanding, you intentionally STRAWMANED me, as I noted in one of my previous posts.
Meanwhile, all the points I made in previous posts still stand.
Quoting Gnomon
In my own words, "You're vastly better at quoting songs than you are at making sense."
:rofl:
That's the funniest thing I've seen in quite some time. I probably should not be promoting it, but damn... that was funny. I momentarily lost control of myself.
In that post, Gnomon makes a number of statements about mathematics qua mathematics. Attempting defintitions (thery're botched) and making claims. About mathematics. Yet Gnomon begrudges discussion of mathematics in relation to a topic couched by the original poster who him(or her)self mentioned mathematics and even explicitly as technical. But that's just typical poster hypocrisy and incoherence.
Amen!
I don't know what set Tones off on his "Gnomon said" rant. Gnomon didn't say or mean whatever knocked the chip off his shoulder. Maybe the chip fell off by itself. I certainly had no intention to insult him, or to debate the technicalities of higher math with him. But he seems to be determined to make it all about the numbers.
I was about to mention that he's gnawing on an imaginary bone, with no nutritional value. But such a light-hearted tongue-in-cheek remark might just throw more fuel on the "he said --- she said" flame. So, instead, since this thread long ago veered off-topic, I'll take your advice to just laugh quietly and walk away. Thanks for the Aristotle??? quote. :joke:
PS___Since he's bursting at the seems, I'll let Tones have the last word : fill-in the blank [ . . . . . . . ]
Laughter is not the involuntary response provoked here.
And, in and of itself, posters should not feel obligated to desist in defending themselves nor to desist in flagging when posters post lies, falsehoods, misrepresentations, ignorance, confusion, fallacies, speciousness and other forms of intellectual dishonesty and intellectual irresponsibility.
And I believe it is worthwhile to resist the essentially censorious insistence that people should not follow up on certain aspects of a discussion. Discussions naturally go down subpaths that deserve discussion as components of a larger subject. So when mathematics is brought into a discussion it is eminently worthwhile to talk about whether a poster's presentation of mathematical aspects is coherent, informed or true.
In a discussion about political philosophy, if a poster makes certain claims and interpretations regarding the U.S. Constitution as part an argument toward a philosophical view, then it is eminently worthwhile to discuss whether those claims are true and those interpretations coherent and fair.
In a discussion about philosophy concerning cosmology, if claims and interpretations about general relativity are brought in, then of course there may be follow-ups.
In a discussion about first cause and infinite regress, if a poster makes certain claims and interpretations about mathematics, then of course there may be follow-ups. And that is poignantly true when a poster is spreading confusion, misunderstanding and falsehood on the subject of mathematics. It is definitely worthwhile to flag that, and, even better, to supply correct information and explanation.
That post is so densely, richly packed in error, speciousness and hypocrisy that a lot of unpacking awaits an ambitious unpacker.
But first, yes, a risible moment:
Quoting Gnomon
Nice. Bannon suggests that Gnomon has been so laughable that it's best just to walk away from him (or her). Then Gnomon says, "Amen!"
Quoting Gnomon
(1) 'rant' is again argument by characterization. It might as well be paraphrased as "My posts are reasoned commentary; your posts are rants". It's an instance of a generalization of an insight George Carlin articulated so brilliantly in his wonderfully trenchant routine:
https://youtu.be/JLoge6QzcGY
[2:02 - 2:22 on the point, though the whole clip is quintessential comedy]
It's absurd and egregious for Gnomon to characterize my posts as "rants", presumably in contradistinction with his posts. Moreover, Gnomon's own posts included ad hominem claims, would be mind reading, about people's motives.
(2) Gnomon says he doesn't know what started the "Gnomon said" track. Thus, Gnomon lacks awareness even of what he(or she) said. The track started when Gnomon falsely and bizarrely claimed that I had added something to a quote. Of course it is reasonable for me to refute that false claim and then to continue to refute Gnomon's stubborn and incorrect insistence that I share fault with him (or her) anyway.
And it is a worthwhile lesson highlighting brazen intellectual dishonesty, to the point of a poster trying to prevail in a claim even if it means denying a plain bald fact as to what the subject and predicate are in a simple sentence.
And the track originated in Gnomon declaring that jgill's comment was "Irrelevant!" when jgill's comment was not irrelevant; and generally presuming to say for other posters what aspects of the discussion they need to regard as not apropros, especially when Gnomon him(or her)self talked about those aspects before I even posted in the thread, and doubly especially as the original poster him(or her)self first introduced that aspect and later explicitly made challenges to other posters for exactness about that aspect.
(3) In greatest generality: If Poster P and Poster Q sequentially reply back and forth, then it is incorrect and unfair to say or to insinuate that just one of them is too persistent.
Quoting Gnomon
(1) No chip here. On the other hand, it's tempting to say that there is probably a chip behind insisting that posters should not follow up on certain aspects of a conversation, and possibly behind categorically declaring "Irrelevant!" to a poster's report of his study rather than allowing that what one personally is interested in does not subsume all that is relevant, let alone possibly saying "Tell us more about those studies".
(2) I stated explicitly what I dispute in Gnomon's posts to me. For Gnomon to say he doesn't know is nuts. Suggesting that my dispute with him (or her) came out of nowhere as some kind of lashing out from having a chip on my shoulder is wrong.
(3) And it was Gnomon who first disputed me in this thread, not vice versa. Again, the hypocrisy.
Quoting Gnomon
I didn't claim Gnomon insulted me. But after I asked Gnomon to please indicate that bolding is added when he (or she) adds bolding to my quotes, Gnomon finally replied by childishly adding gratuitous bolding to that very quote of me asking him (or her) not to do that; as far as I can tell, his (or her) point was merely to scoff at my request, which was a reasonable request to respect a universal convention that one notes that emphases have been added to a quote. Gnomon was childishly insulting in that instance. He (or she) showed his (or her) stripes. Then he (or she) follows with the protestation, "Aw shucks; I ain't said nothing against Tones; I've just been minding my own business" [not a quote]. Like I said, laughter is is not the involuntary response provoked here.
Quoting Gnomon
Dig it when someone says "I'm not going to say X" thereby saying X. It's sophomorically sneaky. Politicians and lousy writers on politics especially like to do it.
Quoting Gnomon
That would be advice that Gnomon laugh at him(or her)self.
And it's delicious irony that Gnomon says he (or she) will walk away when he (or she) just then did NOT walk away. If banno's advice where actually taken to heart, then Gnomon would have indeed just walked away rather than posting more digs against his (or her) interlocuter.
Quoting Gnomon[italics original]
I don't know whether it was intended to spell 'seams' as 'seems', but as to 'bursting', I am thorough point by point; I provide ample explanations and adequate steps in my arguments, so that they are convincing and to evince that they are transparent; and I reiterate points, especially refutations, that dishonest posters try to pretend have not been made as they deploy the tactic of SKIPPING.
Quoting Gnomon
I guarantee that that is not true. Fill in the blank [ . . . . . . . ]
By way of possibly dragging this thread back to the topic - causation...
The grain of coherence within Invicta's ridiculous OP might have been the old idea that while each element of an infinite causal chain has a cause, it is stil open to ask what caused the chain as a whole. From memory, it's found in the famous debate between Russell and Coplestone, where Russell points out that it makes sense to ask, of any particular human, who the mother is, but it does not make sense to ask who the mother of the human race as a whole is. As I alluded earlier, I share some of Russell's scepticism towards the notion of causation, so I'm reasonably happy with that argument.
If Invicta had had the wherewithal to put together an argument, they may have applied Coplestone's point to a circular causal sequence, by asking what it is that causes the circle as a totality. Invicta says, "asking where the circle came from is a valid question". To my eye that carries the visual analogue too far, since if we did have a circular causal chain every element of the chain would have a cause, and so no further explanation is needed.
Those who uncritically accept the notion of causation could have a field day with such an argument. It might garner some wider attention for this abortive thread. For my own part, I've already expressed scepticism towards causation. I don't think that a sufficiently coherent account of causes can be provided, nor is it necessary. Instead we may use something broader, the sort of thing we might call a model or a schema or a narrative.
Edit: RussellCoplestone debate.
Interesting dialogue at that link.
, I can't apologize on behalf of the TPF forum. But personally, I'm sorry you got mired in the quicksand of the Literal Mind; of which there are several pits on this "meeting place of ideas". Personally, I saw some merit in your hypothetical, metaphorical, and symbolic approach to a "perennial" philosophical conundrum : "how did the observed chain of causation get started?". Or, in other words, "why is there something instead of nothing"?
Unlike Plato & Aristotle, some pseudo-philosopher posters are limited in their thinking to finite physical Reality : no place for metaphysical Ideality. Consequently, intimations of anything outside the physical/material system of Cause & Effect amounts to blasphemy against their personal belief system (their creed). As you've seen, they sometimes react with "furious anger and righteous indignation". (note -- don't look for links to the quotes, just take them literally, at face value)
Space-time Causation is obviously not a physical object in the real world. It is instead, an abstract idea conceived in the mind of observers to explain why one event is followed by another as-if by a transfer of momentum (conserved quantity of energy). But the energy itself is an idea (qualia), not a tangible substance (quanta) that could be poured into a bottle. Aristotle defined "Energy" (ergon) as a mysterious unseen "power" to act on objects. Modern physicists may have different terminology, but Causation is still an ideational attribution, not a tangible thing bounded by space-time.
The conventional symbol*1 for Infinity*2 is not a literal/physical example of a thing-without-beginning-or-end. Instead, it's a circle folded-over into a laid-over symbol of the number eight*3. Before that convention was adopted, some thinkers used the circle itself to represent something without beginning or end. Your Ouroboros image is another version of the same concept. Likewise, in modern times, we sometimes use a Mobius strip*4 to represent the imaginary concept of Infinity. But, literally & in reality, its just a finite strip of paper folded-over into a single surface topographic system, where you can draw a line, but never come to an edge. In another sense, the Mobius represents a seemingly impossible object, like a Klein Bottle*5.
I don't know about you, but I don't conceive of the postulated First Cause as a thing existing in space-time, and bound by the rules of Reality. Instead, it was imagined by the ancient philosophers as an Ideal solution to the seemingly impossible notion of Infinite Regress in a finite world. :smile:
*1. Symbol : a thing that represents or stands for something else, especially a material object representing something abstract.
*2. Infinity : a state or quality, not a specific quantity
*3. A FOLDED FIGURE EIGHT, representing a never-ending circle
*4. A FOLDED CIRCULAR STRIP, representing a single-edged geometric surface with only one side
*5. A FOLDED FOUR-DIMENSIONAL SURFACE, with no inside or outside
Quoting Gnomon
Quoting Gnomon
Still laughing.
In this thread? Which posters do you claim are limited in their thinking to only physical reality? And what have they posted that allows you that claim, and to the extent that they have claimed that disagreement is anything like blasphemy?
Copleston seemed not to be familiar with the thinking behind Russell's point that he eschews 'necessary' and 'contingent' as adjectives to describe entities as opposed to propositions. But I am curious what Russell meant by "a logic that I reject".
It's hard to see how the arguments there could be parsed in terms of boxes and diamonds in such a way as to overcome some considerable ambiguity, especially if we were to add Russell's explication of individual identify in terms of definite descriptions. Beyond my pay grade. We might write ?x[(Kx & ?y(Ky ? y=x)) & Bx], but where to put the diamond that indicates the thing that is K only exists contingently?
I think Russell is saying that you don't put modal operators in front of terms, only in front of formulas. So you could have:
NEx(Kx & Ay(Ky -> y=x) & Bx)
or
PEx(Kx & Ay(Ky -> y=x) & Bx)
But he also requires that
NEx(Kx & Ay(Ky -> y=x) & Bx) holds only if Ex(Kx & Ay(Ky -> y=x) & Bx) is logically true.
/
Quoting Banno
Be careful. The diamond ('P' in my notation above) says that the statement is possibly true, but it doesn't say that the statement is not necessarily true.
I thought the same thing, but could not quite see how to fit it together. Jan Dejnoka has argued that Russell had a quite sophisticated modal logic, and given that Russell was the authority on Leibniz this seems inevitable. Leibniz is after all the originator of possible worlds. Further, Russell's admonition of Leibniz is modal, that Leibniz did not follow the logic of modality to the (for Russell) inevitable conclusion of the world being necessarily as it is, even as Spinoza did. Speaking roughly, Russell held that necessity begets only necessity, and contingency begets only contingency, and hence if there are contingencies in the world then the world is contingent, and if god is necessary then all his creations are by that fact also necessary. But the academic discussion on the issue is bulky and indecisive.
A large part of the issue here is that the language of modality was understood less formally then - up to a hundred and twenty years ago - than now. This is I think the core of Russell's argument in Necessity and Possibility in whch he writes:
Earlier he makes it clear that
Russell puts much of the blame for the confusion down to Kant. In this, at least, he seems to be in agreement with Kripke.
Good post. Interesting.
I'd need to read that essay, but meanwhile, what does he mean by "fundamental logical notion"? And why does he say there is not such a thing? As you mentioned, modal logic has come a long way since 1905, and the debate with Copleston was in 1948 by which time modal logic had been much better explicated but not nearly as robust as with Kripke semantics that came later. If Russell had kept up with such improvements (maybe he did? but I doubt it since, if I'm not mistaken, Russell's attention was generally turning to subjects other than logic or mathematics), then I wonder whether his views would have changed.
"We must distinguish between a necessary proposition and a proposition which predicates necessity" - Russell
Of course.
Well, were diamonds and boxes used back then? Given that there was not at that stage even a standard notation for predicate calculus, I doubt there was much by way of agreement on how to parse modal operators.
What we tend to lose from our "post-formal" perspective is an understanding of the accomodations that have to take place in order to follow a particular formal approach to parsing sentences although we get a reminder when dealing with initiates into logic, where even otherwise clever folk have difficulty in parsing simple sentences. That is, the development of a logical notation includes, usually implicitly, injunctions to only represent certain things in certain ways, and to reject other representations; these are injunctions to think about the sentences in a particular way, rejecting other options that are less amenable to the logical notation.
So developing a logical notation involves seeing sentences in a certain way, amenable to those logical notations. To be sure, I take this as a good thing, the removal of inept and inaccurate parsings.
And keep in mind that Russell was 76 in 1948.
Thus he was blessed with the Wisdom of the Ancients. Right? :cool:
Kripke was 8.