An all encompassing mind neccesarily exists
1. True statements can only exist as cognitive content
Reason : Whatever theory of truth you pick (Correspondence theory, pragmatic theory, coherence theory, deflationary theory etc) , its definition and operation can only be the evaluation of a mind. So to say, "X is true" is to evaluate X as T in your mind in reference to some truth-criterion
2. Cognitive content depends on the existence of a mind which can comprehend it
Reason : This should be relatively uncontroversial. Intentional content (ideas, beliefs etc) cannot be comprehended or sustained by extended matter due to the fact that immaterial and non-extended entity cannot have any causal or supervenience relation to material and extended entity. If not, we need an explanation of HOW it is possible and HOW it works.
3. There are infinitely many statements that are necessarily true, independent of spacetime itself
Laws of logic ( LNC for eg ) , Mathematical axioms and theorems. To anyone who says this is wrong, we ask.
Reason 1 : How can our physical theories which describe our universe to a great degree of accuracy prior to the existence of any symbolic language be true if the mathematical entities they refer to or depend on constructions which never even existed ? Your physical theory is definitely false if its meaning and truth-falsity depends on something which is non-existent.
Reason 2 : Let's suppose mathematical statements are just symbols we draw with some rules. Given the fact our universe can only contain finite information, there can only be finite mathematical statements that are true, but this is false on face value ( There is no logical impossibility in adding additional axioms and theorems to the most comprehensive mathematical system )
4. All neccesarily true statements exist as cognitive content (from 1,2)
Conclusion :
Therefore , an all encompassing mind neccesarily exists
Note : Given this mind comprehends statements that were true before the universe or spacetime even came into existence, this mind can be equated to an impersonal God.
Reason : Whatever theory of truth you pick (Correspondence theory, pragmatic theory, coherence theory, deflationary theory etc) , its definition and operation can only be the evaluation of a mind. So to say, "X is true" is to evaluate X as T in your mind in reference to some truth-criterion
2. Cognitive content depends on the existence of a mind which can comprehend it
Reason : This should be relatively uncontroversial. Intentional content (ideas, beliefs etc) cannot be comprehended or sustained by extended matter due to the fact that immaterial and non-extended entity cannot have any causal or supervenience relation to material and extended entity. If not, we need an explanation of HOW it is possible and HOW it works.
3. There are infinitely many statements that are necessarily true, independent of spacetime itself
Laws of logic ( LNC for eg ) , Mathematical axioms and theorems. To anyone who says this is wrong, we ask.
Reason 1 : How can our physical theories which describe our universe to a great degree of accuracy prior to the existence of any symbolic language be true if the mathematical entities they refer to or depend on constructions which never even existed ? Your physical theory is definitely false if its meaning and truth-falsity depends on something which is non-existent.
Reason 2 : Let's suppose mathematical statements are just symbols we draw with some rules. Given the fact our universe can only contain finite information, there can only be finite mathematical statements that are true, but this is false on face value ( There is no logical impossibility in adding additional axioms and theorems to the most comprehensive mathematical system )
4. All neccesarily true statements exist as cognitive content (from 1,2)
Conclusion :
Therefore , an all encompassing mind neccesarily exists
Note : Given this mind comprehends statements that were true before the universe or spacetime even came into existence, this mind can be equated to an impersonal God.
Comments (41)
How does it follow from your premises that the statements (already) exist?
Quoting Echarmion
Yes. You would have to establish some kind of necessary connection between the existence of a necessary truth and the existence of the conditions that make the necessary truth true.
I do agree that necessary truths implicate a cognizer though.
That (which exists as pixels on a screen) is not a true statement?
To show : All (neccesarily) true statements exist as cognitive content
Reason : Whatever theory of truth you pick (Correspondence theory, pragmatic theory, coherence theory, deflationary theory etc) , its definition and operation can only be the evaluation of a mind. So to say, "X is true" is to evaluate X as T in your mind in reference to some truth-criterion
I will elaborate on the paragraph above
A true statement presupposes a truth-criterion. A truth-criterion doesn't tell us what is the case, only how it is to be determined. Moreover, truth-criterion requires the existence of a language in which the world can be described. Language rests on intentional content (esp meaning). Intentional content is a cognitive content, even though it can be determined by the world.
Note : I am not saying our mind plays the only role in determining the intentional content, but that intentional content doesn't exist without the mind.
It doesn't follow from any of this that any particular statement (concerning a necessary truth or something else) necessarily exists.
I would like you to imagine a world in which there are no minds. You will imagine our world as it exists minus the minds, and you will use the knowledge we have ( intentional content ) to infer what would be true in such a world, depending on whether you are a direct/indirect realist or irrealist and your metaphysical commitments to what exists independent of the mind
But hold on.
All you did in this thought experiment is imagine a mind less world from a world in which there are minds and languages. In other words, you mentally allocated to the world which had no minds with your mind to describe it.
Using your mind to describe a mindless world ( in which a mind doesn't exist ) is a wrong step.
This tells us there cannot be any true or false statements about a world in which there no minds.
Possible Retort : But you just made a true statement about this world. No, l haven't. I have stated a condition for semantics. If such a world existed, its description would be impossible
Can you point out the specific flaw. Saying the conclusion doesn't follow isn't helpful.
I actually want to improve this argument. So you can even critique the weak point and suggest how l can improve it.
What change to this argument would convince you its correct ?
Sure, I can't imagine without using my mind.
Quoting Sirius
Then why did you ask me to make a wrong step?
(I know, I know, that's how the presuppositionalist game is played.)
This reduces to the true statements that exist depend on the existence of a mind that can comprehend them.
Whats to say the mind on which the cognitive content depends, is the same kind of mind which comprehends cognitive content? From which follows, what may be true cognitive content existing in one kind of mind, is incomprehensible given the cognitive content of another kind. Or, which is the same thing, there are as many true statements as there are minds that exist on which the comprehension of true statements depends.
There is nothing contained in the conclusion that there are necessarily a multiplicity of kinds of minds, given the relative incomprehensibility of cognitive content, that there is therefore a singular all-encompassing mind to which all true statements belong.
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That true statements can only exist as cognitive content, is true; that cognitive content depends on the existence of a mind, is true, that true statements depend on a truth-criterion, is true. Parsimony suggests, then, any mind that exists comprehends only its own cognitive content, insofar as the mere existence of a mind is insufficient for a truth-criterion which grants to true statements their validity, and, more importantly, denies to the totality of all cognitive content the validity of truth.
An all-encompassing mind does not necessarily exist. It might, but not necessarily.
Lets change this real quick: Known statements can only exist as cognitive content.
Truth is what exists whether we know it or not. Lets say you didn't know that the heart pumped blood through your body. Does it make it untrue? No. Lets say you are educated and know that the heart is "the source of thoughts". Does that make it true? No. Knowledge and truth are not the same thing. Knowledge is your best reasoned approximation of what appears to be true, but it is not truth itself.
Your second point in general works as long as you understand that it is knowledge which needs a mind, not truth. Your third point is irrelevant because knowledge is what we can grasp, and it is unknown that we can grasp any one truth, let alone an infinite truths.
Nice try though! A good approach that is only marred by the common mistake of thinking that truth and knowledge are the same thing.
The content of a statement is mental content. This includes the "truth" of the statement, or the truth evaluation.
But not all possible statements already exist. You would need to show that the statement about the necessary truth also necessarily exists.
What do you mean by true statements? Propositions? If so, I see no reason to believe that propositions could not exist as platonic forms (or something like that) independently of any mind.
For example, why cant the true proposition p > q not exist acausally as the a part of the form of reality?
Another route, is to just deny:
For your argument to work, one has to be a mathematical and logical realisti.e., one has to believe that math and logic pertain to the structure of reality and are not our mere estimations of itwhich I am not seeing why this would be implausible.
You are conflating the map with the territory: just because I can measure a door with a ruler and get a rough estimate of its size it does not follow that the door has a fixed size (mathematically). However, if one is a mathematical realist, again, they could just say that numbers, math operators, etc. are platonic forms (or something similar), which doesnt require a universal mind.
What we estimate about reality will always be an finite underestimate of what is happening: no matter how precise it is.
Not just propositions, but true propositions. Here is 2 reasons we should prefer true propositions to be cognitive content over platonic forms
1. Platonic forms lack intentional content. There is no meaning to them in refrence to themselves. Platonic forms don't think they are true. We with our minds do.
2. Let's suppose true statements existed as Platonic forms, then we would only be able to access true statements by coming into contact with platonic forms, but our minds cannot contact them or comprehend them. Furthermore, we do have experience of minds evaluating true statements, what evidence is there for the existence of platonic entities, how do you know they exist ?
Mathematics isn't an estimation of the world. You are confusing physics with mathematics. Yes, numbers may represent apples and chairs, but it's ludicrous to conflate them.
Mathematical theorems rest on axioms and inferences our minds derive from them. That's it. The axioms are taken as self-evident, not some a posteriori fact about the world.
If you say your door is 2 meters long and "2" doesn't exist, then your statement is false. But you do have a mind which can conceptualize "2", even if it's a rough approximation, so your statement is somewhat right. If you improved your instrument, you would get a better measurement, but it still depends on the existence of some number inside your head.
Now, look at physics. It describes the universe with numbers before any mind existed in the universe. Such a theory is wrong if there were no numbers, the theory can't even be approximately correct. So there must have been some mind which comprehended mathematical numbers/concepts
As for numbers being platonic entities, refer to my objection above
And ? Are you saying there are only finitely true mathematical statements because of that ? If not, then it's a point in my favor. There must be a mind beyond the universe which can comprehend all the infinite true mathematical statements. ( I have already objected to platonism, so it is not a reasonable alternative )
I never claimed all contingent truths must exist, only logically neccesary truths. I have already given reasons why mathematical truths can not depend on material representation ( refuting logicism )
If a statement is logically neccesary, then it exists irrespective of whether there is a physical world or not, since it isn't about the physical world.
Here is a proof of the existence of neccesarily logically true statements and a mind :
Definition :
Existence for neccesarily true statements means "X is neccesarily" exists as an evaluation.
If it doesn't, then we can't say "X is neccesarily true", but X is neccesarily true, so an evaluation neccesarily exists. But if an evaluation neccesarily exists, a mind neccesarily exists for the evaluation.
As far I can see you are just begging the question that there is no such thing as a mind-independent reality. I'm sure lots of people would say that: just because truths can only be evaluated by a mind, doesn't mean there isn't some kind of objective reality beyond it.
You need to re-read my first point. My conclusion is compatible with a mind-independent reality, given a mind exists to comprehend it as a reality apart from itself
True statements are not equivalent to reality, they describe reality in a way that satisfies some "truth" criterion. But any truth criterion is mind-dependent
Mind dependent in what sense ? Its conception and operation rests on a mind
Once more, I never denied a mind-independent reality, in fact, it is compatible with my conclusion. What l claim is you cannot sensibly talk of a world in which there wasn't a single neccesary mind (whether it existed alongside the universe, beyond it, as itself )
Then l show this mind must be all encompassing and infinitely powerful given neccesarily true mathematical statements.
What does it mean for truths to exist? Are truths metaphysically real "states of affairs"? Or are they constructions of a particular mind?
Quoting Sirius
This does not make sense to me. The content of a statement doesn't change its ontological status.
Quoting Sirius
This proof only works conceptually if truths are the results of evaluation, which is to say truths are (mental) constructs.
But this means also that necessary truths only ever exist for specific minds, and a mindless world has no truths, necessary or otherwise. So a mindless world is perfectly self consistent, and necessary truths only arise for specific minds.
Only implicate? I think cognition is a necessary condition for necessary truths. Are there necessary truths in a possible world without minds? If so, what is their existence like, if not in some mind? As some Platonic Form?
Only if a mind is observing the pixels on the screen. Otherwise, they're just pixels on a screen. It takes mentation to turn the pixels into something else (i.e., to attach meaning to the pixels on the screen). Whenever we get into this area, I always ask, "is a simulation of a tornado a simulation if no one is observing it?" If there's no mind interpreting the results of the simulation of the tornado, it's just pixels and noise. How could it be anything else?
I addressed this in the beginning. Given any theory of truth, whether it assumes the truth criterion is a metaphysical representation or otherwise, its conception and operation depends on a mind.
Here is a concrete example. Take the correspondence theory
Before there was any mind, how would you tell, X states of affairs was in correspondence with actual facts of a world ? You cannot
Why ? Because to evaluate whether some statement is true or false in some world is to be a mind in that world, conceptually or actually.
This makes the correspondence theory useless. If a criterion can never be implemented, it is meaningless. The entire purpose and meaning of a criterion rests in it's possible implementation.
Ask yourself. Does it make sense to say X statement was always true, but it never always existed. How can a statement be true and not exist ? And if a true statement an an evaluation must exist, it will exist in a mind
True statements are a mental evaluation, but what they represent isn't. A mindless world may have truths, but we cannot speak of them, which is no different from not having any truths.
Let's suppose there is no God. We can do without him actually. The only difference is we will get an infinite gradation of minds, instead of an all encompassing mind
Was "Big bang just occurred" a true statement when the big bang occurred ? Here is the tricky part. We can say it is a true statement from an evaluation in our time w.r.t the time when the big bang occurred, but it involves us taking our mind to the time when the big bang occurred CONCEPTUALLY. But even if we didn't exist, It is neccesary condition for this universe that there be a mind in the relative distant future which can evaluate the conditions of the past when there were no minds.
How is this possible ?
As you know from special relativity, the past/present/future exists on the same ontological plane. So when the big bang occurred, we were thinking of it having occurred in the future from the refrence of big bang. But even if we didn't exist, there must have been someone in the future who was thinking of the big bang. As we have eliminated God, we will need to take this universe to be infinite to have all the minds represent the infinitely many true mathematical statements and have them evaluated. So instead of an all encompassing mind, we have an infinite gradation of minds, given each mind is limited.
To sum it up, the existence of a mind is a neccesary condition for the existence of neccesarily logical truths, but not a sufficient condition.
Excellent reply.
People confuse data with information. The latter is meaningful. I was tempted to bring up information realism and pancomputationalism , the "It from bit" hypothesis of John Wheeler, but didn't since it would cause more confusion. Nevertheless, it is a stronger version of my conclusion, in which reality emerges from an immaterial reality where Yes/No decisions take place. I am simply content with claiming the existence of a mind is a neccesary but not sufficient condition for the truth evaluation of all true statements.
Thank you. I was thinking about Searle's Wall when I wrote that. But it may be too tangential to your argument.
Right, but if only the evaluation of a truth depends on a mind, then it doesn't follow that necessary truths also necessitate a mind.
Quoting Sirius
It does make sense, but it does also easily get confusing. The problem imho is that you're adding another meta layer. Now we're taking about the statement about the statement about X. Obviously if you make a statement about a statement the latter must already exist. But this doesn't tell us that it must always have existed.
Quoting Sirius
Well it's possible because this universe is the one with humans in it. This is an application of the anthropic principle. From the perspective of a mind experiencing their universe, that universe must necessarily contain the conditions for minds to exist.
There could be a universe where that isn't the case, but we wouldn't be experiencing it.
Quoting Sirius
The big bang is a human concept though, so as such it only exists in a universe that has humans (eventually).
And saying that there are infinitely many true mathematical statements to be evaluated seems to be at odds with your position that truth is created by evaluation. Since the statements don't all already exist, they're merely indefinite, not infinite.
Why would a proposition existing need have intentional content about itself? That doesnt make sense to me. The platonic form doesnt need to think itself as true: it is true iff our assertion that it exists corresponds to reality. So a true proposition, like 1+1=2, would exist and our statement 1+1=2 is true because it corresponds to that platonic form.
Why? We come to know platonic forms, assuming they exist, by reverse engineering the form of the reality of which we experience.
I was just noting that your argument presupposes mathematical realism, which is the view that mathematics pertains to the form of reality. Physics uses math, and for mathematical realist those physics equations work in virtue of roughly corresponding to actual mathematical relationships between entities (e.g., forces, objects, etc).
Then, perhaps I misrepresented your view: maybe you are a mathematical anti-realist. If you think that math is just derived from our modes and means of cognition, then it doesnt pertain to the actual structure of reality.
But how do you reconcile this with your view that there are infinitely true statements which exist in reality? Why not, then, just believe that mathematical statements, for example, are only true in virtue of how we cognize? Then you dont need to posit a universal mind.
Nah...2 meters is a valid estimation, its a tool that our faculty of reason has, of the door length. For mathematical anti-realists, they are just going to say that there is no 2 out there because theres no math: its our faculty of reason that conceptualizes things mathematically.
Now I think you may be a realist afterall (: Do you think math pertains to the real structure or at least exists out there mind-independently?
I can say that it is dependent on a number in my head and say that the number doesnt exist outside of heads. Mathematical anti-realism in a nutshell.
I disagree. We can create models of what the universe was before any mind, and those are estimations: they do not entail that reality actually abides by math. It simply does not follow.
Yeah, I just dont see why a mind needs to comprehend it for their to be numbers.
No, I am saying that there does not exist, if we go the mathematical anti-realist route, an infinite amount of mathematical propositions in reality--hence there is nothing needing to be comprehended by a universal mind. Just because we can generate an infinite amount of true mathematical statements from our basic mode of cognition it does not follow that there exists such math statements in reality.
I don't see why stopping here wouldn't be the reasonable solution.
Because it involves a contradiction. To say there exists ineffable truths about X world is to contradict yourself. Hence, there is no world which has ineffable truths. But a true statement depends neccesarily (not sufficiently ) on a mental evaluation, hence there must always be a mind to evaluate it
How could truth exist except in a mind? Here's a true statement: "The Earth is round". Now suppose all the minds in the universe disappear. Are the pixels on the screen showing "The Earth is round" still showing something that's true? If so, what makes it true? That the statement "The Earth is round" corresponds with reality, right? But if there are no minds to establish the correspondence between the statement and the world, how is the pattern of pixels "The Earth is round" a true statement?
I want to flag an objection from the perspective of one sympathetic to the Platonic intuitions behind this post. And that is the sense in which it can be said that such an all-encompassing mind exists. Because it seems clear to me that whatever exists is composed of parts and has a beginning and an end in time. To challenge that would require proving the existence of something that doesn't exhibit those attributes, and I cannot conceive of such a thing. Everything I am aware of, that exists, exhibits these attributes.
You might say that intelligible objects, such as logical principles and real numbers, don't come into or go out of existence, nor are composed of parts. And that is true - but do they exist? You can tell me they do, but to demonstrate them you would need to explain them to me, and I would need to understand them. But they certainly don't exist as do rocks, trees, and stars. They are real as elements of rational thought, but they're not phenomenally existent. And I'm of the view that 'what exists' pertains to or describes the domain of phenomena.
I noticed this passage from Bertrand Russell's discussion of universals:
Quoting Bertrand Russell, The World of Universals
I sense this is close in meaning to your OP, and something I fully agree with. The problematical part, is the meaning of the word 'exists' in this context, so also of the existence of the mind which comprehends such relations. Which is not to say that such a mind does not exist, but that it must necessarily transcend the distinction between existence and non-existence, a distinction which characterises everything that exists.
One will sometimes encounter the terminology in philosophical theology of God as 'beyond being' - and I think this is what this expression is driving at, although strictly speaking, the expression ought to be 'beyond existence', as there is a distinction, albeit one not commonly made, between 'being' and 'existence'. What is necessarily so, cannot not be.
Ideas clearly exist. Ideas are not composed of parts. You can't divide an idea. It comes as a whole. Yes, you may have an incomplete idea or it may transform into something else as you think, but the idea as an immaterial object cannot be divided. To give an analogy from physics, think of fields. They cannot be divided into parts. Therefore, whatever exists is not neccesarily composed of parts.
( Additional remarks, our minds are also indivisible, but they exist. Though we do speak of minds in the plural, the barrier between a mind and another mind can be best described as our brain filtering out other minds, as a radio picks one signal and filters out other the rest. But this is a bit speculative )
If you still insist, then this will take you down a very narrow road. For eg, "good" and "evil" as properties are not divisible. Do they exist ? If they don't, then claiming "Murder is wrong" becomes false. You can escape this conundrum by being a non-cognitivist, but the Frege-Geach problem awaits you.
Secondly. The parts of the whole can be contingent, without the collection or the container of the parts being contingent. As for our universe having a beginning and an end in time, if time is just one of its dimension and a relational feature between events, then it's a property of events within the universe, not the universe itself. The universe itself is atemporal / aspatial. The universe doesn't exist in time or space.
Let's talk about universals. Russell's argument primarily rests on concepts being the object/essence of things around us, even though they are comprehended as ideas. I will use some insight from Wittgenstein and Berkeley to refute this misconception. Let's take the famous example offered by Wittgenstein, "game". Can we give a description of "game" which is an object/essence of all games ? We cannot. Or take the example of Russell , i.e "whiteness". There is no other concept which has taken different meanings across cultures and history. It could not have belonged to objects.
On a side note, l don't believe numbers neccesarily exist as platonic entities, though they must exist in some infinite all encompassing mind. I won't be defending mathematical platonism ( with small p, espoused by the likes of Quine )
Why should we believe in the existence of mathematical entities. Well, one of my argument in OP is the well known indispensability argument offered by Quine-Putnam
It goes as follows
(P1) We ought to have ontological commitment to all and only the entities that are indispensable to our best scientific theories.
(P2) Mathematical entities are indispensable to our best scientific theories.
(C) We ought to have ontological commitment to mathematical entities.
I would like to modify this argument a bit to your taste
(P1) We have ontological commitment to all entities that are deeply intertwined in our (non-illusory) phenomenal experience and shape it
P(2) Mathematical entities are deeply intertwined in our (non-illusory) phenomenal experience and shape it
(C) We have ontological commitment to mathematical entities
Reasoning for P(1) and P(2) , Without mathematical concepts/intuiton already existing in our minds, we would not look at a triangular shape and see it as a triangle. We would not look at 3 apples and 2 oranges and think, there are 5 fruits infront of me. Moreover, when it comes to geometrical shapes, you cannot seperate your seeing of something as a figure from the concept of the figure.
I would like to emphasize, l don't think there is any explanation as to how material objects, such as trees, can instantiate a mathematical number. It appears to me that our minds project mathematical concepts onto the world and shape our phenomenal experience for us. Not the other way round.
Now imagine there were no minds in this world. But it surely makes sense to say, there would still be gazillions of stars in the sky. But this is information, a true meaning embedded statement viewed from the perspective of a mind which has access to mathematical concepts. Hence, even if our minds didn't exist, there must be some mind in whose conception the number describing all the stars in our universe exists.
As for existence, l believe we need to go back to the medieval philosophers, and mystics esp. If we follow their method, then to claim 'X exists' is to claim 'X can be found by a mind'
There exists a box on the table
A box on the table can be found by a mind
There exists a number "2"
The number "2" can be found by a mind
A square circle does not exist
A square circle can never be found by a mind ( except as an example of something never to be found )
There exist beauty
Beauty can be found by a mind
There exists good and bad
Good and bad can be found by a mind
There exists a mind
Each mind can be or is found by itself ( self-reflexive). As for the existence of other minds, l will show it follows quite easily.
If an object around you finds you, it has a mind. Books and chairs don't find you, people and animals do. How do we know something finds us out ? From its language and behavior ( for animals it's only behavior ) which is similar to ours when we find something.
The next obvious question from an interlocutor would be what is the difference between the existence of an idea, an object out there, a value judgment and an illusion ?
The way you find it and the way your mind experiences it. Your experience is non-reductive, you cannot analyze it further. As for the mind, we can say the mind isn't a physical object, it isn't an abstract entity, it isn't a moral property, it isn't an aesthetic property. In other words, the mind can only be defined as a negation of all it experiences as other than itself. Can our minds be positively described as consciousness ? I'm not sure. So l stick with the negative approach.
On the one hand, as soon as some sufficiently capable intelligence wants to know of various attributions of how many, the material thing is that which instantiates both the object of such intellectual want in general and the means of satisfying it in particular.
On the other hand, material objects are not so much the instantiation of mathematical objects, but only serve as the occasion for an intelligence to instantiate by its own means, a method sufficient for that which it wants to know about those objects, from which arises the construction of mathematical objects.
What would be a reason for mathematical objects at all, if not for an intelligence that seeks judgement on certain kinds of relations, given between real, physical things? Perhaps, then it is neither the material object itself, not the intelligence itself, that instantiates mathematical objects, but it is merely the occurrence of natural relations between the two, that demands them.
It never was the question of explanation, but only the affirmative power of whatever it may be.
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Quoting Sirius
Yep, just like that. But the instantiation of them remains unexplained by the mere projection.
I don't think its a contradiction to say that there is an objective world and I just don't have access to it.
I dispute this. There may be infinitely many facts, but it does not follow that there are infinitely many true statements. Some facts just arent talked about.
At the very least you can say that there are infinitely many possible true statements, but I dont think that requires an all-encompassing mind.
If a fact isn't talked about (or held in some mind) is it a fact?
Also, there are infinitely many numbers, right? But there is a limit to the biggest number a finite brain can think of. No matter what notation is used, there will be a number that a finite brain just cannot conceive- it will be overwhelmed. The neurons/transistors/logic gates will be overwhelmed. So does that mean there aren't infinitely many numbers?
I take it you are willing to accept there can be infinitely many mathematical facts.
You take facts to be possible states of affairs, which must either be true or false. So given there can be infinitely many facts, an infinitely many of them are either true or false. By the law of non-contradiction, an infinitely many of them are true, likewise an infinitely many of them are false. An infinitely many true statements cannot be expressed by a universe which contains finite information. Hence, an infinitely many true statements exist independent of the universe
Note : Possible states of affairs can be false, for eg, 1+1=3 is F , given the usual notation. All actual statements are just true possible statements
If by possibly true you mean possible statements which are not actual but true, then it's a self contradiction. But if you mean the possible statement can be true or false, then you have said nothing. You are just repeating the law of non-contradiction, which is even true of actual statements.
Statements are true, states of affairs obtain. A statement is true if it describes a state of affairs that obtains, and false if it describes a state of affairs that doesn't obtain.
There are a finite number of statements but (possibly) an infinite number of states of affairs. Statements depend on "cognitive content" but (some) states of affairs don't.
Quoting Sirius
But do they? That's the question I'm raising. The point I'm making is that they exist in a different way than do phenomenal objects. As I said, the only way to communicate an idea is to explain it to someone capable of understanding it, and as you yourself say:
Quoting Sirius
But whose is the mind on which those facts depend? In what sense does that exist? And if it does exist, then why can't any empirical evidence be adduced to demonstrate it?
As you conclude, this 'mind' corresponds to 'an impersonal God' (although the 'impersonal' caveat might simply serve to defray the accusation of defending religious apologetics.) But fathoming that mind is another matter. That mind is not 'out there somewhere', it is not a phenomenal existent. So in what sense can it be said to be real? I think you're actually coming up against a pretty profound philosophical issue with deep roots in the tradition.
Forgive the length of the quotation below. It's from Dermot Moran's entry on Scotus Eriugena on SEP, slightly edited by me, and I provide it, because it's about the only source I'm aware of that makes this point in modal metaphysics. Note in some passages I've substituted 'to exist' for 'to be', to support the polemical point.
Quoting SEP, John Scotus Eriugena
My bolds. I think this reflects the hierarchical metaphysics of the 'chain of being' (scala naturae) which later fell into disrepute with the 'flattening' of ontology which characterises the advent of modernity. I think it stands for something real, but not empirically intelligible.
Quoting Sirius
But what prompted that argument? Why were they obliged to defend the importance of mathematics in the first place? According to the IEP entry on same,
So, what are our 'best epistemic theories', and why do they deny that such knowledge is possible?
This is just the point I'm making about sense in which number exists.
It goes on:
My bolds. According to our 'best epistemic theories', mathematical insight should't be possible - because it contradicts naturalism! We are, after all, evolved animals, right? Nothing like that anywhere else in the animal kingdom! Hence Quine and Putnam's convoluted argumentation to defend something that should never have been called into question in the first place, but which seems to contradict the naturalist orthodoxy of the Academy. As SEP puts it,
(I would have more to say about the nature of the one mind you're proposing but it's already far too long a post so will come back to that.)
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1.This type of dialectic is encountered in apophatic theology, see for instance God does not Exist and What is the Ground of Being?
Not in the Platonic sense. Numbers don't exist. Rather, when we say that there are infinitely many numbers we are just saying that we can (in principle) keep adding 1 forever.
I believe there is a fundamental disagreement between us regarding the ontological and logical status of possible states and actual states of affairs.
Here is what l hold onto
1. If A is a possible state of affairs, it was always possible. Possible states of affairs don't come into existence as a possibility.
2. Before this universe or any other universe existed, the possible states of affairs in reference to our universe and other universes out there existed, alongside all the possible states of affairs of universes which never came into existence.
3. Each possible state of affairs is either true or false. For mathematical statements, this is determined by logical necessity. As for empirical statements, they are assigned T/F in a brute manner, whether you believe in a God or not. Even if God assigned truth values to possible states of affairs related to the physical reality, it would be brute.
4. A true possible state of affairs is actual. What is actual, was never not actual. What is not actual is false. Otherwise, a possible states of affairs would be true and false.
What do 2, II, { { }, { { } } } , apple apple
all share ?
These objects don't belong in the list just because we wanted them to be in this list. The symbols are designed by us, but they represent something which isn't our construct, or else we would be able to do anything with them, such as equate 2 with 3, given the usual notation, bit this isn't possible.
If you are a strict nominalist who believes math is entirely our own construction, then you will need to explain why mathematical statements are not contingent and why do the laws of physics depend on them ?
As for infinity. Mathematicians never state, there are infinite possible numbers. Nope. They say
Take N = { 1, 2, 3... } , then N HAS an infinite number of elements
When we write lim x -- > inf 1 / x = 0 , we don't only mean as x approaches infinity, then 1 / x approaches 0, but when x approaches infinity, 1/ x does approach 0
The equality sign isn't there to represent an approximation. It isn't the job of philosophers to tell mathematicians what they can or cannot say.
Yes, there is a fundamental disagreement. My take is that truth is a "property" of expressions, i.e. speech, writing, thought, etc. As such, as you say, "true statements can only exist as cognitive content," given that speech, writing, and thought can only exist as cognitive content. But there's more to the world than speech, writing, and thought, and so that speech, writing, and thought can only exist as cognitive content isn't that the rest of the world can only exist as cognitive content.
But you seem to be arguing that truth is a property of other things (e.g. the states of affairs that speech, writing, and thought are about). It's not a position I agree with.
Even if I were to accept that truth is a property of these other things, note that these other things aren't statements. A true state of affairs isn't a true statement, and so that true statements can only exist as cognitive content isn't that true states of affairs can only exist as cognitive content. Your argument appears to equivocate.
If truth is mind-dependent even if about mind-independent objects, how are we assessing what is true in terms of definition?
If true statements are merely a mind communicating a mind-independent truth then none of this really works because were just discussing the subjectivity of lnguahe but if true is actually taken as a relation between the mind-independent world (ie any given object) and the mind who would potentially make a statement about it - ie that true just means the clearest transition from the world, to the mind, then the statements considered true require there to be nothing more than minds that can achieve a relation with the world to such a degree that other minds consider their statements to in fact carry that relation which is, to be very gentle, unhelpful in my estimation