4. All neccesarily true statements exist as cognitive content (from 1,2) — Sirius

How does it follow from your premises that the statements (already) exist?

How does it follow from your premises that the statements (already) exist? — 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.

1. True statements can only exist as cognitive content — Sirius

That (which exists as pixels on a screen) is not a true statement?

How does it follow from your premises that the statements (already) exist? - Echarmion

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.

That (which exists as pixels on a screen) is not a true statement?

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

It doesn't follow from any of this that any particular statement (concerning a necessary truth or something else) necessarily exists.

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 ?

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. — Sirius

Sure, I can't imagine without using my mind.

Using your mind to describe a mindless world ( in which a mind doesn't exist ) is a wrong step. — Sirius

Then why did you ask me to make a wrong step?

(I know, I know, that's how the presuppositionalist game is played.)

1. True statements can only exist as cognitive content.
2. Cognitive content depends on the existence of a mind which can comprehend it. — Sirius

This reduces to…the true statements that exist depend on the existence of a mind that can comprehend them.

What’s 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.
————-

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.

1. True statements can only exist as cognitive content — Sirius

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.

Can you point out the specific flaw. Saying the conclusion doesn't follow isn't helpful. — Sirius

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.

1. True statements can only exist as cognitive content
2. Cognitive content depends on the existence of a mind which can comprehend it

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 can’t the true proposition ‘p > q’ not exist acausally as the a part of the form of reality?

Another route, is to just deny:

3. There are infinitely many statements that are necessarily true, independent of spacetime itself

For your argument to work, one has to be a mathematical and logical realist—i.e., one has to believe that math and logic pertain to the structure of reality and are not our mere estimations of it—which I am not seeing why this would be implausible.

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.

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 doesn’t require a universal mind.

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 )

What we estimate about reality will always be an finite underestimate of what is happening: no matter how precise it is.

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 can’t the true proposition ‘p > q’ not exist acausally as the a part of the form of reality?

Another route, is to just deny:

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 ?

Another route, is to just deny:

3. There are infinitely many statements that are necessarily true, independent of spacetime itself

For your argument to work, one has to be a mathematical and logical realist—i.e., one has to believe that math and logic pertain to the structure of reality and are not our mere estimations of it—which I am not seeing why this would be implausible.

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.

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 doesn’t require a universal mind.

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

What we estimate about reality will always be an finite underestimate of what is happening: no matter how precise it is.

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 )

But not all possible statements already exist. You would need to show that the statement about the necessary truth also necessarily exists.

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.

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.

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 ) — Sirius

What does it mean for truths to exist? Are truths metaphysically real "states of affairs"? Or are they constructions of a particular mind?

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. — Sirius

This does not make sense to me. The content of a statement doesn't change its ontological status.

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. — 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.

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. — Pantagruel

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?

1. True statements can only exist as cognitive content
— Sirius

That (which exists as pixels on a screen) is not a true statement? — wonderer1

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?

:up:

What does it mean for truths to exist? Are truths metaphysically real "states of affairs"? Or are they constructions of a particular mind?

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.

This does not make sense to me. The content of a statement doesn't change its ontological status.

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

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.

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.

Only if a mind is observing the pixels on a screen. Otherwise, they're just pixels on a screen. It takes mentation to turn the pixels into something else. 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?

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.

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. — Sirius

Thank you. I was thinking about Searle's Wall when I wrote that. But it may be too tangential to your argument.

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. — Sirius

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.

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 — 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.

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.

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 ? — 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.

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.

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. — 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.

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.

Why would a proposition existing need have intentional content about itself? That doesn’t make sense to me. The platonic form doesn’t 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.

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.

Why? We come to know platonic forms, assuming they exist, by reverse engineering the form of the reality of which we experience.

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.

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).

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.

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 doesn’t 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 don’t need to posit a universal mind.

If you say your door is 2 meters long and "2" doesn't exist, then your statement is false.

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 there’s no math: it’s our faculty of reason that conceptualizes things mathematically.

But you do have a mind which can conceptualize "2", even if it's a rough approximation, so your statement is somewhat right

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?

If you improved your instrument, you would get a better measurement, but it still depends on the existence of some number inside your head.

I can say that it is dependent on a number ‘in my head’ and say that the number doesn’t exist ‘outside of heads’. Mathematical anti-realism in a nutshell.

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.

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.

So there must have been some mind which comprehended mathematical numbers/concepts

As for numbers being platonic entities, refer to my objection above

Yeah, I just don’t see why a mind needs to comprehend it for their to be numbers.

Are you saying there are only finitely true mathematical statements because of that ?

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.

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. — Sirius

I don't see why stopping here wouldn't be the reasonable solution.

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

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. — Echarmion

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?

Therefore , an all encompassing mind necessarily exists — Sirius

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:

Consider such a proposition as 'Edinburgh is north of London'. Here we have a relation between two places, and it seems plain that the relation subsists independently of our knowledge of it. When we come to know that Edinburgh is north of London, we come to know something which has to do only with Edinburgh and London: we do not cause the truth of the proposition by coming to know it, on the contrary we merely apprehend a fact which was there before we knew it. The part of the earth's surface where Edinburgh stands would be north of the part where London stands, even if there were no human being to know about north and south, and even if there were no minds at all in the universe. ...We may therefore now assume it to be true that nothing mental is presupposed in the fact that Edinburgh is north of London. But this fact involves the relation 'north of', which is a universal; and it would be impossible for the whole fact to involve nothing mental if the relation 'north of', which is a constituent part of the fact, did involve anything mental. Hence we must admit that the relation, like the terms it relates, is not dependent upon thought, but belongs to the independent world which thought apprehends but does not create.

This conclusion, however, is met by the difficulty that the relation 'north of' does not seem to exist in the same sense in which Edinburgh and London exist. If we ask 'Where and when does this relation exist?' the answer must be 'Nowhere and nowhen'. There is no place or time where we can find the relation 'north of'. It does not exist in Edinburgh any more than in London, for it relates the two and is neutral as between them. Nor can we say that it exists at any particular time. Now everything that can be apprehended by the senses or by introspection exists at some particular time. Hence the relation 'north of' is radically different from such things. It is neither in space nor in time, neither material nor mental; yet it is something.

It is largely the very peculiar kind of being that belongs to universals which has led many people to suppose that they are really mental. We can think of a universal, and our thinking then exists in a perfectly ordinary sense, like any other mental act. Suppose, for example, that we are thinking of whiteness. Then in one sense it may be said that whiteness is 'in our mind'. ...In the strict sense, it is not whiteness that is in our mind, but the act of thinking of whiteness. The connected ambiguity in the word 'idea', which we noted at the same time, also causes confusion here. In one sense of this word, namely the sense in which it denotes the object of an act of thought, whiteness is an 'idea'. Hence, if the ambiguity is not guarded against, we may come to think that whiteness is an 'idea' in the other sense, i.e. an act of thought; and thus we come to think that whiteness is mental. But in so thinking, we rob it of its essential quality of universality. One man's act of thought is necessarily a different thing from another man's; one man's act of thought at one time is necessarily a different thing from the same man's act of thought at another time. Hence, if whiteness were the thought as opposed to its object, no two different men could think of it, and no one man could think of it twice. That which many different thoughts of whiteness have in common is their object, and this object is different from all of them. Thus universals are not thoughts, though when known they are the objects of thoughts. — 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.

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 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.