Are all things trivial conditions of themselves?

[Birdmanman]

I hold that God, in His Divine Nature, is not a thing whose existence is caused. I further hold that nothing can be the real condition of its own existence, otherwise it would need to exist prior (either temporally or even causally) to its own existence, which is impossible.

But it appears that everything that does exist already has its own existence as a trivial condition of its own existence. That is, it seems always to hold that “If X, then X” is trivially true.
For example “If the ball exists, then the ball exists” is true. But the first portion of that (“If the ball exist”) was a logical condition of the second portion of that statement (“then the ball exists”).
But would this not apply to God as well, so that, although we may say God has no actual (external) condition of His existence, He Himself is the logical condition of His own Existence (in a trivial way)?

Also, would it be heretical to hold that God Himself is also Logic? It seems that, because God cannot negate Himself (cause Himself not to exist), even He is subject to logic; but it would be improper to call Him subject to anything other than Himself; so it would seem more proper to say that He is also Logic (or at least that Logic is an aspect of (a way of looking at?) Truth, and that He is Truth).

 

[KyrieEleison17]

I hold that God, in His Divine Nature, is not a thing whose existence is caused. I further hold that nothing can be the real condition of its own existence, otherwise it would need to exist prior (either temporally or even causally) to its own existence, which is impossible.

But it appears that everything that does exist already has its own existence as a trivial condition of its own existence. That is, it seems always to hold that “If X, then X” is trivially true.
For example “If the ball exists, then the ball exists” is true. But the first portion of that (“If the ball exist”) was a logical condition of the second portion of that statement (“then the ball exists”).
But would this not apply to God as well, so that, although we may say God has no actual (external) condition of His existence, He Himself is the logical condition of His own Existence (in a trivial way)?

Also, would it be heretical to hold that God Himself is also Logic? It seems that, because God cannot negate Himself (cause Himself not to exist), even He is subject to logic; but it would be improper to call Him subject to anything other than Himself; so it would seem more proper to say that He is also Logic (or at least that Logic is an aspect of (a way of looking at?) Truth, and that He is Truth).

You seem about right here but I will make a few comments.

We know full well that baseballs do not cause themselves to exist. Baseballs are artefacts and no artefact is the cause of its own existence. In fact we don’t know of anything that can or could cause its existence and, as you said, it’s still held to be impossible as it would require the thing’s already existing in some way to do so. So that’s nothing trivial: you can’t do science without accepting this (i.e. the principle of causality).

 

[polytropos]

I further hold that nothing can be the real condition of its own existence, otherwise it would need to exist prior (either temporally or even causally) to its own existence, which is impossible.

The argument you are giving here seems to be the argument that Aquinas gives to the effect that a thing cannot be its own efficient cause. Is that what you mean by real condition? The other thing that the term suggests to me is the real distinction between essence and existence (in created things). To know what a man is is not to know that a man exists.

But it appears that everything that does exist already has its own existence as a trivial condition of its own existence. That is, it seems always to hold that “If X, then X” is trivially true.

“If X, then X” is a tautology, for it is logically equivalent to “not X or X”.

For example “If the ball exists, then the ball exists” is true. But the first portion of that (“If the ball exist”) was a logical condition of the second portion of that statement (“then the ball exists”).
But would this not apply to God as well, so that, although we may say God has no actual (external) condition of His existence, He Himself is the logical condition of His own Existence (in a trivial way)?

For the above reason, “If the ball exists, then the ball exists” does not actually give a “condition” for the ball’s existence. (And likewise, the similitude of the claim about the ball with the claim about God does not really have any implications–they are both tautologies.)

It seems to me like you are over-reifying logic. The rules of logic are beings of reason, entia rationis, mostly of use in reasoning and dialectic (both of which, God has no use for, since he is unchangingly omniscient). That does not mean that they admit of exceptions or anything like that, but it does mean that there is more to God’s simplicity and subsistence than a logical relationship.

Also, would it be heretical to hold that God Himself is also Logic? It seems that, because God cannot negate Himself (cause Himself not to exist), even He is subject to logic; but it would be improper to call Him subject to anything other than Himself; so it would seem more proper to say that He is also Logic (or at least that Logic is an aspect of (a way of looking at?) Truth, and that He is Truth).

As I said above, I think logical entities are mind-dependent beings of reason. At least under that construal (I suppose there could be others), logic would not be one of the transcendentals (as truth is). The transcendentals are the various “aspects” of being, which are really the same thing viewed by humans under different conceptual schemes… namely being, goodness, truth, beauty, etc. Hence God is Being Itself, God is Goodness Itself, God is Truth Itself, and God is Beauty Itself. I wouldn’t number logic among the transcendentals.

 

[Oreoracle]

It seems problematic to me to suppose that logical statements “exist”. One difficulty is that there are multiple varieties of logic, each equipped with its own set of axioms. When you choose the axioms, you choose what propositions mean, in the same way that choosing a definition determines the meaning of a word.

Because of this, there are statements that are true in classical logic but not in intuitionist logic, or ones that are true in a paraconsistent logic but not in classical logic. To say that propositions exist would require us to explain why they exist in some logics but not in others. It seems easier to admit that the truth of a proposition is just a consequence of your choice in axioms rather than some deeper, metaphysical framework.

 

[KyrieEleison17]

To say that propositions exist would require us to explain why they exist in some logics but not in others. It seems easier to admit that the truth of a proposition is just a consequence of your choice in axioms rather than some deeper, metaphysical framework.

I don’t know about this. By a proposition could be understood almost anything being predicated of a subject: ‘Oreoracle exists’. The proposition is a judgement formed in my mind - so it exists ‘there’, at least in some sense; moreover, it wouldn’t seem pointless to inquire as to why that is a true proposition.

 

[Birdmanman]

The argument you are giving here seems to be the argument that Aquinas gives to the effect that a thing cannot be its own efficient cause. Is that what you mean by real condition? The other thing that the term suggests to me is the real distinction between essence and existence (in created things). To know what a man is is not to know that a man exists.

“If X, then X” is a tautology, for it is logically equivalent to “not X or X”.

For the above reason, “If the ball exists, then the ball exists” does not actually give a “condition” for the ball’s existence. (And likewise, the similitude of the claim about the ball with the claim about God does not really have any implications–they are both tautologies.)

It seems to me like you are over-reifying logic. The rules of logic are beings of reason, entia rationis, mostly of use in reasoning and dialectic (both of which, God has no use for, since he is unchangingly omniscient). That does not mean that they admit of exceptions or anything like that, but it does mean that there is more to God’s simplicity and subsistence than a logical relationship.

As I said above, I think logical entities are mind-dependent beings of reason. At least under that construal (I suppose there could be others), logic would not be one of the transcendentals (as truth is). The transcendentals are the various “aspects” of being, which are really the same thing viewed by humans under different conceptual schemes… namely being, goodness, truth, beauty, etc. Hence God is Being Itself, God is Goodness Itself, God is Truth Itself, and God is Beauty Itself. I wouldn’t number logic among the transcendentals.

I had this concern as well (about over-reifying logic); I appreciate your response and it has helped me greatly. I might ask though, why something being a tautology precludes it from also being a conditional statement (that is, why does it follow that, if “if X then X” is a tautology, then “if the ball exists then the ball exists” does not provide us with a condition of the ball’s existence) ?

It seems problematic to me to suppose that logical statements “exist”. One difficulty is that there are multiple varieties of logic, each equipped with its own set of axioms. When you choose the axioms, you choose what propositions mean, in the same way that choosing a definition determines the meaning of a word.

Because of this, there are statements that are true in classical logic but not in intuitionist logic, or ones that are true in a paraconsistent logic but not in classical logic. To say that propositions exist would require us to explain why they exist in some logics but not in others. It seems easier to admit that the truth of a proposition is just a consequence of your choice in axioms rather than some deeper, metaphysical framework.

Thanks for your response! I am not a logician and mean no disrespect to you by this, but under what logical system and axioms did you determine it was true that it is “easier to admit that the truth of a proposition is just a consequence of your choice of axioms”, and why should I hold the axioms that you do in support of this?

It also seems that logical statements, their meaning, or at least their representation in sentences or concepts, do exist (in one way or another). Otherwise, what are we talking about when you imply that logical statements don’t exist? *

(I think that the laws of logic (X is X; Not X is not X; X is not not X) are the basest axioms held, at least implicitly, by all humans who think, and that attempting to deny any of them will lead to a self-refutation or inconsistency. Of course, why anyone should care about truth or consistency at all seems to be more of a moral question outside the scope of this thread).*

 

[polytropos]

I had this concern as well (about over-reifying logic); I appreciate your response and it has helped me greatly. I might ask though, why something being a tautology precludes it from also being a conditional statement (that is, why does it follow that, if “if X then X” is a tautology, then “if the ball exists then the ball exists” does not provide us with a condition of the ball’s existence) ?

Well, the first reason is that we should not expect the logic to project so simply onto the metaphysics. The main reason, though, is that “If the ball exists, then the ball exists” is true even if the ball does not in fact exist. The tautology “If X, then X” can’t explain both “X” and “not X”.

 

[Birdmanman]

Well, the first reason is that we should not expect the logic to project so simply onto the metaphysics. The main reason, though, is that “If the ball exists, then the ball exists” is true even if the ball does not in fact exist. The tautology “If X, then X” can’t explain both “X” and “not X”.

I’m sorry, you must think me rather slow, but is it possible to explain any further why “If X, then X” cannot explain both “X” and “not X”? I don’t see why not…the contrapositive of the statement shows that “If not X, then not X” which appears true…and the positive shows that “if X, then X” which also appears true.

 

[polytropos]

I’m sorry, you must think me rather slow, but is it possible to explain any further why “If X, then X” cannot explain both “X” and “not X”? I don’t see why not…the contrapositive of the statement shows that “If not X, then not X” which appears true…and the positive shows that “if X, then X” which also appears true.

Sure.

Ostensibly, if “If X, then X” is a “condition” for “X” being the case, then one is taking the truth of “If X, then X” to be in some way explanatory of “X” (I am assuming that this is related to the way you are using the term “condition”). But then, suppose “X” is not the case. “If X, then X” is still true. So in what sense is it explanatory of “X”, which is false?

You are right that the contrapositive is also a tautology, but that seems to cause the same issue. If “If X, then X” is explanatory of “X” and “If not X, then not X” is explanatory of “not X”, then why should both tautologies be the case when only one “X” or “not X” is true. There is no relationship between the allegedly explanatory claims and what they are supposed to be explaining.

Another reason seems simply to be that a conditional “If p, then q” gives you a logically sufficient reason for q. But that does not preclude there being some other logically sufficient reason for p, namely r: “If r, then p”. So then you would have “If r, then q”. So we can admit that “If X, then X” is a tautology, but that does not necessitate that X is the only logically sufficient condition of X, ie. that X is subsistent. If some other logically sufficient condition exists and is disclosed, for example, by sound metaphysics, then we need not make any comparison between God and the ball.

Yet another reason would be that a proposition like “the ball exists” discloses a state of affairs. Material conditionals are just truth functions. While we are used to using conditionals in our daily life to disclose causal and explanatory relations, those are quite irrelevant to classical logic. It is also true that “If the sun is blue, then the sun is green”, because the antecedent is false. It is true, furthermore, that “If water is H2O, then Barack Obama is president of the United States of America”. But it is a mistake to think that either conditional discloses an explanatory condition. The ball’s existence need not be subsistent in any sense just because “If the ball exists, then the ball exists” is true.

 

[Birdmanman]

Sure.

Ostensibly, if “If X, then X” is a “condition” for “X” being the case, then one is taking the truth of “If X, then X” to be in some way explanatory of “X” (I am assuming that this is related to the way you are using the term “condition”). But then, suppose “X” is not the case. “If X, then X” is still true. So in what sense is it explanatory of “X”, which is false?

You are right that the contrapositive is also a tautology, but that seems to cause the same issue. If “If X, then X” is explanatory of “X” and “If not X, then not X” is explanatory of “not X”, then why should both tautologies be the case when only one “X” or “not X” is true. There is no relationship between the allegedly explanatory claims and what they are supposed to be explaining.

Another reason seems simply to be that a conditional “If p, then q” gives you a logically sufficient reason for q. But that does not preclude there being some other logically sufficient reason for p, namely r: “If r, then p”. So then you would have “If r, then q”. So we can admit that “If X, then X” is a tautology, but that does not necessitate that X is the only logically sufficient condition of X, ie. that X is subsistent. If some other logically sufficient condition exists and is disclosed, for example, by sound metaphysics, then we need not make any comparison between God and the ball.

Yet another reason would be that a proposition like “the ball exists” discloses a state of affairs. Material conditionals are just truth functions. While we are used to using conditionals in our daily life to disclose causal and explanatory relations, those are quite irrelevant to classical logic. It is also true that “If the sun is blue, then I will paint my house yellow”, because the antecedent is false. It is true, furthermore, that “If water is H2O, then Barack Obama is president of the United States of America”. But it is a mistake to think that either conditional discloses an explanatory condition. The ball’s existence need not be subsistent in any sense just because “If the ball exists, then the ball exists” is true.

I may not have been clear in my original post. I identify (for the sake of this thread) the “trivial condition” of the existence of X as the existence of X itself. That is, the thing itself is its own trivial condition. I do this because the conditional proposition “If X, then X” is true, where X (in the first part of the proposition) is both identical to and the condition of X (in the second part of the proposition). I did not mean to say that the proposition “If X, then X” is a condition for X being the case. (That is, I am saying that X is the [trivial] condition of X, not that the proposition is the trivial condition of X).

Otherwise, I thank you for your most recent post, and will chew over what you have said there (which seems to answer my question).

 

[polytropos]

I may not have been clear in my original post. I identify (for the sake of this thread) the “trivial condition” of the existence of X as the existence of X itself. That is, the thing itself is its own trivial condition. I do this because the conditional proposition “If X, then X” is true, where X (in the first part of the proposition) is both identical to and the condition of X (in the second part of the proposition). I did not mean to say that the proposition “If X, then X” is a condition for X being the case. (That is, I am saying that X is the [trivial] condition of X, not that the proposition is the trivial condition of X).

I see. In that case I think the last two paragraphs of my post are relevant. If X is the trivial condition of itself, then any true statement should also be a “material condition” of X (assuming X is true). But there seems to be no reason to regard that as metaphysically significant.

 

[Birdmanman]

I see. In that case I think the last two paragraphs of my post are relevant. If X is the trivial condition of itself, then any true statement should also be a “material condition” of X (assuming X is true). But there seems to be no reason to regard that as metaphysically significant.

Thanks for your help! I thought that this kind of reasoning (that a true statement implies all other true statements, and that a false statement implies all other statements both true and false) was unique to analytical logic. My dilemma may be more easily laid out below:

1. The conditional proposition “If X exists, then X exists” is true (tautologically).
2. In this conditional proposition, X’s existence is a condition of X’s existence. (This is what is meant by a conditional proposition, the first object (or object’s existence) identified is the condition, the second object (or object’s existence) identified is dependent on that condition (the first object) being fulfilled (or existing)).
3. Therefore, it is true that X’s existence is a condition of X’s existence. (From 1 and 2)
4. But it is impossible that something’s existence should be a condition of its existence (for something cannot be logically prior to itself). (Premise)
5. Thus, there is a flaw in the argument.