Objection to Aquinas' Five Proofs

[Betterave]

It might be possible for you to come up with a statement about reality which seems logically undeniable, but it will never actually be logically undeniable.

And so, since this is surely a statement about reality, it is not actually logically undeniable?

Similarly, you might be able to find a logically undeniable statement which seems like it’s about reality, but it can never truly be about reality.

This too appears to be a statement about reality…

The reason for this is that tautologies do not tell us about reality, and statements are logical theorems if and only if they are tautologies.

…and this too.

The latter relationship was proved in two metatheorems, the completeness theorem and its converse the [soundness theorem](http://philosophy.wisc.edu/velasco/211/Soundness Theorem for SL.pdf).

Could you be more specific with your reference here? Copy and paste a relevant passage maybe?

 

[The_Exodus]

You might want to let x be a propositional constant which references the real world. Then finally you could say that it is not possible that x and not-x is a statement about reality. However, as a theorem in (informal) propositional logic, it is a tautology, and does not actually give us meaningful information about metaphysical systems outside the domain of logic itself.

My position (against the idealists) is that principle of contradiction is not a tautology, but rather the fundamental law of being, which is intuited by the mind upon perceiving reality. This causal order of aquisition is free from tautology.

My question to you remains, however. When you use the word “logic,” what mental process are you refering to, and why should we think it valid for gaining truth?

hatsoff:

In other words, it doesn’t help us predict and control our experiences outside our use of logic, nor does it give us information about what other real objects might exist, nor what relationship they might have to each other.

Why doesn’t it; could you be more specific?

I intuit object a is object a, and not object not-a. This relationship of identity seems enormously useful to me, for understanding reality, living practically, etc.

 

[The_Exodus]

It might be possible for you to come up with a statement about reality which seems logically undeniable, but it will never actually be logically undeniable.

What do you mean here by “logically undeniable?” I can think of all sorts of statements about reality which are against this claim: the sun is shining, I exist, my car needs gas, etc.

hatsoff:

Similarly, you might be able to find a logically undeniable statement which seems like it’s about reality, but it can never truly be about reality. The reason for this is that tautologies do not tell us about reality, and statements are logical theorems if and only if they are tautologies.

The law of identity is not a tautology, as stated in my previous post, since it is gained by the mind upon perceiving being. This is the classical epistemology of the Scholastics. Now, if you want to put up the Kantian impassible bridge between reality “as it is” and reality “is it appears to us” then you are free to do so, but if you do, none of your statements about reality “as it is” can be meaningful. And neither can reality’s “unknowableness” be proved. It can only be asserted, and even this on the supposition that reality “as it is” exists in the first place, since we have no reason to think our mind is not all there is.

 

[hatsoff]

What do you mean here by “logically undeniable?” I can think of all sorts of statements about reality which are against this claim: the sun is shining, I exist, my car needs gas, etc.

By “logically undeniable,” I mean that it is a law or theorem in (informal) predicate logic.

The law of identity is not a tautology, as stated in my previous post, since it is gained by the mind upon perceiving being. This is the classical epistemology of the Scholastics. Now, if you want to put up the Kantian impassible bridge between reality “as it is” and reality “is it appears to us” then you are free to do so, but if you do, none of your statements about reality “as it is” can be meaningful. And neither can reality’s “unknowableness” be proved. It can only be asserted, and even this on the supposition that reality “as it is” exists in the first place, since we have no reason to think our mind is not all there is.

The law of identity is indeed true in every interpretation, which is precisely what it means to be a tautology. If it were false in some interpretation, then it wouldn’t be a logical law, by Godel’s completeness theorem.

 

[The_Exodus]

The law of identity is indeed true in every interpretation, which is precisely what it means to be a tautology. If it were false in some interpretation, then it wouldn’t be a logical law, by Godel’s completeness theorem.

Again, could you explain your statement (examples, how it relates to my claims, etc)?

 

[hatsoff]

Again, could you explain your statement (examples, how it relates to my claims, etc)?

You claimed that the laws of identity and noncontradiction are not tautologies, but that is incorrect. The laws of identity and noncontradiction are tautologies. Why? Because they’re true in every interpretation, which is precisely what it means to be a tautology.

 

[The_Exodus]

You claimed that the laws of identity and noncontradiction are not tautologies, but that is incorrect. The laws of identity and noncontradiction are tautologies. Why? Because they’re true in every interpretation, which is precisely what it means to be a tautology.

I could have simply re-read your previous posts if I wanted to hear you say the same thing again.

What do you mean when you say “they’re true in every interpretation”? Does this imply there is no such thing as a false interpretation? Further, how are the laws of identity and contradiction aquired by the mind?