Objection to Aquinas' Five Proofs

[The_Exodus]

i don’t understand relativity, but the top physicists do. and i accept the scholarly consensus on the truth of the matter. if there were any such scholarly consensus on the validity of aquinas’s proofs among philosophers and logicians as there is on einstein’s relativity then the existence of god and all his attributes would be a matter of settled fact in academia. how do you explain the fact that the existence of god is not a settled fact among academics and that they are less likely than your uneducated masses to be catholic?/

Physicists sure don’t agree my friend. Any field, the higher you go, the more difference there is in opinion. This is the case with Aquinas scholars and physicists. It’s an error to think “relativity” is a closed case. This is mostly because, just because someone labels them an “Aquinas” scholar or a “follower of Einstein” doesn’t mean they truly are. A guy can call himself whatever he wants and be following his own thought instead of another’s. A Ph. D doesn’t change this. It just makes it more subtle and more shocking. Furthermore, don’t rely on authority if you haven’t looked into that authority for yourself. If you don’t know a lick about physics, it’s irresponsible just to accept what someone says on his say-so. Be agnostic about it.,

The existence of god, how much of his being can be known and what kind of knowledge we can have of it has been a divisive issue for ages. Catholic teaching, however, says that the existence of god can be known as certain by natural reason. Now, a lotta guys wanna say that our reason can’t be certain of anything. Starting from Descartes with the cogito (which is never where the Scholastics started), they go on to say that our reason can’t be certain of anything. So a huge chunk of modern philosophy is caught up in this whole Cartesian/Kantian Idealism. Of course, they’re going to say we can’t prove or be certain that God exists. But they also concede we can’t be certain that other minds or matter exist, or even our own selves, so there you go. Now, if you want to know what the real thinkers of Catholicism thought – what the philosophy of the Church is built on – read the Scholastics and Aristotle. Then read their traditional commentators. They have an entirely different view of the intellect than the Idealists and Sensualists/Pragmatists.

It really all gets messy cause people disagree about what they mean by “proof” and “certainty.” Needless to say, there is no short response to the differences implied by each school of thought on these issues.

 

[hatsoff]

My friend, read St. Thomas’ commentators before you jump to this conclusion. One has to understand the root of his thought before one can make a serious criticism of his proofs. Any rejection of his proofs, furthermore, result in a sor of mass scale rejection of certain types of knowledge (as a matter of fact I would say all knowledge)and change one’s entire epistemology. Hegel, for instance, who rejected the proofs, also had to reject the principle of contradiction, and thought that reality was “the joining of two contradictories” (whatever that means.) Anyway, read Garrigou-Lagrange. He’s a great, recent commentator on St. Thomas.

Thomists frequently ask me to read more material if I observe that what I have read seems ridiculous. Although it’s always possible that I really don’t understand Aquinas, and that I just have to study further his work, what reason have I to think that this is so?

If you think that my denial of that one of Aquinas’ ways, quoted previously, requires me to reject the principle of contradiction, then you are welcome to explain why. However—and I hope you will understand—I just don’t want to read some dry and dense commentary which, from my perspective, is very likely to contain more of the same nonsense I’ve encountered with other Thomists. In short, you Catholics have to do a better job convincing me that he is worth reading!

 

[Rocinante]

Physicists sure don’t agree my friend. Any field, the higher you go, the more difference there is in opinion. This is the case with Aquinas scholars and physicists

true. once you get into a field there are always controversial areas, but we are not talking about “the higher you go” here. we are talking about the legitimacy of a simple logical proof. the higher you go the more likely it is that you will find things that experts disagree on, but they don’t disagree on simple things like this matter of the validity of a simple proof any more than mathematicians disagree on the validity of a proof of the pythagorean theorem.

my understanding is that the scholarly consensus among philosophers is that these 5 proofs have real problems. these proofs are simple, but they turn out to be too simple.

there is a reason why religion is thought to be a matter of faith. it were a matter of reason, then the people with the most powerful reasoning skills (academics) would be the most religious among us. but of course that is not the case. it takes more than such “proofs” to convince us of the existence of the divine or at least to argue the point in a way that stands up to rational scrutiny on the highest levels.

rocinante

 

[The_Exodus]

we are talking about the legitimacy of a simple logical proof. the higher you go the more likely it is that you will find things that experts disagree on, but they don’t disagree on simple things like this matter of the validity of a simple proof

This isn’t the case at all. As a matter of fact, the word “proof” is one of the most disagreed on words in the history of western civilization.

Nearly every person you will ever ask will give you a different definition of what a “simple proof” is. Your definition, I’m sure, is probably quite different than mine for starters. And each of ours probably quite different from everyone on this forum.

rocinante:

my understanding is that the scholarly consensus among philosophers is that these 5 proofs have real problems.

You have to understand that “scholarly consensus” has a particular perspective, which is epistemologically different than scholars of the past, or other current scholars. There is no simple appeal to “modern scholarship” in the cases of the 5 proofs. It really takes a sort of historically broad understanding of philosophy to see why there are disagreements, and what those disagreements imply.

rocinante:

there is a reason why religion is thought to be a matter of faith.

This is true, but faith doesn’t destroy reason. This, however, is the divisive question: is theism fideistic? And again, there’s no quick answer to this question.

 

[The_Exodus]

Although it’s always possible that I really don’t understand Aquinas, and that I just have to study further his work, what reason have I to think that this is so?

You can think you’ve discovered, on a quick purview, holes in the mind of one of the greatest philosophers in the history of the world. Does that not strike you as unreasonable, just a little? Suppose a 6th grader read Einstein and thought “this can’t be so and so!” Would you think the 6th grader reasonable?

Further, it doesn’t really matter to me whether or not you think it’s reasonable to read further his work. All I’m saying is that (particularly since you appeal to Dawkins) you probably have a very convoluted understanding of him.

hatsoff:

If you think that my denial of that one of Aquinas’ ways, quoted previously, requires me to reject the principle of contradiction, then you are welcome to explain why.

How is the principle of contradiction verified or known to be true?

 

[hatsoff]

You can think you’ve discovered, on a quick purview, holes in the mind of one of the greatest philosophers in the history of the world. Does that not strike you as unreasonable, just a little? Suppose a 6th grader read Einstein and thought “this can’t be so and so!” Would you think the 6th grader reasonable?

I see no reason to suppose that Aquinas was “one of the greatest philosophers in the history of the world.” On the contrary, he seems to me to be a poor philosopher, at least by modern standards.

He is quite famous, but fame is not greatness.

Further, it doesn’t really matter to me whether or not you think it’s reasonable to read further his work. All I’m saying is that (particularly since you appeal to Dawkins) you probably have a very convoluted understanding of him.

I guess I just would rather have an interactive experience than go read some dry text. If you think Dawkins has garbled Aquinas, then I invite you, or indeed anyone else here, to explain how.

How is the principle of contradiction verified or known to be true?

That depends on the system of logic in context. Informally, it’s just a property of certain (though not all) natural language games. Formally, it’s true as a theorem, axiom or schema thereof, depending on the system.

 

[The_Exodus]

I see no reason to suppose that Aquinas was “one of the greatest philosophers in the history of the world.” On the contrary, he seems to me to be a poor philosopher, at least by modern standards.

That’s fine. You’re free to hold whatever opinion you want.

hatsoff:

That depends on the system of logic in context. Informally, it’s just a property of certain (though not all) natural language games. Formally, it’s true as a theorem, axiom or schema thereof, depending on the system.

Erm… ok. So, again, how is it we verify the principle of contradiction, or how is it we know it is true?

Or do you suppose it is a subjective phenomena? (“That depends on the system of logic in context.”)

I’m interested to know what system of logic does not presuppose the principle of contradiction’s validity?

 

[_Locke]

I’m interested to know what system of logic does not presuppose the principle of contradiction’s validity?

“As is true of all axioms, the law of non-contradiction is alleged to be neither verifiable nor falsifiable, on the grounds that any proof or disproof must use the law itself prior to reaching the conclusion.” (Wikipedia)

hatsoff:

Thomists frequently ask me to read more material if I observe that what I have read seems ridiculous. Although it’s always possible that I really don’t understand Aquinas, and that I just have to study further his work, what reason have I to think that this is so?

I think the Courtier’s Reply would be an excellent one; that is, to point out that one need not have the “detailed discourses of Count Roderigo of Seville on the exquisite and exotic leathers of the Emperor’s boots” nor approach “schools dedicated to writing learned treatises on the beauty of the Emperor’s raiment” nor be “trained in the shops of Paris and Milan, until learn to tell the difference between a ruffled flounce and a puffy pantaloon” just to say that the emperor is naked.

 

[awatkins69]

The law of non-contradiction is not a logical principle only. It is a metaphysical principle about reality. Metaphysics precedes logic. Yes, there are formal logics where there are valid contradictions. That says absolutely nothing about reality. For example, euclidean geometry is a real formal mathematical system, but it is falsified and doesn’t conform to reality (cf. theory of relativity). Likewise, dialetheist logics do not conform to reality.

So they may be interesting to study for their own sake, in the same way it is interesting to study Euclid’s Elements. And like Euclid’s Elements, they can help us to understand the true logics better. Logic that is used in actual debate needs to conform to reality. So before anything, we’re going to have to agree on some metaphysical principles about reality. If we agree on those then whatever other formal logical systems have to say is completely irrelevant for our purposes.

 

[hatsoff]

The law of non-contradiction is not a logical principle only. It is a metaphysical principle about reality. Metaphysics precedes logic. Yes, there are formal logics where there are valid contradictions. That says absolutely nothing about reality. For example, euclidean geometry is a real formal mathematical system, but it is falsified and doesn’t conform to reality (cf. theory of relativity). Likewise, dialetheist logics do not conform to reality.

So they may be interesting to study for their own sake, in the same way it is interesting to study Euclid’s Elements. And like Euclid’s Elements, they can help us to understand the true logics better. Logic that is used in actual debate needs to conform to reality. So before anything, we’re going to have to agree on some metaphysical principles about reality. If we agree on those then whatever other formal logical systems have to say is completely irrelevant for our purposes.

I’m sorry, but this is not correct at all. The law of noncontradiction is indeed a logical principle, and logical systems such as Euclidean geometry or group theory are not “true” or untrue, nor can they be falsified by empirical observation. Logic is about inference, i.e., about how certain statements follow from other statements.

 

[awatkins69]

I’m sorry, but this is not correct at all. The law of noncontradiction is indeed a logical principle, and logical systems such as Euclidean geometry or group theory are not “true” or untrue, nor can they be falsified by empirical observation. Logic is about inference, i.e., about how certain statements follow from other statements.

Euclidean geometry can be falsified, insofar as one posits it as being consistent with the actual physical world. Hyperbolic geometry is more consistent with the special theory of relativity. On the other hand, if you don’t propose that Euclidean geometry is the way we describe our physical world, then yeah, we’ve got no problem.

Likewise, logics can be falsified, insofar as we posit them as being consistent with reality. If you don’t think that dialetheist logics can be applied to reality, and that it is just a fun consistent system, we’ve got no problem here either. The law of non-contradiction (LNC) still stands. But if you want to argue that the LNC doesn’t apply because of dialetheist logics, then you have to prove that dialetheist logics are the logics consistent with reality. You have to prove that there are *real *valid contradictions, outside of the formal system. And this is metaphysically impossible because the LNC is always true.

Even Graham Priest, the proponent of paraconsistent logic, agrees with this. He draws a strict distinction between proposing a formal logical system with valid contradictions and proposing this system as conforming to reality.

 

[hatsoff]

Euclidean geometry can be falsified, insofar as one posits it as being consistent with the actual physical world. Hyperbolic geometry is more consistent with the special theory of relativity. On the other hand, if you don’t propose that Euclidean geometry is the way we describe our physical world, then yeah, we’ve got no problem.

Likewise, logics can be falsified, insofar as we posit them as being consistent with reality. If you don’t think that dialetheist logics can be applied to reality, and that it is just a fun consistent system, we’ve got no problem here either. The law of non-contradiction (LNC) still stands. But if you want to argue that the LNC doesn’t apply because of dialetheist logics, then you have to prove that dialetheist logics are the logics consistent with reality. You have to prove that there are *real *valid contradictions, outside of the formal system. And this is metaphysically impossible because the LNC is always true.

Even Graham Priest, the proponent of paraconsistent logic, agrees with this. He draws a strict distinction between proposing a formal logical system with valid contradictions and proposing this system as conforming to reality.

Either Prof. Priest is mistaken or else you have misunderstood him. Logic, as I mentioned previously, is about language and inference, not physical systems.

 

[The_Exodus]

Either Prof. Priest is mistaken or else you have misunderstood him. Logic, as I mentioned previously, is about language and inference, not physical systems.

Yes but logic at root is nothing more than the principle of contradiction, which is a metaphysical principle, gained from reality by the mind intuiting being; or, more particularly, this or that being. When the mind individuates and identifies a particular being, it does so through grasping, without any illative reasoning process, the law of contradiction. It is not reasoned to. It is intuitively grasped. And the law of identity must not be a Kantian category, else we have no way of supposing reality is any different from ourselves. Further, we have prima facie evidence that reality is not uniform, and, if our mind grasped things merely categorically, there would be no reason why various categories are employed now here, now elsewhere. In the end, we must admit multiplicity to reality.

The question for idealists is, of course, how does one come to know the principle of contradiction? It cannot be an a priori, or else universal skepticism follows.

 

[hatsoff]

Yes but logic at root is nothing more than the principle of contradiction, which is a metaphysical principle, gained from reality by the mind intuiting being; or, more particularly, this or that being.

Logic the study of inference, which is part of language games, and while noncontradiction is an essential theorem of many logical systems, it is not the “root” of all logic, nor is it a “metaphysical” principle.

 

[Betterave]

Logic the study of inference, which is part of language games, and while noncontradiction is an essential theorem of many logical systems, it is not the “root” of all logic, nor is it a “metaphysical” principle.

It seems that from your opponents’ p.o.v. you’re positing a false dichotomy: LNC pertains to logic, not metaphysics. It also seems that you’re failing to respond to this point, and instead just insisting on your position.

 

[The_Exodus]

Logic the study of inference, which is part of language games, and while noncontradiction is an essential theorem of many logical systems, it is not the “root” of all logic, nor is it a “metaphysical” principle.

Would you care to explain your position a bit more?

 

[awatkins69]

Logic the study of inference, which is part of language games, and while noncontradiction is an essential theorem of many logical systems, it is not the “root” of all logic, nor is it a “metaphysical” principle.

Inference is different in different systems. For instance, in this paraconsistent logic which we were talking about earlier, there are fewer inferences than a quantificational logic for instance. That’s what makes it so fun to read about.

Now, the LNC, as I posit it, is a metaphysical principle. I posit it thus: With x as a random variable, it is not possible that both x and not-x.

That’s a metaphysical statement about reality. Any logic which contradicts that proposition, and says that there are true contradictions (whatever that means), contradicts my metaphysics and, by extension, reality. Contradiction of reality is what most people take falsehood to be. Thus, those logics are false. So, as long as we are trying to find truth and *valid *inference (not just consistency of inference in an arbitrary system), our metaphysics precedes our logic.

 

[hatsoff]

Inference is different in different systems. For instance, in this paraconsistent logic which we were talking about earlier, there are fewer inferences than a quantificational logic for instance. That’s what makes it so fun to read about.

Now, the LNC, as I posit it, is a metaphysical principle. I posit it thus: **With x as a random variable, it is not possible that both x and not-x. **

That’s a metaphysical statement about reality. Any logic which contradicts that proposition, and says that there are true contradictions (whatever that means), contradicts my metaphysics and, by extension, reality. Contradiction of reality is what most people take falsehood to be. Thus, those logics are false. So, as long as we are trying to find truth and *valid *inference (not just consistency of inference in an arbitrary system), our metaphysics precedes our logic.

(boldface emphasis added)

The words in bold do not make any sense. A random variable is a kind of mathematical function, not a logical statement. Your “statement” has the same syntax as this: It is not possible that both tree and not-tree.

Maybe you want us to take x as a propositional variable. But in that case, it is not possible that x and not-x is not a statement about reality, because it does not make reference to the real world (except of course insofar as it is a theorem schema for informal propositional logic).

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. 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.

Would you care to explain your position a bit more?

Hopefully the above is a sufficient response to this query as well.

 

[awatkins69]

Hi hatsoff. You’re right, I used the totally wrong terminology there. Sorry about that. I should say “propositional constant”. Also, I think you might be right about me having only proposed it as a tautology, making it insufficient for anything other than logical purposes. But anyways, how about the following proposition:

“The same attribute cannot at the same time belong and not belong to the same subject in the same respect.”

This talks about *things *rather than logical sentences. That’s a metaphysical claim about reality, and it is correct. Thus, any “true” logic is going to have to incorporate it as an axiom (maybe in the form of “not-possibly x and not-x”, with x as a propositional constant?).

 

[hatsoff]

Hi hatsoff. You’re right, I used the totally wrong terminology there. Sorry about that. I should say “propositional constant”. Also, I think you might be right about me having only proposed it as a tautology, making it insufficient for anything other than logical purposes. But anyways, how about the following proposition:

“The same attribute cannot at the same time belong and not belong to the same subject in the same respect.”

This talks about *things *rather than logical sentences. That’s a metaphysical claim about reality, and it is correct. Thus, any “true” logic is going to have to incorporate it as an axiom (maybe in the form of “not-possibly x and not-x”, with x as a propositional constant?).

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. 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 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).