- Ouros
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Re: Retorsion argument, first principles and non-classical logic
John West wrote:
Too bad for metaphysics then.
What argument exactly?
Haha. Come on, Ouros! Bill writes in good, clear English. (He's giving counterexamples to the thesis that retorsion arguments for theses establish those theses as laws of reality.)
Oops! Sorry, I wasn't trying to be mean, I was sincerely asking what you were talking about because of the distance beetween the two messages, and I wasn't sure what were the initials "BV" standing for. :D
Well, I think that, in fact, what he suggest IS transcendental idealism. That's basically what was Kant arguing for: that first principles were only epistemically necessary, and not metaphysically necessary.
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Re: Retorsion argument, first principles and non-classical logic
Oops! Sorry, I wasn't trying to be mean, I was sincerely asking what you were talking about because of the distance beetween the two messages, and I wasn't sure what were the initials "BV" standing for.
I'll quote next time.
Well, I think that, in fact, what he suggest IS transcendental idealism. That's basically what was Kant arguing for: that first principles were only epistemically necessary, and not metaphysically necessary.
But Vallicella doesn't argue that we can't prove the theses are metaphysical laws (cf. example 4). Only that we can't prove they are by retorsion.
- Ouros
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Re: Retorsion argument, first principles and non-classical logic
But Vallicella doesn't argue that we can't prove the theses are metaphysical laws (cf. example 4). Only that we can't prove they are by retorsion.
I think we can. Of course, I'm no expert, but for me, every attempt to apply them only to thought is condemned to be meaningless.
Kant was a prime example for that: even if he wanted to show that we can only use the PSR for phenomens, he used it also, in a more subtle way, on the things-in-themselve.
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Thread Starter- SapereAude
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Re: Retorsion argument, first principles and non-classical logic
But Vallicella doesn't argue that we can't prove the theses are metaphysical laws (cf. example 4). Only that we can't prove they are by retorsion.
No, I don't think BV meant that the theses are metaphysical laws, but rather that they are truths simply on logical grounds. No ontology is specifically engaged (cf. example 6 which requires some ontology but not too much also). Upshot:
My tentative conclusion is that retorsion has merely a transcendental significance, not a metaphysical one.
So, we can believe that a thesis is a metaphysical law, but we cannot prove it. All "proofs" revolve in the framework of the "first principles" of which we can only believe that they are true. Done properly, "proofs" are unassailably valid but only within the starting framework. Has that framework anything to do with reality?—that's another question.
Kant was a prime example for that: even if he wanted to show that we can only use the PSR for phenomena, he used it also, in a more subtle way, on the things-in-themselve.
Kant is not an idol to blindly worship. The whole conception of the things-in-themselves was ill-devised and should be discarded in favour of much stronger notion of the Noumenon (but not Noumena!).
Every proposition of geometry is absolutely necessary, and in this way one talked about an object lying entirely outside the sphere of our understanding as if one understood quite well what one meant by this concept. The unconditioned necessity of judgments, however, is not an absolute necessity of things.
- Greg
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Re: Retorsion argument, first principles and non-classical logic
As far as I understand, Hegel's project aims to create a dynamic philosophy, a philosophy of process. Aristotle's static logic demonstrably leads to paradoxes (Zeno), so, being a complete system in itself, it poorly grasp things as they are in reality, i.e. in time, in motion. Sure, we use AL on a daily basis, but that only on condition that we consider objects as being static. It's a bit like Newton's physics to be enough for everyday calculations than to use Einstein's. Nobody is quite sure how to implement Hegel's dialectical logic, but it just cannot be bypassed in modern philosophical reasoning.
I find this potted history utterly perplexing and implausible. How are you formulating Zeno's paradox such that it is an ineluctable consequence of Aristotle's logic (as opposed to some deceptive folk premise about motion)? How are you understanding Aristotle's logic such that it counts as "a complete system in itself," which tries at all to grasp things? And how are you understanding 'static' such that Aristotle's logic assumes objects are static and Hegel's logic, by dropping that assumption, is uniquely suited to avoid Zeno's paradox? (If no one knows how to implement Hegel's logic, why should we be confident that it has any of the advantages claimed for it?)
In any case, none of this constitutes an answer to the question of whether, if we accept Hegel's logic, we should also believe some contradictions. Frankly, I don't see that, here at least, talk about static and dynamic logics and dropping the principle of non-contradiction has risen above rhetoric.
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Re: Retorsion argument, first principles and non-classical logic
@Greg
I readily admit that I'm not a mathematician or logician and even if I were, it would be just impossible to properly address such a question in a mere comment. My problem with PC lies in the qualification: "one cannot say of something that it is and that it is not in the same respect and at the same time". That "in the same respect and at the same time" seems doubtful to me—we do know precisely what it means in the proposition but what about reality? Already Plato questioned it: "According to both Plato and Aristotle, Heraclitus was said to have denied the law of non-contradiction. This is quite likely if, as Plato pointed out, the law of non-contradiction does not hold for changing things in the world. If a philosophy of Becoming is not possible without change, then (the potential of) what is to become must already exist in the present object. In "We step and do not step into the same rivers; we are and we are not", both Heraclitus's and Plato's object simultaneously must, in some sense, be both what it now is and have the potential (dynamic) of what it might become." According to some interpretations of Zeno's paradoxes, "all of Zeno's motion paradoxes are resolved by the conclusion that instants in time and instantaneous magnitudes do not physically exist." Aristotle himself argued that "Time is not composed of indivisible nows any more than any other magnitude is composed of indivisibles." Alas, modern physics posits exactly that: "Another proposed solution is to question one of the assumptions Zeno used in his paradoxes, which is that between any two different points in space (or time), there is always another point. Without this assumption there are only a finite number of distances between two points, hence there is no infinite sequence of movements, and the paradox is resolved. The ideas of Planck length and Planck time in modern physics place a limit on the measurement of time and space, if not on time and space themselves." Is it possible or not to somehow connect logic, maths and physics in this question I do not know, I admit that, but presumably Zeno based his endeavor on Aristotle's logic and nobody has ever accused him to be illogical. Hegel is of no help here, of course, but perhaps only because of the lack of proper formalization, the existing forms of non-classical logic being just the first examples of and which are to grow in importance significantly as AI studies progress.
TLDR: "in the same respect and at the same time" - are we able to define these conditions rigorously in reality?
Every proposition of geometry is absolutely necessary, and in this way one talked about an object lying entirely outside the sphere of our understanding as if one understood quite well what one meant by this concept. The unconditioned necessity of judgments, however, is not an absolute necessity of things.
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Re: Retorsion argument, first principles and non-classical logic
My problem with PC lies in the qualification: "one cannot say of something that it is and that it is not in the same respect and at the same time". That "in the same respect and at the same time" seems doubtful to me—we do know precisely what it means in the proposition but what about reality? ... In "We step and do not step into the same rivers; we are and we are not", both Heraclitus's and Plato's object simultaneously must, in some sense, be both what it now is and have the potential (dynamic) of what it might become." (italics added)
I don't know or care whether every defender of PNC has said what I am about to say. But I see PNC like this. It's true that one sometimes utters "p" and utters "not p". One way in which there is no problem here is if one utters them at different times. But then there are cases here one also wants to say "p" and "not p" at the same time. A standard way of absolving oneself is by saying, for instance, "in some sense p and not p"; one might, for instance, say that one won and did not win a competition, when one means that one lost by a technicality (or because the other team got away with cheating) but deserved to win. One is in such a case not saying anything genuinely contradictory.
It is when one says "No, I mean by 'p' exactly the same thing in 'p' and 'not p', when I say 'p and not p'," that one is guaranteed to be wrong.
This is why the untenability of denying PNC is drawn out by asking the denier to produce a proposition which he wants us to affirm and deny. There's no way he actually wants both to represent, and not to represent, the world to his hearers, unless he's confused. Change doesn't supply any counterexample. Whether you are saying of my fence that it is white and not white, because it's white before I paint it but not white after, or you are saying that it is white and not white, because it is actually white but also contains a potential for not being white, you are not denying the same thing you are affirming. Philosophers sometimes do express themselves with the schema "p and not p", where it is thereby understood that they are equivocating in order to make their point (and that we wouldn't read them charitably if we took them not to do so). Take, for instance, the principle lex iniusta non est lex, or the statement "a decoy duck is not a duck". These aren't counterexamples to PNC.
I don't see that the meaning of "in the same respect and at the same time" "in reality" is what's at issue here. "When we say, mean, that such-and-such is the case, then, with what we mean, we do not stop anywhere short of the fact, but mean: such-and-such - is - thus-and-so." I don't have to get beyond what I say; it's just a question of whether what I say is a denial of the same thing I'm affirming. Whether in "Citizens Bank is a bank and is not a bank" I am affirming and denying something of Citizens Bank in the same respect depends on whether, for instance, I mean the same thing by "bank" in both of its occurrences. If in the second, I mean that Citizens Bank is not a river bank, then I'm not saying anything false.
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Re: Retorsion argument, first principles and non-classical logic
I'm not sure how you're using “metaphysical laws”, Sapere:
No, I don't think BV meant that the theses are metaphysical laws, but rather that they are truths simply on logical grounds. No ontology is specifically engaged (cf. example 6 which requires some ontology but not too much also).
But this is at most a bad choice of words on my part. I had been up all night trying to wrap up some research, and needed a term to mark off “necessary truth[s] […] true independently of any mind” from truths grounded in minds.
So, we can believe that a thesis is a metaphysical law, but we cannot prove it. All "proofs" revolve in the framework of the "first principles" of which we can only believe that they are true. Done properly, "proofs" are unassailably valid but only within the starting framework. Has that framework anything to do with reality?—that's another question.
This comment goes beyond what Vallicella says in the article. I only have one goal in this thread: to get people to face up to Vallicella's argument against retorsion on its own terms, without becoming embroiled in a lengthy back and forth.
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Re: Retorsion argument, first principles and non-classical logic
@Greg
Here's my point—it's madness to attack PNC per se, it's impossible, and I'm not interested in abstract formal reasoning at all, I'm interested in reality. My question is whether PNC as a tool is applicable through and through and whether we can justify its application at all in some cases. Kant, Kierkegaard and Shestov deny that for different reasons. The simplest point is made by Kierkegaard and Shestov (irrationalism). As Kierkegaard famously said, there is nothing impossible for God. We might take it as a definition, actually. So, if according to PNC we can't say that God does and doesn't exist "in the same respect and at the same time," let alone that He is and is not good, omniscient, and so forth.... and that's the case because PNC is unassailable..... what we are stating, in effect, is that God is subject to the Necessity of PNC. But that's absurd - God cannot be subject to anything.... except for Himself perhaps.... and even if so, there always exists a nonzero possibility that such a world might come into existence where He was not, should there to be His will. Or take, e.g. time - if God just cannot make the past "non-ever-happened" it follows that He is subject to the irreversibility of time, so He is a false god and Gnostics were right after all. Show me the entity who laid down that PNC is unassailable, that time is irreversible, that 2+2 always equals 4 - that's true God.
As Bill Vallicella put it:
Given the identity of the Second Person and the man Jesus, if a man was raised bodily from the dead by the power of God, and this man is God, then God raises himself.
This doctrine violates our ordinary canons of reasoning. It is, to put it bluntly, absurd in the logical sense of the term: logically contradictory. (Tertullian, Kierkegaard, and Shestov would agree.) Or so it seems to me and Dale Tuggy and many others. But others, equally sharp and serious and committed to the truth, think that if one makes the right distinctions the Incarnation doctrine can be shown not to be in violation of the ordinary canons. I think their fancy footwork avails nothing. Tuggy thinks the same.
Well, suppose Tuggy and I are right. Then it seems there are two ways to go, the Tuggy way and the way of mystery. Tuggy, if I undertand him, rejects the Trinity and the divinity of Jesus. Standing firm within what I call the Discursive Framework he argues cogently that the doctrines in question are logically impossible.
But there is this 'possibility.' There are true propositions that appear to our intellects as either logically self-contradictory or as issuing by valid inferences in logical contradictions. They are not contradictory in themselves, but they must appear contradictory to our fallen intellects here below. It is not just that these propositions are true, but we cannot understand how they could be true; it is that they seem to us as evidently not true. And yet they are true, and contradiction-free in themselves.
Last edited by SapereAude (4/08/2018 9:27 am)
Every proposition of geometry is absolutely necessary, and in this way one talked about an object lying entirely outside the sphere of our understanding as if one understood quite well what one meant by this concept. The unconditioned necessity of judgments, however, is not an absolute necessity of things.
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Re: Retorsion argument, first principles and non-classical logic
My question is whether PNC as a tool is applicable through and through and whether we can justify its application at all in some cases. Kant, Kierkegaard and Shestov deny that for different reasons. The simplest point is made by Kierkegaard and Shestov (irrationalism).
I don't think that Kant denies the complete generality of PNC. (Whether he denies what you say will depend on what it would be to "justify [PNC's] application" in a particular case. Taking 'justification' in the way standard among philosophers, virtually no philosopher would hold that PNC needs to be "justified", if that means that one needs to argue for its applicability from more basic premises.)
As Kierkegaard famously said, there is nothing impossible for God. We might take it as a definition, actually. So, if according to PNC we can't say that God does and doesn't exist "in the same respect and at the same time," let alone that He is and is not good, omniscient, and so forth.... and that's the case because PNC is unassailable..... what we are stating, in effect, is that God is subject to the Necessity of PNC. But that's absurd - God cannot be subject to anything.... except for Himself perhaps....
Indeed, the same view was taken by Descartes:
I do not think we should ever say of anything that it cannot be brought about by God. For since every basis of truth ... depends on his omnipotence, I would not dare to say that God cannot make a mountain without a valley, or bring it about that 1 and 2 are not 3. I merely say that he has given me such a mind that I cannot conceive a mountain without a valley, or a sum of 1 and 2 which is not 3; such things involve a contradiction in my conception.
I'm a Christian, but I do not see the need for such an excess of piety. And it surprises me greatly that you mention Kant together with Descartes and Kierkegaard on this point. For Kant the laws of logic are the "absolutely necessary rules of thought without which there can be no employment whatsoever of the understanding" (A52/B76). The entertainment of the unapplicability of PNC is not even thought for Kant. The thought that PNC's constraining God's action and therefore cognition would be a limitation of his freedom and power is also a decidedly un-Kantian thought (as, indeed, is that this should be described in terms of "constraint" at all). (You of course say that Kant doesn't have the same reasons as Kierkegaard and Shestov and, we can add, Descartes, which would be true, but it's not clear how all the appealing to authority is supposed to help since the rest of Kant's philosophy is supposed to undermine views like those of Descartes and Kierkegaard.)
More positively, I would say that if the only conception of omnipotence available to the philosophical theist is that according to which an omnipotent being can do the logically impossible, then so much the worse for the theist. Which alternative should be preferred is a long-standing topic in the philosophy of religion. But the irrationalist position is really not very tempting. It is not as though Scripture forces it on us, and it is not as though any of the arguments for God's existence from his effects even tend to suggest that he could do what is logically impossible.
I'm with Tuggy in thinking that if we must hold the doctrines of the Trinity or of the Incarnation to contain a contradiction, then they should be rejected; I just hold that we need not.