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hen comments on Infinite Certainty - Less Wrong
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Comments (114)
You could be mistaken about logic, a demon might be playing tricks on you etc.
You can say "Sherlock Holmes was correct in his deduction." That does not rely on Sherlock Holmes actually existing, it's just noting a relation between one concept (Sherlock Holmes) and another (a correct deduction).
What would you say, if asked to defend this possibility?
This is true, but (at least if we're channeling Descartes) the question is whether or not we can raise a doubt about the truth of the claim that something exists. Our ability to have this thought doesn't prove that it's true, but it may well close off any doubts.
The complexity based prior for living in such a world is very low, but non-zero. Consequently, you can't be straight 1.0 convinced it's not the case.
A teapot could actually be an alien spaceship masquerading as a teapot-lookalike. That possibility is heavily, heavily discounted against using your favorite version of everyone's favorite heuristic (Occam's Razor). However, since it can be formulated (with a lot of extra bits), its probability is non-zero. Enough to reductio the "easily 100%".
Well, this is a restatement of the claim that it's possible to be deceived about tautologies, not a defense of that claim. But your post clarifies the situation quite a lot, so maybe I can rephrase my request: how would you defend the claim that it is possible (with any arbitrarily large number of bits) to formulate a world in which a contradictions is true?
I admit I for one don't know how I would defend the contrary claim, that no such world could be formulated.
Probably heavily depends on the meaning of "formulate", "contradiction" and "true". For example, what's the difference between "imagine" and "formulate"? In other words, with "any arbitrarily large number of bits" you can likely accurately "formulate" a model of the human brain/mind which imagines "a world in which a contradiction is true".
I mean whatever Kawoomba meant, and so he's free to tell me whether or not I'm asking for something impossible (though that would be a dangerous line for him to take).
Is your thought that unless we can (with certainty) rule out the possibility of such a model or rule out the possibility that this model represents a world in which a contradiction is true, then we can't call ourselves certain about the law of non-contradiction? I grant that the falsity of that disjunct seems far from certain.
I am not a mathematician, but to me the law of non-contradiction is something like a theorem in propositional calculus, unrelated to a particular world. A propositional calculus may or may not be a useful model, depends on the application, of course. But I suppose this is straying dangerously close to the discussion of instrumentalism, which led us nowhere last time we had it.
It seems more like an axiom to me than a theorem: I know of no way to argue for it that doesn't presuppose it. So I kind of read Aristotle for a living (don't laugh), and he takes an interesting shot at arguing for the LNC: he seems to say it's simply impossible to formulate a contradiction in thought, or even in speech. The sentence 'this is a man and not a man' just isn't genuine proposition.
That doesn't seem super plausible, however interesting a strategy it is, and I don't know of anything better.
This seems like a version of "no true Scotsman". Anyway, I don't know much about Aristotle's ideas, but what I do know, mostly physics-related, either is outright wrong or has been obsolete for the last 500 years. If this is any indication, his ideas on logic are probably long superseded by the first-order logic or something, and his ideas on language and meaning by something else reasonably modern. Maybe he is fun to read from the historical or literary perspective, I don't know, but I doubt that it adds anything to one's understanding of the world.
Well, his argument consists of more than the above assertion (he lays out a bunch of independent criteria for the expression of a thought, and argues that contradictions can never satisfy them). However I can't disagree with you on this: no one reads Aristotle to learn about physics or logic or biology or what-have-you. To say that modern versions are more powerful, more accurate, and more useful is massive understatement. People still read Aristotle as a relevant ethical philosopher, though I have my doubts as to how useful he can be, given that he was an advocate for slavery, sexism, infanticide, etc. Not a good start for an ethicist.
On the other hand, almost no contemporary logicians think contradictions can be true, but no one I know of has an argument for this. It's just a primitive.