formulate a world in which a contradictions is true?
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).
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”.
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.
[in] a world in which a contradiction is true, then we can’t call ourselves certain about the law of non-contradiction?
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.
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.
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.
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.