[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 If this is any indication, his ideas on logic are probably long superseded by the first-order logic or something, and his ideas on language and meaning by something else reasonably modern.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.
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.