What does it mean for modus ponens to “do worse” than something? It might “do badly” in virtue of there not being any relevant statements of the form “A” and “if A then B” lying around. That would hardly make MP “fallacious” though. It might be that by deducing “B” from “A” and “if A then B” we thereby deduce something false. But then either “A” or “if A then B” must have been false (or at least non-true), and it hardly counts against MP that it loses reliability when applied to non-true premises.
Well, look at the Problem of Identity. I start with an apple or a boat, and I brush molecules off the apple or replace the boards on the boat, and end up with something other than an apple or a boat. This shouldn’t be a problem, except that I’ve got a big Modus Ponens chain (this is an apple; an apple with a molecule removed is still an apple) that fails when the chain gets long enough. To fix my problem, I’ve got to:
a. Say actually, there are almost no apples in the world. Modus Ponens rarely applies to the real world because almost no premises are perfectly true. When someone asks “is this delicious-looking fruit an apple”, I have to say “Dunno, probably not.”
b. Say actually, there are apples, and an apple missing a molecule remains an apple, and Modus Ponens works except in rare corner cases. And experience/tradition/etc can help us know where those corner cases are, so we can avoid mistakenly applying Modus Ponens when it will lead from correct premises to incorrect conclusions.
Here you’re talking about Euclidean geometry as an empirical theory of space (or perhaps space-time), as opposed to Euclidean geometry as a branch of mathematics
Well, Euclidean geometry is extremely interesting because it works relatively well as a theory of space, without actually relying on empirical data.
Users of a language have to agree on the meanings of primitive words like ‘and’, ‘if’, ‘then’, or else they’re just ‘playing a different game’.
I hope that logic (like Euclidean geometry) is actually telling us something about the world, not just about the words/rules we started with. If modus ponens is purely a linguistic trick rather than a method of increasing our knowledge, then it’s as useful as chess. I think it’s far more useful, and lets us obtain better approximations of the actual world.
Well, look at the Problem of Identity. I start with an apple or a boat, and I brush molecules off the apple or replace the boards on the boat, and end up with something other than an apple or a boat. This shouldn’t be a problem, except that I’ve got a big Modus Ponens chain (this is an apple; an apple with a molecule removed is still an apple) that fails when the chain gets long enough. To fix my problem, I’ve got to:
a. Say actually, there are almost no apples in the world. Modus Ponens rarely applies to the real world because almost no premises are perfectly true. When someone asks “is this delicious-looking fruit an apple”, I have to say “Dunno, probably not.”
b. Say actually, there are apples, and an apple missing a molecule remains an apple, and Modus Ponens works except in rare corner cases. And experience/tradition/etc can help us know where those corner cases are, so we can avoid mistakenly applying Modus Ponens when it will lead from correct premises to incorrect conclusions.
Well, Euclidean geometry is extremely interesting because it works relatively well as a theory of space, without actually relying on empirical data.
I hope that logic (like Euclidean geometry) is actually telling us something about the world, not just about the words/rules we started with. If modus ponens is purely a linguistic trick rather than a method of increasing our knowledge, then it’s as useful as chess. I think it’s far more useful, and lets us obtain better approximations of the actual world.