Your second answer is the nearest to being right, but I wouldn’t put it quite like that.
An alternate answer, that a believer in absolute morality or logic might like, is that logic actually deserves a higher place than Euclidean geometry. Where geometry can be tested and modified wherever the data support a modification, logic can’t.
Just to clarify: 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. Here is how ‘empirical’ and ‘mathematical’ Euclidean geometry come apart: The latter requires that we make methodological decisions (i) to hold the axioms true come what may and (ii) to refrain from making empirical predictions solely on the basis of our theorems.
I don’t think there is any important sense in which logic is ‘higher’ than Euclidean-geometry-as-mathematics.
No matter how many times our modus ponens does worse than an Appeal to Tradition or Ad Populum in some area of inquiry, we still don’t say “ok, alter the rules of logic for this area of inquiry to make Ad Populum the correct method there and Modus Ponens the fallacious method there”
I don’t think this makes sense.
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.
(You might want to object to the (“loaded”) terminology of “truth” and “falsity”, but then it would be up to you to say what it means for MP to be “fallacious”.)
Going back to prase’s question:
What, in your opinion, makes modus ponens better than appeal to authority, independently of its persuasiveness?
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’. (If your knights are moving like queens then whatever else you’re doing, you’re not playing chess.) What makes MP ‘reliable’ is that its validity is ‘built into’ the meanings of the words used to express it.
There’s nothing ‘mystical’ about this. It’s just that if you want to make complex statements with many subclauses, then you need conventions which dictate how the meaning of the whole statement decomposes into the meanings of the subclauses.
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
This is key. I like to say that we play logic with a stacked deck. We’ve dealt all the aces to a few logical rules. This doesn’t mean that logic isn’t in some sense absolute, but it removes any whiff of theology that might be suspected to be attached.
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’.
True, but there is more to being logical than just following linguistic convention. The philosophers’ classic “tonk” operator works like this: From A, one is licensed to infer “A tonk B”. From “A tonk B” one is licensed to infer B. Luckily for language users everywhere, there is no actual language with these conventions.
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.
Your second answer is the nearest to being right, but I wouldn’t put it quite like that.
Just to clarify: 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. Here is how ‘empirical’ and ‘mathematical’ Euclidean geometry come apart: The latter requires that we make methodological decisions (i) to hold the axioms true come what may and (ii) to refrain from making empirical predictions solely on the basis of our theorems.
I don’t think there is any important sense in which logic is ‘higher’ than Euclidean-geometry-as-mathematics.
I don’t think this makes sense.
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.
(You might want to object to the (“loaded”) terminology of “truth” and “falsity”, but then it would be up to you to say what it means for MP to be “fallacious”.)
Going back to prase’s question:
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’. (If your knights are moving like queens then whatever else you’re doing, you’re not playing chess.) What makes MP ‘reliable’ is that its validity is ‘built into’ the meanings of the words used to express it.
There’s nothing ‘mystical’ about this. It’s just that if you want to make complex statements with many subclauses, then you need conventions which dictate how the meaning of the whole statement decomposes into the meanings of the subclauses.
I agree but with some spin control.
This is key. I like to say that we play logic with a stacked deck. We’ve dealt all the aces to a few logical rules. This doesn’t mean that logic isn’t in some sense absolute, but it removes any whiff of theology that might be suspected to be attached.
True, but there is more to being logical than just following linguistic convention. The philosophers’ classic “tonk” operator works like this: From A, one is licensed to infer “A tonk B”. From “A tonk B” one is licensed to infer B. Luckily for language users everywhere, there is no actual language with these conventions.
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.