All my answers to this are flawed.
My best is: It’s like Euclidean geometry: humans (and other species) are constructed in a way that Euclidean geometry fits fairly well. The formalized rules of Euclidean geometry match spacial reality even better than what we’ve evolved, so we prefer them… but they’re similar enough to what we’ve evolved that we accept them rather than alternate geometries. Euclidean geometry isn’t right—reality is more complex than any system of geometry—but the combination of “works well enough”, “improves on our evolved heuristic”, and “matches our evolved heuristic well enough” combine to give it a privileged place. Just so, that system of formal logic works well enough, improves on our evolved reasoning heuristics, and yet matches those heuristics well enough… so we give formal logic a privileged place. The privilege is sufficient that many believe logic is the basis of Truth, that many theists believe that even angels or deities cannot be both A and not-A, and that people who use fallacies to convince others of truths are frequently considered to be liars.
This does not sufficiently satisfy me.
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. 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”, we just question our premises, our methods of detection of answers, etc. So logic is special and is above the empirical method.
I am unsatisfied by the above paragraph as well.
A third possibility is that it’s not—it’s just a code of conduct/signalling. We agree to only use logic to convince one another because it works well, because the use of other methods of persuasion can often be detected and punished, and because the people who can rely on logic rather than on other methods of persuasion are smarter and more trustworthy. In specific instances, logic might not be the best way to learn something or to convince others, but getting caught supporting or using contraband methods will be punished so we all use/support logic unless we’re sure we can get away with the contraband.
This is an unsatisfying explanation to me as well.
Another answer (which I’m not sure is the answer) is that in logic or mathematics, a person is more likely to be convinced by a random correct proof than a random flawed proof; and if a person is convinced by a flawed proof it is easy to change their mind by pointing out the flaw in the proof; but if a person is convinced by a correct proof, then it is difficult to change their mind by incorrectly claiming there is a flaw. Of course I am being sloppy and nontechnical here; I bet there is a subtle, technical sense in which, under reflection, Modus Ponens is more appealing than Appeal To Justin Bieber.
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.
I like the first answer. The second one uses rather mystical “higher place”. It decouples logic from the real world, making it “true” without regard to observations. But logic is represented in human brains which are part of the world. The third answer seems too much instrumental. I don’t think punishment plays important role in establishing the status of logic. After all, “contraband” methods of persuasion are rarely punished.
Expanding on your first answer, it seems that logic is based on the most firm intuitions which almost all people have—maybe encoded in the low level hardware structure of human brains. People often have conflicting intuitions, but there seems to be some hierarchy which tells which intuitions are more basic and thus to be prefered. But this is still strongly related to persuasion, even if not in the open way of your third answer.
If this view of logic is correct, the generalisation to ethics is somewhat problematic. The ethical intuitions are more complicated and conflict in less obvious ways, and there doesn’t seem to be a universal set of prefered axioms. Any ethical theory thus may be perceived as arbitrary and controversial.
After all, “contraband” methods of persuasion are rarely punished
Contraband methods of persuasion are weakly punished, here and elsewhere, by means of public humiliation along with repudiation of the point trying to be made. Some people go so far as to give fallacious defenses of positions they hate (on anonymous forums) in order to weaken support for those positions. Interestingly, the contexts where we think logic is most important (like this site) are much less tolerant of fallacies than the contexts where we think logic is less important (politics or family dinner). So while I’d love to dismiss that cynical explanation, I can’t quite so easily.
People often have conflicting intuitions, but there seems to be some hierarchy which tells which intuitions are more basic and thus to be preferred.
Actually, there is indeed such a hierarchy in moral reasoning, and it has been better studied/elucidated (by Kohlberg, Rest, et al) than logical reasoning has.
All my answers to this are flawed. My best is: It’s like Euclidean geometry: humans (and other species) are constructed in a way that Euclidean geometry fits fairly well. The formalized rules of Euclidean geometry match spacial reality even better than what we’ve evolved, so we prefer them… but they’re similar enough to what we’ve evolved that we accept them rather than alternate geometries. Euclidean geometry isn’t right—reality is more complex than any system of geometry—but the combination of “works well enough”, “improves on our evolved heuristic”, and “matches our evolved heuristic well enough” combine to give it a privileged place. Just so, that system of formal logic works well enough, improves on our evolved reasoning heuristics, and yet matches those heuristics well enough… so we give formal logic a privileged place. The privilege is sufficient that many believe logic is the basis of Truth, that many theists believe that even angels or deities cannot be both A and not-A, and that people who use fallacies to convince others of truths are frequently considered to be liars. This does not sufficiently satisfy me.
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. 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”, we just question our premises, our methods of detection of answers, etc. So logic is special and is above the empirical method. I am unsatisfied by the above paragraph as well.
A third possibility is that it’s not—it’s just a code of conduct/signalling. We agree to only use logic to convince one another because it works well, because the use of other methods of persuasion can often be detected and punished, and because the people who can rely on logic rather than on other methods of persuasion are smarter and more trustworthy. In specific instances, logic might not be the best way to learn something or to convince others, but getting caught supporting or using contraband methods will be punished so we all use/support logic unless we’re sure we can get away with the contraband. This is an unsatisfying explanation to me as well.
Another answer (which I’m not sure is the answer) is that in logic or mathematics, a person is more likely to be convinced by a random correct proof than a random flawed proof; and if a person is convinced by a flawed proof it is easy to change their mind by pointing out the flaw in the proof; but if a person is convinced by a correct proof, then it is difficult to change their mind by incorrectly claiming there is a flaw. Of course I am being sloppy and nontechnical here; I bet there is a subtle, technical sense in which, under reflection, Modus Ponens is more appealing than Appeal To Justin Bieber.
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.
I like the first answer. The second one uses rather mystical “higher place”. It decouples logic from the real world, making it “true” without regard to observations. But logic is represented in human brains which are part of the world. The third answer seems too much instrumental. I don’t think punishment plays important role in establishing the status of logic. After all, “contraband” methods of persuasion are rarely punished.
Expanding on your first answer, it seems that logic is based on the most firm intuitions which almost all people have—maybe encoded in the low level hardware structure of human brains. People often have conflicting intuitions, but there seems to be some hierarchy which tells which intuitions are more basic and thus to be prefered. But this is still strongly related to persuasion, even if not in the open way of your third answer.
If this view of logic is correct, the generalisation to ethics is somewhat problematic. The ethical intuitions are more complicated and conflict in less obvious ways, and there doesn’t seem to be a universal set of prefered axioms. Any ethical theory thus may be perceived as arbitrary and controversial.
You are certainly at least partly right. But:
Contraband methods of persuasion are weakly punished, here and elsewhere, by means of public humiliation along with repudiation of the point trying to be made. Some people go so far as to give fallacious defenses of positions they hate (on anonymous forums) in order to weaken support for those positions. Interestingly, the contexts where we think logic is most important (like this site) are much less tolerant of fallacies than the contexts where we think logic is less important (politics or family dinner). So while I’d love to dismiss that cynical explanation, I can’t quite so easily.
Actually, there is indeed such a hierarchy in moral reasoning, and it has been better studied/elucidated (by Kohlberg, Rest, et al) than logical reasoning has.
So do you think aliens would develop a non-isomorphic system of logic?
I think it is possible.