I both resonate with this sentiment, but am also hesitant since you could say similar things about linear algebra or prime factorizations, or most of mathematics:
You first come up with a theory of how to determine something is a prime number, based on the ones you know are primes, then you apply that theory to some numbers you intuitively thought were not primes to show that they are indeed prime, and then you impose that mathematical knowledge on others, even though there might currently not be a single person on earth who actually thinks the number you highlight is prime.
Or maybe a more historically accurate example is non-euclidian geometry, which if I remember things correctly, was assumed to be inconsistent since the 16th century, and a lot of the people who developed non-euclidian geometry actually set out to prove its inconsistency. But based on the methods they applied to other mathematical theorems, they then applied those methods to non-euclidian geometry and found that it should actually be consistent, and then they imposed that feeling of shouldness onto others, even though at the time the dominant mode of thinking was to believe non-euclidian geometry was inconsistent.
This is not an accurate comparison, for the simple reason that “prime number” is a formally defined concept. The reason we think that 2 or 5 or 13 are prime isn’t that we have an un-formalized (and perhaps un-formalizable) intuition that they’re prime; it’s that we have a formal definition, and 2 and 5 and 13 fit it!
So when we consider a number like 2,345,387,436,980,981, our “intuitions” about whether it’s prime, or whether anyone “thinks” it’s prime, are just as irrelevant as they are to the question of whether 2 is prime. Either a number fits the formal definition, or it doesn’t fit the formal definition, or we are as yet unable to determine whether it fits the formal definition. Nothing else matters.
With moral intuitions, obviously, things could not be more different…
I think you are overestimating the degree to which we have formal definitions for core mathematical concepts, or at least to what degree it was possible to make progress before we had formalized a large chunk of modern mathematics.
While I agree that morality is generally harder to formalize than mathematics, I do think we are only talking about a difference in degree, instead of a difference in kind. The study of mathematics is the study of our intuitions about certain types of relationships between mental object we have in our mind (which are probably informed by our real-world experience). We tend to develop mathematics in the areas where peoples intuitions about their mental objects agree with one another, or where we can reliably induce similar intuitions with the use of thought experiments or examples (i.e. counting apples, number lines, falling objects, linear transformations, dividing pies between friends, etc.).
The study of morality is similarly the study of a different set of relationships, which might be less universal, but not qualitatively differently universal than our intuitions about mathematical relationships. Good moral philosophy similarly tries to find out what moral intuitions people share, or induce shared intuitions with the help of examples and thought experiments, and then tries to apply the standards of consistency (which is just another aesthetic intuition), logical argument (also just based on aesthetic intuitions) and conceptual elegance, to extend their domain, similarly to mathematicians extending our intuitions about dividing pies to the concepts of the rational and real numbers.
Edit: A related point is that a proof in mathematics is just the application of a set of rules that seem self-evidently true to other mathematicians. If you for some reason you do not find the principle of induction, or the concept of proof-by-contradiction intuitively compelling, then those proofs will not be compelling to you. Mathematics is just built on our intuitions of how logical reasoning is supposed to work. Good moral ethics is trying to establish the foundations of our intuitions of how moral reasoning is supposed to work, and then apply those foundations to come to a deeper understanding of morality, similarly to how mathematics applied its foundation to come to a much deeper understanding of what logical truth is.
I disagree with your evaluation of both mathematics and morality, but it seems like we’ve wandered into somewhat of a tangent. I think I prefer to table this discussion until another time, with apologies.
I both resonate with this sentiment, but am also hesitant since you could say similar things about linear algebra or prime factorizations, or most of mathematics:
You first come up with a theory of how to determine something is a prime number, based on the ones you know are primes, then you apply that theory to some numbers you intuitively thought were not primes to show that they are indeed prime, and then you impose that mathematical knowledge on others, even though there might currently not be a single person on earth who actually thinks the number you highlight is prime.
Or maybe a more historically accurate example is non-euclidian geometry, which if I remember things correctly, was assumed to be inconsistent since the 16th century, and a lot of the people who developed non-euclidian geometry actually set out to prove its inconsistency. But based on the methods they applied to other mathematical theorems, they then applied those methods to non-euclidian geometry and found that it should actually be consistent, and then they imposed that feeling of shouldness onto others, even though at the time the dominant mode of thinking was to believe non-euclidian geometry was inconsistent.
This is not an accurate comparison, for the simple reason that “prime number” is a formally defined concept. The reason we think that 2 or 5 or 13 are prime isn’t that we have an un-formalized (and perhaps un-formalizable) intuition that they’re prime; it’s that we have a formal definition, and 2 and 5 and 13 fit it!
So when we consider a number like 2,345,387,436,980,981, our “intuitions” about whether it’s prime, or whether anyone “thinks” it’s prime, are just as irrelevant as they are to the question of whether 2 is prime. Either a number fits the formal definition, or it doesn’t fit the formal definition, or we are as yet unable to determine whether it fits the formal definition. Nothing else matters.
With moral intuitions, obviously, things could not be more different…
I think you are overestimating the degree to which we have formal definitions for core mathematical concepts, or at least to what degree it was possible to make progress before we had formalized a large chunk of modern mathematics.
While I agree that morality is generally harder to formalize than mathematics, I do think we are only talking about a difference in degree, instead of a difference in kind. The study of mathematics is the study of our intuitions about certain types of relationships between mental object we have in our mind (which are probably informed by our real-world experience). We tend to develop mathematics in the areas where peoples intuitions about their mental objects agree with one another, or where we can reliably induce similar intuitions with the use of thought experiments or examples (i.e. counting apples, number lines, falling objects, linear transformations, dividing pies between friends, etc.).
The study of morality is similarly the study of a different set of relationships, which might be less universal, but not qualitatively differently universal than our intuitions about mathematical relationships. Good moral philosophy similarly tries to find out what moral intuitions people share, or induce shared intuitions with the help of examples and thought experiments, and then tries to apply the standards of consistency (which is just another aesthetic intuition), logical argument (also just based on aesthetic intuitions) and conceptual elegance, to extend their domain, similarly to mathematicians extending our intuitions about dividing pies to the concepts of the rational and real numbers.
Edit: A related point is that a proof in mathematics is just the application of a set of rules that seem self-evidently true to other mathematicians. If you for some reason you do not find the principle of induction, or the concept of proof-by-contradiction intuitively compelling, then those proofs will not be compelling to you. Mathematics is just built on our intuitions of how logical reasoning is supposed to work. Good moral ethics is trying to establish the foundations of our intuitions of how moral reasoning is supposed to work, and then apply those foundations to come to a deeper understanding of morality, similarly to how mathematics applied its foundation to come to a much deeper understanding of what logical truth is.
I disagree with your evaluation of both mathematics and morality, but it seems like we’ve wandered into somewhat of a tangent. I think I prefer to table this discussion until another time, with apologies.
Seems good. It does seem pretty removed from the OP.