Insofar as I am an optimist about the scientific method, I put my trust in the existence of objective incontrovertible tests for different theories in the field. All humans tend to play politics with beliefs, so there will be consensuses and contrarians and cliques in every field. But in fields that agree on tests, those consensuses will correspond to the actual outcome of the tests; while in fields with no tests, politics will overwhelm any signal produced by armchair reasoning.
Mathematicians have excellent tests for the correctness of a proof, so they rarely disagree for long. Physicists have good empirical predictions, so they only disagree about some things.
Linguists might agree on a test, but most of the time that test is not doable in practice, so they can’t really know if there are biological universals of language; and so they keep on disagreeing about theories more (I predict) than they disagree about any actually observable fact.
And philosophers, by definition, mostly work on things that have no empirical tests, at least not actually executable ones. So they are used to disagreeing, and also to sometimes agreeing (coming to consensus), without actual objective proof of the thing they agree on. And that’s why I expect that “how many philosophers believe X” is a poor tests for “is X true”, more so than for mathematicians or physicists or even linguists.
edit : this disagreement is about an actual meaningful question with an answer, not things like B vs F (which are arguments about taste, as far as I can tell).
Mathematicians have excellent tests for the correctness of a proof, so they rarely disagree for long.
I’m not a mathematician, but my impression impression is that this has gotten less true, as the typical proof published in mathematics journals has gotten more convoluted and harder to check. Mathematicians are now often forced to rely on trusting their colleagues to know whether a proof is correct or not. See here.
Not that this makes mathematics any worse off than other fields. I’m pretty sure all fields these days require people to trust their colleagues.
Interesting. What about machine proof checking? Why don’t mathematicians publish all results in a formal notation (in addition to the human-oriented one) that allows all proofs to be checked, and entered into an Internet repository available to automated proof assistants?
For the same reason not all software is written in Coq/Agda/other proof systems: it would be incredibly expensive, slow, and demand very rare skills.
Insofar as I am an optimist about the scientific method, I put my trust in the existence of objective incontrovertible tests for different theories in the field. All humans tend to play politics with beliefs, so there will be consensuses and contrarians and cliques in every field. But in fields that agree on tests, those consensuses will correspond to the actual outcome of the tests; while in fields with no tests, politics will overwhelm any signal produced by armchair reasoning.
Mathematicians have excellent tests for the correctness of a proof, so they rarely disagree for long. Physicists have good empirical predictions, so they only disagree about some things.
Linguists might agree on a test, but most of the time that test is not doable in practice, so they can’t really know if there are biological universals of language; and so they keep on disagreeing about theories more (I predict) than they disagree about any actually observable fact.
And philosophers, by definition, mostly work on things that have no empirical tests, at least not actually executable ones. So they are used to disagreeing, and also to sometimes agreeing (coming to consensus), without actual objective proof of the thing they agree on. And that’s why I expect that “how many philosophers believe X” is a poor tests for “is X true”, more so than for mathematicians or physicists or even linguists.
Seemingly longstanding disagreements in quantitative fields exist, see e.g.:
http://andrewgelman.com/2009/07/05/disputes_about/
edit : this disagreement is about an actual meaningful question with an answer, not things like B vs F (which are arguments about taste, as far as I can tell).
How does that dispute stand today? Is it still running, have the parties reached agreement, or are they not talking to each other?
I will see what I can find out. My guess is there was no resolution.
I’m not a mathematician, but my impression impression is that this has gotten less true, as the typical proof published in mathematics journals has gotten more convoluted and harder to check. Mathematicians are now often forced to rely on trusting their colleagues to know whether a proof is correct or not. See here.
Not that this makes mathematics any worse off than other fields. I’m pretty sure all fields these days require people to trust their colleagues.
Interesting. What about machine proof checking? Why don’t mathematicians publish all results in a formal notation (in addition to the human-oriented one) that allows all proofs to be checked, and entered into an Internet repository available to automated proof assistants?
For the same reason not all software is written in Coq/Agda/other proof systems: it would be incredibly expensive, slow, and demand very rare skills.
Because it takes a lot of extra time and work to formalize a proof to the level where it can be automatically checked.