In old mathematics texts, at the end of a proof one sometimes sees the expression “Q.E.A.”, abbreviating “quod est absurdum”, that is, “which is absurd”. It isn’t used nowadays, because in mathematics, it is now known precisely what is absurd: a contradiction. Nothing else is absurd. The only reductio ad absurdum in mathematics is proof by contradiction. While intuition may inform one’s search for theorems and their proofs, an actual proof must not depend on any intuitions beyond the common acceptance of the universal language of mathematics (i.e. first-order predicate calculus).
In former times, before that universal language had been discovered, this was not so. People trying to prove Euclid’s Fifth Postulate would start by supposing it to be false, derive a great many conclusions from this, and eventually either give up, or declare victory by dismissing as absurd or repugnant some conclusion they thought especially bizarre.
In science, there is a second type of absurdity: contradiction by experimental data. This is not quite as reliable a message that your theory is wrong as self-contradiction, since sometimes it is the experiment that is wrong, but still, you can get a long way with science. When establishing scientific results, intuition does not count as evidence, only consistency of the theory and agreement with observation.
19th century introspectionist psychology failed because its practitioners found themselves unable to agree on the basic data of their introspections, such as whether every colour is a psychologically primitive sensation, or some are compounds of others (link). Here’s a link to the beginning of a scientific account (containing a link to a book-length account near the foot).
So in both mathematics and science, intuition plays a role in the conduct of the discipline, but always has to be cashed out when it comes to determining what is true. When it cannot be, the subject is in a confused state. Philosophy is very confused. If intuition is evidence, as Kripke would have it (quoted in the paper that Prismattic linked):
Some philosophers think that something’s having intuitive content is very inconclusive evidence in favor of it. I think it is very heavy evidence in favor of anything, myself. I really don’t know, in a way, what more conclusive evidence one can have about anything, ultimately speaking.
then how does one proceed when different people’s intuitions are irreconcilable? The Chinese Room does/does not understand. One should/should not switch the trolley. A perfect copy is/is not me. Reality does not contradict itself, only our beliefs about reality. Therefore intuitions on these matters, however strongly held, are poor evidence.
What good is a discipline in which anyone can respond to an argument by just trotting out a contrary intuition, and have this count as a substantial response?
In old mathematics texts, at the end of a proof one sometimes sees the expression “Q.E.A.”, abbreviating “quod est absurdum”, that is, “which is absurd”. It isn’t used nowadays, because in mathematics, it is now known precisely what is absurd: a contradiction. Nothing else is absurd. The only reductio ad absurdum in mathematics is proof by contradiction. While intuition may inform one’s search for theorems and their proofs, an actual proof must not depend on any intuitions beyond the common acceptance of the universal language of mathematics (i.e. first-order predicate calculus).
In former times, before that universal language had been discovered, this was not so. People trying to prove Euclid’s Fifth Postulate would start by supposing it to be false, derive a great many conclusions from this, and eventually either give up, or declare victory by dismissing as absurd or repugnant some conclusion they thought especially bizarre.
In science, there is a second type of absurdity: contradiction by experimental data. This is not quite as reliable a message that your theory is wrong as self-contradiction, since sometimes it is the experiment that is wrong, but still, you can get a long way with science. When establishing scientific results, intuition does not count as evidence, only consistency of the theory and agreement with observation.
19th century introspectionist psychology failed because its practitioners found themselves unable to agree on the basic data of their introspections, such as whether every colour is a psychologically primitive sensation, or some are compounds of others (link). Here’s a link to the beginning of a scientific account (containing a link to a book-length account near the foot).
So in both mathematics and science, intuition plays a role in the conduct of the discipline, but always has to be cashed out when it comes to determining what is true. When it cannot be, the subject is in a confused state. Philosophy is very confused. If intuition is evidence, as Kripke would have it (quoted in the paper that Prismattic linked):
then how does one proceed when different people’s intuitions are irreconcilable? The Chinese Room does/does not understand. One should/should not switch the trolley. A perfect copy is/is not me. Reality does not contradict itself, only our beliefs about reality. Therefore intuitions on these matters, however strongly held, are poor evidence.
What good is a discipline in which anyone can respond to an argument by just trotting out a contrary intuition, and have this count as a substantial response?