On this I think we agree. I’ll just add that sometimes “intuitions” points to “a short mental calculation” and some other times to “a biased heuristic”.
It can mean either of those, but it can also mean an assumption you can neither prove nor do without.;
Some axioms are more basic than others.
If what you want is convergence on objective truth, it is the existence of axioms that people don’t agree on that is the problem.
And indeed challenged axioms produce strong revolutions.
And pluralism. Intuitonistic and classical maths co-existing, Euclidean and non-Euclidean geometry co-exisitng.
. Truth table are useful as long as they agree on the axioms. Or one could say that truth tables are based on intuition...
Truth tables give you a set of logical functions, some of which resemble traditional logical connectives, such as “and” and “implies” to some extent. But only to some extent. The worry is that they don’t capture all the features of ordinary langauge usage.
It can mean either of those, but it can also mean an assumption you can neither prove nor do without.;
If what you want is convergence on objective truth, it is the existence of axioms that people don’t agree on that is the problem.
And pluralism. Intuitonistic and classical maths co-existing, Euclidean and non-Euclidean geometry co-exisitng.
Truth tables give you a set of logical functions, some of which resemble traditional logical connectives, such as “and” and “implies” to some extent. But only to some extent. The worry is that they don’t capture all the features of ordinary langauge usage.