Re:Turing and Wittgenstein on Logic and Mathematics [pdf]
by ukj on Wednesday July 22, 2020 @12:12PM
(#23918541)
If you trawl Girard’s papers you will find him saying at least these two things:
Logic is subjective.
Logic is implicit - will never be explicit.
“The symbol speaks for itself” is the notion of denotational semantics mathematicians use. I am in the camp of “symbols mean whatever you interpret them to mean”.
We have said that some things are arbitrary in the symbols that we use and that some things are not. In logic it is only the latter that express: but that means that logic is not a field in which we express what we wish with the help of signs, but rather one in which the nature of the absolutely necessary signs speaks for itself.