[FOM] Classical logic and the mathematical practice

[Andrej Bauer]

Timothy Y. Chow wrote:
> It generally takes considerable philosophical education before
> someone seriously entertains the notion that if there is no way to
> decide whether X happened or not, then maybe X neither happened nor
> didn't happen.

I suspect Tim did not want to say what he said in this paragraph, namely
that "people of considerable philosophical education" might entertain
the possibility that "not (X or not X)" is valid. Well, perhaps people
of considerable philosophical education might actually do precisely
that, but I am sure there is no mathematician, constructive or
classical, who would seriously attempt to believe such a falacy.

I have seen this mistake before: people think that "not accepting the
law of excluded middle" means "accepting the negation of the law of
excluded middle". In fact, I suspect most mathematicians think precisely
that. Naturally they would then conclude that constructivist mathematics
is garbage.

Best regards,

Andrej