Thanks! I’m not an amazing writer like Eliezer, but I enjoy being on LW and I want other people to enjoy it as well.
The definition of implication is actually a bit more complex, you need to take the largest open subset of “not-P or Q”. Similarly, negation isn’t just complement, but the largest open subset of the complement. That’s what makes the intuitionistic stuff work, otherwise you get classical logic as Alex said. But topology isn’t everyone’s cup of tea, so I left it out.
Thanks! I’m not an amazing writer like Eliezer, but I enjoy being on LW and I want other people to enjoy it as well.
The definition of implication is actually a bit more complex, you need to take the largest open subset of “not-P or Q”. Similarly, negation isn’t just complement, but the largest open subset of the complement. That’s what makes the intuitionistic stuff work, otherwise you get classical logic as Alex said. But topology isn’t everyone’s cup of tea, so I left it out.