Talk:Brouwer–Heyting–Kolmogorov interpretation

How can a function convert a thing into something that does not exist(proof of absurdity)? 2.53.1.233 (talk) 03:31, 28 January 2020 (UTC)


 * Yes, there seems to be some inconsistency here (section "The interpretation"):
 * The formula $$\neg P$$ is defined as $$P \to \bot$$, so a proof of it is a function f that converts a proof of $$P$$ into a proof of $$\bot$$.
 * There is no proof of $$\bot$$ (the absurdity, or bottom type (nontermination in some programming languages)).
 * Which would imply we can never have a proof of $$\neg P$$, since there are no functions $$f\colon X \to \varnothing$$. I'm sure this is just a matter of imprecise phrasing - perhaps someone familiar with the topic could help. --Jordan Mitchell Barrett (talk) 09:13, 28 October 2020 (UTC)


 * A function $$f\colon X \to \varnothing$$ exists precisely when $$X$$ itself is empty. ChurchBishop (talk) 03:35, 2 April 2021 (UTC)