4 ms·
Suppose, I choose "This sentence is false" as an axiom. having it as an axiom allows me to reason from its content that it is false and thus I have a contradict
by thethirdone 10y ago
Suppose, I choose "This sentence is false" as an axiom. having it as an axiom allows me to reason from its content that it is false and thus I have a contradiction.
In this way at least, that axiom is "wrong".
- monochromatic 10y agoBut the Axiom of Choice doesn't lead to contradictions (unless Zermelo Fraenkel set theory itself contains contradictions). The Axiom of Choice just leads to some non-intuitive results.