You need to add some assumptions to make it work. For example, I believe the following works:
“In second order arithmetic, we can prove that NP1 implies NF, where NP1 is the statement ‘there exists no first order proof of the conjecture’ and NF is the statement ‘the conjecture isn’t false’.”
You need to add some assumptions to make it work. For example, I believe the following works:
“In second order arithmetic, we can prove that NP1 implies NF, where NP1 is the statement ‘there exists no first order proof of the conjecture’ and NF is the statement ‘the conjecture isn’t false’.”