Philosophy Now Forum

Gödel’s 1st theorem is meaningless as Godel cant tell us what makes a maths statement true
http://gamahucherpress.yellowgum.com/wp ... DEL5.pdf
Gödel’s 1st theorem states

a) “Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true,[1] but not provable in the theory (Kleene 1967, p. 250)


note
"... there is an arithmetical statement that is true..."

In other words there are true mathematical statements which cant be proven
But the fact is Godel cant tell us what makes a mathematical statement true thus his theorem is meaningless

anne wrote: ↑Wed Jan 23, 2019 7:46 am But the fact is Godel cant tell us what makes a mathematical statement true thus his theorem is meaningless

If you accept this conclusion then you are going to have a hard time putting together any arguments.

No human being can tell us what makes ANY statement true without tripping over infinite regress.

As in English so in Mathematics, you simply accept some things as axiomatic truths.

Logik wrote: ↑Wed Jan 23, 2019 8:17 am

anne wrote: ↑Wed Jan 23, 2019 7:46 am But the fact is Godel cant tell us what makes a mathematical statement true thus his theorem is meaningless

If you accept this conclusion then you are going to have a hard time putting together any arguments.

No human being can tell us what makes ANY statement true without tripping over infinite regress.

As in English so in Mathematics, you simply accept some things as axiomatic truths.

Actually Godel's incompleteness theorem can be applied to Godel's incompleteness theorem and a contradiction occurs as his theorem becomes a proof subject to the fallacy of circularity where all axiomatic states are subject to a self-referentiality.

Godel, by default, necessitates all mathematical statements as circular. I cover this in the mirror calculus thread.

She is right.