GÃ¶delâ€™s 1st theorem is meaningless

http://gamahucherpress.yellowgum.com/wp-content/uploads/GODEL5.pdf

GÃ¶delâ€™s 1st theorem

a) â€œAny 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 can't be proven.

But the fact is GÃ¶del can't tell us what makes a mathematical statement true thus his theorem is meaningless.

http://gamahucherpress.yellowgum.com/wp-content/uploads/GODEL5.pdf

GÃ¶delâ€™s 1st theorem

a) â€œAny 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 can't be proven.

But the fact is GÃ¶del can't tell us what makes a mathematical statement true thus his theorem is meaningless.

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