Gödel’s 1st theorem is meaningless

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Gödel’s 1st theorem is meaningless

Postby bas on January 25th, 2019, 7:09 pm 

Gödel’s 1st theorem is meaningless

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

Gödel’s 1st theorem

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
bas
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Re: Gödel’s 1st theorem is meaningless

Postby Lomax on January 25th, 2019, 7:38 pm 

I'm rusty on mathematics, but:
bas » January 26th, 2019, 12:09 am wrote:But the fact is Godel cant tell us what makes a mathematical statement true thus his theorem is meaningless

If this is the case then surely the vast majority of what most people say is meaningless. How many people can adequately define truth? We only need to be able to say that G follows from the axioms.
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