The Instigator
shakuntala
Pro (for)
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The Contender
lightingbolt50
Con (against)
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All proven maths statements cant be true-fron Godels theorem

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Voting Style: Open Point System: 7 Point
Started: 5/20/2014 Category: Science
Updated: 3 years ago Status: Post Voting Period
Viewed: 569 times Debate No: 55126
Debate Rounds (3)
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shakuntala

Pro

australias leading erotic poet colin leslie dean notes

All proven maths statements cant be true-fron Godels theorem
(if there is only one definition of truth in mathematics)

godel proved that there are true mathematic statements which cant be proven

http://www.scribd.com...

http://en.wikipedia.org...

?Any effectively generated theory cap
?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)
For each consistent formal theory T having the required small amount of number theory
? provability-within-the-theory-T is not the same as truth; the theory T is incomplete.?

this means then Godels theorem means All provable mathematics statements cant be true including his own theorem

godel proved that there are true mathematic statements which cant be proven

so that entails then that what ever a true mathematics statement is a condition on it being true must be that it cant be proven
(if there is only one definition of truth in mathematics)

that means then
that all provable mathematic statements cant be true
as a condition on being true is that it must be non-provable

corollary
Thus godel giving a proof of his theorem means his theorem cant be true as a condition on being true is that it must be non-provable

This place godels theorem in a paradox

Godels theorem is considered true but if it is true then it cant be true as he has proved his theorem but his theorem means then his theorem cant be true as a condition on being true is that it must be non-provable
lightingbolt50

Con

For something to be true, it must be provable, not un-provable. That is a highly flawed definition of truth. Btw, why are you so obsessed with Colin Dean, it get's so annoying. Stop talking about her on all of your debates.
Debate Round No. 1
shakuntala

Pro

con says
"For something to be true, it must be provable, not un-provable"
please address these two points

1)godel proved
http://en.wikipedia.org...
"arithmetical statement that is true,[1] but not provable"

therefore your statement that
"For something to be true, it must be provable" is wrong

2)godel proved
"arithmetical statement that is true,[1] but not provable"
so by a simple use of logic it entails
that
for a mathematics statement to be trues a condition on it being true must be that it cant be proven

that entails
(if there is only one definition of truth in mathematics)
All provable mathematics statements cant be true including his own theorem
lightingbolt50

Con

By the way you said it, you made it seem like you think for something to be true it must be un-provable, something can be true without being provable, but being unprovable isn't a requirement to be true, like you entailed.
Debate Round No. 2
shakuntala

Pro

con says
", something can be true without being provable,"

thus as dean says

so that entails then that what ever a true mathematics statement is a condition on it being true must be that it cant be proven
(if there is only one definition of truth in mathematics)

that means then
that all provable mathematic statements cant be true
as a condition on being true is that it must be non-provable
lightingbolt50

Con

Something CAN be true without being provable, but it's not a requirement to be true. There are plenty of things that are true and are provable.
Debate Round No. 3
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