if set theory ie ZFC is incomplete it cannot prove anything

[pam69ur]

That a statement or argument is conjectural does not imply that it is false or invalid, and it is not a criticism of such a statement of argument that it might be false or invalid.

complete besides the point
wiles if he offered a proof of the fermats theorem with an unproven Taniyama–Shimura conjecture it would not have been accepted as a proof at all

same applies to ZFC if there are statements which canot be proven -like the once Taniyama–Shimura conjecture- then ZFC cant be used to prove anything but only give conjectures


you ask

If you actually have a criticism of ZFC, rather than the trivial fact that it could possibly be mistaken, please provide it.

i have given it
same applies to ZFC if there are statements which canot be proven -like the once Taniyama–Shimura conjecture- then ZFC cant be used to prove anything but only give conjectures


if it applies to wiles proof
it then applies to ZFC
ie with out proof of all the statements -ieTaniyama–Shimura conjecture- then ZFC cant proove anything

[Professer Frost]

Pam69ur,
Look, if you want to start a thread on the overall philosophy of Colin L. Dean go ahead, but I get the distinct impression that everyone on the forum is sick of your endless harping on this particular topic.
- The Prof.

[Aedes]

Originally Posted by pam69ur

same with 1+1=2 untill it is proven all you can do with it is giive conjectures

What's to prove? 1+1=2 is a completely closed tautology.

[Nocturne]

pam69ur,

The hypotheses of science will be forever unproven. That is, the past success of a scientific hypothesis does not imply its future success, and so by convention scientists hold every scientific hypothesis open to refutation. However, the elementary fact that scientific hypothesis are unproven is not generally considered a cause for alarm, and neither is it thought a damning criticism. In other words, the unprovable status of scientific hypotheses does not imply that they are false, and since scientific investigation is concerned with discovering true theories, and not provably true theories, the unprovability of scientific theories is not something to be too worried about.

In a like manner, there are statements about some formal languages which cannot be proven to be true by that language--else the language must be inconsistent. Therefore, if a language is consistent then it is impossible to construct a proof for every statement of that language, and so mathematicians, like scientists, by convention hold their hypotheses open to refutation. However, that it is impossible to prove, once and for all, that such a language is consistent is not a cause for alarm, and neither is it a damning criticism. In other words, the unprovable status of some mathematical languages does not imply that they are inconsistent, and since it is their consistency which we are concerned with, that they might be unprovable is not something to be too worried about.

[pam69ur]

The hypotheses of science will be forever unproven. That is, the past success of a scientific hypothesis does not imply its future success, and so by convention scientists hold every scientific hypothesis open to refutation. However, the elementary fact that scientific hypothesis are unproven is not generally considered a cause for alarm, and neither is it thought a damning criticism. In other words, the unprovable status of scientific hypotheses does not imply that they are false, and since scientific investigation is concerned with discovering true theories, and not provably true theories, the unprovability of scientific theories is not something to be too worried about.

In a like manner, there are statements about some formal languages which cannot be proven to be true by that language--else the language must be inconsistent. Therefore, if a language is consistent then it is impossible to construct a proof for every statement of that language, and so mathematicians, like scientists, by convention hold their hypotheses open to refutation. However, that it is impossible to prove, once and for all, that such a language is consistent is not a cause for alarm, and neither is it a damning criticism. In other words, the unprovable status of some mathematical languages does not imply that they are inconsistent, and since it is their consistency which we are concerned with, that they might be unprovable is not something to be too worried about.

all irrelevant

as colin ****** dean has noted

ZFC cannot prove anything as it has statements which cant be proven

in ZFC if there are statements which canot be proven -like the once Taniyama–Shimura conjecture- then ZFC cant be used to prove anything but only give conjectures


if it applies to wiles proof
it then applies to ZFC
ie with out proof of all the statements -ieTaniyama–Shimura conjecture- then ZFC cant proove anything

if wiles gave a proof using an unproven Taniyama–Shimura conjecture-mathematicians would have said he did not give a proof as one of his statements was itself unproven

so
mathematicans must then say ZFC cant give any proof as some of its statements are unproven
VERY SIMPLE
what applies to wiles must then apply to ZFC

[Nocturne]

pam69ur,

I agree. However, this is only a problem if you are attempting to achieve a secure proof, something which I am not particularly concerned with. In short, that a derivation may not be a proof in the sense which you mean does not mean that the same derivation is invalid, and so until someone produces an critical argument which purports to show that a language is inconsistent, I am not going to hold the mere possibility that it is inconsistent against it. In other words, the problem which seems to concern you is not inherent to mathematics, but with what you want to do with mathematics, and since I do not share the same goals I do not share the problem which afflicts you. Therefore, the result of the Godelian theorem doesn't concern me in the same way that it concerns you, since what you seek to do by mathematical argument is not something which I am interested in achieving.

If you want to argue that ZFC, or any other formal language is inconsistent then I am all ears. If, however, you simply want to rant on about how "proofs" in these languages do not provide the security which you would like then I am not interested--that is your problem, not mine.

[VideCorSpoon]

Originally Posted by pam69ur

all irrelevant

as colin ****** dean has noted

ZFC cannot prove anything as it has statements which cant be proven

in ZFC if there are statements which canot be proven -like the once Taniyama–Shimura conjecture- then ZFC cant be used to prove anything but only give conjectures


if it applies to wiles proof
it then applies to ZFC
ie with out proof of all the statements -ieTaniyama–Shimura conjecture- then ZFC cant proove anything

if wiles gave a proof using an unproven Taniyama–Shimura conjecture-mathematicians would have said he did not give a proof as one of his statements was itself unproven

so
mathematicans must then say ZFC cant give any proof as some of its statements are unproven
VERY SIMPLE
what applies to wiles must then apply to ZFC

Here we go again...