in any self-consistent set of axioms, there exist theorems which can neither be proved or disproved..Godel?

Question

A few thoughts Many years ago as a maths/physics undergrad I was discussing this in the pub with other students. At the time we argued whether certain mathematical propositions belonged to the class of 'undecidables', eg Fermat's Last Theorem, Goldenbach's Conjecture etc My argument was that if these were undecidable it would be inconsistent with them being false, therefore they were either true but unprovable or false but no counterexamples had been found.This caused great consternation and dispute- I was accused of depriving humanity of free-will: after all, if everything is capable of being known,(even theoretically), then all our actions can be pre-determined. In the end we settled the debate with an arm wrestling tourney- I won! Much more satisfactory than a lot of casuistry, stupid diagrams and equations.Stephen Hawking has problems with 'naked singularities' as does Pope Ratzinger over the existence of 'limbo'. I'd take the pair of them! Force!- the best way to settle arguments

Answer 1

doesn't the statement contradict itself? If it is a theory that can be proved, then it proves itself wrong. If it cannot be proved then it again may be wrong.

Answer 2

Yes, I've read about this recently. Mathemathicians were SO shocked! They were shocked at the possibility that in a carefully contructed, perfectly logical system (and we mean here mathemathical logic, the most exact ever), propositions can be formulated that cannot be either proved or disproved. Your argument sounds interesting, but I wouldn't venture to judge it. I wonder, however, what could possibly mean for those propositions to be true or false, if the value of true or false for a proposition, in mathemathical logic, means nothing more that its truth or falsity can be attained from the premises (which we know to be true) by performing a series of correct logical operations. Then, indecidability means no truth and no falsity whatsoever! So, what your friends were possibly trying to tell you is that absolute knowledge is not possible, not even in mathemathics. All of you should have been familiar with Heisenberg's principle of indetermination in nuclear physics, which already means the dearest dream of 19th century determinists, that of ultimately knowing the equations of all particles and thus supposedly being able to predict the future, has been already shattered to pieces. So what were you arguing about, then?
But you won the other argument, which means somehow that, as an empirical rule, lack of subtlety in reasoning is compensated by physical strength. Poor Hawking... (I hope you won't take it as a personal offence since you know it's a joke.)
The Pope however looks relatively strong; does this mean we should let him decide about those singularities? I wonder if the Roman Catholic doctrine on papal infallibility covers physics too.
About the limbo issue, what the pope could do would be to go to his really, really cool Vatican Library and read from the Holy Fathers of the Church: what do they say about afterlife?

Answer 3

the super undertaking approximately philosophy is that on the sides that's impossible to tell who rather is conscious it and who's conversing finished rubbish. even with the undeniable fact that, you're no longer rather on the sides. Your argument is tosh: in the event that they're undecidable then it rather is inconsistent with them being fake OR authentic. that's style of the factor. as though as an occasion the intensity of your fake impression, Fermat's final Theorem is neither authentic yet unprovable nor fake: it became shown by ability of Andrew Wiles (status on the shoulders of giants) - a dozen years in the past now. A fool can ask greater questions than a smart guy can answer, and a fool in a communicate of mathematical pholosophy will frequently think of he has come out on appropriate, purely because of the fact people who understand greater could no longer knock down his arguments in a fashion he might desire to comprehend. and you are able to desire to take a seventy 8-3 hundred and sixty 5 days-previous guy and a guy in a wheelchair? Bully for you!

Answer 4

Have you tried the hangdem diagrams? they suggest that the intercropual formation of eclecticism's as a diopetual underpinning of all matter, and furthermore that all pintonagosysts are wrong. well that's according to the study carried out by yessam salohcin m.d Cm pl.

Answer 5

Pardon me --- this has WHAT to do with religion and spirituality (apart from the fact that a Pope gets mentioned once)?

Answer 6

isnt a godel one of those things that sticks to your butt after you wipe