Hi all, Why say that the following phrase is nonsense? “The consistency of axioms cannot be proved within their own system.” Because: A system which has axioms for itself, in order for the system to call them axioms for itself, the system has to have a consistent behavior around those axioms and so when it behaves inconsistently with regard to those axioms, the inconsistency between those axioms and the system’s behavior the system can prove to itself. If what is written above is false, then when a system behaves inconsistently with regard to some axioms it has for itself, that inconsistency it cannot prove to itself, and it keeps behaving inconsistently with regard to those axioms…but… if the system keeps behaving inconsistently with regard to some axioms and cannot prove to itself that it does so with regard to those axioms, then it doesn’t seem to me it can consistently keep regarding them as axioms for the system, and then something else replaces them, and that something else is what the system calls axioms for itself. The way humans make sense of the world around them, is either one that is funny for them, or it is one that is not funny for them. If the way humans make sense of the world around them is not funny for them…for a long time, those people don’t have a good time…for a long time, and they may forget that… The way one makes sense of the world around one, is funny for one, or it wouldn’t be funny for one... check comments under youtube song "Sarah Silverman in London" , you will find there, how this relates to you,just follow the money... Kind regards, Alex
oh...didn't you read the 2nd line of the message? Why say that the following phrase is nonsense? “The consistency of axioms cannot be proved within their own system.” now did you find the question we are discussing in this thread...geniues?
That seemed pretty rhetorical. Other than you, who said that phrase is nonsense? Do you think it requires genius to comprehend these ideas?
(Kolmogorov) probability axioms can be disproven in physics. ( https://en.wikipedia.org/wiki/Probability_axioms ) E.g. they allow to derive Bell-like Mermin's inequality: "tossing 3 coins, at least 2 are equal" - for 3 binary variables ABC: Pr(A=B) + Pr(A=C) + Pr(B=C) >=1 Specifically, choosing any probability distribution for 8 possibilities sum_ABC pABC=1 Pr(A=B) = p000 + p001 + p110 + p111 Pr(A=C) = p000 + p010 + p101 + p111 Pr(B=C) = p000 + p100 + p011 + p111 Pr(A=B) + Pr(A=C) + Pr(B=C) = 2p000 + 2p111 + 1 >= 1 However, QM formalism allows to violate this inequality, e.g. https://arxiv.org/pdf/1212.5214
google the phrase first...in order to understand what we are talking about then read my argument then really, REALLY put some time and effort to think before you reply to me
Why say that the following phrase is nonsense? “The consistency of axioms cannot be proved within their own system.” Because: A system which has axioms for itself, in order for the system to call them axioms for itself, the system has to have a consistent behavior around those axioms and so when it behaves inconsistently with regard to those axioms, the inconsistency between those axioms and the system’s behavior the system can prove to itself. If what is written above is false, then when a system behaves inconsistently with regard to some axioms it has for itself, that inconsistency it cannot prove to itself, and it keeps behaving inconsistently with regard to those axioms…but… if the system keeps behaving inconsistently with regard to some axioms and cannot prove to itself that it does so with regard to those axioms, then it doesn’t seem to me it can consistently keep regarding them as axioms for the system, and then something else replaces them, and that something else is what the system calls axioms for itself. any of you think you can prove me wrong? go ahead, but....geniuses...stay on the subject (the subject we are discussing here is right above geniuses)
It's not nonsense. It's sort of half of one of Godel's famous proofs. Are you saying you think it's nonsense? Any mathematical system that is entirely self-consistent must also be incomplete, in that true statements can be expressed within the system but not proved within it. Does that help you?
