Tortoise answered but backtracked when he realised the consequences for Godels theorem
is the axiom of reducibility invalid-as Ramey says
are self referencing statements invalid -as text books on logic say
you all disparge colin leslie dean called him a crackpot etc when he claims godels theorems are invalid because he use the axiom of reducibilty and self refetrencing statements
You all say Godels theorems are not invalid because he uses the axiom of reduciciblity-which Russell Wittgentien and ramsey and most mathematicians say is invalid.
And you say godels theorems are not invalid because he constructs self referential statements-which text books on logic say are invalid
So come on have the courage to put your reputation on the line [as Tortoise did] and gives us a yes or no to my questions 1) & 2
if you say 1 & 2 are invalid then you must admit godels theorems are invalid- and thus admitt colin leslie dean is correct
or
if you say 1 & 2 are not invalid then you are saying Russell Wittgenstien Ramsey and most mathematicians are wrong as well as text books on logic
I’m no expert on either of these, but I assume, that like most things, a simple yes or no would be insufficient for an explanation. It’s probably a matter of the context in which one or the other is applied. One might be valid and the other not given certain conditions or stipulations.
Another thing, logical validity isn’t god. How do you think progress is made in the field of logic? People show that certain things just “are” in spite of the limits of our descriptive mechanisms. Then we get better logic. Right?
not good enough
ramsey wittgenstien russell et al have all said axiom of reducibility is invalid regardless of context
text books on logic say self referential statements are invalid regardless of context
you making that statement is only trying to avoid making a statement which might reflect badly on your reputation -come on be couragoues as ramsey at al have done and give us a yes or no
come on gives us a answer -u take einstien to be an authority
u take godel
u take hawkins to be an authority
so if you cant find an authority to say AR and impredicative statements are valid -be couragoes and you say so if you have courage
u say 1=1 based on some authority u believe u cant divide by zero based on some authority
so wat is your authority for that-and use that authority to answer my questions
If there was a way to answer your question properly with a yes or no, then I would, but philosophy isn’t so black and white. If you think that calling me uncourageous is going to somehow appeal to my ego and that you can force me to join in on a silly, and ill defined debate, then you’re just wrong. I think you have to realize that both concepts exist, and in different contexts both can be useful, neither can be simply true or false w/ out some context. And arguing that one is better than the other shows that you’re just looking for an unporductive “debate” about something upon which you feel yourself to be an authority.
Come back with better questions. Have the courage.
hey ramsey russell wittgenstien [both philosophers]et al and text books on logic have no problem in saying no ie they are invalid
so i cant see why u cant give a yes or no
Invalid in what context? The fact is that both sides of your “debate” can be boiled down to the same metaphysical uncertainty, and they both rest on the same logical grounds. Saying one is True, and the other False, is a claim that can’t be proven. We don’t know if the universe has boundaries. That’s the fact of the matter.
Godel’s theorem makes three points. One contradicts itself in that the metaphysical may exist, under certain rigid circumstances. When he is all done saying nothing can be proved, he leaves wiggle room, best explained by the work of Nagel and Newman- dannyreviews.com/h/Godel_Proof.html
Godel says that nothing is provable because the proof rests upon an ultimate postulate that is outside that system that is to be proved. This is the argument that mathematics cannot be proven and why physicists are petrified to admit that the standard model relies on mathematics as much as it depends on force definitions.
I argue that Godel is wrong on this point because I believe that integers are derived naturally from the harmonic geometry of nature’s quantum.
GIT also implies that only a negative is provable. This is why infinity, as I use it (motion), is provable.
GIT is scattered and has points I agree with and points I disagree with.
What most do not realize is that GIT toppled Logical Positivism and ultimately philosophy, as it is not at the academic level it once was at. Theology has not suffered because it doesn’t care about proof. GIT split things up. This was applied to theology and theologists were stuck, so they simply began to ignore proof itself.
In my opinion the goal is to unite Philosophy, Theology and Science. Perpetualty does this…
I get it, you don’t get what I’m saying. He is saying that all numbers that are based on the value of ‘one’ cannot be established from within a specific system. The value must be obtained from outside the system/set from which all of the values of the set are to be determined. All mathematics is unprovable until ‘one’ can be proven from within any system.
Peano Axioms do not assign a value to ‘one’, they only state that it exists. Other numbers are functions of ‘one’.
All mathematical numbers represent values that are functions of an arbitrary value for ‘one’. The arbitrary value must be proven.
So he is saying we must define ‘one’ in a way that is not circular. This has already been done by establishing the natural source of numbers. It just wasn’t done in his lifetime.
His theorem is not about validity, it’s about consequence. It’s a numbers interpretation. The entire point of his proof is that you cannot avoid self-referential statements in any logical system that is strong enough to embody a number theory.
To ‘invalidate’ the theory misses the point of the theory. Remember…math is man-made…
