your the one saying 1=1 is true so tel us why it is true
you can prove
1+1=2
but tell us why it is true
But the jokes on you: our reality is irrelevant. The way we apply math to reality is the problem of physicists and other scientists, not of mathematicians.
Again, Godel may have had a conception of true which yielded a particular interpretation of his results, but this is not relevant to the proof. The proof as implied by the title of the article is merely to show that a given system to model our notion of arithmetic contains “undecidable propositions.” i.e. it is a well formed string of symbols that constitutes a number theoretic “proposition” for which there exists neither a series of “statements” corresponding to a “proof” of either its affirmation or negation. Everything he did can be rephrased into a tautologous mathematical language.
We don’t need to reference some kind of abstract notion of “truth” of the statement unless someone lets a logically illiterate philosopher near it.
Point 1 - dealt with.
Point 2 - I’m still not certain about this as I don’t have a reputable source to go on for no longer using it. Not that it matters given alternative formulations of the same proof.
Point 3 - You still don’t understand the way mathematical induction works. It is a well accepted, well understood axiom used in deductive proofs that everyone in undergraduate level math is quite familiar with. It is absolutely not a form of “induction” in the common sense of the term, and by definition of the term “axiom” it isn’t an argument so it can’t be “circular”.
Now, 1=1 follows immediately from the definition of “=”.
- A(a): a=a
- A(a,b): a=b => b=a
- A(a,b,c): (a=b&b=c) => a=c
Now, ~(1=2) follows directly and immediately from our definitions of “=”, 1, and 2. All of this stuff is completely and utterly tautologous. If we’re arguing about it, someone doesn’t know the meaning of the terms.
No. Your proof isn’t invalid. You just aren’t proving anything about the accepted thing known as the “number system”.
sorry euclidean geometry was worked out assuming reality was eculidean -it aint so the 5th is wrong
as i say
mathematicians cant tell us what “true”
sorry godel says there are true statements which cant be proven
but
he cant tell us what true statements are
thus his proof is meaningless
and
we have no way of knowing if his proof is true
it may be accepted
but
following poincare it is circular as his peanos 5th - as poincare even saw
thats your problem to busy accepting the standard view of things- thats why you will never amount to much
sorry if you use invalid premeses then your conclusions are invalid
in this case 1+1= 5 cant prove anything about the number system as it is invalid
just as the axiom of reduciblity cant prove anything about maths as it is invalid
for fu//k sake go look at godels proof
i have given quotes from it showing he uses AR what fu…king more reputable source do you want
Ignoring your amazing capacity to repeat your stance and ignore my actual arguments…
I know Godel used AR. I sludged through the proof onetime. He spells it out IIRC. What I don’t see is why this discredits the proof; the fact that Goedel’s proofs are considered valid generally is evidence that either a)AR is kosher, or b)no one cares because we can arrive at the conclusions anyway. And attacking it on a technicality like that when alternative formulations of the proof are available is something akin to a strange vendetta against a logician whom philosophers have an unhealthy preoccupation with.
You may be taking issue with a particular school of thought of interpreting his results, but you should distinguish this from the actual proof itself. Otherwise you’re simply spreading your debating resources unnecessarily thin.
AR is not kosher
when i meantioned 1+1=5
you said
so by using AR godel arent proving anything about mathematics
it does not matter what has been so called proven since -or that alternative formulations of the proof are available-for when godel did is proof his proof was the only one on the market and it is invalid as he uses the invalid axiom AR as my quotes show you
and what is more godels theorem is meaningless as he cant tell us what makes a statement true
when he tells us there are true statements which cant be proven
Because 1 represents my left testicle, and 1 represents by right testicle, and 2 represents the state of my testicles. I have two of them, because there is one on the left, which when added to the one on the right equals 2.
sorry that is physics
1+1=2
are just meaningless symbols connected by a rule
it could look like !+! = *
so tell us why it is true
Hmm, while most of your points run the gamut from bunk to bland and back again, the AR question presents something more interesting. I’ll have to do more research before I pummel your inexplicably Godel centric mind, but alas, I have more pressing issues…
Still, it doesn’t really tell us anything at all. It seems that everyone except the philosophers tacitly agree with the use of AR, and Godel is much more highly thought of as a mathematical logician than Russel or especially Big W. Again, there is no such thing as reality here, so if we here in math land can all agree we like AR, that’s just too bad for you 
And you can argue the definition of ‘true’ till you’re blue in the face, but it really isn’t going to get interesting. Just another language game m’dear.
Still perseverating on that topic eh? I daresay, your understanding of formal proofs doesn’t equal your knowledge. Riding the crest of someone else’s discoveries are we? Please refer to my prior response; the mathematical proof needs no comment on truth (and in fact, in many and myriad interpretations used, it doesn’t say a thing on the subject). Truth is a philosophical notion which is quite irrelevant to the meaningless manipulation of symbols. Again, you clearly are trying to attack a particular philosophical position on his results, but you are unfortunately conflating the proof with the interpretation.
Again.
mathematicians like
ramsey did not like it
Ramsey says
Such an axiom has no place in mathematics, and anything which cannot be
proved without using it cannot be regarded as proved at all.
This axiom there is no reason to suppose true; and if it were true, this
would be a happy accident and not a logical necessity, for it is not a
tautology. (THE FOUNDATIONS OF MATHEMATICS* (1925) by F. P. RAMSEY
and even the mathematician editors of godels works did not like it
From Kurt Godels collected works vol 3 p.119
books.google.com/books?id=gDzbuU … #PPA119,M1
“the axiom of reducibility is generally regarded as the grossest philosophical expediency “
so it aint just philosophers he say AR is invalid
godel is meant to have made a distinction between proof and true
thus destroying the hilbert programme
to prove statement is not the same as that statement being true
Because the two symbols are identical, and the sign in between them means add them together and the number 2 on the other side of it means that that’s what you get when you add them together.
rubbish
it could be boolean algebra in which case the * = 0
How do you know that’s what it would look like if you don’t even know what it means?
just throwing your comments down your throoat
if i cant know its boolean
then
u cant know its normal arithmetic
so the point still stand
why is !+!=*
or
1+1= 2
true as distinct from proven
How about this, 1=1 because everyone, (for the most part) agrees that it does. Is that it?
so truth is what the majority agree upon
the majority once agreed gallelio was wrong
most people in the world agree there is a god
so that means god is true then
so tell us what every mathematician says makes a statement true- bear in mind since godel this must be independent of proof
as godel made a dictinction between true statements and proven statements
and he is said to have destroyed the hilbert idea that true was proven from axioms
Janie - tell me this - what are the consequences of the point you are making here? Why does it matter?
for one thing it means as colin leslie dean has said godel theorem is meaningless babble as he tells us there are true statements which cant be proven -but he cant tell us what makes a statement true
And the consequences of that are?
- mathematics ends in meaninglessness- like all products of human thinking
- Godels theorem is a fraud -what godel did