colin leslie dean’s attack on godel’s proof does not demonstrate anything about godel’s proof
he claims that godel uses the axiom of reducibility in his proof, which was declared invalid by ramsay
but in the paper cited by dean himself it is stated that the axiom schema used is not itself the reducibility axiom, but merely a weaker schema that performs a similar function
it is clearly stated that the given axiom schema is not the reducibility axiom but merely fulfills a similar function
thus it is not clear whether ramsay’s pronouncement applies to it
dean has therefore not shown that godel’s proof has any problem
the quote “i.e. from the reducibility axiom” is simply speaking loosely, it is an annotated translation after all so it need not speak precisely
the supposed reducibility axiom referred to there may not even be the same as the reducibility axiom ramsay denounces
besides all the other quotes including the one i gave indicate that the given axiom schema “takes the place of”, “represents”, or “plays the role of” the axiom of reducibility
these phrases are clearly meant to convey the idea that the axiom schema is similar in function but not identical to the axiom of reducibility
i wonder if you can tell the difference between a thing and the representation of that thing
if you go to shakespeare’s play henry V and see the actor playing henry do you think that henry has risen from the dead lol
just using your own experts to show your argument ends in meaninglessness
obviously that’s not necessarily the case
have you ever spoken something imprecise in your life, i bet you have
does that mean that everything you say is imprecise
of course not
the clear and prevailing assertion from all the different sources you cited is that godel’s axiom is not the same as the axiom of reducibility
you just want it to be the same so you can win your little meaninglessness argument
well sorry it doesn’t quite work
just shoving your own authorities down your throat to show your argument ends in meaninglessness
your example of w and cos x is only one example of how representation is used
it can also be like with henry V
in that case the thing and the representation are not the same
in fact they are completely different
if w = actor of henry V and cos x = henry V and w plays role as cos x do you think w = cos x then
hahahaha
you did not answer my point
just because a source talks loosely once doesn’t mean it always talks loosely
just because you have lied before doesn’t mean everything you say is lies
if you continue to use this argument i can just turn it against you to dismiss you:
you’ve almost certainly lied once, therefore everything you say is lies lol
you did not answer my point
i pointed out that “represents” and “plays the role of” can mean different things in different contexts
if w = actor of henry V and cos x = henry V and w plays role as cos x do you think w = cos x then
it looks like your plan is to not answer my points and repeat the same thing over and over
well that will certainly end in meaninglessness lol
your sources clearly indicate axiom 1v plays the role of reducibility axiom, not that they are identical
only once it seems to imply that they are the same in a very offhand way
since you are big on democracy how about we put it to a vote
3-1 i win, axiom 1v plays the role of reducibility and is not the same as reducibility
the problem here is that you are not an expert in the sources you are reading
and hence are incapable of understanding author’s point
you read godel’s paper like it was the infallible bible or something
if you are a real scientist you know that there are mistakes and imprecise sayings in nearly every paper
yet despite being imperfect they still carry much meaning
but you have to get out of infallible perfectionistic religious bible mindset to grasp it
you did not answer my point
your algebra example only uses one meaning of “represent” and “plays the role of”
you have not shown that the meaning you use is the same as the meaning used in the paper
the paper could mean represent like in the henry V way
an actor who plays henry V acts like henry V but is not the same as henry V
if godel’s axiom and axiom of reducibility were the same they would just say that instead of always saying “represent”
now we have setteled that
ie your quote is contradicted by your own source
thus your attack on dean collapses
dean also say godel is invalid as he uses visoius circle statements
which text books on logic say are invalid
not all math is about formulas
representation can mean more subtle things in higher forms of math
for example a representation in linear algebra is a homomorphism from an arbitrary group G to a matrix group M
it is said that M represents group G
but M does not equal G
you cannot force a word to mean only what you want it to mean
it means what the author wants it to mean
unless you are an expert in the authors field you cannot say that representation means what you think it means here
the meaninglessness only exists in your limited mind not in math
you do not understand godel’s proof
read “godel’s proof” by nagel
it is shown there that godel created statements which speak about themselves, however they do so indirectly and hence are not impredicative
godel was well aware of the danger of impredicative definitions
his entire proof is based around creating a way for formulas to refer to themselves indirectly
hence avoiding impredication
nowhere in godel’s proof will you see a statement which actually speaks about itself directly, hence no impredicative statements
as i have said the source was speaking loosely
you are now just repeating yourself endlessly and i will not reply to this assertion again
scientific papers speak imprecisely all the time, they are not the infallible bible
nothing is infallible, lol especially not the bible
no
i am saying your rewrite does not apply to the example at hand
the reference to representation in the paper is not talking about substituting things into formulas
you simply assert that godel meant by “propositions which make statements about themselves” the same thing as russell meant by “impredicative propositions”
you nowhere show this to be the case
in fact i know it to be false since (as nagel notes) godel’s propositions do not contain any references to themselves
they only contain references to numerical equations
godel proposition is something like P = "the equation 500=5100 is a correct factorization of 500"
this of course does not refer to itself
however the equation 500 = 5100 can be interpreted as a proposition using a special godel code
the interpreted proposition turns out to be P itself
however P is just talking about an equation hence is not impredicative in russellian sense
just because the paper contains the word “substitution” does not mean that “representation” is being used in the sense of formula substitution
the word “represents” is nowhere near substitution in the passage you cited
it is in a different sentence expressing a completely different thought about the axiom, unrelated to formula substitution
you can’t just chop up a mathematical paper into a jumble of words and ignore the sentence structure and expect it to mean something
no wonder all your arguments end in meaninglessness lol
