Most mathematician will never have a theorem named after them because they are just hacks doing normal mathematics.

in other words many mathematicians are highly intelligent but they will never be a ponicare or a godel etc because they cant see the cracks in the paradigm.

It takes a very rare person to see the cracks but because most mathematicians just repeat what they are taught they are unable to bring about revolutions in mathematics.

I think this has to do with their education. They just soak up what they are told but never really question or understand the fundamental concepts.

this applies to all areas of life most people are just hacks -highly intelligent but no genius
they just do their work like a technician following allgorythims of research
allgorythms of thinking never being able to think outside the box

most of you reading this will never amount to much in your area not because you are not intelligent but because you will just remain a hack locked in an algorythm of action and thinking -due to your education- with no real imagination or original abilities

most mathematicians can repeat godel proof or skolems solution to his paradox
but they will never have a theorem named after them because they are nothing but intelligent hacks.
take skolem he saw a crack and came up with his paradox
then his solution
but most of you will never see any cracks because your mind is blinded by your education no matter how intelligent you are
you will make lots of money be successful
but
completely forgotten in the historical record
you will amount to nothing but a well paid hack
you might write books but they will be as forgotten as you will be
you will never stand out from the hacks no matter how well you know your maths- because you cant see the cracks

Look Dean, if you’re trying to rally the nihilists, you have to remember, most of them are just stupid teenagers who don’t even understand what they believe. What makes you think they’re going to have the slightest understanding of complex mathematics? Why don’t you bitch about the president or something. That might make you more popular.

To an extent her assessment of creative thought is sort of correct. Your average mathematician doesn’t make a revolution. In general, great mathematics however is not the result of the kind of stuff Godel did. Yes, everyone knows who Godel is, but in the world of math, however interesting, he just isn’t that important. You don’t do great work by challenging the foundations or whathaveyou.

This stuff is the theoretical equivalent of housekeeping.

thats only because like denali you are not good enough to see the cracks so tell me what godel meant by true statements

if you cant then his theorem is meaningless

godel used an invalid axiom thus his proof is invalid
godel admitts he uses imprediative statements -philosophr say these are invalid- thus his proof is invalid

We should really keep these arguments restricted to one thread, but hey, I’m not one to quibble about details.

Irrelevant

Nope.

…Undetermined, but so far the best argument in your arsenal.

Well, I’d be interested to know the definition of impredicativity you’re operating under. Impredicative statements, as per the Wikipedia(yay) definition, are things which are used all the time in math. Now, maybe some people don’t like them, but frankly, they’re fringe.

I mean, no offense, but at least half the things you say are nonsense; do you really think that you are in a better position to challenge a long-since-irrelevant theorem that plenty of people familiar with the field had much to gain by invalidating? To actually make Godel’s proof (or something equivalent, and that is the point here because when you get right down to it a proof is largely just something which satisfies mathematicians) impossible you would need to gut some pretty basic mathematics. Godel used a particular set of axioms and whatnot, but you’re getting lost in the details if you think that it couldn’t be possible otherwise. That was the key and what is powerful and what people pay care about: any mathematical system has holes which can be exploited in a similar fashion.

The fact that alternatives exist is evidence of the fact that everyone knows that even if we start rewriting some foundational stuff the principles of Godel’s proof will still work. Foundational stuff is just housekeeping; no one needs to care about it when they write actual proofs because if it really started fuxing things up, there would be something wrong with the foundational stuff. Calculus existed for hundreds of years before it was done “right”. Basic arithmetic existed thousands of years before Peano penned his axioms; why?

Begging the question is not invalid because it is self-referencing. It is a particular kind of self-reference. You can absolutely reference a statement you mean to prove before you prove it.

But, yeah, I’m with D. Most math isn’t big novelties like Godel.

Wait… are you attempting a priori to rule out the concept of a nested metalanguage? Just because you don’t like it? I think better yet you’re messing up the concept of a nested metalanguage: Godel’s statements referenced themselves in a way which is completely compatible with a number system and that was what was potent about them. You can’t just dismiss the proof without throwing math out the window because Godel’s concepts of computability etc. all follow immediately from the basics of an arithmetical system. What is relevant here is that you can’t disprove Godel without fuxing all of math, in which case your arguing about a result in a system you don’t even believe in. And if you can’t appreciate the absurdity in that you must have a terribly impoverished emotional life.

You are deeply confused about what Godel actually did, lost as it were in the trap of natural language approximations of mathematics.

Still, most of your sources are either long-since-has-beens or never-weres. Nothing that I have read has revealed a genuine understanding of the functioning of mathematics rather than just a pedantic familiarity with the history of logical philosophy. If you want to do mathematics, you’re going to have to come to our level.

By the way, I still think when you get to this level of mathematical philosophy, we’re debating stuff that is neither useful, nor true (i.e. constructs), in which case I can only say that it doesn’t make sense not to defer to the mathematicians. I mean logicians are full of even more shit than mathematicians; who are we going to trust?

godel himself said impredicative statements can make maths false and you cant say he did not have a genuine understanding of the functioning of mathematics

and texts books on logic say they are outlawed

its maths problem if they use outlawed statements- to fucking bad if maths has to be thrown out the window- what maths is immune form criticism just because it works

you see this is why you are just a hack and will be a never-weres
you cant see the cracks for having your face pushed in them

and

we dont defer to mathematicians because they are dumb shits
mathematician cant tell us what numbers are with out being circular ie violating the vicious circle principle

go see my thread called “mathematician cant tell us what numbers are”

Let’s just face it, big G just isn’t as important as people like to think he is. Nor was Russel, or any number of other people. And Wittgenstein (while I respect him philosophically) was a hack and a half mathematically.

Why actually yes. I’m a philosophical skeptic; logicians can say whatever they want but they’re still full of crap. You’re throwing an a prior construct which produces nothing of note against one that produces something; I see no reason to give more credence to the logicians other than the emperor’s clothes are supposed to be even more fabulous in their case.

While the first statement is not necessarily false, the second one is irrelevant because the vast majority of people working in math don’t give a crap about logic; there are any number of more useful and interesting things to do.

just like a religous person says about criticism of his god
and

you sound exactly like a religious person who in the face of logical arguments against god says well it works for me

you have turned maths into your religion and like all religion are impervious to logic
hahahahahhaha bow down in the temple of maths and lick it ass you zealot
you must be very scared and need like all religious people an absolute to give you comfort

You can spin it however you want ladyjane, but when you get right down to it this is nothing but language games. Likening belief in math to belief in God is the grossest silliness you’ve come up with yet. Math gets the job done; it passes all tests you can throw at it when it comes to dealing with anything that isn’t blatantly a figment of the human imagination. This is like saying that you have logically proven that wrenches are useless; if anyone said that, you’d say “WTF?”

You come up with cherry-picked decontextualized quotes, and completely debatable laws of “textbook logic” which are nothing but a priori nonsense anyway. The question of whether or not math means anything is absurd when dissociated from whether or not it is useful.

The question of whether or not math is meaningful is nonsense to begin with. For the position I expressed in my last position to hold, I don’t need to “believe” in math (if that makes an iota of sense anyway); I only need to use math, and have it get me the results I want.

As you’ve pointed out, math is an “ad hoc” discipline. If you expose a flaw, someone can (and will) come along to plug it. You can’t disprove it; you can’t invalidate it; you can’t challenge it. It is immune to logic because if the standards of logic change, the system will change to accomodate it. IT IS A PRIORI.

Preferences change ladyjane; your concept of logic as some sort of thing which can be true or false (as you’ve demonstrated elsewhere on this forum) only shows how naive you are when it comes to this stuff.

PS I’m 90% certain a bunch of your sources/arguments are so confused they don’t know which way is up, but don’t take my word for it; you have your beliefs too, but if you want some empirical evidence about devotion and the individual, consider how many better argued and more eloquent posts on this sight have failed to sway you

PPS: Your capacity to take on the absolute simplest and least charitable position in other people’s posts make your dialectic a bit…grating. You might want to work on that.

PPPS: Now if you’ll excuse me, Calculus demands a burnt offering…

your maths cant even tell us what numbers are with out circularity
or
if they exist or just figments of a mathematicians imagination- just like religiou fictions
hahahaha