did you just have a final on this?

What do you mean?

Oh, a final exam... No. We don't talk about philosophy of mathematics at the university, unfortunately; it's my hobby.

+1

for me it's all set theory. does the category of "all categories" itself fit in a category?

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Same here. I'm not sure about that, but I guess not, since categories are classes, right? And a proper class cannot be a member of any class.

Sets are artificial; mind dependent. As are categories. So it's really not about determining whether "all categories" is belongs in a category as Defining whether it does. ...did I add something?

Not for me, you didn't. By the way, think about this: since classes are abbreviations for formulas and formulas are finite strings of characters in a sense, then there should be only countably many classes, and they would even form a set... of course this is wrong, because classes are arbitrary collections and cannot be exhausted by finite strings of marks on paper. Even all the subsets of the set of natural numbers cannot be described in such a way. But how about INFINITE strings of characters? We may not

be able to write them down, but they exist somewhere out there in a sense.

Oh, that's a shame that I didn't contribute. I don't know that I understand you. Are you thinking of sets as abstractly existing universal entities that are just exhibited at one time or another? Because If that's the case I cannot agree. What we have in the universe is a collection of simple things that we group. The sets do not exist outside of the mind. Incidentally, the only numbers I believe in are zero and one. All other numbers are mere modifications and therefore unreal.

Wow. That's a very peculiar philosophy, there, and I strongly disagree with you. I have no idea how to call this type of thinking, though... Platonists, such as myself, would absolutely dismiss what you're saying; so would formalists, I believe, for it is impossible to have formal systems without the help of arithmetic; and intuitionists regard natural numbers as the underlying foundation of all mathematics and intuition, so they would pretty much disagree, too.

No, I do not think of sets as abstract entities exibiting themselves at one time or another; I regard them as abstract entities that are timeless. Here's a funny argument for the empty set: even if there were no sets at all, there would therefore be nothing, hence, the empty set would exist.

Oh, I'm a nihilist, so I take a lot of sh*t from pretty much all other philosophers. The paradox of the null set is an interesting one, but since I dismiss the notion of sets it is solved: If nothing exists, then the null set does not exist because Nothing exists... Though I admit I'm not very knowledgeable on mathematical philosophy. Can you suggest any decent reading material on the subject?

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Hmm... how about anything written by Gregory Chaitin, like "Meta Math!" or "Conversations with a Mathematician"? He's actually more of a computer scientist, and he advocates a theory called "Digital Philosophy" which basically says that the Universe is a giant computer, and everything is 0's and 1's. His books are very informally written and mixed with humour.

Also, vote 5, please.

Of course, Thanks.

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http://plato.stanford.edu/entries/russell-paradox/

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What does that have to do with the above discussion? That's a very good site, by the way.

Oh, right, the set of all sets...

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I get strange, pleasant Dresden Codak-ish vibes.

+2

This is classy. Also Philosophy of Math was a fun class.

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Wow, you had that? How did the exams look like?

The exams focused a lot on fallacies and how to prove an argument false using different patterns of premise/conclusion and plugging them in as mathematical formulae. It was a pretty interesting class, because it allowed me to prove to someone why their argument was flawed mathematically.

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Also we worked on proofs using complex numbers. http://www.math.toronto.edu/mathnet/falseProofs/second1eq2.html was kind of what we worked on.

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Interesting. So you used mathematical proofs to dismiss someone's philosophical arguments, too? Also, were there discssions where you would present your views on the philosophy of math?

Yes and not really. The class wasn't advanced enough as a whole to do that, the teacher had to curtail most of his discussions in order to better explain proof mechanics. We did however have an open ended paper where we were supposed to pick a philosopher then try and figure out whether his argument was valid then show why/why not. Can't quite remember who I picked atm, the class was 3 years ago. Now that I think about it, it probably should only be offered to upper classmen.

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Look what I found... http://en.calameo.com/read/000003545197ea50ac57f

For a few seconds, it looked like Daniel Craig fighting Sean Connery. Paired with the 007-ish music, this ytmnd is quite confusing.

+2

"I am even most astonished by the fact that even in mathematical circles the power of suggestion of a single man, however full of temperament and inventiveness, is capable of having the most improbable and eccentric effects." -- Hilbert talking about Brouwer in 1927.

Hilbert is the one with the hat, by the way. And he advocated formalism; Brouwer advocated intuitionism.

No two against one match Whitehead and Russell vs. Gödel. You could also do Heidegger vs. Husserl, though their disagreement is more on the level of semantics and not mathematics (both reject the mathematicization of logic - Heidegger initially on the ground that the employment of the concept of function obscures the meaning and meaning changes of judgments).

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Vote 5, please.

Or whatever else you wanna give me.

Were Russell and Gödel really opposed? As far as I know, at least when he was young, Russell was a platonist, too (logicism was a program, not really a view, I believe). And then later something happened to him. At the end of his life, he even quit Mathematics altogether, claiming that all of it is just a heap of tautologies. Forgot about the incompleteness theorems or what...?

Well, they were opposed in the sense that Gödel's theorem undermines the entire project of the Principia Mathematica which was to be the crowning jewel of Russell and Whitehead's work on the foundations of mathematics. I don't know what Russell thought after Gödel showed him to be wrong. I mean, I suppose they agreed in that Russell realized that he was wrong.

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History repeats itself: First it was Russell who sent a letter to frege right after his Grundlagen der Arithmetik was completed, explaining the Russell Paradox and thus destroying his system... And then, 29 years later, comes Gödel and destroys the hopes of Principia Mathematica.

By the way, Russell worked for the NWO. Seriously, he had books where he wrote how in the future there would be a slave class that, in help of eugenics, drugs and various manipulations, could be made into an artificial state of happiness, but in reality, they would be slaves for the elites. And I used to respect the man...

Logicism is a doble edged sword. An the 1 hand you hav deviretions of mat from lojic, witch is kul, but onn the oder hend yuo hev the stupide tipe thery wich gest rid of alot of usefool thinks in matemathisc and iz arfiticial.

I think they were kind of opposed, as Russell was (at least later) a nominalist.

"I think they were kind of opposed, as Russell was (at least later) a nominalist." Really? How do you mean? That term has a long and varied history in philosophy.

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In one of his book (The Principles of Mathematics, I think), he literally says something like, "since numbers and other mathematical objects can be reduced to logic, they are mere fictions" (paraphrasing, of course).

hey guys cool are we takling about philosophy of the matrix because neo in that movie is like a jesus and plus the wachowski brothers read a book once it was the philosophy pop-up book

No, we're talking about philosophy of mathematics. Though there may be some connection...

DUDE YOU DON'T KNOW I SEEN THE MATRIX LIKE 50 TIMES ITS ABOUT PHILOSOPHY I TOOK IT AT THE LEARNING ANNEX ON 89TH & PEACE PIPE LANE IT WAS CALLED ''PHILOSOPHIES AND IDEA IN MATRIX AN READIN BOOKS" I bought the texd buch at the... the book drive

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Vote 5, please.

NO WAY GENTILE

-1

+1 for making me feel, for the briefest of moments, that my philosophy degree wasn't a waste of time

+1

:)

When is the Reptillian Agenda YTMND coming?

started the gif, but work has been crazy lately and i haven't been YTMNDing as much lately. i'm hoping to put a big dent in it this weekend

+1

Waste Management keeping you busy? Lol, philosophy.

+1

McLOL!

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As a B.A. in anthropology, I feel the numbness where your pain once was. McUnemployed.

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That's Just The Power Of The Arts!

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Do what I'm doing and ditch whatever ideals sent you in that liberal arts direction and get your MBA. That's the Power of Love by Chuy Luis and the Blues.

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Well, I chose mathematical studies solely because of my love for Math(s). I don't even know what job will I be able to get, and I do not really care.

An M.S. in math will make you marketable. Before you know it you'll be working as a petroleum engineer for Halliburton. Lol, ideals.

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I got an IT/programming diploma this year and landed a cool job, but I really just want to dance.

+1

I would rather want to become a professional mathematician.

^Without the "want".

And the "to".

and a three and a four and a....

+1

Wouldn't you rather be a philosophical mathematician

+1

No, a philosophically INCLINED mathematician.

*any academic subject* tmnd = 5

+1

*looks around uncomfortably, votes five so he looks smart*

+2

controversy

+1

Oh, I'm a nihilist, so I take a lot of sh*t from pretty much all other philosophers. The paradox of the null set is an interesting one, but since I dismiss the notion of sets it is solved: If nothing exists, then the null set does not exist because Nothing exists... Though I admit I'm not very knowledgeable on mathematical philosophy. Can you suggest any decent reading material on the subject?

F*ck. ignore this, I've moved it.

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david hilbert is a doble edged sword.

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(on the 1 hand you have the 23 probelms wich are hard. on the other hand brower beleved difarently and casued a callous strugle betwen the two. on the other hand godle said "EPIC FALE" and the rich would get richer. the problem is biz markie remixing vapors for corporate sponsers.)

+1

Triple edged sword?

You Must Finish Mechanical Engineering 205 At The University of Texas. Finish it now.

Someone should add Koen and Nedry, really mix it up. I would but I absolutely suck.

Pretentious Site is Pretentious

-1

You don't get it, do you?