Tuesday, July 03, 2012

Thesis, antithesis, synthesis: Hegel is spinning in his grave

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13 comments:

Arelcao Akleos said...

So he wrote the bulk of both sides? Now there is A Man for All Reasons

Arelcao Akleos said...

If he has Hegel spinning in both directions at the same time, won't it be a null thesis?

Tecumseh said...

Spinning like a gee-haw whammy diddle. Or the Coanda spinning top.

Mr roT said...

Hegel had nothing to do with Physics.

Tecumseh said...

Ah, mais non, mais non, says Charly:

The mechanistic empiricists were unable to classify multidimensional geometry in their system and were faced with the choice of recognising a mathematically possible geometry but excluding the rest from mathematics. The formalists, who have transformed mathematics into a sort of chess game with empty symbols, are not in a position to explain its role in technology, science and statistics. The conventionalists (Henri Poincare), who hold that mathematical concepts and operations are merely convenient, mentally economical conventions, thus avoid the question posed and are unable to make any statement about the development of these concepts.

Thus none of these philosophical schools, which all grasp one and only one side of reality, is in a position to understand the link between mathematics and practice and its laws of development. Hegel alone gave mathematics a definition such as grasped the essence of the matter, a definition which, quite independently of Hegel's views, is actually profoundly materialist.

Tecumseh said...

Just like Hegel, Marx is closest to Lagrange in his proof of analysis. But his conception of Lagrange is fundamentally different from Hegel's conception. Hegel conceives Lagrange, as we have already seen, according to the usual shallow interpretation, so that Lagrange appears as a typical formalist and conventionalist introducing the fundamental concepts of analysis into mathematics in a purely external and arbitrary manner. What Marx admires about him, on the contrary, is the exact opposite; the fact that Lagrange uncovers the connection between analysis and algebra and that he shows how analysis grows out of algebra. 'The real and therefore the simplest connections between the new and the old', Marx writes 'are always discovered as soon as the new takes on a rounded-out form, and one can say that differential calculus obtained this relation through the theorems of Taylor and MacLaurin. It thus fell to Lagrange to be the first to reduce differential calculus to a strictly algebraic basis.'

Hah! PDEs are just algebra. Told you so.

Mr roT said...

Formalism schmormalism. What are these fags talkin' about?

Mr roT said...

If PDE are just pédé algebra, then what's alg-top?

Tecumseh said...

Ask Karlie.

Mr roT said...

Hirzebruch was a Fritz, not a Karl.

Tecumseh said...

Watch his last lecture, and let me know if you catch my off-the-top-of-my-head computation.

Mr roT said...

link?

Tecumseh said...

No link. Just go to the House that Fritz Built, and click on things. Second part of the lecture. Or ask Mr Leverkuhn, I think he was there, too.