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Mathematicians vs. Philosophers: Cage Match


maarsen

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Who has the best record of actually getting tangible results as to the nature of reality? Round one. 

Emmanuel Kant publishes a proof for the non-existence of asteroids. Unfortunately it comes three months after their discovery.

Leonard Euler replies that it was the only sensible thing Kant wrote. Score one for the mathemeticians. 

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Round Two :

Gödel's incompleteness theorem : Gödel the Philosopher proved that finding a complete and consistent set of axioms for all mathematics is impossible.

David Hilbert got very angry of the result because he already started a program to set a complete set of axioms for the mathematics

Score one for the philosophers

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1 hour ago, Future Null Infinity said:

Round Two :

Gödel's incompleteness theorem : Gödel the Philosopher proved that finding a complete and consistent set of axioms for all mathematics is impossible.

David Hilbert got very angry of the result because he already started a program to set a complete set of axioms for the mathematics

Score one for the philosophers

Surely Gödel can be counted as a mathematician? I mean, if you want to give credit to the philosophers, how about Bertrand Russell, who first pointed out the problem with Hilberts program?

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Mathematicians ultimately reduced to opinions after spending literally minutes debating the truthiness of philosopher Sam Harris' claim that Mormonism is, to a mathematical certainty, more wrong than Christianity.  

Philosopher Sam Harris declares, "made you look!"  :P

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6 hours ago, Roose Boltons Pet Leech said:

Surely Gödel can be counted as a mathematician? I mean, if you want to give credit to the philosophers, how about Bertrand Russell, who first pointed out the problem with Hilberts program?

Thank you very much for the information, I looked it up and I didn't know that Gödel was also a mathematician

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I cannot find any information on Kant and asteroids. It seems that you mean Hegel who claimed some very odd things in astrophysics on spurious a priori arguments (that there could not be a planet between Mars and Jupiter) and was proven wrong with the discovery of the (now dwarf planet) Ceres. But Euler was long dead by then, so you could not really be bothered to fact check ANYTHING about the erroneous claim you used to start the thread...

If you think of this relation as a "cage match", you obviously do not know much about the history of either field and present the most grotesque distortion of their relationship.

Overall, philosophers have been among the greatest fanboys of mathematics ever. Almost all philosophers in history took maths/geometry as the most brilliant example of knowledge and its rational organization and sometimes strove to model their philosophical systems after Euklid's system of geometry. Supposedly there was an inscription above the portal to Plato's Academy in Athens that nobody unschooled in geometry should enter (mêdeis ageometrikos eisito). The (then contemporary) maths figured prominently in the education proposals for philosophers both in Plato's writings and in the "liberal arts" curriculum of the medieval universities. The "higher" portion (quadrivium) of the seven liberal arts is mathematical: arithmetics, geometry, astronomy and music (which was mostly theory of harmony).

There are probably more philosophers in history who were also mathematicians than there is overlap with any other field: Descartes, Leibniz, Bolzano, Boole, Peirce, Russell, Whitehead, Tarski...

There are  exceptions (i.e. math-critical philosophers) but they are very few and such criticism was often restricted to stating the obvious fact that mathematics does not cover everything and/or arguing against the worst philosopher fanboys who wanted to shape all fields of knowledge as closely as possible according to the example of geometry and maths.

Kant was hugely impressed by maths and (especially) Newtonian physics and while not technically schooled he came up in one of his earliest books (1755, still very far from the famous Critiques) with the speculation on the origin of our solar system that turned out to be roughly correct and was later suggested independently and mathematically made more precise by Laplace (Kant-Laplace/nebular hypothesis). It is also historically remarkable that this is a largely mechanistic model as opposed to the theistic origins of the universe/solar system Newton tended to favor. Of course, there is also some speculation that reads like hilarious 18th century sci-fi, e.g. Kant thought that all planets were inhabited and that their inhabitants would be more virtuous if further from the sun because he suggested a connection between the "coarser" material basis of e.g. the Mercury-dwellers and their moral character. (The point was probably that earthlings are roughly in the middle, made from "crooked timber" that is, capable of moral behaviour but having a hard time with it whereas the Mercurians would be more beast-like and the Saturnians angels hardly in need of morals to guide their behavior) He presented this stuff as speculative hypothesis, not as certain a priori knowledge, so it seems rather petty to hold it against his philosophy. (And one will find similar stuff with almost any great professional physicist of the past, I'd wager.)

Kant was also among the first (and it is quite remarkable for someone without schooling in higher maths) to discover the phenomenon of "orientable spaces"; look it up, I don't have time to summarize all that stuff and correct every sophomoric misconception.

 

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2 hours ago, sologdin said:

dunno, kids.  my phone has a calculator in it, but no categorical imperator, which would of course be the coolest computer phone software ever.

"Ugh, FINE, categorical imperator. I wasn't going to treat him as a means only. You never think about the only. Where's that upgrade?"

You probably meant a categorical imperative generator, but isn't the applied side the real bitch?

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nonono quite correct.  was thinking that an effective categorical-imperator provides the appropriate imperative for any historical conjuncture whereby a course of action is identified as consistent (or not) with a principle to be elevated to universal law.

imperator, tell me if i am acting in accordance with natural law when i snort up all the cocaine.

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9 hours ago, Jo498 said:

I cannot find any information on Kant and asteroids. It seems that you mean Hegel who claimed some very odd things in astrophysics on spurious a priori arguments (that there could not be a planet between Mars and Jupiter) and was proven wrong with the discovery of the (now dwarf planet) Ceres. But Euler was long dead by then, so you could not really be bothered to fact check ANYTHING about the erroneous claim you used to start the thread...

If you think of this relation as a "cage match", you obviously do not know much about the history of either field and present the most grotesque distortion of their relationship.

Overall, philosophers have been among the greatest fanboys of mathematics ever. Almost all philosophers in history took maths/geometry as the most brilliant example of knowledge and its rational organization and sometimes strove to model their philosophical systems after Euklid's system of geometry. Supposedly there was an inscription above the portal to Plato's Academy in Athens that nobody unschooled in geometry should enter (mêdeis ageometrikos eisito). The (then contemporary) maths figured prominently in the education proposals for philosophers both in Plato's writings and in the "liberal arts" curriculum of the medieval universities. The "higher" portion (quadrivium) of the seven liberal arts is mathematical: arithmetics, geometry, astronomy and music (which was mostly theory of harmony).

There are probably more philosophers in history who were also mathematicians than there is overlap with any other field: Descartes, Leibniz, Bolzano, Boole, Peirce, Russell, Whitehead, Tarski...

There are  exceptions (i.e. math-critical philosophers) but they are very few and such criticism was often restricted to stating the obvious fact that mathematics does not cover everything and/or arguing against the worst philosopher fanboys who wanted to shape all fields of knowledge as closely as possible according to the example of geometry and maths.

Kant was hugely impressed by maths and (especially) Newtonian physics and while not technically schooled he came up in one of his earliest books (1755, still very far from the famous Critiques) with the speculation on the origin of our solar system that turned out to be roughly correct and was later suggested independently and mathematically made more precise by Laplace (Kant-Laplace/nebular hypothesis). It is also historically remarkable that this is a largely mechanistic model as opposed to the theistic origins of the universe/solar system Newton tended to favor. Of course, there is also some speculation that reads like hilarious 18th century sci-fi, e.g. Kant thought that all planets were inhabited and that their inhabitants would be more virtuous if further from the sun because he suggested a connection between the "coarser" material basis of e.g. the Mercury-dwellers and their moral character. (The point was probably that earthlings are roughly in the middle, made from "crooked timber" that is, capable of moral behaviour but having a hard time with it whereas the Mercurians would be more beast-like and the Saturnians angels hardly in need of morals to guide their behavior) He presented this stuff as speculative hypothesis, not as certain a priori knowledge, so it seems rather petty to hold it against his philosophy. (And one will find similar stuff with almost any great professional physicist of the past, I'd wager.)

Kant was also among the first (and it is quite remarkable for someone without schooling in higher maths) to discover the phenomenon of "orientable spaces"; look it up, I don't have time to summarize all that stuff and correct every sophomoric misconception.

 

Kant's nebula theory was disproved by Maxwell, using mathematics. Ideas without mathematics behind them tend to be ....nebulous.

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Tolkien contending that the universe was created by the music of the Ainur borne out by the mathematics of string theory, in that the fabric of everything is nought but manifold vibrations?*

 

*of inherently massless sub-Planck-length one-dimensional loops.

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Here is a problem that can be solved using math, but not philosophy. A work schedule needs to be posted that is 6 weeks long, covers three shifts and 2 12 hour weekend shifts with everyone working a weekend, an afternoon shift and a midnight shift once every 6 weeks. All shifts and hours of work have to be fair and equitable as this is a union shop. When you have 12 people, this works out really elegantly. But then someone goes off sick for an extended period. We had hours of discussion, and that is not an exaggeration, on how to create a fair and equitable discussion. It was pointed out by the mathematically inclined that 11 is a prime number and nothing divides into it. No matter how much talk was done, 11 remained a prime number. Finally it went to mediation to be solved.  The mediator immediately realized 11 is prime and told the employer to pay up for posting an inequitable schedule.

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18 hours ago, Maester Drew said:

Do physicists count as mathematicians in this round?

Until the 20th century or so, there was little difference between those two or between either of them and philosophers. Many of the truly great (Leibniz, Descartes, Newton, etc.) made contributions to all three disciplines. Even today, a theoretical physicist is effectively a practical flavor of mathematician and both physicists and mathematicians dabble in philosophy.

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