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Introduction to Mathematical Philosophy

73 points by equilibrium 13y ago

saint-loup 13y ago
>> Week Eight: Quantum Logic (orthocomplemented lattices, projections, Gleason's Theorem, probability and logic). Naive question: wasn't quantum logic a somewhat failed endeavour and a thing of the past?
- bobwaycott 13y ago
  It is not a failed philosophical endeavor, and there are still philosophers engaged in the field. It had an early period beginning in the 1930s, and another strong period from the '50s-70s. It has been helpful to the understanding and development of probability theory, and continues to be applied and investigated, including in current scientific experimentation. The rise of quantum computing has created another contemporary dimension to the field. As it is, it grapples with properly understanding and formulating logic and correct perceptions and descriptions of the world by building on classical logic in light of developments in quantum mechanics. I doubt we'll see it 'fail' and fade into obscurity anytime soon. It's not exactly Cartesian philosophy.
  - Jimmy 13y ago
    And Cartesian dualism is still alive with some philosophers... ideas don't die easily.
    - chrisdevereux 13y ago
      Cartesian dualism (aka substance dualism, the idea that mind and body are distinct objects) isn't particularly popular in mainstream philosophy. Property dualism on the other hand (the idea that eg., mental states and physical states can't be fully explained in terms of each other, but that people possess both) is quite popular.
  - chrisdevereux 13y ago
    Nitpick: Cartesian philosophy might be obscure, but I don't think it's a failed theory in the sense that, say, the phlogiston theory of combustion is a failed theory. Even if it was ultimately discarded by philosophers, it allowed the modern field of epistemology to develop (which wouldn't have really been possible previously), and (arguably) contributed to the development of physics by excluding our mental vocabulary (thoughts, experiences, beliefs, etc.) from the study of the physical world. At the expense of our ability to understand said mental vocabulary perhaps, but an improvement on what had been thought previously. I'd compare it to how a particular module in a program might be important for some time, since it provides some basic functionality that is required in order to develop the rest of the program, but that after some time is no longer needed and refactored out in favour of something more sophisticated.
    - bobwaycott 13y ago
      Of course, and my apologies because I was unclear with my language. I was using Cartesianism as an example of faded, not failed, philosophical field. That was rather foolish of me to word it so lazily. Thanks for the nitpick and pointing out all the great things that resulted.
loevborg 13y ago
Having studied at the same university (though not with either of the professors), I can confirm that both teachers are respected professors and experts in their fields (logic and the philosophy of science). I'm sure it'll be an interesting course.
javert 13y ago
I'm sure there is some interesting and valid material here, but the overall project of doing philosophy via mathematics is nonsense. As a sidenote, you acutally need philosophy to validate mathematics, not the other way around.
- Schiphol 13y ago
  You should probably read more of what these theorists call mathematical philosophy (I recommend reading a couple of numbers of Erkenntnis, edited by Leitgeb, and perhaps taking this course) before passing such a harsh judgement. As a sidenote, the kind of foundationalism about mathematics that you seem to endorse is not the only option in the philosophy of mathematics -- although this issue is largely orthogonal to the prospects of mathematical philosophy.
  - brg 13y ago
    I disagree. There is an asymmetric relationship between philosophy and mathematics that belies the lack of influence and low import of the former. Science, mathematics, and even art can all continue at no diminished pace without input from philosophy's sophists.
- chris_wot 13y ago
  As a sidenote, you acutally need philosophy to validate mathematics, not the other way around. Forgive my ignorance, but why is that?
  - thebooktocome 13y ago
    It was philosophy that saved the world from (classical) infinitesimals, and spurred the development of modern analysis. http://en.wikipedia.org/wiki/The_Analyst http://en.wikipedia.org/wiki/The_Analyst (No, classical infinitesimals bear no resemblance to the infinitesimals of nonstandard analysis.)

73 points by equilibrium 13y ago

>> Week Eight: Quantum Logic (orthocomplemented lattices, projections, Gleason's Theorem, probability and logic). Naive question: wasn't quantum logic a somewhat failed endeavour and a thing of the past?

bobwaycott 13y ago
It is not a failed philosophical endeavor, and there are still philosophers engaged in the field. It had an early period beginning in the 1930s, and another strong period from the '50s-70s. It has been helpful to the understanding and development of probability theory, and continues to be applied and investigated, including in current scientific experimentation. The rise of quantum computing has created another contemporary dimension to the field. As it is, it grapples with properly understanding and formulating logic and correct perceptions and descriptions of the world by building on classical logic in light of developments in quantum mechanics. I doubt we'll see it 'fail' and fade into obscurity anytime soon. It's not exactly Cartesian philosophy.
- Jimmy 13y ago
  And Cartesian dualism is still alive with some philosophers... ideas don't die easily.
  - chrisdevereux 13y ago
    Cartesian dualism (aka substance dualism, the idea that mind and body are distinct objects) isn't particularly popular in mainstream philosophy. Property dualism on the other hand (the idea that eg., mental states and physical states can't be fully explained in terms of each other, but that people possess both) is quite popular.
- chrisdevereux 13y ago
  Nitpick: Cartesian philosophy might be obscure, but I don't think it's a failed theory in the sense that, say, the phlogiston theory of combustion is a failed theory. Even if it was ultimately discarded by philosophers, it allowed the modern field of epistemology to develop (which wouldn't have really been possible previously), and (arguably) contributed to the development of physics by excluding our mental vocabulary (thoughts, experiences, beliefs, etc.) from the study of the physical world. At the expense of our ability to understand said mental vocabulary perhaps, but an improvement on what had been thought previously. I'd compare it to how a particular module in a program might be important for some time, since it provides some basic functionality that is required in order to develop the rest of the program, but that after some time is no longer needed and refactored out in favour of something more sophisticated.
  - bobwaycott 13y ago
    Of course, and my apologies because I was unclear with my language. I was using Cartesianism as an example of faded, not failed, philosophical field. That was rather foolish of me to word it so lazily. Thanks for the nitpick and pointing out all the great things that resulted.

loevborg 13y ago

Having studied at the same university (though not with either of the professors), I can confirm that both teachers are respected professors and experts in their fields (logic and the philosophy of science). I'm sure it'll be an interesting course.

javert 13y ago

I'm sure there is some interesting and valid material here, but the overall project of doing philosophy via mathematics is nonsense. As a sidenote, you acutally need philosophy to validate mathematics, not the other way around.

Schiphol 13y ago
You should probably read more of what these theorists call mathematical philosophy (I recommend reading a couple of numbers of Erkenntnis, edited by Leitgeb, and perhaps taking this course) before passing such a harsh judgement. As a sidenote, the kind of foundationalism about mathematics that you seem to endorse is not the only option in the philosophy of mathematics -- although this issue is largely orthogonal to the prospects of mathematical philosophy.
- brg 13y ago
  I disagree. There is an asymmetric relationship between philosophy and mathematics that belies the lack of influence and low import of the former. Science, mathematics, and even art can all continue at no diminished pace without input from philosophy's sophists.
chris_wot 13y ago
As a sidenote, you acutally need philosophy to validate mathematics, not the other way around. Forgive my ignorance, but why is that?
- thebooktocome 13y ago
  It was philosophy that saved the world from (classical) infinitesimals, and spurred the development of modern analysis. http://en.wikipedia.org/wiki/The_Analyst http://en.wikipedia.org/wiki/The_Analyst (No, classical infinitesimals bear no resemblance to the infinitesimals of nonstandard analysis.)