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No, on the contrary. Mathematics is about structures within, using its own language. Natural language is completely separated from mathematics (although most ma

No, on the contrary. Mathematics is about structures within, using its own language. Natural language is completely separated from mathematics (although most mathematicians use natural language to communicate mathematics).

kragen 1y ago
Only pure mathematics fits your description, and while perhaps it is ontologically prior to applied mathematics and science, the human activity of studying pure mathematics seems to have historically arisen from applied mathematics and never entirely escaped it, while applied mathematics seems to have historically arisen from science. And the first step in reducing some phenomenon of the contingent world, such as "heat" or "work" or "light" or "circle" or "strategy", to an abstraction you can apply math to, is precisely to "take[] some word from the natural language and tries to [invent] a formal definition for it with necessary and sufficient conditions." That's how you start applying the hypothetico-deductive method to anything. You might argue that physics and math aren't "philosophy", but Plato, Newton, Kant, and Gauss would say you were full of shit.
- Retric 1y ago
  That’s more a modern interpretation coloring history. “Applied mathematics” has always disagreed with reality. It’s only recently that we’ve gotten so good at understanding the world that the differences seem less pronounced. Ancient Egyptians didn’t know why the height of a pile of grain doesn’t grow linearly with the amount of grain in a column etc, instead mathematics was seen as a useful shortcut. Which has always been what applied mathematics ends up as. > You might argue that physics and math aren't "philosophy" There’s a far longer list of famous people including philosophers, scientists, etc who disagree with that idea than agree with it. Fundamentally they operate in different directions with philosophy attacking from the top down and science and mathematics from the bottom up. Plato specifically disagreed with the notion that observation alone can lead to truth.
  - kragen 1y ago
    Nonsense. You seem to want to redefine "philosophy" to mean "philosophy that doesn't work", which admittedly is a widespread definition today among the common people. But if we stipulate that definition, it has the practical problem that we cannot tell whether what Chalmers is up to here is "philosophy" or not until we find out whether it was a productive line of inquiry or not, perhaps in two or three hundred years. Whether Plato believed that you could figure out the area of a triangle or the composition of matter from pure logic, or whether that required empirical observation, is irrelevant to the fact that he considered figuring out the area of a triangle or the composition of matter to be properly part of philosophy. This is an assertion that it would never have occurred to anyone to challenge until very recently, with the advent of the useless popular definition of "philosophy" you seem to be championing for some random reason.
    - Retric 1y ago
      Sure, nonsense meanwhile you seem to misunderstand one of the earliest philosophical debates. Plato specifically argued for truth independent of physical reality where Aristotle believed in empiricism. As to your edit> You seem to want to redefine "philosophy" to mean "philosophy that doesn't work", which admittedly is a widespread definition today among the common people. But if we stipulate that definition, it has the practical problem that we cannot tell whether what Chalmers is up to here is "philosophy" or not until we find out whether it was a productive line of inquiry or not, perhaps in two or three hundred years. Hardly, I specifically mentioned that some philosophers are open to observation but they get there as a philosophical stance first. Meanwhile Thomas Aquinas and many others argued that truth flowed from religious text. It’s easy to dismiss such reasoning especially when it disagrees with observed reality but that doesn’t erase such people from history. Edit2: I’m done responding to your edits.
      - dr_dshiv 1y ago
        They are united together in Pythagoreanism. Which Newton, Copernicus and Galileo claimed to be… For a Pythagorean, the world is made of math: “All is Number.” The math exists in immaterial reality — and harmonies in math manifested as harmonies in the material world (ie “harmony of the spheres”). Plato merely critiqued that a focus on empirical mathematical modeling distracted from how geometry and other pure mathematics revealed basic truths about reality. I can provide source texts as well.

kragen 1y ago

Only pure mathematics fits your description, and while perhaps it is ontologically prior to applied mathematics and science, the human activity of studying pure mathematics seems to have historically arisen from applied mathematics and never entirely escaped it, while applied mathematics seems to have historically arisen from science. And the first step in reducing some phenomenon of the contingent world, such as "heat" or "work" or "light" or "circle" or "strategy", to an abstraction you can apply math to, is precisely to "take[] some word from the natural language and tries to [invent] a formal definition for it with necessary and sufficient conditions." That's how you start applying the hypothetico-deductive method to anything. You might argue that physics and math aren't "philosophy", but Plato, Newton, Kant, and Gauss would say you were full of shit.

Retric 1y ago
That’s more a modern interpretation coloring history. “Applied mathematics” has always disagreed with reality. It’s only recently that we’ve gotten so good at understanding the world that the differences seem less pronounced. Ancient Egyptians didn’t know why the height of a pile of grain doesn’t grow linearly with the amount of grain in a column etc, instead mathematics was seen as a useful shortcut. Which has always been what applied mathematics ends up as. > You might argue that physics and math aren't "philosophy" There’s a far longer list of famous people including philosophers, scientists, etc who disagree with that idea than agree with it. Fundamentally they operate in different directions with philosophy attacking from the top down and science and mathematics from the bottom up. Plato specifically disagreed with the notion that observation alone can lead to truth.
- kragen 1y ago
  Nonsense. You seem to want to redefine "philosophy" to mean "philosophy that doesn't work", which admittedly is a widespread definition today among the common people. But if we stipulate that definition, it has the practical problem that we cannot tell whether what Chalmers is up to here is "philosophy" or not until we find out whether it was a productive line of inquiry or not, perhaps in two or three hundred years. Whether Plato believed that you could figure out the area of a triangle or the composition of matter from pure logic, or whether that required empirical observation, is irrelevant to the fact that he considered figuring out the area of a triangle or the composition of matter to be properly part of philosophy. This is an assertion that it would never have occurred to anyone to challenge until very recently, with the advent of the useless popular definition of "philosophy" you seem to be championing for some random reason.
  - Retric 1y ago
    Sure, nonsense meanwhile you seem to misunderstand one of the earliest philosophical debates. Plato specifically argued for truth independent of physical reality where Aristotle believed in empiricism. As to your edit> You seem to want to redefine "philosophy" to mean "philosophy that doesn't work", which admittedly is a widespread definition today among the common people. But if we stipulate that definition, it has the practical problem that we cannot tell whether what Chalmers is up to here is "philosophy" or not until we find out whether it was a productive line of inquiry or not, perhaps in two or three hundred years. Hardly, I specifically mentioned that some philosophers are open to observation but they get there as a philosophical stance first. Meanwhile Thomas Aquinas and many others argued that truth flowed from religious text. It’s easy to dismiss such reasoning especially when it disagrees with observed reality but that doesn’t erase such people from history. Edit2: I’m done responding to your edits.
    - dr_dshiv 1y ago
      They are united together in Pythagoreanism. Which Newton, Copernicus and Galileo claimed to be… For a Pythagorean, the world is made of math: “All is Number.” The math exists in immaterial reality — and harmonies in math manifested as harmonies in the material world (ie “harmony of the spheres”). Plato merely critiqued that a focus on empirical mathematical modeling distracted from how geometry and other pure mathematics revealed basic truths about reality. I can provide source texts as well.