• Gurgeh
    8
    First there was philosophy, which was about finding out about the world by postulating, then science became a subbranch of philosophy, which is about finding out things about the world by postulating which you can empirically verify, then maths became a subbranch of science, which is about finding out things about the world from first principles. So will the leading branch of philosophy now be a subbranch of mathematics, and then the most cutting edge branch will be a subbranch of that, and so on? Like maybe from here it could get into the methodical establishment of first principles.
  • Pfhorrest
    2.5k
    That’s not an accurate historical account. Philosophy wasn’t and isn’t always just about speculating, and mathematics is older than the branching of science off of philosophy, and used to be mixed up with philosophy itself (as with Pythagoras).
  • Gurgeh
    8
    But the subbranches are correct and they acquired general interest in that order.
  • Adam's Off Ox
    52
    While I don't fully subscribe to the order of the history of the concepts you have laid out, I also don't deny that some subbranches of older disciplines bring about more interesting discoveries.

    Would you be willing to float that Probability emerges from Mathematics and that Probability offers cutting edge solutions for the contemporary era?
  • Gurgeh
    8
    I mean the scientific approach applies to all of philosophy and verifies or repudiates it, while not all philosophy applies to science, mathematics applies to all of science and everything in science shows a mathematical framework, but not all science applies to maths. First principles of maths applies to all of maths, while not all of maths applies to first principles. So what comes after first principles? What subbranch of first principles will apply to all of first principles, while not all first principles applies to that subbranch?
  • Adam's Off Ox
    52
    When you speak of first principles, I think of first-order logic. Mathematical objects focus on definitions, concepts, axioms, and proofs.

    But we may come to investigate the deeper workings that bring about the concepts and postulates that make up mathematical inquiry.

    "How do we come up with definitions?" may be a different category than which concepts we adopt.

    I'm thinking of what processes are required before we even arrive at first principles. There may be some psychological digging involved, which goes beyond laws of thought or formalism.
  • SophistiCat
    1.3k
    then maths became a subbranch of science, which is about finding out things about the world from first principlesGurgeh

    Math as such is not about finding out things about the world. Math is about finding out things about math, nothing more, nothing less.

    Sure, the direction in which we take mathematical research can be motivated by our desire to find things out about the world by applying mathematics to science. (It can also be influenced by psychology, social pressures, esthetics, or whatever else.) But in that instance mathematics is just a tool of science. Science is still ultimately responsible for what we take to be our findings.
  • Gurgeh
    8
    With "math is about finding out things about the world" I was referring to the fact that everything in the world is modellable, simulatable and many things are formalisable. Any given phenomenon can be modelled or simulated, moreover anything in maths is applicable to the real world and tells you absolute truths about the real world, and there is no other source of absolute truth.
  • SophistiCat
    1.3k
    With "math is about finding out things about the world" I was referring to the fact that everything in the world is modellable, simulatable and many things are formalisable.Gurgeh

    That is the responsibility of science though. Mathematics in this case is only a tool and a language of science.

    moreover anything in maths is applicable to the real world and tells you absolute truths about the real world, and there is no other source of absolute truth.Gurgeh

    Well, that is a very strange thing to say. If this is a personal belief, fine. But if (in the spirit of the OP) this is intended to express a generally accepted idea, then definitely no.
  • Gurgeh
    8

    moreover anything in maths is applicable to the real world and tells you absolute truths about the real world, and there is no other source of absolute truth.

    Well, that is a very strange thing to say. If this is a personal belief, fine. But if (in the spirit of the OP) this is intended to express a generally accepted idea, then definitely no.
    Empiricism is always to be refined. Every part of empiricism is temporary. Every part of maths is absolute truth. And if it's not empirical, as in theories which you don't test, then you haven't supplied evidence for it.

    With "math is about finding out things about the world" I was referring to the fact that everything in the world is modellable, simulatable and many things are formalisable.

    That is the responsibility of science though. Mathematics in this case is only a tool and a language of science.
    Finding out things about the world isn't as important as finding out about structure. Without structure you won't understand what you're trying to find out about the world, let alone make reasonable postulations about it.
  • SophistiCat
    1.3k
    Empiricism is always to be refined. Every part of empiricism is temporary. Every part of maths is absolute truth. And if it's not empirical, as in theories which you don't test, then you haven't supplied evidence for it.Gurgeh

    I don't see how this is addresses the part of the discussion that you quoted. Also I am not sure what "it" refers to in the last sentence.

    Finding out things about the world isn't as important as finding out about structure.Gurgeh

    Finding the structure of what?
  • Gurgeh
    8
    Finding out things about the world isn't as important as finding out about structure.
    Finding the structure of what?
    Structure is independent of reality. Reality is dependent on structure.

    Empiricism is always to be refined. Every part of empiricism is temporary. Every part of maths is absolute truth. And if it's not empirical, as in theories which you don't test, then you haven't supplied evidence for it.

    I don't see how this is addresses the part of the discussion that you quoted. Also I am not sure what "it" refers to in the last sentence.

    Name one truth which isn't mathematical but is absolute.
  • SophistiCat
    1.3k
    Name one truth which isn't mathematical but is absolute.Gurgeh

    Again, you are quoting something but not addressing what you quote.

    And again, it is unclear what you are aiming at with your posts. If you are just stating your beliefs, then whatever. If you made a case for or against something, then there would be something to discuss - otherwise we are done.
bold
italic
underline
strike
code
quote
ulist
image
url
mention
reveal
youtube
tweet
Add a Comment