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      Questions tagged [mathematical-philosophy]

      Philosophical aspects of logic and set theory; truth status of mathematical axioms; Philosophy of Mathematics; philosophical aspects of mathematics in general; relation of mathematics to philosophy; etc. Consider also posting at http://philosophy.stackexchange.com/, where philosophy-of-mathematics is one of the most popular tags.

      6
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      332 views

      Constructivist defininition of linear subspaces of $\mathbb{Q}^n$?

      Let me preface this by saying I'm not someone who has every studied mathematical logic or philosophy of math, so I may be mangling terminology here (and the title is a little tongue in cheek). I (and ...
      -4
      votes
      2answers
      338 views

      Is the notion of measurable cardinal definable from the perspective of set-theoretical potentialism?

      Consider the definition of measurable cardinal (this definition was found in Neil Barton's paper, "Large cardinals and the iterative conception of set"): Definition 8. A cardinal $\kappa$ is ...
      7
      votes
      5answers
      1k views

      Is there any physical or computational justification for non-constructive axioms such as AC or excluded middle?

      I became interested in mathematics after studying physics because I wanted to better understand the mathematical foundations of various physical theories I had studied such as quantum mechanics, ...
      7
      votes
      1answer
      519 views

      Explaining the consistency of PRA and ZF from predicative foundations

      Recently I got interested in predicative foundations, mostly because of Laura Crosilla's work and because Agda employs a predicative type theory. From the point of view of a predicative foundation to ...
      14
      votes
      0answers
      434 views

      Does inner model theory seek canonical models for large cardinals?

      Like the author of this question, I have heard that a main goal of inner model theory is building canonical inner models for large cardinals. My questions are: (a) Is this accurate? (b) If so, in ...
      15
      votes
      1answer
      719 views

      Axiom of Choice versus V=L in opposition to large cardinals

      Consider the following two observations: The axiom $V=L$ is incompatible with large cardinal axioms that are somehow "too large", like measurable cardinals. The axiom of Choice is incompatible with ...
      2
      votes
      0answers
      257 views

      Does this axiomatic system satisfy requirements for founding mathematics?

      In this article, the author, F.A.Muller, suggests criteria for a founding theory of mathematics (pp:14-16). The author proposes $ARC$ Class Theory to embody these requirements. The motivation is ...
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      votes
      2answers
      1k views

      Complex analytic vs algebraic geometry

      This is more of a philosophical or historical question, and I can be totally wrong in what I am about to write next. It looks to me, that complex-analytic geometry has lost its relative positions ...
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      votes
      1answer
      385 views

      “Mathematics is the science of the infinite” [closed]

      The title is the first sentence of Hermann Weyl's 1930 essay, "Levels of Infinity." He focuses on "the distinction between actuality and potentiality, between Being and Possibility." He opines ...
      5
      votes
      0answers
      298 views

      Theorems conditional on false conjectures

      What is an example of a theorem that was conditional on a conjecture that later turned out to be false?
      22
      votes
      4answers
      1k views

      Does Zorn's Lemma imply a physical prediction? [duplicate]

      A friend of mine joked that Zorn's lemma must be true because it's used in functional analysis, which gives results about PDEs that are then used to make planes, and the planes fly. I'm not super ...
      10
      votes
      1answer
      617 views

      Quantum functional analysis

      Can one explain some philosophy behind "quantum functional analysis" (or "quantized functional analysis") which was initiated and developed by such researchers as: Ruan Z.-J., Pisier J., Effros E.G., ...
      5
      votes
      3answers
      410 views

      Counting without one-to-one correspondence? [closed]

      Ash and Gross in their wonderful book Fearless Symmetry found it worth mentioning (and thus suggesting) another way of counting for which "we do not even need to know how to count" (in the sense of ...
      8
      votes
      0answers
      512 views

      What's the point of cubical type theory?

      I have been following through the development of homotopy type theory since 2013 because I was really interested in the foundation of mathematics. The novel idea of combining programming with homotopy ...
      0
      votes
      1answer
      230 views

      Criterion of completeness

      Wittgenstein (PR 181) talks about a criterion of completeness for the irrationals. I am trying to understand what this might mean. Completeness of the reals, in the decimal number system, is the ...

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