Mathematics uses deductive methodology to produce results called theorems that are indisputable truth by logical necessity, with respect to the axioms of the starting axioms and definitions.


  1. Does philosophy, nowadays, proceed with this deductive methodology?
  2. If yes, what are other currently "acceptable" ways of doing philosophy?
  • @Conifold I don't agree with respect to mathematics. What I think is true is that people do mathematics without continuously referring to the axioms, for simplicity. The hypothetical-deductive structure remains, and this necessarily implies a starting point, the axioms.
    – Lilla
    Nov 9, 2020 at 7:52
  • 1
    No, this is not how people do mathematics, there have been extensive studies on this. The reasoning is mostly semantic from definitions and constructions rather than deductive from axioms, explicit or implicit. Axiomatic method makes verification of the proofs more reliable, but that is not how they are either found or checked in practice. Nor are axioms a starting point even in principle, mathematical theories are very malleable as to their deductive structure, and the same theorems can be derived from any number of dissimilar collections of axioms chosen for convenience or elegance.
    – Conifold
    Nov 10, 2020 at 20:53
  • To add to Conifold's comment, mathematics has existed for over 3000 years and for most of that time (with the exception of Euclid) mathematicians mostly didn't bother with axiomatizing things. Axiomatization is a fairly recent obsession encouraged by Hilbert in the late 19th/early 20th centuries. Axiomatization is valuable, but it's not required for mathematics to be mathematics.
    – Bumble
    Oct 22, 2021 at 18:21
  • @Bumble (As a deductionist) Proper mathematics require deduction. Nov 1, 2021 at 19:01
  • @ErdelvonMises Well, I agree that mathematics uses deduction, but that does not require axiom systems. You can teach someone how to use simple algebra to deduce the value of x in an equation without either you or them knowing how to axiomatize algebra.
    – Bumble
    Nov 3, 2021 at 10:43


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