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I think you are both getting lost in the weeds trying to make this metaphor work, or not work. Math is simply the logical conclusion of a set of conditions som

• naasking 3y ago
  I think this conflates logic and mathematics. Some would dispute that logic underpins mathematics. Counting can be analyzed logically, but it does not in any meaningful sense seem to depend on logic.
  • jplusequalt 3y ago
    Sure it does. How else would you prove that one number follows or precedes another? I think you are conflating the act of physically counting with the logical foundation of our number systems.
    • naasking 3y ago
      It doesn't seem correct to equate mathematics with proof. If I express a mathematical construction like the whole numbers (let Whole = Zero | Succ Whole), and I build further constructions on that foundation, am I doing mathematics? If so, then it seems mathematics does not depend on logic, as logic depends on propositions and there are no propositions to be seen. Certainly you can analyze such constructions using logic, but that's again conflating logic with mathematics. There's overlap, but they aren't strictly the same.
      • jplusequalt 3y ago
        I would say that a mathematical construction is based in logic, maybe not in the traditional sense, but there is definitely logic behind the construction itself. I think we are talking past one another, what I mean by logic here is more nebulous than predicate calculus. There is an innate logic behind the philosophy of mathematics and I believe you cannot divorce mathematics from logic.