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Certainly! I am not performing mathematics when I am reading a fiction book and (unconsciously or consciously) mentally simulating the actions and internal stat

Certainly! I am not performing mathematics when I am reading a fiction book and (unconsciously or consciously) mentally simulating the actions and internal states of the characters. I never said anything like "all thought is mathematics", merely "not all mathematics is symbolic thought".

lisper 5y ago
> I am not performing mathematics when I am reading a fiction book How do you know? You said that thinking about the objects referred to by mathematical formalisms is performing mathematics. How can you be sure that your fiction book can't be described by some mathematical formalism, but you are simply as yet unaware of it?
- Smaug123 5y ago
  Maybe you'll come along in ten years and convince me that I was performing mathematics all along! Maths has expanded to embrace other fields in the past. Archimedes probably would have called work on the nature of truth "philosophy" and very much not "mathematics". I, for one, do not wish to adopt any stance that rules out future progress.
  - lisper 5y ago
    I don't have to wait ten years. Unless you reject the Church-Turing thesis, then on your definition everything is math, which makes your definition vacuous.
    - Smaug123 5y ago
      I shall quote myself: > I never said anything like "all thought is mathematics", merely "not all mathematics is symbolic thought".
      - lisper 5y ago
        We're going around in circles. If not all mathematics is symbolic thought, then, unless you're a dualist, there is nothing that can be meaningfully distinguished as "not mathematics" (because Turing completeness) and the whole concept of mathematics becomes vacuous and useless.
        Smaug123 5y ago
        Well, you're extrapolating to the claim that since humans can be emulated by machines, which are in the domain of mathematics, every aspect of human thought is mathematics. I deny this extrapolation. Merely writing something down does not make it literature; merely encoding something into a Turing machine does not make it mathematics.

lisper 5y ago

> I am not performing mathematics when I am reading a fiction book How do you know? You said that thinking about the objects referred to by mathematical formalisms is performing mathematics. How can you be sure that your fiction book can't be described by some mathematical formalism, but you are simply as yet unaware of it?

Smaug123 5y ago
Maybe you'll come along in ten years and convince me that I was performing mathematics all along! Maths has expanded to embrace other fields in the past. Archimedes probably would have called work on the nature of truth "philosophy" and very much not "mathematics". I, for one, do not wish to adopt any stance that rules out future progress.
- lisper 5y ago
  I don't have to wait ten years. Unless you reject the Church-Turing thesis, then on your definition everything is math, which makes your definition vacuous.
  - Smaug123 5y ago
    I shall quote myself: > I never said anything like "all thought is mathematics", merely "not all mathematics is symbolic thought".
    - lisper 5y ago
      We're going around in circles. If not all mathematics is symbolic thought, then, unless you're a dualist, there is nothing that can be meaningfully distinguished as "not mathematics" (because Turing completeness) and the whole concept of mathematics becomes vacuous and useless.
      - Smaug123 5y ago
        Well, you're extrapolating to the claim that since humans can be emulated by machines, which are in the domain of mathematics, every aspect of human thought is mathematics. I deny this extrapolation. Merely writing something down does not make it literature; merely encoding something into a Turing machine does not make it mathematics.