4 ms·

(For anyone else reading this who might be misled, note that OP's position is generally considered to be "crank" mathematics)

schoen 10y ago
It is definitely not a standard or mainstream view, but it could be a flavor of https://en.wikipedia.org/wiki/Finitism https://en.wikipedia.org/wiki/Finitism which has been defended by a very small but not infinitesimal :-) number of professional mathematicians and which isn't a logically inconsistent position.
- 4ad 10y ago
  Personally, I am an ultrafinitist. By that I mean that I believe that physical systems can be completely described by constructive mathematics based on intuitionistic logic[2] operating on computable reals[3]. I believe that any other kind of mathematics, e.g. classical logic with axiom of choice can create unphysical models. That being said, I don't object to classical logic as a purely abstract concept. Everything proved in ZFC is certainly true in ZFC! And I don't think any finitist will contest that. [1] https://en.wikipedia.org/wiki/Ultrafinitism https://en.wikipedia.org/wiki/Ultrafinitism [2] https://en.wikipedia.org/wiki/Intuitionistic_logic https://en.wikipedia.org/wiki/Intuitionistic_logic [3] https://en.wikipedia.org/wiki/Computable_number https://en.wikipedia.org/wiki/Computable_number
pierre_d528 10y ago
What a rigorous way to defend your position! Calling names! I bet you are an infinitely good Cantorian ! Did you speak with God recently?
- mikeash 10y ago
  You got as much rigor as you gave. Disproving every wacky position with a careful analysis is impossible, nobody has that much time.
  - xenadu02 10y ago
    Indeed, there are an almost infinite number of crank theories because they don't require logic, evidence, or proof - just belief. One crank can churn out a hundred nonsense theories in the time it takes someone to validate one scientific idea or mathematical proof. This has a corollary in the startup world: everyone has an idea, what matters is execution.
GregBuchholz 10y ago
For anyone who might be misled, here are some links that people can use to judge for themselves how "crank" someone is: Professor Norman Wildberger's homepage: http://web.maths.unsw.edu.au/~norman/ http://web.maths.unsw.edu.au/~norman/ ...a paper by Wildberger tackling some of the issues in this thread: Set Theory: Should You Believe? http://web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf http://web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf Some interesting works by Gregory Chaitin Meta Math! The Quest for Omega https://arxiv.org/abs/math/0404335 https://arxiv.org/abs/math/0404335 Exploring Randomness https://www.cs.auckland.ac.nz/~chaitin/ait/ https://www.cs.auckland.ac.nz/~chaitin/ait/ How Real are Real Numbers? https://arxiv.org/abs/math/0411418 https://arxiv.org/abs/math/0411418 People who are interested in ultrafinitism would also want to check out Doron Zeilberger http://www.math.rutgers.edu/~zeilberg/ http://www.math.rutgers.edu/~zeilberg/ and Edward Nelson https://web.math.princeton.edu/~nelson/ https://web.math.princeton.edu/~nelson/

schoen 10y ago

It is definitely not a standard or mainstream view, but it could be a flavor of https://en.wikipedia.org/wiki/Finitism https://en.wikipedia.org/wiki/Finitism which has been defended by a very small but not infinitesimal :-) number of professional mathematicians and which isn't a logically inconsistent position.

4ad 10y ago
Personally, I am an ultrafinitist. By that I mean that I believe that physical systems can be completely described by constructive mathematics based on intuitionistic logic[2] operating on computable reals[3]. I believe that any other kind of mathematics, e.g. classical logic with axiom of choice can create unphysical models. That being said, I don't object to classical logic as a purely abstract concept. Everything proved in ZFC is certainly true in ZFC! And I don't think any finitist will contest that. [1] https://en.wikipedia.org/wiki/Ultrafinitism https://en.wikipedia.org/wiki/Ultrafinitism [2] https://en.wikipedia.org/wiki/Intuitionistic_logic https://en.wikipedia.org/wiki/Intuitionistic_logic [3] https://en.wikipedia.org/wiki/Computable_number https://en.wikipedia.org/wiki/Computable_number

pierre_d528 10y ago

What a rigorous way to defend your position! Calling names! I bet you are an infinitely good Cantorian ! Did you speak with God recently?

mikeash 10y ago
You got as much rigor as you gave. Disproving every wacky position with a careful analysis is impossible, nobody has that much time.
- xenadu02 10y ago
  Indeed, there are an almost infinite number of crank theories because they don't require logic, evidence, or proof - just belief. One crank can churn out a hundred nonsense theories in the time it takes someone to validate one scientific idea or mathematical proof. This has a corollary in the startup world: everyone has an idea, what matters is execution.

GregBuchholz 10y ago

For anyone who might be misled, here are some links that people can use to judge for themselves how "crank" someone is: Professor Norman Wildberger's homepage: http://web.maths.unsw.edu.au/~norman/ http://web.maths.unsw.edu.au/~norman/ ...a paper by Wildberger tackling some of the issues in this thread: Set Theory: Should You Believe? http://web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf http://web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf Some interesting works by Gregory Chaitin Meta Math! The Quest for Omega https://arxiv.org/abs/math/0404335 https://arxiv.org/abs/math/0404335 Exploring Randomness https://www.cs.auckland.ac.nz/~chaitin/ait/ https://www.cs.auckland.ac.nz/~chaitin/ait/ How Real are Real Numbers? https://arxiv.org/abs/math/0411418 https://arxiv.org/abs/math/0411418 People who are interested in ultrafinitism would also want to check out Doron Zeilberger http://www.math.rutgers.edu/~zeilberg/ http://www.math.rutgers.edu/~zeilberg/ and Edward Nelson https://web.math.princeton.edu/~nelson/ https://web.math.princeton.edu/~nelson/