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Godel's theorem applies to all systems strong enough to do arithmetic. When we talk about "powerful" systems, it will inevitably have to do arithmetic. One of

by sn41 3y ago

Godel's theorem applies to all systems strong enough to do arithmetic. When we talk about "powerful" systems, it will inevitably have to do arithmetic. One of the unprovable statements of any such formal system will be that "this system is consistent", which is an important property. [Godel's second incompleteness theorem] I feel that AI in general is headed towards the direction of saying that provability is not really important, let's just head in a pragmatic direction.

keithalewis 3y ago
Prior to Euclid people seemed to be concerned with valid arguments. Mathematical proofs are limited to true or false statements. Math is great when modeling physics, but quite lacking when applied to other human endeavours.
- zmgsabst 3y ago
  Facebook disagrees: Math lets them manipulate your emotions on behalf of advertisers and spy agencies, alike. As does Midjourney: Math lets them turn a loose description into a high quality picture of that scene.
  - DiscourseFan 3y ago
    I don't think its useful to refer to every symbolic structure that people employ to build machines as "math." There is more to Facebook and Midjourney than the equations used to represent their operation.
    - zmgsabst 3y ago
      Computers compute — they’re a replacement for people doing arithmetic on paper forms. Fundamentally, there’s a mathematical representation of their computational system. Also, you admit that equations are driving the core of both systems I described: - algorithmic manipulation - SD images
      - DiscourseFan 3y ago
        >equations are driving the core of both systems I described Everything in society uses symbolic representation, but is not driven by symbolic representation, but the people who create those representations.
casey2 3y ago
>unprovable statements Nonsensical is better in modern discussions than "unprovable". It shows that statements that were previously (and currently by some) thought to be mathematical are actually nonsense just like "x tastes like chicken" but more devious. Asking if a Turing machine with M memory halts in less than N steps is sane and provable. http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/enquiry.pdf http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/e...
- bmacho 3y ago
  > Did Gödel Really Prove That There Exist True yet Unprovable Statements? > Of course not! All his “statements” were meaningless! > Every statement that starts : “for every integer n . . .” or “there exists an integer n . . .”, is completely meaningless, since it tacitly assumes that there are infinitely many integers. Of course, there are only finitely many of them, since our worlds, both the physical and the mathematical, are finite. .. > The statement “n + n = 2n for every integer n” is meaningless. It is only true for every _finite_ integer. It is also true for symbolic n. Eehrm? This is not the modern view on math. In modern math Gödel's theorems are currently regarded as its wiki article talks about it : https://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems https://en.wikipedia.org/wiki/Gödel's_incompleteness_theorem... .

by sn41 3y ago

keithalewis 3y ago

Prior to Euclid people seemed to be concerned with valid arguments. Mathematical proofs are limited to true or false statements. Math is great when modeling physics, but quite lacking when applied to other human endeavours.

zmgsabst 3y ago
Facebook disagrees: Math lets them manipulate your emotions on behalf of advertisers and spy agencies, alike. As does Midjourney: Math lets them turn a loose description into a high quality picture of that scene.
- DiscourseFan 3y ago
  I don't think its useful to refer to every symbolic structure that people employ to build machines as "math." There is more to Facebook and Midjourney than the equations used to represent their operation.
  - zmgsabst 3y ago
    Computers compute — they’re a replacement for people doing arithmetic on paper forms. Fundamentally, there’s a mathematical representation of their computational system. Also, you admit that equations are driving the core of both systems I described: - algorithmic manipulation - SD images
    - DiscourseFan 3y ago
      >equations are driving the core of both systems I described Everything in society uses symbolic representation, but is not driven by symbolic representation, but the people who create those representations.

casey2 3y ago

>unprovable statements Nonsensical is better in modern discussions than "unprovable". It shows that statements that were previously (and currently by some) thought to be mathematical are actually nonsense just like "x tastes like chicken" but more devious. Asking if a Turing machine with M memory halts in less than N steps is sane and provable. http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/enquiry.pdf http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/e...

bmacho 3y ago
> Did Gödel Really Prove That There Exist True yet Unprovable Statements? > Of course not! All his “statements” were meaningless! > Every statement that starts : “for every integer n . . .” or “there exists an integer n . . .”, is completely meaningless, since it tacitly assumes that there are infinitely many integers. Of course, there are only finitely many of them, since our worlds, both the physical and the mathematical, are finite. .. > The statement “n + n = 2n for every integer n” is meaningless. It is only true for every _finite_ integer. It is also true for symbolic n. Eehrm? This is not the modern view on math. In modern math Gödel's theorems are currently regarded as its wiki article talks about it : https://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems https://en.wikipedia.org/wiki/Gödel's_incompleteness_theorem... .