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Gödel’s incompleteness theorem says that pink elephants may indeed well exist.
by strogonoff 2y ago
Gödel’s incompleteness theorem says that pink elephants may indeed well exist.
- exe34 2y agono it doesn't.
- strogonoff 2y agoThis is only true if you reject the pink elephant argument as straw man in the first place. As long as you consider it a figure of speech (a charitable interpretation indeed), then existence of pink elephants (or ghosts, or what have you) is exactly the implication of the theory in context of scientific method.
- exe34 2y agoGödel's theorem deals with the axioms of mathematics. the scientific method deals with the physical universe. a small part of mathematics is useful in describing the universe, but most of it isn't.
- strogonoff 2y agoThe theorem is about formal systems in general. You may want to take a look at https://en.wikipedia.org/wiki/Scientific_method#Science_of_complex_systems https://en.wikipedia.org/wiki/Scientific_method#Science_of_c..., though I recommend to read, for example, GEB to inderstand the implications of the theorem.
- anon291 2y agoThat's really not what it says. Godel's incompleteness theorem applied to AI would say something like 'There are statements about the model's behavior we cannot prove without relying on statements that cannot to be proven' (this is because obviously the AI algorithms are based on elementary arithmetic).
- strogonoff 2y agoThe theorem applies beyond elementary arithmetic to any formal system. If we try to be rigorous in that way with our models of the universe, the theorem would say that no matter how formally sound our models are they will have to be incomplete, incorrect, or non-provable; that is, we would not be able to rule out the existence of consciousness or figurative pink elephants. (And if they are not formally sound in that way, our models can be safely considered to be incorrect/incomplete simply because they are not formally sound in that way.)