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> The argument that those that find something beyond formalism must formalise it in order to be regarded as serious is not a serious argument! Eh; waving your

> The argument that those that find something beyond formalism must formalise it in order to be regarded as serious is not a serious argument! Eh; waving your hands around and claiming, without much evidence, that of course there's "something beyond formalism" isn't a "serious argument" either. It seems like you, being presented with The Mystery of Consciousness, and having the option to either explain, worship, or ignore it, are opting to worship it. Hence: > > polynomial time heuristic search algorithm. > > Like create culture, write the works of Shakespeare or create a workable theory of the mind of others? Or fall in love, teach a child to play cricket or understand (and act on) an Opera?

sgt101 9y ago
Am I wrong that incompleteness demonstrates that there are systems that cannot be completely described in formal terms?
- Elrac 9y ago
  I'm no expert, but yes, I think you're wrong about that. This explanation https://www.scientificamerican.com/article/what-is-godels-theorem/ https://www.scientificamerican.com/article/what-is-godels-th..., a little closer to layperson level, uses integer arithmetic as a simple example. Peano's axioms completely describe integer arithmetic - easy peasy! What Gödel says is that there are, nevertheless, statements about results in this system that cannot be proved true (or false). The problem appears to be not describing the system but proving every possible conjecture about it.
  - blackflame7000 9y ago
    There are certain logical traps (paradoxes) than cannot be formalized by a computer. For example, given the statement, "This sentence is False", it is not possible to deduce a boolean value describing the sentence. Thus there is some property of the sentence that is not describable to a purely logical system. Human consciousness allow us to spot the paradox where as a polynomial search algorithm could not.
    - dTal 9y ago
      Formalizing or describing something is not the same as "deducing a boolean value". But I can ask GNU Maxima to give me a list of all numbers that satisfy the equation x+1=x-1, and it will happily tell me that there is no such number. Maxima doesn't support self-referential propositional logic, but a solver that can identify that no truth value can support "this sentence is false" doesn't need to do anything more mystical than test both cases - no "polynomial search algorithm" required. You are suggesting that "human consciousness" is a separate, ineffable thing from a "purely logical system", but I don't see any reason a computer couldn't do what your brain is doing. You can't tell me the truth value of the sentence either.

sgt101 9y ago

Am I wrong that incompleteness demonstrates that there are systems that cannot be completely described in formal terms?

Elrac 9y ago
I'm no expert, but yes, I think you're wrong about that. This explanation https://www.scientificamerican.com/article/what-is-godels-theorem/ https://www.scientificamerican.com/article/what-is-godels-th..., a little closer to layperson level, uses integer arithmetic as a simple example. Peano's axioms completely describe integer arithmetic - easy peasy! What Gödel says is that there are, nevertheless, statements about results in this system that cannot be proved true (or false). The problem appears to be not describing the system but proving every possible conjecture about it.
- blackflame7000 9y ago
  There are certain logical traps (paradoxes) than cannot be formalized by a computer. For example, given the statement, "This sentence is False", it is not possible to deduce a boolean value describing the sentence. Thus there is some property of the sentence that is not describable to a purely logical system. Human consciousness allow us to spot the paradox where as a polynomial search algorithm could not.
  - dTal 9y ago
    Formalizing or describing something is not the same as "deducing a boolean value". But I can ask GNU Maxima to give me a list of all numbers that satisfy the equation x+1=x-1, and it will happily tell me that there is no such number. Maxima doesn't support self-referential propositional logic, but a solver that can identify that no truth value can support "this sentence is false" doesn't need to do anything more mystical than test both cases - no "polynomial search algorithm" required. You are suggesting that "human consciousness" is a separate, ineffable thing from a "purely logical system", but I don't see any reason a computer couldn't do what your brain is doing. You can't tell me the truth value of the sentence either.