Robin
Penultimate Amazing
- Joined
- Apr 29, 2004
- Messages
- 14,971
Peter Soderqvist:
The weather is, as you say, a chaotic system. It is not an algorithmic system although we can employ algorithms to solve the systems of equations involved. So the weather is not a Turing computable system even if some mathematical approximation of it might be.
There appear to be many contradictory versions of the Turing-Church thesis, but it definitely does not say this. This is the only version that Turing and Church themselves actually endorsed:
So a thing might not be Turing computable, but still decidable.
So if I say that cognitive states are not Turing computable it is not the same as saying it is undecidable. It is not the same as saying it is non-deterministic.
There are machines that are not Turing machines.
I tend to the "mind as machine" side of the debate, I can't see anything about consciousness or free-will that could not be produced mechanically.
See you on Monday
The weather is, as you say, a chaotic system. It is not an algorithmic system although we can employ algorithms to solve the systems of equations involved. So the weather is not a Turing computable system even if some mathematical approximation of it might be.
Soderqvist1: it must, because a Turing machine works with bits and can compute every possible physical state, except undecidable propositions, and uncomputable numbers etc, which are abstract phenomena, according to the Turing-Church principle!
There appear to be many contradictory versions of the Turing-Church thesis, but it definitely does not say this. This is the only version that Turing and Church themselves actually endorsed:
Whatever can be calculated by a machine (working on finite data in accordance with a finite program of instructions) is Turing-machine-computable.
So a thing might not be Turing computable, but still decidable.
So if I say that cognitive states are not Turing computable it is not the same as saying it is undecidable. It is not the same as saying it is non-deterministic.
There are machines that are not Turing machines.
I tend to the "mind as machine" side of the debate, I can't see anything about consciousness or free-will that could not be produced mechanically.
See you on Monday