On Wed, Aug 22, 2012 at 10:48 AM, benjayk <[email protected]>wrote:
> > > Bruno Marchal wrote: > > > >> > >> Imagine a computer without an output. Now, if we look at what the > >> computer > >> is doing, we can not infer what it is actually doing in terms of > >> high-level > >> activity, because this is just defined at the output/input. For > >> example, no > >> video exists in the computer - the data of the video could be other > >> data as > >> well. We would indeed just find computation. > >> At the level of the chip, notions like definition, proving, inductive > >> interference don't exist. And if we believe the church-turing > >> thesis, they > >> can't exist in any computation (since all are equivalent to a > >> computation of > >> a turing computer, which doesn't have those notions), they would be > >> merely > >> labels that we use in our programming language. > > > > All computers are equivalent with respect to computability. This does > > not entail that all computers are equivalent to respect of > > provability. Indeed the PA machines proves much more than the RA > > machines. The ZF machine proves much more than the PA machines. But > > they do prove in the operational meaning of the term. They actually > > give proof of statements. Like you can say that a computer can play > > chess. > > Computability is closed for the diagonal procedure, but not > > provability, game, definability, etc. > > > OK, this makes sense. > > In any case, the problem still exists, though it may not be enough to say > that the answer to the statement is not computable. The original form still > holds (saying "solely using a computer"). > > For to work, as Godel did, you need to perfectly define the elements in the sentence using a formal language like mathematics. English is too ambiguous. If you try perfectly define what you mean by computer, in a formal way, you may find that you have trouble coming up with a definition that includes computers, but does't also include human brains. Jason -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
