On Wed, Aug 22, 2012 at 1:07 PM, benjayk <benjamin.jaku...@googlemail.com>wrote:
> > > Jason Resch-2 wrote: > > > > On Wed, Aug 22, 2012 at 10:48 AM, benjayk > > <benjamin.jaku...@googlemail.com>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. > > > > > No, this can't work, since the sentence is exactly supposed to express > something that cannot be precisely defined and show that it is intuitively > true. > > Actually even the most precise definitions do exactly the same at the root, > since there is no such a thing as a fundamentally precise definition. For > example 0: You might say it is the smallest non-negative integer, but this > begs the question, since integer is meaningless without defining 0 first. > So > ultimately we just rely on our intuitive fuzzy understanding of 0 as > nothing, and being one less then one of something (which again is an > intuitive notion derived from our experience of objects). > > So what is your definition of computer, and what is your evidence/reasoning that you yourself are not contained in that definition? 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@example.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.