Jason Resch-2 wrote:
> On Wed, Aug 22, 2012 at 10:48 AM, benjayk
>> 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
>> holds (saying "solely using a computer").
> For to work, as Godel did, you need to perfectly define the elements in
> 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
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).
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