|From:||William Frank <williamf.frank@xxxxxxxxx>|
|Date:||Fri, 13 Feb 2015 12:49:40 -0500|
On Thu, Feb 12, 2015 at 10:43 PM, Steven Ericsson-Zenith <steven@xxxxxxx> wrote:
Interesting. I understand a proof to provide one piece of certain knowledge : *if* their are no errors in the proof, then its conclusion is true. and as a result, a proof provides one piece of practical knowledge: to the degree that I ann a community of others I trust are convinced there are no errors in the proof, I can rely on the conclusion in making decisions. In other words, I always thought, the only practical effect of a proof is a rational feeling of confidence in certain expectations, and that the use of the proof was therefore to *act* on that confidence. I would like to know of another use a proof might have, other than perhaps its esthetic enjoyment.
I was just using the incorrectness of Copi's 'proofs' of the consistency of his logic as evidence that just because there is a purported and widely accepted proof, even of something that one might take as obvious, is no absolute proof that the conclusion of the proof is true, and, for people, and complex systems, there is never such an absolute proof.
I would agree that this is electrical engineering, an application of computational mathematics, And as such, is to be trusted only with caveats. I am not so concerned with quantum effects as I am with the effects of fires, asteroids, faulty materials, electromagnetic effects, vandalism, .... on how that physical device will actually behave.
Ah, so here, we are speaking at cross purposes. I had no intention of bringing in metaphysics, and I think that even mentioning escaping it is bringing it in. But, in this regard, to each his own. I thank you for your patience in answering.
Right. But some call mathematics a science. Mathematical science and natural science being the two types. That is the source of the problem with 'computer science'. Maybe compuational mathematics would be clearer.
Of course not.
But it makes some aspects of computer engineering not engineering but rather pure mathematics. Turing machines and context - sensitive grammars are abstract things of interest in their own right, as much as are categories and fractals and other mathematical topics that from time to time turn out to have practical applications.
My point was that it would be ***infinitely*** expensive, as being logically impossible, and showing an impossibly arrogant attitude toward nature and its vicissitudes. Rather, as you say, the appropriate approach is to establish, to the degree cost effective, within the realm of the controllable and a certain set of rare events, a strong expectation that the bridge will not fall down,
Sure. If you prove something about one layer, and not the one below, the value of the proof about the higher layer is greatly diminished, especially because any of us using a 'modern
computer to even write email messages is well aware that the system is so hopeless convoluted as to guarantee frequent, unpredictable breakage. This, however, does not make the higher level proof 'useless'. I would rather know that **at least** my nice little program has been examined under the microscope of a proof method and not found wanting. I like to see this happen because I fear that the 'modern' direction is to abandon all such attempts, since we can't have everything, and continually make bigger mess all the way up and down the stack.
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