|From:||William Frank <williamf.frank@xxxxxxxxx>|
|Date:||Thu, 12 Feb 2015 19:47:11 -0500|
"Let me just note a couple of peripheral issues.
1. Proof of a software program is only of use to you if the behavior of the underlying hardware is formally proven and that proof is compatible with the proof of the program. "
This is one of the most puzzling sentences I have ever read.
a. Why is a proof useless because it does not prove that everything is also OK in the world to which the thing proven might be related and by which it might be affected? The use of a proof helps convince you that *at least that part* of the problem is less likely to cause us trouble.
b. Even the proof does not guarantee that we have absolute certainty, since of course many proofs that convince many people prove to be incorrect. If I recall, the *consistency* proof on Copi's Symbolic Logic was for sure wrong for the first two editions, as each edition had been shown to be inconsistent, in a more convincing manner. (The consistency proof in edition three has stood.)
c. the idea that we could prove anything about underlying hardware is amazing. I though that the physical sciences were of their very nature inexact, and that the behavior of all physical objects was unpredicatable, to one degree or another. If I am wrong, something awfully big has happened in science that passed me by. I would truly love to hear it named.
d. this seems to be related to your claim, Steven, that there is 'no such thing' as 'computer science.' Where I went to school, 'computer science' was defined to be a branch of **pure mathematics** that had many (as always) inexact applications in computer engineering. This idea fell on deaf ears last time I raised it in this forum, and I have continued to wonder why. I can't imagine why it is a controversial view, except perhaps that there are all those computer science departments out there that teach a little computer science, and alot of computer engineering, and don't make the distinction they should. (Then, I taught for a while at a school that had a department of 'poultry science', which likewise did not distinquish the specialized zoology from the engineering).
But, it is am important distinction. After all, if we could prove things about physical machines, as well as theoretical ones, then why would not all engineering actually be science? Perhaps because we built it, rather than found it by the side of the road? (Well, as I said before, I never found any Turing machines on the side of the road, and I never expect to.) I If somebody told me, I can prove my bridge will never fall down! I can prove no one can every hack this cypher! I would have said, let me hire somebody who knows his business better than to say either of those things. But, again, maybe something awful big has happened in science while I was not looking.
e. finally, though it has been more than 30 years since I was a professional in proof theory, I do continue to dabble and publish in the philosophy of logic, and i was even interested in the head-of-a-pin question of whether two proofs concatenated was also a proof. But, I did not ever hear of the concept of proofs being 'compatable' and can't find it on the web, or in the Stanford Encyclopedia of Philosophy. So, again, it is an idea I would find very interesting, if it has a definition.
On Thu, Feb 12, 2015 at 6:52 PM, Ravi Sharma <drravisharma@xxxxxxxxx> wrote:
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