Message from discussion "Friendly Premises"

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From: "Acme Diagnostics" <LFinezapt...@partpostmark.net>
Newsgroups: sci.logic
Subject: Re: "Friendly Premises"
Date: 3 Aug 2005 22:09:03 -0500
Organization: Newscene Usenet News Service, http://www.newscene.com/
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Jim Spriggs  wrote:
>Acme Diagnostics wrote:
>> Jim Spriggs  wrote:
>>>Jesse Alama wrote:
>>>
>>>> Torkel ignored much of the post
>>>> <42eb8beb$0$91626$bb4e3...@newscene.com> and called attention to the
>>>> part about "self-proving procedures" and "recursive proof".  That may
>>>> have been a snarky move, but I think Torkel's question needs to be
>>>> answered if we are to fully understand your original post.  To be
>>>> honest, I am with Tokel on this one: I too don't know what you mean by
>>>> "self-proving procedures" or "recursive proofs".  I presume other
>>>> readers of sci.logic are in the same boat.  For our sake, tell us what
>>>> you mean by "self-proving procedure" and "recursive proof".
>>>
>>>My guess was that "recursive proof" was an honest mistake for "proof by
>>>induction".  "self-proving procedure" intrigues me, where can I buy one?
>>
>> Hi Jim,
>>
>> Seeing George's message reminded me that I had intended
>> to compliment your two statements, before getting sidetracked.
>>
>> "Honest mistake" is exactly correct.
>
>So, when you wrote "recursive proof" you meant precisely "proof by
>induction"?

No, I only referred to the "honest mistake" part. I have no idea
what "proof by induction" means. It sounds like an oxymoron
to me, but I have seen it legitimately used in context of
some logic somewhere, so I know it is not an oxymoron in some
sense. I vaguely remember some textbook somewhere saying
something like "this is called a proof by induction but that's a
misnomer because it is really a deductive process" or something
like that. This goes back a while, and was (probably still is)
irrelevant to my goals in logic.

>> I obviously made a mistake there too, since I
>> intended to use a phrase that posters could figure out easily
>> enough, failing miserably.
>
>Can you give an alternative to "self-proving procedure"?  Or give an
>example, or a reference?  Do you mean something like:
>
>  Mathematicians use mathematics to prove things about logic
>  while at the same time founding their mathematics on logic.

No, not at all.

There are systems of logic where results can be changed from
outside the system. "Results" are often called proofs, though
not in the same sense as a theoretical math proof. For instance,
in business, or in the military including in the most complex
systems imaginable, someone will often say "prove it" and someone
will just produce some empirical evidence which is then accepted
as "proof," or it could just a point of short logic. Well, to get
closer to what some people would be more willing to accept as a
"logic system," it also happens in the programming world. There
you prove your logic with the "run" button. A more "theoretical"
example would be statistical prediction of stocks or commodity
prices. There you make theoretical calculations which are proved
in the sense of exact probability calculations. But when applied
in the real-world, new logic can completely invalidate that
"theory." (I know some statistical formulas are unproven
mathematically but lets not go there. It's just a "more
theoretical" example than the business example.) Then there are
dogmas of all varieties including religious dogmas, and you'll
find that "logic" occurs as every third word (or whatever) in
some of them. They are routinely "disproved" from outside those
systems. I think you get the idea.

In logic or math theories never intended to apply in the
real-world (and perhaps some that are - I don't know), a system
can be constructed so that there is no possibility of anything
outside the system changing results, or at least that's what I've
been told, including here. That is what I meant by
"self-proving." That has been called "self-proving" at various
points thoughout my life from a variety of sources. None of them
being in predicate or math logic, though.

Since the idea of "proofs" had to be introduced into logic
at some point, there is no reason for me to conclude that
they were introduced as the "theoretical" self-provng kind
all at once. For all I know, there may be other or intermediate
logics that have some other definition of "proved" that can
in some circumstance whatsoever be affected from outside
the system. I think that would be a foolish assumption to
make until one exhausts the historical record. I haven't even
started on the historical record. <g>

"Procedure" just means a step-by-step process. Lot's of
synonyms could have been used. Some word seemed necessary
to complete the phrase "self-proving..." since by itself it's
just an adjective. Other than that, I didn't mean to attach any
special importance to the word. "Self-proving mechanism" or
"self-proving process" or "self-proving method" or "self-proving
system" all would probably have worked as well in my mind. I saw
no reason not to use "procedure," since that's one thing that a
deductive proof is according to my textbook excerpt. I had
probably read that excerpt (and others) in the past and probably
"finite successive step-by-step process" (and variations) was
just read as "procedure" in my mind, since that's what it is.

Larry