Message from discussion "Friendly Premises"

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From: Martin Shobe <msh...@sbcglobal.net>
Newsgroups: sci.logic
Subject: Re: "Friendly Premises"
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Date: Sun, 31 Jul 2005 20:59:51 GMT

On 31 Jul 2005 14:57:03 -0500, "Acme Diagnostics"
<LFinezapt...@partpostmark.net> wrote:

[Snip]

>3. "Self-"
>
>The prefex "self-" can mean anything I want it to mean among
>all the common definitions of the prefix "self-" as long as it
>is sufficient to describe any logic system whatsoever.
>
>I choose for it to mean "self-contained" in the context of a
>"logic system," and to simply refer to any logic system
>whatsoever that does not require input from outside that system
>to apply any of it's rules of inference; and additionally this
>implies that all elements needed for that application are within
>the system.
>
>For instance, in a system of syllogisms composed of syllogistic
>arguments, or in the whole system of syllogistic logic, if the
>premises are true, then in all valid arguments the conclusions
>must be true. Nothing from outside the system, i.e. the
>syllogisms, (or syllogistic logic) is needed to infer that.
>Additionally, nothing from outside the system can change it
>without changing the system itself, and my definition including
>"a system" precludes that one thing. Thus, "self-" in this
>context implies a self-contained system.
>
>4. "Procedure".
>
>A procedure is a finite successive sequence of steps, also
>sometimes described as a finite successive step-by-step process.
>
>That's probably obvious enough, since it only needs to apply
>to any logic system of any kind.
>
>5. "Proving."
>
>Note: In logical argumention, the quantifiers "some" and
>"sometimes" minimally require one case.
>
>Accurately condensing, but not paraphrasing, more text than I
>care to type until further challenged, another quote from a logic
>textbook:
>
>"A deduction in logic is sometimes defined as a finite successive
>step-by-step process applying rules of a logic system to a series
>of premises or formulas. In some of these cases where deduction
>is so defined, the word "deduction" is used synonymously with the
>word 'proof'. The two terms will be used interchangeably in this
>text."
>
>This textbook is well-distributed. Whether it is accurate or not
>is irrelevant. I don't need to prove that the concept occurs in
>"correct" logic, just that it occurs in logic. Any
>well-distributed logic textbook occurs "in logic."

In other words, a "self-proving procedure" is nothing other than a
proof.  

[Snip]

Martin