Re: "Friendly Premises"


Martin Shobe <mshobe@xxxxxxxxxxxxx> wrote:
>On 1 Aug 2005 13:17:01 -0500, "Acme Diagnostics"
><LFinezapthis@xxxxxxxxxxxxxxxx> wrote:
>>Martin Shobe <mshobe@xxxxxxxxxxxxx> wrote:
>>>On 31 Jul 2005 14:57:03 -0500, "Acme Diagnostics"
>>><LFinezapthis@xxxxxxxxxxxxxxxx> 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.
>>
>>I can't really know since I am grossly unqualified, but it
>>naively seems to me that if there's such a thing as a
>>self-proving procedure in logic, then it would be a proof, and
>>that the word "self" would imply a little more information than
>>just "proof." I only proved that the "concept" existed within
>>logic, just playing with words, i.e. logic.
>
>Not really.
>
>Your definition of "procedure" is directly included in
>your definition of "proof".

Yes of course. The definitions are obviously a build. One is to
be used in the next.

No, as implied in the rest of your comment (below), there is no
occurence of "procedure" in the (full) text I used for "proof."
I connected the phrase in the textbook with "procedure" myself.

I did just copy the definition out of the proof definition and
include it in the previous definition of "procedure." And I
purposely tacked it onto the end of another definition in an
off-handed way, "...also sometimes described as..." And I did
that for a very good reason: hostile reviewers.

When reading the definition of "procedure" and encountering "a
finite successive step-by-step process," the hostile reviewer,
not knowing what is to come in the next definition, is expected
to accept that as one legitimate definition of "procedure." And
why not, since it is, and since they have no reason not to (yet).

But then when they get to the definition of "proof" and encounter
that same exact wording, and realize they've already accepted it,
then they cannot refuse the definition in honesty.

Whether you approve of that tactic or not, it is no point of
logic. The refutation stands.

>Since you pulled your definition of
>"proof" from a logic textbook, it is almost certain that your
>definition of "self" is included in the definition of proof as well.

Nope. That was not included anywhere. "Self-proving" in context
of math is just a phrase I've always known and encountered
throughout my life.

>(Somewhere, it almost certainly states that the formulas must either
>be things proven already, or axioms. At that point, your definition
>of "self" is included.)

Thanks for demonstrating an instance of the concept of "self-"
occuring in logic. I hereby incorporate that into the refutation
under definition "3. 'Self-'".

Larry
.

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