Re: "Friendly Premises"


Jesse Alama <alama@xxxxxxxxxxxx> wrote:
>"Acme Diagnostics" <LFinezapthis@xxxxxxxxxxxxxxxx> writes:
>> Torkel Franzen <torkel@xxxxxxxxxx> wrote:

Sorry for the delay. As usual, it took longer than expected.

>>> There is no concept of "self-proving procedure" or "recursive
>>>proof" in logic.
>>
>> That statement is incorrect.
>
>How?

Ah, more typing practice! <g> Actually, I type about 3,000 wpm.
(Perhaps I exaggerate slightly.)

"a concept...in logic" can be interpreted in two ways: 1) the
concept is a logic concept, or 2) the concept is any concept that
occurs anywhere in a logic process, e.g. a logical argument, i.e.
any concept in the universe.

Obviously, there do not exist particular logic terms for each
concept in the universe.

In a logical argument, which is certainly "in logic," the
"informal logic" branch to be exact, any concept in the universe
can be described with any words sufficient to make the argument
"reliable." (Skip 20 pages on what "reliable" means in this
sense, as it will not apply here.)

That's the easy proof that Torkel's statement is incorrect, and
in fact the one I noticed immediately. It's also why I was so
confident that his statement was logically incorrect that I used
the strongest appropriate denial, "That statement is incorrect."

But "good faith" argumentation requires me to volunteer that,
while that proof is certainly and famously sufficient in context
of Torkel, most qualified real debate judges would not pass that
proof, and I am presenting this proof to others besides Torkel.

The reason it would not usually pass is that it is a
*theoretical* interpretation (commonly, "splitting hairs"), and
logical arguments using language, even one's as short as Torkel's
one statement, are *real world.* (Excluding textbook examples,
etc.)

If you are unfamiliar with "real-world reasoning," just think
"informal logic." Close enough, but keep in mind the there
are parts of rhetoric not primarily intended to be logical, also
very big real-world parts of formal logic like probability,
statistics (inductive) and minor parts of classical logic which
are typically studied in "formal logic" courses, books, etc.

I would be making the exact same mistake that Torkel made
when, upon reading the following sentence:

[Goedel] proved that any set of axioms at least as rich
as the axioms of arithmetic has statements which are true
in that set of axioms, but cannot be proved by using that
set of axioms.

he excerpted "true in that set of axioms" out of context, changed
it (like in 5 or 10 repetitions even after being corrected) to
read "true in a set of axioms" (thus removing the reference to
the context), and interpreting that phrase *theoretically*. Of
course after those changes it makes no sense theoretically.
(Actually, I'm told, but am unqualified to even "think I know,"
that it does in some rare context(s), but I conceded that point
anyway since it doesn't matter).

However, the statement was always intended in the real-world
sense considering venue and intended readers. That was explained
myriad times in myriad ways, including in its original
presentation here. Further, in a sufficient number of
*real-world* tests (one now being fortunately linkable)
the entire sentence was inferenced correctly every time.

Now getting back to Torkel's assertion at the top, most qualified
judges would instead require me to assume that Torkel was not so
stupid as to make that mistake, even though he seems challenged
enough at reasoning, e.g. the Goedel example, to make it. Thus I
volunteer to supply charity to improve his assertion to admit
only interpretation #1. The simplest way to improve his assertion
for that is (emphasis added):

>>>There is no *logic* concept of "self-proving procedure"
>>>or "recursive proof" in logic.

This is the statement that I will prove incorrect. Unfortunately
for any readers, that takes a bit longer. I get to practice my
logical refutations.

This is the end of Torkel's lesson. Whether correct or
incorrect, the rest is over his head by about 10 stories. I see
no reason why it should be over anyone else's head. It's length
should not be a reading challenge for any readers qualified to
post here except those for whom English is a second language.
I apologize to them for length. I'd probably do a summary if one
should ask. One of my medical textbooks has paragraphs as long
as this whole post, for instance, and about a 25-character
average word length. Perhaps I exaggerate slightly again.<g>

- - - - -- - - - -

REFUTING THE ASSERTION:

"There is no logic concept of 'self-proving procedure' or
'recursive proof' in logic."

First I will explicate the definitions of words in the above
statement only to clarify them and open up my proof to criticism.
I will then show that, using these words, a true statement
can be constructed "in logic" that contradicts the assertion.

The contradicting statement that I construct will contain the
exact phrasing I used, which phrasing the assertion labels a
"concept," now improved to "logic concept," and will demonstrate
that the phrasing does in fact describe a logic concept, and that
this logic concept does in fact occur "in logic."

These facts will be demonstrated within the definitions because,
in this particular refutation, they are highly related.

There will be no attempt whatsoever to show that either of the
two quoted phrases occur in any glossary of logic terms because
I would not be so stupid as to refute a completely different
assertion from the one I was given to refute, e.g. "There is no
logic glossary containing the terms 'self-proving procedure' or
'recursive proof' in logic." I mention this only because I
suspect that at least one reader expects this to be the assertion
to be refuted. There is a good well-known logic term for that:
"Wishful Thinking." <g>

1. "Logic"

This will be a logical refutation of Torkel's above (improved)
statement proving it to be incorrect. This logical refutation
will use language and thus be governed by the rules of logical
argumentation.

Such a logical refutation is within the logic branch of logical
argumentation which is, in at least one standard logic
definition, within the logic branch of informal logic, which is
within logic. This satisfies the condition "in logic" for these
definitions.

2. "In"

This has already been partly defined at the top. To refute the
improved version of Torkel's assertion, I must demonstrate a
"logic concept." This can be any logic concept that occurs
in logic, Since Torkel has quantified over his entire complex
proposition with the universal "no," and since in context we
can eliminate the usual real-world "soft universal"
interpretation, I need only demonstrate one counter-example. I
will choose the logic concept of "logic system" for my
counter-example.

I personally know this to be a standard concept in at least one
area of logic and I believe it passes as a fact on shared
experience.

However, "to crack unreasoning resistance" as we sometimes
say in the real debate world, I quote from a logic textbook:

"These rules form a system called the propositional
calculus. (The term means simply 'system for performing
calculations with propositions.')"

Note that the word "system" is used as a general
word, twice, using it's common definition, not a technical
defintion. Also note that a logic textbook occurs "in logic,"

Of course the terms "axiom system" or "axiomatic
system" are often used in sci.logic, also on the web, and I'm
sure that mathematical theories are described generally as
"systems" in at least one textbook somewhere, though I don't have
an example, nor do I need one. Torkel didn't say "in XYZ logic,"
he said "in logic."

Because I need to anyway, I will provide an additional example
of "system" used in a general sense along with the next
definition.

Thus I am satisfied that any qualified debate jury would accept
"logic system" as a legitimate example of a "logic concept" "in
logic."

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."

[End definitions]

Now using these words and the explicated definitions all from
within logic, and assuming agreement for the meaning of "there,"
"is," and "of," I can construct the sentence: "There is a
logic concept of 'self-proving procedure' in logic" which is a
meaningful sentence in a logical refutation (but perhaps not
in any theoretical or symbolic logic), thus qualifies as
"occuring in logic," as defined. It is meaningful because it is
at least sufficient to disprove by counter-example the universal
assertion, "There is no logical concept of 'self-proving
procedure' in logic."

According to the "OR" operator as used in logical argumentation,
Torkel has asserted that neither of the two quoted terms occurs
in logic. Thus I need only prove that one of them occurs to
provide the counter-example proving his statement incorrect.

A proper refutation, even of this size, would take at least a
week and better a month. This is not my best work. I reserve the
right to correct any errors that may be found.

To my assertion "That statement is incorrect," which now stands
proved in this group until refuted, Torkel said:

> OK, so you've invented them.

I did not invent any concepts. All concepts herein were well
establish long before I arrived on the planet. That goes for
all the words in the assertion and counter-example as well.

Nor did I invent any terms. My use of the phrases were not
"quoted" (below). *Torkel* added the quotes. The confusion about
both concepts *and* terms is his own doing.

And a big reason for that is his constant habit of *snipping
necessary context* and *inaccurate quoting*.

- - - - -

Now for the benefit of the three posters who have so far asked,
I will explain the meaning of the two phrases *in context*.

Quoting myself, the context is as follows:

>>For this I submit...

<snip some of what I "submit" and continuing with the rest of
what I "submit">

>>1. Existential import had to go because otherwise math
>> could not be supported without the "empty set," i.e. in
>> common understanding the number 0.
>>2. Replace the word "premise" with "axiom."
>>3. Replace the word "conclusion" with "theorem."
>>4. Support self-proving procedures, and perhaps recursive
>> proofs though I'm not that far along yet.
>>
>>Now, I don't know these things for sure, and I'm certain to have
>>made historical and terminological mistakes <snip>

Notice that I only "submitted," and did not "assert." Notice that
I don't know these things for sure. Notice that, re: "recursive
proofs" - "perhaps...not that far along yet." Notice that "I'm
sure to have made terminological mistakes."

Most of all, notice the lack of quotes around those two phrases.

Additional important context is that I posted this to a troll,
but who is however an expert who knows answers. I may thus
legitimately overstate my "submission" to provoke a reply
which might tell me something about the accuracy of these
statements.

Given all that context, there is no use for an explanation. I
don't know anything about Frege or Russell or predicate logic or
how it applies to mathematical logic. I've picked up the
"recursive proof" lingo on Usenet. It googles and obvious
variations google, but not that many pages. Do that and you'll
know what I know.

I've known that math is self-proving, as people from outside the
field of math often say not needing to split any Goedel hairs,
forever. For reasoning in a philosophical sense, it's the main
distinction between math and most other professions.

Thanks Jesse for the opportunity to present my case on
these issues.

Larry
.

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