Re: "Friendly Premises"


"George Dance" <georgedance04@xxxxxxxx> wrote:
>H. J. Sander Bruggink wrote:
>> George Dance wrote:

First, let me compliment you on your much stronger
demonstration that "proof" is not equivalent to "Self-proving
procedure" that occurs in Torkel's (reduced) assertion:

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

by constructing the necessary inference from the assumption
"'proof' is equivalent to 'self-proving procedure'":

"There is no concept of 'logic' in logic."

which is obviously absurd. In my reply to Mr. Shobe, I could
only say it "naively seems to me" that "self-" implied more
information than just "proof." I'm can make a proof by
absurdity, but I just didn't see it!

Also, I compliment H. J. Sander Bruggink who appears to
be arguing cooperatively and knowledgeably for the opposition
here. Maybe we can make some progress, then, as opposed to
just being "silly."

>>> Surely not. I am pointing out that, if Mr. Shobe is correct that the
>>> concepts of 'self-proving procedure' and 'proof' refer to the same
>>> things, then asserting (as you did) "There is no concept of
>>> 'self-proving procedure' in logic" is equivalent to asserting "There is
>>> no concept of 'proof' in logic."
>>
>> Let's do a little word game:
>>
>> I am pointing that, if the words 'bloem' and 'flower'
>> refer to the same things, then asserting "there is no
>> word 'bloem' in English" is equivalent to asserting
>> "there is no word 'flower' in English."
>>
>> Do you agree with this? :-)
>
>Well, yes, but we weren't talking about words but concepts. The fact
>that an English-speaker doesn't use the word 'bloem' does not show that
>English-speakers have no such concept. In fact they do, even though
>they use a different word ('flower') for it.

Doesn't the analogy also contain a level-of-description (LOD)
error?

For background, I remind other readers that 1) LOD is a test in
real-world logical reasoning (RW) 2) RW includes everything in
the real-world, i.e. it includes "theory." The two are not
mutually exclusive. 3) LOD is only ever valid in a context, I'll
try to make context obvious where necessary.

Mr. Shobe, who made the (paraphrase) "'self-proving procedure' is
equivalent to 'proof.'" assertion, appeared to use "proof" only
in the sense of a deductive formal logic proof. For one thing he
was commenting on a textbook quote about the "deductive" process
that seemed obviously within formal logic.

"Self-proving procedure" is RW. The latter contains the word
"proof" but that word is used in the RW sense, and includes both
formal deductive proofs and other kinds of "proofs" as (loosely
and perhaps incorrectly) used in other logic contexts. "Self-"
and "procedure" are both intended (regardless of how poorly) to
invoke the formal deductive interpretation of proof in context of
predicate/math logic (and don't forget I was confused about that
relationship), by readers who are assumed to be qualified to make
that conversion, by someone (me) who doesn't know the correct
terminology to use and thus cannot make that conversion. (As I
clearly stated with the original introduction of the phrase.)

"Proof" is then "formal deductive logic in English" while
"self-proving procedure" is "English," even though it was
(attempted to be) shaded to the best of my meager ability
in such a way as to induce the above hoped for conversion.
Also note that, since I wanted to induce that conversion, I also
needed it to be somewhat obviously incorrect - and that should go
down in Usenet history as one of the most tortured excuses ever
for confused terminology!).

The LOD for "proof" is "formal deductive logic in English"
The LOD for 'self-proving procedure' is "English"
Because "formal deductive logic," when containing English
language (at least), occurs within "English," there is an LOD
change to the next higher LOD. Thus the comparison "proof" v.
"self-proving procedure" contains a change in LOD.

The two terms cannot be equivalent if there is a change in
LOD.

Also, it was recently explained to me that, linguistically, the
word "Formal" excludes language by definition. I don't know if
that applies here, but if it does, then that's another end of the
story (besides yours). 'Self-proving procedure" cannot be
equivalent to 'proof" in the formal deductive sense.

I continue with an aside about this proof (refutation) by analogy.
If there is indeed an LOD change between 'proof' and
'self-proving procedure' then I think the analogy must fail
because I don't think there is an LOD change in the analogy.
However, if the LOD change above does fail, then the analogy
would hold with respect to LOD only.

I don't know all the things that would be in a higher
LOD for "English." But I'm speculating that the obvious one
in context of the jumbled word in the analogy would be
"character set." Here, the context includes: character set,
words, resulting meaning, logic using words, natural language
using words, theory v. RW.

Both "Bloem" and "flower" occur in "character set." That
alone does not establish that they are in the same LOD
(what I wish to demonstrate). But it establishes that they
are in the same system, i.e. if there is a difference in LOD
in context of "characters set," one is contained within the
other (which I suspect is not the case.)

The LOD for 'Flower" is "English."
The LOD for 'bloem" is "Nonsense."
But "English" does not occur within "Nonsense" (I speculate.)

"English" does not occur within "nonsense" because you
cannot have "Nonsense" without "English" (whereas you
*can* have English without formal deductive logic in the original
comparison which is being analogized).

In other words, the character set "abcde...", however arranged
is not "nonsense." It remains just a character set, and it's
perfectly sensible to invent a character set. It cannot be
"nonsense" until "sense" is introduced, i.e. "English." "Sense"
(i.e. English) is in the same level of description as "nonsense."

Thus (I speculate) the analogy fails because: 1) there is a
failure to maintain LOD in the analogy, and 2) LOD is one of the
attributes of the comparison being analogized, i.e. "proof" v.
"self-proving procedure." which is a deciding attribute of the
proposition in question, i.e. whether the two terms are
equivalent.

Again, this whole line of reasoning, presented for George's
(or anyone's) review, is speculative.

Larry
.

Quantcast