Rich, (01)
Let me start with the last line of your last note on this thread: (02)
RC> I would like to see a full philosophical structuring of this
> very basic thing we call logic. (03)
That has been done in great depth, and if you want to begin
that study, I completely agree with Pat Hayes: Start by
studying truth tables. When you make one statement P, and you
later make another statement Q, you have two statements: P, Q. (04)
One of the basic rules of inference of Boolean logic: (05)
P, Q |- P&Q (06)
The turnstile symbol "|-" is an abbreviation for the phrase (07)
"from the previous, it follows that" (08)
That inference is true independently of any context or any
implicit assumptions about narratives or time sequence. (09)
As I said before, an implicit assumption about time would
imply that the sequence of two statements P,Q implies
"P and then Q". But that in no way negates the previous
point, because "P and then Q" also implies "P and Q". (010)
This is not deep philosophy. This is the most baby philosophy
you can imagine. There is immensely more to say about context,
presupposition, time, etc. But Boolean logic is more basic. (011)
RC> John... stated that you can build a philosophy (logic,
> algebra, ?) on the basis of establishing the following:
>
> 1. Existence
> 2. Conjunction
> 3. Negation by omission (012)
To begin at the end, I was definitely *not* recommending
"negation by omission". More precisely, I was claiming
something very much simpler: (013)
1. You can observe something. (In logic, "there exists an x") (014)
2. You can also observe something and you can observe something
else. (In logic, "there is an x, and there is a y") (015)
3. You can observe something about something you observe.
(In logic, "there is an x, and there is a property P,
and P(x)") (016)
4. You can observe a relation among two or more things.
(In logic, "there is an x, and there is a y, and
there is a relation R, and R(x,y)") (017)
Note that the only Boolean operators and quantifiers that
appear in those statements are existence and conjunction. (018)
All other Boolean operators and the quantifier "every" or "forall"
can only be *inferred*. They can never be observed directly. (019)
For example, it is impossible to observe a negation such as
"There are no bacteria in this room." (020)
You might be able to claim such a statement after applying
some strong chemicals to the room or by heating it to a
very high temperature. But that claim results from an
inference from some properties that you assume about
bacteria. It is not a direct observation. (021)
Russell once joked that he could not get Wittgenstein to
admit "There is no hippopotamus in this room." That is
because Russell failed to understand the point that W. was
trying to make: We can never observe a negation directly. (022)
Failure to observe something is not equivalent to a negation.
But given other information, a failure to observe *might*
imply a negation. Given our previous knowledge about the
size and smell of hippos, and our failure to see or smell
one in the room, it would be safe to *infer* that no hippo
is present. (023)
But that is an *inference*, not an observation. (024)
I was not *recommending* negation as failure. I was simply
observing that nobody has ever observed a negation, or an
implication, or a disjunction, or a universal generalization
directly. Those logical combinations are always justified by
some kind of reasoning -- induction, deduction, or abduction. (025)
I was not expressing any kind of deep philosophy. (026)
The only algebra I was using is elementary Boolean algebra. (027)
I was just stating the obvious. (028)
Sometimes, it takes effort to appreciate the obvious. (029)
John (030)
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