Re: SUO: Thoughts and judgments
Robert,
Some system or theory X only gives you an advantage over some
person P if and only if all of P's insights are subsumed by X.
I very much doubt that those two theories you mention give anyone
any advantage over Peirce.
REK> We have the advantage over Ockham, Peirce and Tarski of the
Information Flow
> theory of classification and the theory of Formal Concept Analysis.
The following is a very simple concept that was familiar to Peirce,
Tarski, and even Ockham, but with different notation & terminology:
> In the truth classification and the associated truth concept lattice, where
> L-structures are instances (tokens), L-sentences are types and L-incidence
> is satisfaction (structure models sentence), we can define the concept of
> logical consequence as follows: The sentence X follows logically from the
> sentences of the class K if and only if the formal concept generated by the
> class K is at or below the formal concept generated by the sentence X.
To emphasize the point, there is an anecdote about Richard Feyman,
who made a bet with a colleague who happened to be an algebraic
topologist:
1. Feyman bet that if his colleague (I'll call him C) would take any
proposition about algebraic topology (either a theorem or the
negation of a theorem) and answered all of F's questions about
the definitions and intuitive meaning of the terms, then F would
tell C whether the proposition was true or false.
2. C scoffed at the claim, since he believed that it was impossible
for a nonspecialist to determine whether any such proposition
was true or false without carrying out a lengthy proof that used
all the machinery of category theory, etc.
3. But F persuaded C to take the bet.
And of course, I wouldn't be telling you this if F hadn't won.
For every theorem or its negation, F asked C about the meaning of
each term, and after F was satisfied that he had an intuitive
feeling for the proposition, he answered whether it was true or
false. And F's answer was correct for every one.
Unfortunately, I don't remember the source where I first read about
this anecdote. If I can find it, I'll send another note about it.
I tried Google to search for this anecdote, but no luck. However,
I did find the following two quotations along the way, which
reinforce my point that the really good people in math, logic,
and related fields have a strong intuitive feeling for the results
long before they happen to write them down in any notation.
Bottom line: Most logicians today have gone a lot farther than
Peirce, Tarski, and Ockham in many technical ways. But in many of
the fundamental insights about what it all means, they haven't begun
to "go beyond" Peirce, and even Ockham would give them a real run
for their money if he showed up at one of their seminars. As an
example, just look at Ockham's treatment of puzzles such as the baldness
of the present king of France and compare it to what Russell, Strawson,
Kripke, etc., have said. For a summary, see Section 4 of my paper:
http://www.jfsowa.com/pubs/signproc.htm
John Sowa
PS: That doesn't mean that I don't think those theories you cited
are useless. They are good exercises for developing the intuitions
in students and in designing software to be run on computers that
have no intuitions at all.
_______________________________________________________________________
"Mathematics -- this may surprise or shock some -- is never deductive in
its creation. The mathematician at work makes vague guesses, visualizes
broad generalizations, and jumps to unwarranted conclusions. He
arranges
and rearranges his ideas, and becomes convinced of their truth long
before he can write down a logical proof ... the deductive stage,
writing the results down, and writing its rigorous proof are relatively
trivial once the real insight arrives; it is more the draftsman's work
not the architect's."
- Paul Halmos
"We have a habit in writing articles published in scientific journals
to make the work as finished as possible, to cover up all the tracks, to
not worry about the blind alleys or describe how you had the wrong idea
first, and so on. So there isn't any place to publish, in a dignified
manner, what you actually did in order to get to do the work."
- Richard Feynman