Re: All Hope Of Logic Becoming Useful (Was Lost In Translation)
Jon,
I certainly share your concerns, and so would Peirce,
Whitehead, and Wittgenstein. The only people who
think logic, by itself, can solve any serious
problems are those who were deluded by people like
Frege, Russell, and Carnap. (Poor old Wittgenstein
was one of those people, and he spent the second half
of his life trying to recover from his earlier malady.)
JA> My concern is whether our logical calculi, formalisms,
> and languages will ever begin to serve the actual work
> of reasoning on significant practical questions in any
> meaningful way. As a matter of course, that will take
> their efficient computational implementation. However,
> there are some preliminary questions about what logic is,
> what it's supposed to be good for, and what it will take
> to design a computational calculus that is good for that.
I think that GOFOL (Good Old First-Order Logic) is part
of the answer, but only one part. Much more is needed.
Just one observation: GOFOL is sufficient to specify
a Turing machine; in fact, you only need the Horn-clause
subset to do that. Ergo, anything that is computable
on any digital computer can be specified in GOFOL.
But mere sufficiency is not sufficient.
JA> We have a hundred years of mostly wrong answers to
> these questions. You can tell they are wrong because
> nobody actually uses them for any significant practical
> purpose in everyday real-world research on real hard
> questions in any field.
There is an enormous difference between research and
practice. If you want to do siginficant research,
abduction is the most important reasoning method.
But if you want to do practical computation, GOFOL is
extremely practical. Just look at SQL -- it is one
of the worst notations for logic (it was *the* worst
before OWL came along), but the entire world economy
runs on SQL. You can't beat that for practicality.
JA> It is a sad fact of history that I have to go back
> to Peirce to find anybody who shows the least signs of
> recognizing the problem of scientific inquiry as something
> that isn't hacked already, but it's a fact, nonetheless.
>
> One of the causes of this sad condition, and its persistence,
> seems to be the detachment of our current excuse for logic
> from the realities of "experience and logical reflexion".
Peirce is always a good starting point for any kind of
inquiry, but following are some quotations from Whitehead
that are worth noting (_Modes of Thought_, 1938):
- "The conjunction of premises, from which logic proceeds,
presupposes that no difficulty will arise from the conjunction
of the various unexpressed presuppositions involved in those
premises. Both in science and in logic, you have only to develop
your argument sufficiently, and sooner or later you are bound
to arrive at a contradiction, either internally within the
argument, or externally in its reference to fact." (p. 14)
- "It should be noticed that logical proof starts from premises,
and that premises are based upon evidence. Thus evidence is
presupposed by logic; at least, it is presupposed by the
assumption that logic has any importance." (p. 67)
- "The premises are conceived in the simplicity of their individual
isolation. But there can be no logical test for the possibility
that deductive procedure, leading to the elaboration of
compositions, may introduce into relevance considerations from
which the primitive notions of the topic have been abstracted....
Thus deductive logic has not the coercive supremacy which is
conventionally conceded to it. When applied to concrete instances,
it is a tentative procedure, finally to be judged by the self-
evidence of its issues." (p. 144)
- "The topic of every science is an abstraction from the full
concrete happenings of nature. But every abstraction neglects
the influx of the factors omitted into the factors retained."
(p. 196)
JA> Can we design computational calculi that will actually help
> with these tasks? Perhaps. But it will take waking up to the
> near total inutility of current systems, along with the near-
> sighted philosophies of logic that went into producing them,
> before we can even begin.
There is no shortage of people who have long ago given up on
logic. Unfortunately, they are reacting against logicians
who have no idea about how logic should be used. The major
problem is to convince logicians that deduction is only one
part of reasoning and by no means the most important part.
For some related points, following are the slides I presented
at the ICCS 2003 conference in Dresden:
http://www.jfsowa.com/talks/iccs2003.htm
Analogical Reasoning
Following is the full paper from the proceedings:
http://www.jfsowa.com/pubs/analog.htm
Analogical Reasoning
And following is a more philosophical analysis of the
shortcomings of 20th-century analytical philosophy:
http://www.jfsowa.com/pubs/signproc.htm
Signs, Processes, and Language Games
John Sowa