Death and Syntaxes
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John,
The tendency to fixate on the mere possibility of expression
in a given form of representation is a symptom of expressivism,
which was begat by syntacticism, which was begat by nominalism.
The one thing that you have to give nominal thinkers credit for
is their ability to keep changing their names. Now scepticism
toward hypothetical objects, like Complex Numbers, the English
Language, and Planet Earth, is entirely appropriate, but there
are lots and lots of hypothetical objects that have paid back
the overhead of their speculative investments, and bona fide,
non-trivial, objective-oriented formal thought is just not
possible without them.
My initial up-piping on this thread was concerned with the sorts of
properties that deserve to be called "objective", as they variously
say in mathematics, "coordinate basis free", "frame of reference or
label independent", "transformational invariant", "universal", etc.
Generally speaking, one does not normally consider a definition of
an object or a property to be properly objective unless it can be
given a notation invariant form.
Some buzz that I was googling about "logical order", as in "k^th order logic",
made me think that this is really more like some kind of "linguistic order",
and that we are at the stage where we lack a properly objective measure
of the putative complexity.
Part of this problem, or the inability to recognize that there is a problem,
appears to be due to the lack of homework doing that some schools of logic
so notoriously permit, if not incite. So I back-tract to a point in time
when logicians still had a clue what they were talking about, and I think
it remains clear that what Aquinas and Peirce and Company were talking
about is simply lost in the so-called "reading" that tries to explain
it in terms of this syntactibund measure of "order".
Jon Awbrey
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John F. Sowa wrote:
>
> 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
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