Ron, Rich, and Chris, (01)
RS> May I toss a little pebble into the semantics pool? (02)
That's more than a pebble. It's a much needed agitation of a
stagnant pond. I frequently make waves that disturb the basic
paradigms of many people's pet projects. I am always happy to
have fellow wave generators take the heat so that I can appear
as a conciliator. I have a great deal of sympathy with the two
papers on your web site: (03)
http://web.me.com/rstamper/Site/PHILOSOPHY_.html
Stumbling across a "Soft Mathematics"?
while Exploring some Issues of Organisation, Law and Metaphysics (04)
http://web.me.com/rstamper/Site/MEASUR.html
Measur methods outlined (05)
RS> Perhaps I have misunderstood the discussion but it appears to
> concern the use of languages, especially forms of logic, to
> solve problems of meaning. (06)
I am frequently diverted into such details because those details
are critical for computation. But I definitely *do not* consider
Tarski's model theory to be adequate as a definition of meaning
for natural languages. I frequently quote the title of Tarski's
major paper, because it spells out *all* and *only* what his
model theory can contribute: (07)
"The concept of truth in formalized languages" (08)
For full natural languages, truth is certainly important, and
Tarski's model theory can address some of the issues, but not
all. Even then, there is far more to meaning than just truth. (09)
RS> Kowalski and his PROLOG team at Imperial College dismissed our
> work on semantics at the London School of Economics. Another
> professor of computer science, at about the same time, rebuked
> me for using the terms 'ontology' and 'epistemology' and warned
> me against falling into a 'philosophical bog'. I’m worried that
> most Otologgers belong in the same camp. (010)
Many do belong to that camp, and others are confused about what
camp they belong to. But some also have a broader perspective. (011)
RS> Kowalski put it clearly on p.9 of his book "Logic for Problem
> Solving":
>
> "It follows that it is unnecessary to talk about meaning
> at all. All talk about meaning can be reexpressed in terms
> of logical implication."
>
> To us this declared their retreat into either a world of pure
> symbol manipulation or a rarefied Platonic reality accessible
> to some privileged minds. (012)
I have a very high regard for Kowalski's technical contributions
to the use of logic in general and Prolog in particular. But
his philosophy is deeply mired in the stagnant pond. (013)
At the end of this note is a copy of a message I sent to the
BISC mailing list -- Berkeley Initiative in Soft Computing,
which was founded by Lotfi Zadeh and includes many people
who support fuzzy logic and other "soft" methods. (014)
RS> For work on semantics, do we not need a kind of logic that keeps
> the agents in the picture? one that starts from responsibility and
> existence as primitives and then leads to truth and falsity as
> derived concepts. I guess that it will resemble FOL with a twist. (015)
Yes. And that twist gets into metalanguage about language and about
the agents that use language. Tarski also discussed metalanguage,
but much more is needed. (016)
RC> Yes, agents act purposefully while nonagents are physical objects.
> So I agree that the agent concept and its various applications, are
> needed to properly process English text. (017)
Indeed. Purpose is critical to any theory about how agents use
language in connection with what they do. Those connections,
which are usually lumped under the term 'pragmatics', are a
component of "meaning" that is at least as important as truth. (018)
CM> I don't have the book [by Kowalski], but one natural, and fairly
> innocuous, interpretation is simply that the meaning of a sentence
> (in a given theory) is characterized by the set of sentences it
> logically implies. This is more or less the axiomatic approach
> to ontologies. (019)
I agree that is probably Kowalski's intention. But it assumes
that the axioms are magically plucked out of thin air and dumped
into a theorem prover. By dismissing anything that cannot be
expressed in terms of deduction as a "philosophical bog", Kowalski
ignores the all-important question of how those axioms are derived.
He cannot deal with questions about observation, interpretation,
testing, induction, abduction, learning, belief revision, or
anything that can turn a theorem prover into an intelligent agent. (020)
CM> If your purpose is simply to provide a semantics for the basic
> operators of FOL — which is all the basic model theory of FOL
> purports to do — then you don't really need any specific ontology
> at all. (021)
That's true. But it's not sufficient for building an intelligent
agent. (022)
RS>> I guess that it will resemble FOL with a twist. (023)
CM> Maybe. Show us a theory. (024)
The kinds of theories one might implement in IKL, for example --
or the still undefined theories (in IKL or other notations)
that can support systems that can really be said to "understand"
natural languages by responding in the way that people do. (025)
John
__________________________________________________________________ (026)
Note to BISC mailing list, dated 1 July 2009: (027)
Dear Lotfi and Stuart, (028)
As someone who has long been associated with formal systems of logic
and reasoning, I would like to emphasize that I definitely *do not*
subscribe to the Frege-Russell-Carnap dogma that logic is somehow
superior to natural languages. (029)
When it comes to logic, my philosophical heroes are Peirce, Whitehead,
and the later Wittgenstein -- who are in no way inferior to and, I
believe, far and away superior to the previous three. I claim that
the majority of the weaknesses of both 20th century analytic philosophy
and many of the AI developments inspired by it are the direct result
of the F-R-C dogmas. Furthermore, I believe that those weaknesses
could be corrected by giving at least equal time to the philosophical
and logical writings by CSP, ANW, and LW. (030)
A few comments: (031)
SHR> The open-world issues need to be visited for they will prove to
> eclipse the closed-world issues. Here, the approximate solution of
> the class of problems you outline will necessarily shed much light
> on how the brain works - not through neurochemsitry, but through
> approximate constraint-based reasoning of the open-world sort. (032)
I mostly agree with that point, but I'd like to rephrase it in terms
of Wittgenstein's language games. In his first book, which LW wrote
under the influence of his mentors, Frege and Russell, he adopted
their dogmas about the primacy of logic and a kind of model theory. (033)
In his Philosophical Remarks of 1929-1930, LW began to break with
his mentors, and he introduced two fundamental terms: 'Satzsystem'
(system of sentences or propositions) and 'Beweissystem' (system
of proof). LW came to the conclusion that there is an open-ended
number (possibly infinite) of Satzsysteme, and for each Satzsystem
there is an open-ended number of proof systems. What we now call
a logic is a combination of a Satzsystem with a Beweissystem. (034)
In his later writings, LW adopted the now more familiar term
'Sprachspiel' (usually translated 'language game') as the
equivalent of a Satzsystem plus a Beweissystem. But he also
included a much more open-ended range of language games, which
did not have to have anything that remotely resembled the kinds
of formalisms used in the Satzsysteme and their Beweissysteme. (035)
When talking about the open-world assumption and closed-world
assumption, I prefer to use LW's terminology: Any given
notation for logic defines a Satzsystem. That notation with
the classical rules of inference (closed-world assumption)
is one Beweissystem that can be used with that Satzsystem. (036)
However, that same notation with the modified rules of
inference necessary for the open-world assumption provides
a different Beweissystem for the same Satzsystem. And it
is quite possible that there could be other Beweissysteme
that might be used with that same notation for other purposes. (037)
That same discussion could be repeated with the term
'language game' as a replacement for 'Satzsystem' plus
'Beweissystem'. In short, all logics are language games,
but many language games go far beyond the Beweissysteme
espoused by most logicians. (038)
SHR> Burnstein has written that the solution of such inherently
> inexact models will derive from multiple analogies, which of
> course is an inexact form of reasoning itself. Inexact reasoning
> brings with it another advantage in that it allows for the use
> of faster inexact hardware for some of the processing... (039)
First of all, I would emphasize that many eminent logicians,
starting with Leibniz and including Peirce, Whitehead, and
the later Wittgenstein, would qualify that term 'inherently
inexact'. They would point out that the rules of inference
together with the closed world assumption are only "exact"
for mathematics. For any empirical subject, *no* system of
logic can be truly exact. The rules of inference might give
the "appearance" of exactness, but the uncertainty in the
measurements and the applicability of the axioms imply that
absolute certainty in the conclusions is impossible to achieve. (040)
Leibniz, of course, did not use our modern logics and
terminology, but he made that point by saying that human
reasoning can only be certain about pure mathematics.
For any empirical subject, only the infinite mind of God
is capable of comprehending the infinite detail necessary
for exact reasoning, and human reasoning is inevitably
limited and fallible. (041)
As for analogies, many modern logicians call deduction
"reasoning from first principles". However, CSP, ANW, and
LW all emphasized that for any empirical subject, deduction
is only as reliable as the assumptions. If the assumptions
and the measurements were derived by the usual methods of
observation, induction, and abduction, it is impossible to
assign any greater reliability to the conclusions than to the
starting assumptions. (042)
Peirce and others made the point that analogy is more primitive
than the other three methods of reasoning: deduction, induction,
and abduction. But "more primitive" does not imply "worse".
Analogy is a one-step method of reasoning that can replace the
multistep reasoning of induction, abduction, and deduction.
If the analogy is based on exactly the same observational data
as the multistep methods, it can be just as reliable as
and sometimes more reliable than the multistep reasoning. (043)
But I would add an important qualification: Many theories,
especially in physics, have been established on the basis of
so many observations, that it is practically impossible to
recreate all their conclusions by using multiple analogies. (044)
In many of the "soft" sciences, however, the theories are
less well established, and reasoning by analogy is far more
important -- especially in applications that go beyond the
areas where the theories were tested. (045)
In economics, for example, the recent disasters were caused
by people who applied their familiar theories in areas where
they had not been tested. Most of the proposed applications
of ontology are to areas that more closely resemble economics
than physics. (046)
LAZ> In realistic settings, mathematically rigorous theories may
> founder on the rocks of incomplete information. (047)
I completely agree, and so would Leibniz, Peirce, Whitehead,
and Wittgenstein. (048)
John Sowa (049)
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