Dear Chris,
You make my point. Let me explain lest we continue to inhabit parallel never
meeting worlds.
On Jun 30 Ronald Stamper wrote:
Perhaps I have misunderstood
the discussion but it appears to concern the use of languages,
especially forms of logic, to solve problems of meaning.
You can do that with FOL
provided that you are prepared to deal only with the self-contained world
to which it gives access.
CM: I have no idea what you mean by a
"self-contained world", but there are no restrictions whatsoever on the
subject matter that can be represented in FOL (though it may not be the
most appropriate logic for certain domains, e.g., quantum
mechanics).
RS responds: Exactly: the use of
( , ), and, or, not etc are restricted but you can freely insert any names for predicates,
P, Q, R, . . . or individuals x, y, z, . . . etc, that you choose. The former have meanings in a purely
syntactic sense supplied by the rules for forming and manipulating expressions
containing them. The symbols for predicates
and individuals have no meanings within the logical language.
No amount of
manipulating logical expressions will connect them to anything in any real or
imaginary world. Such connections
(meanings in the sense that interests me), if any, are supplied when readers
imagine those names connect to real or imaginary predicates or individuals. FOL imposes no restrictions on those
imaginings: that’s its weakness semantically (in the sense that interests me). One cannot step outside the
self-contained world of FOL without the imaginative interpreter of the
logically meaningless symbols.
RS; Kowalsik 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
re-expressed 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.
CM:
I suspect you are grossly misinterpreting the remark. I don't have
the book in question, 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.
RS responds: Make no mistake, I admire Kowalski and
happily discussed this problem with him.
In different words he told me the same thing face to face, at least a couple
of times. In his concern
with the programming of computers, his position is quite correct. But anyone concerned with running a
steel works or administering an arm of government would be foolish to adopt
that position.
A manager says of a stock
report: “I don’t know what this means.” or a judge says the same of a day’s
evidence. Would you instruct
either of them, “Simply look for the set of sentences these logically imply.”? As stockyard manager you would get the
boot or as counsel you would teeter on the brink of contempt of court.
RS: So: no semantics without ontology (RS
emphasises: I use ‘ontology’ in the metaphysical sense of a commitment to what
exists.)
CM:
Well, that depends on the kind of semantics you have in mind. 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.
RS responds: Exactly, I agree. If your priority is the manipulation of
logical formulae using a computer, then a semantics for its basic operators
will suffice together with an ontology that presumes that nothing else exists
but the logical constants and symbols with no constant meaning WITHIN the
language. But I want to help run
steel works and administer the law and I know that managers, judges and others involved
in most practical affairs need to know who supplies the information they use,
whether they can be trusted, what intentions may lie behind their choice of
words, what they might omit . . . etc.
I’m all in favour of logic but
we need something more. So I
suggested
RS: and no semantics without responsible agents.
RS adds: because without them, we have no bridge
between the other symbols and what they stand for. And if those agents are not responsible and open to cross
examination and character references, we can place little trust in anything
generated by even the best and most reliable logic engine.
CM:
Simply false for the semantics of first-order logic. Perhaps true
if you have a different notion of semantics in
mind.
RS: Exactly! That
other notion of semantics is the one that interests me.
RS: For work on semantics, do we not need a kind of logic that
keeps the agents in the picture?
RS adds: That’s why I’ve struggled with ontology
of a rather different kind from that dominating the discussions related to the
Semantic Web.
CM:
Again, it depends on what you mean by "semantics". There
is so much that falls under that term that the question
as it stands is simply ill-formed. This literature on logic-based
approaches to agency is absolutely huge.
RS: I believe that our
discussion has made it clear that we should contend with at least two different
meanings of “meaning” and of “semantics”. A veritable army of scholars has resolved
the semantics of logical formalisms, especially during the last century. Scholarly work on the kind of semantics
that interests me – linking signs to real things – is vast, varied, fascinating
and challenging but yet shows little sign or resolution. The literature on software agents is
irrelevant; I’m concerned with responsible agents, including the authors of the
software but not with their ‘mechantical devices.
Hence I have chosen to work from
a new(ish) ontology towards a logical formalism,
RS: 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.
Maybe. Show us a theory.
RS: Happily! If you
are seriously interested in this other semantics and I’ll also show you some of
the practice – it works well for developing and designing information
systems. The notion of ontological
dependency is well developed but the logical formalism needs lots more work.
Thanks for you comments. As a minor disciple of Popper I always
seek refutations but I must agree with John Sowa that I would not, in other
respects, swap Peirce for Popper.
Semiotics plays an even more important role in the work we have been
doing.
Ronald
-chris