Re: SUO: Re: Axiomatization of Modularity
Jon,
I sympathize with your concerns:
JA> Axioms : Theory :: Grammar : Language?
>
> But this is only true if we have a decent axiom set
> for a content domain and when we have a full grammar
> for a language, which we may have in artificial cases,
> but never really have in the empirically natural cases.
I agree. In my earlier note, I waa using the term "theory" in the
sense of a deductive closure of a set of axioms. That means that
all the theories I was discussing (and the contexts, which contain
them) are artificial in the same sense that predicate calculus is
an artificial language compared to English or any ohter NL.
JA> So the claim that any accumulated empirical corpus of
> information about being, data about what is, which is
> to my way of thinking the primal form of any ontology,
> can be supplanted by any of our currently developed
> and very partial theories about being, well, that
> is just not a sensible suggestion. And yet this
> working assumption is explicitly set out by some
> and even more presumptively taken for granted as
> an unreflective and uncritical rationale by others.
Any artificial theory (and its formally specified domain of discourse)
is at best an approximation to some natural domain, which can never
be fully axiomatized in any finite representation. That is also true
of every theory in every branch of science and every engineering design
that has ever been (at best partially) implemented in some artifact.
JA> The notion that logic is just a species of semiotic...
> and so I have to treat
> the genesis of ontology as prior to theory proper.
I would prefer not to use the word "ontology", except as a buzzword
that has become popular in circles that are providing research funds.
Aristotle didn't use it, and the nineteenth century Germans who made
it popular in philosophy were trying to distinguish theories of
"being as such" from the study of beings in the natural sciences.
I regard that move as fundamentally flawed -- Aristotle properly
placed metaphysics after physics, and I don't believe that ontology
can be or should be separated from physics (except as an expedient for
keeping any single book from becoming too big to be held in one hand).
JA> 3. As far as context goes, then, I cannot treat it
> in the first instance primarily as a parameter
> indexing theories, though maybe something more
> like a constraint on the POV of a given agent,
> but I have to see it as a factor that affects
> the transition from sign to interpretant sign
> in the relevant sign relation, and all of this
> stage-setting prologues the entrance of logic
> and theory, as full-blown characters, at least,
> onto the scene.
I was using the word "context" as a technical term. My preferred
definition is given in the CG standard: a concept node that contains
a nested conceptual graph. I am willing to generalize that term to
include any notation for bracketing an excerpt of language (any kind
of language) that is under discussion.
Following is the beginning of my context paper, which discusses the
ambiguity of the word "context" and my preferred interpretations:
http://www.bestweb.net/~sowa/ontology/contexts.htm
The technical term refers to the purely syntactic function of
bracketing some text in a natural or artificial language. The
other, derived uses, are even more important, but I would prefer
to use other terms for them.
John Sowa
________________________________________________________________________
1. Search for a Theory of Contexts
The notion of context is indispensable for any theory of meaning, but
no consensus has been reached about the formal treatment of context.
Some of the conflicting approaches result from an ambiguity in the
informal senses of the word. Dictionaries list two major senses:
* The basic sense is a section of linguistic text or discourse that
surrounds some word or phrase of interest.
* The derived sense is a nonlinguistic situation, environment, domain,
setting, background, or milieu that includes some entity, subject,
or topic of interest.
The word context may refer to the text, to the information contained
in the text, to the thing that the information is about, or to the
possible uses of the text, the information, or the thing itself. The
ambiguity about contexts results from which of these aspects happens
to be the central focus. These informal senses of the word suggest
criteria for distinguishing the formal functions:
1. Syntax. The syntactic function of context is to group, quote,
delimit, or package a section of text.
2. Semantics. The quoted text of a context may describe or refer to
some real or hypothetical situation. That nonlinguistic referent,
which may also be called the context, constitutes the derived
meaning of the term.
3. Pragmatics. The word "interest", which occurs in both senses
of the English definition, suggests some reason or purpose for
distinguishing the section of linguistic text or nonlinguistic
situation. That purpose is the pragmatics or the reason why the
text is being quoted.