ONT Re: Intension & Extension
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JA = Jon Awbrey
RK = Robert Kent
JA: people who are realists about attributes, intensions, properties,
qualities, types, ..., have trouble saying that attributes are
sentences. an attribute is an abstract object, a sentence is
a syntactic thing, and many sentences could denote the same
attribute. it's not that a sign couldn't be a property of
a thing, but it's not a general rule. is this anything
to which you can accommodate your thinking?
i sense that i may have confused the issue with that penultimate sentence.
so let me go through your comments, and then try to clarify what i meant.
RK: The IFF is situated at the metalevel. It talks about the content of
the object level. In particular, the IFF Model Theory Ontology treats
models (model-theoretic structures), first-order type languages,
expressions (= formulas), sentences of such languages, etcetera,
as abstract things.
yes, but we already do that in our natural discourse.
as soon as we talk or think about anything, even signs,
they become prospective objects of conception, discussion,
and thought, and objectively so if our treatment of them is
logically consistent. and we are always really talking about
things as types that exist at a higher level than the multitude
of tokens that might be distinguished, so the questions of "meta"
or not or "abstract" or not are not the issues i am worried about.
i confess that i do not know what "content" means to folks hereabouts.
it just sounds like a collapse of the denotational or referential dimension,
in other words, a confounding of the object and sign roles, to identify the
sentence with the attribute that it is intended to denote or to describe.
RK: The abstract sentence in the IFF represents the concrete
syntactic sentence of any appropriate object-level logical
language, such as DAML or OIL. Perhaps much like vector
spaces and linear transformations represent Euclidean
vectors and matrices.
no, that sounds exactly backwards to me. the more concrete things,
like matrices and the sorts of sentences that parsers have to parse,
represent the more abstract things, like linear transformations and
the "propositions" or the logical equivalence classes of sentences
that correspond to them.
okay, usage varies here. among the words that i have seen used a lot:
1. idea, 2. logos, 3. lekton, 4. proposition, 5. statement, 6. expression, 7. sentence.
abstract object .............^...............^.............^............ concrete sign.
most folks seem to put the fulcrum somewhere between 3 and 6.
only just recently, as a compromise, i have been locating it between 4 and 5.
RK: Now the use of these abstract sentences as "formal attributes"
occurs in the mathematical context of the *truth classification*.
question here. some people, when they attach the word "formal" to another term,
act as though that is the act that changes it into an abstract object of thought.
for my part, when we construct a mathematical system to serve as an analogue model
of something, the rising tide of formal abstraction lifts all boats at once, and
so i tend to think of the comparative relation-ships as being preserved thereby.
hence, a formal attribute, concept, language, object, ..., remains as it was
in relation to other things, an attribute, concept, language, object, ...
so i try to use mathematical models in a "holistic" way, avoiding as
much as possible the introduction of local or piecemeal distortions.
RK: There they function as properties of the "formal objects" of this
truth classification, which are the models (for the particular
fixed abstract first-order logical language L in question.
A particular L-model 'M' has a particular L-sentence 's'
when it satisfies it, namely when 'M |= s'; that is, the
sentence 's' is true when given the abstract interpretation of
the model 'M'; as you will see, the models in the IFF Model Theory
Ontology are different from traditional models, being based on the
ideas of classification and hypergraph, but they are mathematically
equivalent to the traditional models. So, perhaps in the context of
the truth classification, the sign-like thing called a "sentence"
functions as the property of a thing called a "model".
yes, that's the sort of thing that can happen, but the more usual case is that
the sign (sentence or term) "denotes" an attribute of the situation or thing.
jon awbrey
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