SUO: Re: Intension & Extension
> 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?
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. The
abstract sentence in the IFF represents the concrete synatactic 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. Now the use of these abstract sentences as "formal
attributes" occurs in the mathematical context of the *truth
classification*. 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."
Robert E. Kent
rekent@ontologos.org