A Note From My Dad

> Dad, do you know anything about "intensional" logic or
> semantics? I don't.

Yes, I know about intensional logic/semantics.

I guess for a Platonist, an intension is a projection from an
expression into the space of meanings, whereas a cognitivist
would probably call it a mental representation. The basic idea
is to distinguish the realm of expression from the realm of
semantics/meaning (and a far cry from approaches like Lakoff's
Philosophy in the Flesh, which anchors meanings more closely to
our physical makeup).

Intensions are distinguished from expresions by putting an
apostrophe after the expression, so _dog_ is an expression and
_dog'_ is the corresponding intension. Nothing exciting there.

The payoff comes from "intensional predicates" like _believe_.
For example, in _John believes he is president._ what John
believes is an intension (I am president') for which there is no
corresponding reality.

Various theories of syntax assume that as expressions are
"composed" by rules of grammar, there is a parallel composition
of intensions. E.g., _I like vanilla icecream_ would start by
syntactically composing the adjective _vanilla_ and the noun
_icecream_, simultaneously composing the intentions vanilla' and
icecream' into something like vanilla'(icecream'). [Read" the
intension of vanilla is predicated of the intension of
icecream.]

OR SOMETHING LIKE THIS.

> I want to explore the potential use of the word "intensional"
> as a "pomo" contrast to "intentional." -- along the lines of,
> we should live intensional lives (we need to live in the
> tension of life). Have intensional faith ... and be an
> intensional church ... etc.

I don't think it has anything to do with "tension." Rather, it
is probably cognate with Spanish "entender".

The expressions you mention would, for me, mean something like
"we should be conscious about how we live (rather than just
coast along without giving things due thought)."

> I didn't realize that the word was used in
> mathematics/linguistics. Any thoughts?

You can probably think up a much better way to get your
important point across.

Best, --Dad