SUO: Re: Lifecycle Integration Schema
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LIS. Discussion Note 66
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JA = Jon Awbrey
MW = Matthew West
Matthew,
I'm not sure I understood your comment below.
And I need to correct one lapse of a tension,
to wit, extension, that is liable to lead to
misunderstanding if not attended to 4th-with.
JA: In this context, then, I listed the following four dimensions,
that have been recognized over time, historically speaking,
as providing a frame of reference for describing the
phenomenon or the problem that we have in view:
JA: 1. The Term.
For example, "sweetness", the noun form of the adjective "sweet".
JA: 2. The Concept.
For example, "sweetness", something like a noun in the mind.
JA: 3. The Property.
For example, sweetness, that may also be referred to
as an intension or a quality of the thing in question,
though some will make further distinctions among these.
JA: 4. The Set.
For example, the set of sweet things, that comprises
the extension of either the term "sweetness" or the
concept "sweetness", according to one's taste.
Cut me a little bit of slack at this point, as I learned this bit about
equivocal names, general denotations, and plural references rather late
in life, long after I had gotten habituated to the set-theoretic way of
thinking about things, and so it's easy to slip up, namely, up to a set
of objects as a hypostatically abstract object in its own right or meta-
category, when in fact a more nominal strategy would not admit any such
things to its theatre of operations.
The right way to say it, in the nominal sense of "right", if you choose
to speak of the extensions of terms and concepts without wanting to pay
the price of buying a token for the type <set>, goes somewhat like this:
5. The Extension of a Term or a Concept.
For example, the extension of the term or the concept "sweet"
is all of the things in the pertinent universe of discourse,
or all of the things known at a given state of information,
of which the general term "sweet" is evalued as being true.
Here I have been careful not to invoke, at least, not formally,
not in the "object language" as some would say, the apparently
invidious notion that there is over and above sweet things, an
abstract object that is what all the (rest of the) world would
call the "set" of sweet things.
Nevertheless, we are still free, under carefully circumscribed
engagements of terms, to use our informal language and manners
of speaking about sets, just so long as we never use, formally,
what we thus mention in scary quotations.
In this circumloquacious manner, one is supposed to be able to
say that the extension of the term or the concept "sweet" is
all of the things in the set of sweet things, without being
ontologically committed to saying that the extension of the
term or the concept "sweet" 'is' the set of sweet things.
Or so it is said. And here we begin to see what really
burdens the architexture of nominal thinking, not the
burden of excess ideas but the burden of words, for
all of the circumlocutions that are necessary to
maintain its manor are far more encumbering and
far more exorbitant in their upkeep than the
few spare economies that may be provided by
setting the right ideas in the right places.
At any rate, it is still a good idea to start from a nominal start,
if for no better reason in the end than that it gives us a chance
to see how the run of "hypostatic abstraction" (HA) gets going,
and just so long as we do not mistake the starting gate for
the finish line.
Finally, nobody but nobody would want to say, if they stop
for a moment to think about it, that the term or the concept
"sweet" denotes the set of sweet things. It either denotes in
a singular number the property of being sweet or it denotes in
a plural number the things that are in the set, but it does not
denote in a singular number the set itself. Non-nominal thought
engages the term "set of sweets" for that properly singular role.
JA: And at this point you have said that you see a way
to dispense with 1 of these 4 dimensions, or maybe
to collate 2 of them into 1, leaving 3 as the only
3 dimensions that we need to save the appearances.
JA: Sound familiar?
JA: My question is: How can we be assured that you are
collating dimensions, and not just conflating them?
MW: Well if the property is in the axiom, then it may just be
that it is the piece of work that is left, since we only
have taxonomic and structural axioms at present.
This is the comment that I did not understand.
Jon Awbrey
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