SUO: Re: Lifecycle Integration Schema
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LIS. Discussion Note 65
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JA = Jon Awbrey
MW = Matthew West
JA: It is common to recognize distinctions among a number of things:
1. The word "sweetness", the noun form of the adjective "sweet".
2. The concept "sweetness", something like a noun in the mind.
3. The property sweetness, also known by the term "intension".
4. The set of sweet things, which constitutes the "extension"
of either the term "sweetness" or the concept "sweetness",
according to one's taste.
MW: By extension do you mean the enumeration e.g. {A, B, C} and
by concept do you mean TheSetABC? We do have both of those.
The intension would be the axiom that defined it. Presently
that is only in words in the definition of the concept.
I will describe the Classical version and the Peircean version
of these concepts, very roughly in both cases. The underlying
theme in each variation is that all of the canonical concepts --
comprehension, enumeration, extension, individual, intension,
and so on -- have meaning and make sense only in relation to
a suitable context of interpretation. In the classical vein
from Aristotle to Venn, this theme is tacit in either one of
the ideas of a language community or a universe of discourse.
In Peirce's reworking of this material, the theme of meaning
in relation to a setting of interpretation gets a new twist,
weaving together objects and properties in a relation to his
invention of "information", and all of the above predicables
now become relative to an interpreter's state of information.
Extension of a Concept or a Term. Classically, this is "all"
of the things that fall under a given concept or term, as taken
in a given context of discussion. For Peirce, this is "all" of
the things that one knows to fall under a given concept or term.
Enumeration of a Concept or a Term. Classically, this amounts
to what we would call a "dataset", a concrete empirical listing
of things that one has observed to fall under a concept or a term.
This is inherently relative to a state of knowledge, and so Peirce's
notion is pretty much the same, as I gather from the way that he uses
Aristotle's idea of "enumerative induction" in his theory of inquiry.
Concept. Classically and for Peirce, a concept is a mental sign.
More precisely, a concept is is a mental "symbol", where a symbol
is a type of sign that has the meaning that it does or will have
by virtue of the circumstance than an interpreter interprets or
will interpret it to have the meaning that it does or will have.
As a type of sign, a concept is specified on the parameters of
extension and enumeration in the same way as any other sign.
Intension of an Object. The word "intension" is a synonym for "property".
So an intension of an object is just a property of an object. That is the
primary sense. By virtue of the circumstance that some objects are denoted
by signs and some properties are denoted by signs, the properties of objects
can be associated with the signs that denote those objects, and a panoply of
subtle relationships arise from this that tend to muddy the waters greatly,
so I will leave it at that for now. The business of conflating intensions
with the axioms that define properties appears to be yet another hangover
of nominal thinking bouts that go back to notorious UK party schools.
YUK, YUK,
Jon Awbrey
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