ONT Re: Intension & Extension
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AC = Alonzo Church
JA = Jon Awbrey
RK = Robert Kent
RK: Compare Alonzo Church's discussion (below) of the intension and extension of
a concept with the mathematical (Formal Concept Analysis) (Rudolf Wille and
Garrett Birkhoff) definitions of the intent and extent of a formal concept
on the middle of page 30 in the IFF Classification Ontology document:
RK: http://suo.ieee.org/IFF/versions/20020102/IFFClassificationOntology.pdf
RK: As an illustrious example, see the 19 formal concepts (with
explicit intent and extent) in the concept lattice of the
"Living Classification" on pages 74-76 of the same IFF
Classification Ontology document.
Robert,
I think that people can coin whatever usages they can get away with,
and mathematicians certainly get away with more than normal mortals,
and my ethics of nomenclature is nowhere near as orthodox as a good
Peircean ought to be -- but -- I would still like to see some token
of respect for the continuities of various traditions of usage, and
I can't help thinking that these prospective coin-passers will have
to certify the good intention of what they tender and pay their due
respect to assaying what they mint, if they expect to back up their
usurage, even to render it the common coin of currency in our realm.
On this score, I have several difficulties with the terms "extent" and "intent",
and I also find it difficult to use the word "concept" in the way that it seems
to be intended here, if I'm reading it right, which may be a tenuous assumption.
For me, and most of the people that I understand easily,
a concept is a type of sign, to be specific, a symbol.
So I often speak of the extensions and intensions of
concepts alongside the extensions and intensions of
terms with very slight sense of sleight at the
rate of exchange between concepts and terms.
For me, an intension is always just a property or a quality.
When people speak of "the" intension of a concept or a term,
I usually take them to mean the conjunction of "all" of the
intensions that it has in the relevant context of discourse,
which is more properly called the "comprehension", though
I myself seldom speak this carefully either.
If "intent" is supposed to be the analogue of "intension",
then I can only remark that its suggestion of "intention"
is just plain asking for trouble.
There are historical reasons that explain why otherwise decent scholars
feel like they can play so fast and loose with such delicate traditions,
and it has much to do with the circumstance that we have just been thru
a hundred years of unabashedly dogmatic reductionism. With so many old
wine bottles laying about, supposedly emptied of all meaningful content
by the purges of the intellectual prohibitionists and tea-totalitarians,
it is only natural that enterprising vagabonds will try to make capital
of their residual deposits, or else refill them with whatever they will.
Jon Awbrey
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JA, citing AC:
| Intension & Extension
|
| The 'intension' of a concept consists
| of the qualities or properties which
| go to make up the concept.
|
| The 'extension' of a concept consists of the things
| which fall under the concept; or, according to another
| definition, the 'extension' of a concept consists of the
| concepts which are subsumed under it (determine subclasses).
|
| This is the old distinction between intension and extension,
| and coincides approximately with the distinction between
| a monadic 'propositional function' (q.v.) in intension
| and a 'class' (q.v.).
|
| The words 'intension' and 'extension' are also used in connection
| with a number of distinctions related or analogous to this one, the
| adjective 'extensional' being applied to notions or points of view which
| in some respect confine attention to truth-values of propositions as opposed
| to meanings constituting propositions. In the case of (interpreted) calculi
| of propositions or propositional functions, the adjective 'intensional' may
| mean that account is taken of modality, 'extensional' that all functions
| of propositions which appear are truth-functions. The extreme of the
| extensional point of view does away with propositions altogether and
| retains only truth-values in their place.
|
| Alonzo Church, in Runes, pages 147-148.
|
| Dagobert Runes (ed.), 'Dictionary of Philosophy',
| Littlefield, Adams, & Company, Totowa, NJ, 1972.
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