ONT Re: Intension & Extension
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RK = Robert Kent
RK: I quote from the text by Ganter and Wille (page 17):
GW: | The basic notions of Formal Concept Analysis are
| those of a *formal context* and a *formal concept*.
| The adjective 'formal' is meant to emphasize that
| we are dealing with mathematical notions, which
| only reflect some aspects of the meaning of
| *context* and *concept* in standard language."
Yes, I understand that. I am fully cognizant and quite
familiar with that particular "turn" of thought, both
here and in numerous other places where it manifests
itself, having been trained in that way of thinking
long before I came of an age to reflect on it and
eventually to criticize it. I am also aware of
some of the motives behind it, motives that
I have come to suspect and no longer share.
I use a different framework for thinking
about these sorts of issues, namely, the
pragmatic theory of signs. I believe
that it has many advantages over the
concept of concept that derives from
not very careful readings of Frege.
I use the word "formal" to mean
"pertaining to form", not as
an honorific like "objective",
"rigorous", or "my precious",
well, anyway, I try to.
RK: The purpose of my original message to you:
RK: http://suo.ieee.org/email/msg07729.html
RK: was to invite people to consider how well
these mathematical notions represent the
intuitive notions discussed in the passage
from Alonzo Church that you quoted.
Are these "formal" notions? Are formal notions the same as formal concepts?
I do not use the word "intuitive" to mean "informal", at least, not if I am
using the term "intuition" in the formal sense of the corresponding concept.
Also, my analysis of the parameter of context finds it to be of derivative
and incidental importance relative to the parameters of the interpreter,
and more fundamentally, the interpretant.
RK: I feel that these matters should be fully discussed.
In that light, consider the following excerpts
from your message and Church's passage.
I also feel that these issues need to be fully discussed.
AC was trying to be a good lexicographer,
which means that he tried to give two or
three closely related, but not exactly
simply or trivially related usages.
JA: 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
RK: Suppose we make the identification:
RK: FCA formal context
= IF classification
= the relevant context of discourse
I think that context is only one of the factors that affect
semiotic interpretation, that is, the interpretant that will
be formed by an interpreter, and that the sign relation that
involves this interpretant is the proper unit of analysis and
ultimate frame of reference for understanding the whole process.
So I only invoke context as a transitional sop to interpretants.
In my previous studies of this issue, I found that most thinkers
were looking to "the" context to serve as the determiner and the
disambiguater of meaning, but that this search always turns into
an expanding regress, as there is no such thing as "the" context.
Peirce discussed these issues in his "Note on a Limited Universe of Marks".
RK: And we further make the identifications
RK: FCA attribute
= IF type
= an intension is always just a property or a quality
RK: Then
RK: "the" intension of a concept or a term
= the "comprehension" of the concept
= (Church) the qualities or properties which go to make up the concept.
= the conjunction of "all" of the intensions that it has in the relevant
context of discourse
RK: would seem to correspond exactly to the FCA notion of intent
of a formal concept defined as
RK: the intent of a formal concept (within a formal context)
= all attributes that are shared by all the objects
of the formal concept (its extent)
RK: So, does not the FCA intent seem to fit the intuitive idea
of conceptual intension or comprehension. What do you think?
I think that it is a bad idea to use the word "intent" this way.
It is inviting even more confusion into an already confused area.
Generally speaking, I approach these issues "personalistically" (as in statistics),
and "constructively", where the construction is carried out by, and relative to
a particular agent. So "all" and "the" are relative to an agent. Just as
there is no such thing as "the" meantime meaning of a sign or a concept,
there is no fact of the matter about "the" comprehension of a term --
hence the fun of the pun. One of the features of the reductionism
that I criticize is this notion that one can arrive at objectivity
by simply ignoring the participatory relativity to interpreters.
All of the "hard" sciences have already learned, the "hard" way,
of course, that the facile pretensions of objectifying discourse
are just not the way. I keep wondering when logic will catch on.
Not waiting to exile ...
Jon Awbrey
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