SUO: Re: Relations And Their Divisitudes
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RATD. Note 17
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Tom,
I have recently been reading the writing of a contemporary philosopher
who evidently thinks that a thing without a proper name does not exist.
Out of politeness, the noted philosopher shall remain nameless in this.
Still, it reminds me of an issue that's been in the background of these
discussions, namely, the expressiveness of this or that formal language,
and especially the expressiveness of ordinary "natural" language, which
isn't to say that it isn't just as "nurtural" if the full truth be told.
Strangely enough, that question strikes me as being connected with your
last set of thoughts, and so I will try to tackle them all in one arena.
TJ: My own thoughts about the difference between a row of
a table (a tuple) and the table itself (a relation) is
that the former is part of the extension of the relation,
while the latter (more specifically, the set membership
conditions which define it) represents the intension of
the relation. Next, that one cannot always infer the
intensional rules from the extensional instances because,
at any given moment, the set of all those instances may
not define the boundary conditions of all those rules.
To take a simple example, if one column of the table is
a status-code column, whose domain is the letters A - X
inclusive, it might be that the status-code value of P
is not instantiated in any tuple. Or: a column might
be defined as nullable, although all of the current rows
have a value in that column. In short: that intensional
rules might be inferrable from the full Cartesian Product
of a set of columns (if we knew it was the full Cartesian
Product), but are not inferrable from any subset of the
full Cartesian Product.
Sticking to my method, I will take on the easy things first.
One of the first things to get used to in reading Peirce is that he
may not always be playing that intellectual volleyball game that we
all learned at school, where we set up a net on some beach or field,
divide the massed company into opposing teams, and the fans thereof,
like Extensionalists vs. Intensionalists, or something of that sort --
a whistle blows and we proceed to go at it, hammer and tongs, setup
and spike, with the aim and the full understanding that the ground
rules are always to the death, so to speak, until one side or the
other is utterly trounced, with the ultimate pay-off to winners
and losers alike being the reductive savings that nobody will
have to worry themselves thinking about, much less uttering,
the name of the losing side, except in final dismissal of
the differential feature they so hopelessly defended.
But realities have a way of persisting, no matter
how often people create, preserve, or destroy,
as the case may be, their proper names.
Getting to the point of present application, Extensions and Intensions,
more rounds than I know how to count of the Exteam/Inteam tournament
were played throughout the 20th Century, with the mediate outcome
as of this moment, and as we may speak for the immediate future,
being that the two words in contention no longer have anything
like meaningful contents on the sands of our academic beaches.
In Peirce's work, on the contrary, one finds that extension and,
more properly to name it, comprehension, are but two aspects or
facets of a more integral reality, that he dubbed "information".
Moreover, the usual contest between extensions and intensions,
so earnest in the mind of the average philosopher both before
and after Peirce's effort on behalf of our plane of existence,
is all a bit beside the point when it comes to applying logic
to the real world, caught, according to Peirce, as I read him.
between the ideal world and the sensible world. But see here:
http://suo.ieee.org/ontology/msg05054.html
To be continued ...
Jon Awbrey
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