ONT Re: Relations And Their Divisitudes
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RATD. Note 19
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TJ = Tom Johnston
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.
TJ: 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.
Let's see if we can clear up one of the things that got messed over
somewhere in last ten rounds of the Exteam/Inteam volleyball game.
Namely, what the heck is denoted by the word "intension" anyway?
Intensions, generals, properties, qualities, universals, etc.,
of imagination were all compact, one upon a time, at any rate.
But nominal thinkers seek to reduce the number of things they
grant existence to, as if it were really up to them, and so
they picked on all such airy notings as things that looked
like easy pickings for elimination. Their notorious motto:
"Do not confuse a general name with the name of a general".
And of course they were not talking about Alcibiades or
Franco or individuals of that rank, but the rank of
generals that Plato most notoriously mustered up.
The corollary maxim: "A general is just a name".
By which the nominal thinker means that the name
is enough for all practical purposes, hence the
general as an indpendent entity is "dispatched",
and they meant that in the "extreme prejudice"
sense of the word, hence the name that this
crew bears in general, "nominal thinkers",
or "thinkers in name only", one and all.
But the ghost of the dispatched general will not rest.
Obviously, no sensible thinker can get by in any sort
of life of thought by building up every set that needs
to be thought of by means of enumeration, or the making
of explicit lists, and so it is necessary to muster up
many assemblies by rule -- but what is a rule, anyway?
And here we face the whole abstract/concrete question
all over again. A nominal thinker of the extremely
dedicated sort will say: "A rule is just a writ".
But that "writ" must be taken quite literally as
written out: bull, certificate, dictum, edict,
instruction, order, program, recipe, warrant,
et cetera, but get it in writing is the key.
Weirdly enough, a funny thing can happen at
this point: the guilt-ridden, need-driven
nominal thinker may attempt to resurrect
the long-dead general, in name only,
of course, and breathe the name of
"intension" into the signoid bits.
So let's watch out for that.
Jon Awbrey
TJ: To take a simple example, if one column of the table is a status-code
column, whose domain is the letters A to X inclusive, it might be that
the status-code value of P is not instantiated in any tuple.
TJ: Or: a column might be defined as nullable, although
all of the current rows have a value in that column.
TJ: 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.
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