Category Archives: Logical

Logical Pairings

In previous posts I’ve tried to interpret the canonical Tagalog sentence (e.g., maganda si Taylor Lautner) in terms of an equality relation, GORGEOUS_EQUALS_GORGEOUS.  Conceptually, the relation is formed by logically pairing each member of the set GORGEOUS (MAGANDA) to each of the members, then taking a subset of the set that results from this logical paring.  That subset comprises those logical pairings in which each member of the pair is identical with the other.

What do I mean by ‘logical pairing’?  In the real world, to pair one thing with another is to bring the two things together in some way.  One may pair, for example, some particular matte board, with its particular color, with the painting one is getting framed.  Here, the matte board and painting are getting physically paired.  Or one may pair John with Bill by picturing them in the mind’s eye as together as a couple.  Or one may pair John with John by first seeing him double (i.e., seeing him twice but simultaneously), then by realizing the two Johns are in fact one.

To get a logical pairing, abstract from any concrete form of pairing, that is, ignore any particular way in which the bringing together is done.  Ignore in fact everything about them except that they go under the heading ‘bringing together’ (since maybe that is the only single thing they all have in common.)   Then be content with the fact that, while each member of the set MAGANDA can potentially be brought together with every member of that set,  any actual pairings will be performed just every now and then, and only for a few members.  (For example, in a particular article, Dan Savage pictures Ashton Kutcher and Matt Damon together.)  A logical pairing is a bringing together in which all concrete details of the bringing together (how it is done, in what sense the things are brought together?  Physically?  In the imagination only?  By already knowing that the “objects” of one’s double vision are in fact one and the same?) are ignored.  One salient detail in particular is ignored:  is the pairing actually being done in any given instance, or is it just something that could be done?

If one does not want to rest content with each member of the set being brought together just potentially with every other member of the set, they (plural third person intentionally being used here as a neutral singular third person) are free to imagine a Demiurge ala Plato or a God ala the medievals whose cognitive capacities are sufficiently large as to simultaneously bring together in its mind’s eye every member of the set MAGANDA with every member of that set, so large, in fact, as to be able to see Matt Damon twice with the mind’s eye but already know that Matt Damon is, well, Matt Damon.

I will end by confessing that I like to think of projection as the Demiurge’s ignoring one or more attributes of a relation, and of restriction as the Demiurge’s ignoring one or more tuples in the relation.

Today, my homage to Plato’s SYMPOSIUM (first, gorgeous guys, then the Relational Algebra, then the form Beauty itself) will take the form of a concrete (not just a logical) pairing of Matt Damon and Ashton Kutcher:

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Sigh.  There is too much beauty in the world.

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