Tag Archives: Matt Damon

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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Some More Clean-Up Work: Propositions And States Of Affairs

Following Chisholm, I have been identifying propositions with states of affairs.  A proposition is a subset of the set of states of affairs.  The state of affairs of John grasping a doorknob at time t_0 in Chicago is a state of affairs that always occurs (or always fails to occur).   States of affairs like this one are propositions.  The truth (falsity) of a proposition is nothing but a certain state of affairs occurring (failing to occur).  I am ignoring the question, which is pestering me right now, of why then it seems so awkward to talk about a ‘true’ (‘false’) state of affairs.  From The Stanford Encyclopedia of Philosophy article on Roderick Chisholm:

Consider the state of affairs that is expressed by the sentence ‘Someone is walking’. Chisholm wanted to say that this state of affairs occurs whenever someone walks, and fails to occur at times when no one is walking. Other states of affairs are not like this. For them, it is impossible to sometimes occur and sometimes fail to occur. Chisholm claims that this provides the opportunity for an ontological reduction. We can define a proposition as a state of affairs of this latter sort — it is impossible for there to be times when it occurs and other times when it does not occur. A true proposition is thus one that occurs; and afalse proposition is one that does not occur. Chisholm thinks that we may understand the principles of logic to be about these propositions. By saying that a fact is a true proposition, Chisholm gains yet another ontological reduction ([P&O], 123).

Chisholm thought that in some cases it makes sense to speak of the location at which a state of affairs occurs. Suppose John walks in Chicago at a certain time. Then Chisholm would be willing to say that the state of affairs of John’s walking occurs in Chicago and at that time.

Those states of affairs that are not propositions are events.   I am going through this stuff a bit impressionistically; the chances of my making an error someplace are high.

The tuples in the body of a database relation are propositions.  That is to say, they are states of affairs.  In a conventional database, these are always states of affairs occurring now, and now, and now…. John is an employee of WIDGETS_R_US now, the ‘now’ being implicit in the presence of that tuple in the relation.   In a temporal database as described by Date and Darwen (TEMPORAL DATA AND THE RELATIONAL MODEL),  these are states of affairs that occurred during a time period, or are occurring now (“Since t_0….”), the relevant time periods being explicitly stated in the tuple.

Since propositions are nothing but states of affairs of a certain kind, the operations of the Relational Algebra are operations on states of affairs of that kind.  On the relation ‘Standing_To_The_RIGHT_Of’, for example, we can perform a RESTRICT operation that delivers to us the state of affairs of Don standing to the right of Genghis Khan, then perform a PROJECT operation on that derived relation to obtain just Don.

We will figure out later what to do with Don now that we have him.

My homage to Plato’s SYMPOSIUM for this post will be Matt Damon.  This time we are a bit further along on the way towards eros for mathematical beauty:

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But let’s not forget it all originally stems from eros for gorgeous young men.