Category Archives: Eros

Measles And Wormy Red Apples: IF-THEN Statements And INFORMATION THAT (An Apparent Counter-Example)

It would seem that there are some clear counterexamples to the idea that If p Then q is true when p is information that q.

Consider the following (somewhat gruesome, in the light of the irresponsibility of our contemporary anti-vaxxers) measles example from Fred Dretske.  Dretske, by the way, does not discuss this example in the light of IF-THEN statements.

…an exceptionless uniformity … is not sufficient for the purposes of transmitting information.  Correlations, even pervasive correlations, are not to be confused with informational relations.  Even if the properties F and G are perfectly correlated (whatever is F is G and vice versa), this does not mean that there is information in s’s being F about s‘s being G (or vice versa).  It does not mean that a signal carrying the information that s is F also carries the information that s is G.  For the correlation between F and G may be the sheerest coincidence, a correlation whose persistence is not assured by any law of nature or principle of logic.  All Fs can be G without the probability of s‘s being G, given that it is F, being 1.

To illustrate this point, suppose that all Herman’s children have the measles.  Despite the “correlation,” a signal might well carry the information that Alice is one of Herman’s children without carrying the information that Alice has the measles.  Presumably the fact that all Herman’s children (living in different parts of the country) happened to contract the measles at the same time does not make the probability of their having the measles, given their common parentage, 1.  Since this is so, a signal can carry the information that Alice is one of Herman’s children without carrying the information that she has the measles despite the fact that all Herman’s children have the measles.  It is this fact about information that helps to explain (as we will see in Part II) why we are sometimes in a position to see that (hence, know that) s is F without being able to tell whether s is G despite the fact that every F is G.  Recognizing Alice as one of Herman’s children is not good enough for a medical diagnosis no matter what happens to be true of Herman’s children.  It is diagnostically significant only if the correlation is a manifestation of a nomic (e.g., genetic) regularity between being one of Herman’s children and having the measles.

Fred Dretske, KNOWLEDGE AND THE FLOW OF INFORMATION, Stanford, CSLI Publications, 1999, pp. 73-74

Myself, I would rather choose a less gruesome (given the sometimes horrific consequences of measles), even if still somewhat gross, example.  Suppose that there is a pile comprising red and yellow apples in my grandfather’s orchard.  By pure chance, some of the yellow apples happen to be wormy, while all of the red apples are so.  Given his measles example, Dretske would surely claim that just the fact that a given apple from the pile is red would not constitute information that the apple is wormy.  But suppose that, blindfolded, I handle each apple in the pile one by one, saying each time:

If this apple is red, Then it is wormy.

In my mind’s inner ear, my intuition is shouting to me:  “This is TRUE TRUE TRUE TRUE TRUE!!!!!!”

Likewise, surely the following statement is also true:

If this person loitering here in front of my shop among all these other disreputable-looking lay-abouts is a child of Herman’s, Then she has measles.

This statement would be true, it (strongly) seems to me, even if the person uttering it is talking completely through their hat, even randomly, and has absolutely no evidence that ‘this person’ has the measles, or that she is a child of Herman’s, or that there is any connection at all, even an accidental one, between Herman’s children and the measles.

Therefore, there would seem to be clear cases in which an If p Then q statement is true even when the occurrence of p is not information that q.

Nonetheless, I (at least as of this writing) think I can show in a later post that Dretske’s discussion of the relativity of information drastically undercuts what he thinks his measles example shows.  (I am also thoroughly confident, by the way, that if my doubts are valid, they have already been discussed a thousand times already by everyone and their uncle.)  So the idea that what makes p relevant to q in any true If p Then q statement is an informational relation . . . this idea might find a rescuer after all.

 *****

I hope that today’s homage to Plato’s SYMPOSIUM has never suffered from the measles.  This gorgeous hunk is a math teacher in Great Britain (perhaps hailing ultimately from Italy) who moonlights as a model.

pietronew

I am confident that this math teach will inspire many of his students, both male and female, to start the ascending the platonic ladder whose lowest rung consists in the contemplation of the Beauty of Gorgeous Guys, whose next rungs consist in the contemplation of the Beauty of Math and Logic, and which finally leads to the contemplation of the Form of Beauty Itself.

For now, however, I will linger a bit at the lowest rung, the Contemplation of the Beauty of Gorgeous Guys.  I will get to the Form of Beauty Itself sometime.

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Aristotle’s Sea Battle Argument

In a rough draft of a blog post at work whose real topic had, of course, precious little to do with Aristotle, I playfully tried to explicate his Sea Battle argument to an audience of techies as follows:

The following statement (call it p) is necessarily true:

Either there will be a sea battle tomorrow [at location l], or there will not be a sea battle tomorrow [at location l].

At least one, or possibly both of the constituents of an OR statement must be true if the statement is true.  If the OR statement happens to be an ‘A OR not A’ statement, at most one of  the constituent statements can be true.  What is more, since ‘A OR not A’ must be true, one of the constituent statements must be true.  So either

There will be a sea battle tomorrow [at location l]

is true, or:

There will not be a sea battle tomorrow [at location l]

is true.

But which one?

Suppose that ‘There will be a sea battle tomorrow [at location l]’ is the constituent proposition that is true.  (Call this constituent proposition c1.)  One may already have been struck by the Aha Erlebniss that the sea battle will not  fail to happen (and in fact cannot fail to happen) tomorrow at location l.  (henceforth ‘at location l‘) will be understood.)  But my mind and my imagination feel the presence of a gap between c1 and ‘the sea battle cannot fail to happen tomorrow.’  When I try to jump from the first to the second, I feel a bit as if I were plunging into a void.  The following thought experiment is an attempt to bridge that void,

Start Of Thought Experiment:   To avoid complications involving indexicals, suppose that today, at time t0, I say:

A sea battle happens at time tn.

From the standpoint t0, tn is a point in time that will roll by tomorrow.  Could my statement stop being true at t0+1 (0+1 < n)?  Don’t be silly — of course not.  Someone’s statement ‘The cat (Sylvester, with CAT_ID 347434395) is on the mat (the medieval Persian mat with MAT_ID 84541) at 12:01 pm, October 31, 2014’ never ceases to be true, assuming it was true at 12:01 pm, October 31, 2014.  Ditto my sea-battle statement.  Could my sea-battle statement suddenly stop being true at to+2?  No, of course not.  And so on for every time point starting from t0 and going up to tn.  My statement will be equally true at tn – 1 as well as at time tn. Throughout, it remains true that the sea battle will happen at tn.  There is no room left for the sea battle NOT to happen at tn.

In fact, what would it mean for that statement suddenly to become not true, at some point between to and tn?  Well, suppose — doubtlessly per impossible — that the chain of one set of causes leading to a set of effects serving as causes for yet another set of effects ceases — say, at tn-1 — to be deterministic.  That chain continues unbroken until, abruptly at tn-1, it becomes a flip of nature’s coin whether the sea battle happen or not.  Then, it seems to me, the truth of ‘A sea battle happens at time tn’ ceases to be defined.  The statement is neither true nor false.  Therefore, the statement would be not true, though it would not be false either.

Or again, suppose that the chain continues unbroken until suddenly, at time tn, we end up with (again, per impossible, I am sure) with a weird quantum Schroedinger’s sea battle:  the sea battle is simultaneously in a state of happening and not happening at tn.    In this case, my intuition is, the truth value of my sea battle statement would be undefined at t0 as well as at tn.  End Of Thought Experiment.

So assuming there is a chain of causes working deterministically from t0 to tn, my sea battle statement is definitely true at t0.  And there is no way that the sea battle will fail to happen at tn.  The chain of deterministic causes (assuming this exists) is what gives sense to the idea that my sea battle statement has a definite truth value at t0 — that is is true (false) at that time-point.

This is Fatalism.  Fatalism is often thought to entail that we have no Free Will.  Aristotle comes to this conclusion, and panics.   (At least according to my explication of this stuff to my fellow geek colleagues.)  “Oh my god!!!!!!….er….I mean….oh my Zeus!!!!!  If there is no Free Will, then that loud sucking sound you hear is my ETHICS going down the drain!!!!!  Quick!!! Quick!!!!! Think of something!!!!!!’  (I have to admit that my translation of the ancient Greek here is a trifle free.)  So to save his ethical theory Aristotle decides to assert that while the total original proposition, p, is necessarily true, the truth value of both of its constituents is undefined.  Neither of its constituents is either true nor false.

But I do not see how this (the constituents’ not having a definite truth value) could be so unless the sea battle’s happening (or failing to happen) tomorrow is a matter of nature’s flipping the coin.  Aristotle cannot be right.

I say ‘Aristotle cannot be right’ in full confidence, as a matter of black and white.  Nonetheless, just a little shade of gray, a tiny sliver of doubt, does enter here.  The laws of nature are supposed to be deterministic on the level of apples and triremes, but non-deterministic on the level of protons and electrons (and for all I know on the level of quarks as well). On the micro level, nature is (if I understand this stuff correctly) constantly tossing a coin.  Although one is not supposed to mention quantum physics in a philosophical discussion unless they (intentional use of ‘they’ as a singular gender-neutral pronoun) have completed at least 8 graduate courses in quantum physics (with no grade lower than a B+ in any of them), I do have to at least wonder quantum weirdness might invade the causal chain leading to the sea battle’s occurring (failing to occur) tomorrow in such a way as to make it only 99.9999999999999999999999999999999999999999999999999999999999% probable, not 100% probable, that the sea battle will happen (fail to happen) tomorrow.  Is this enough to blast away the bridge that leads from the present to the future that lets us say that a statement about the future uttered now is either true or false?  I will leave that as a nagging question leaving in its wake just the tiniest whiff of doubt.

* * * * *

If Aristotle were right, then either p is not in fact an OR statement (it only looks like one), which seems rather counter-intuitive to me), or normal classical logic fails to hold for the future.  Contrary to normal, classical logic, it would not be the case that an OR statement is true if and only if at least one of its constituent statements is true.  This would hold only for statements about the present.

But in that case statements such as ‘If this apple drops from the tree under which I am sitting, this apple will splat onto my head in one second’ (call this the ‘apple if-then statement) will not have a defined truth value.  Reducing to ‘Either this apple does not drop from the tree under which I am sitting, OR this apple will not splat on my head in one second’ (‘if p then q’ is the same as ‘not p or q’),  So the truth value of the total apple if-then statement will be undefined because, being a statement about the future, the truth value of ‘this apple will splat on my head in one second’ is undefined.

So if we restrict normal, classical logic to just the present, the number of interesting statements it rules over will become awfully restricted.  Normal, classical logic will become a parlous affair, just as pitiful as the crowning of John Cantacuzenus  and Irene, Andronicus Asen’s daughter in the waning days of the Byzantine Empire.  As related in C.P. Cavafy’s poem Of Colored Glass:

As they had very little in the way of precious stones

(our wretched dominion’s poverty was great

they wore artificial ones.  A heap of bits of glass,

scarlet, green or blue.

I always end my philosphical/logical posts with an homage to Plato’s SYMPOSIUM, for which purpose I will use Ashton Kutcher (swooning, rapturous sigh) yet one more time:

Ashton_Kutcher_0

Look at those stunningly beautiful brown eyes!!!  How can anyone get any work done with beauty like this walking the earth?


Semantic Arguments vs. Adjuncts (Revised)

This is a version of the post below, revised so as to try to eliminate a number of confusions.

The Wikipedia article Argument (linguistics) starts its discussion of the argument/adjunct distinction by asserting that an argument is what is demanded by a predicate to complete its meaning, while an adjunct is not so demanded.  For example, if someone asks me “What is Joe eating?” my answer would be drastically incomplete if I replied “eats.”  My answer would still be drastically incomplete if I supplied just one argument, ‘Joe’, to say ‘Joe eats.’  Only when I supply a second argument, say, ‘a fried egg’, would my reply not create a sense of a question ludicrously left hanging and an answer simply not given.  The predicate _eats_ has two parameters ( shown here as ‘_’) demanding two arguments, such as  ‘Joe’ and ‘a fried egg’ for my reply to make any sense.

( This example, of course, is my own; I am offering it (maybe tendentiously?) in order to make drawing certain conclusions more natural. )

‘[I]n the kitchen’, however, is an adjunct, since nothing would be left ludicrously left hanging in the air were I to leave that phrase out of the proposition “Joe eats a fried egg in the kitchen.”  The predicate eats does not have a parameter demanding something like ‘in the kitchen’ as an argument.

This criterion — i.e., what is demanded by a predicate to complete its meaning … henceforth I will call this the ‘demands criterion’ — runs into trouble when one notices that sometimes eats demands two arguments, but sometimes demands just one.  One might say:  “Joe goes into the kitchen.  Joe is ravenous.  Joe sees food.  Joe eats.”  ( Imagine a novelist or short-story writer working in a certain style.)  The argument ‘a fried egg’ is not demanded in this particular piece of discourse.

But if ‘a fried egg’ is an argument, not an adjunct to eats, it would seem one would  have to abandon the ‘what is demanded by a predicate to complete its meaning’ criterion and find another criterion for what is to count as an argument and what is to count as an adjunct.  This a contributor (doubtlessly not the same person who put forward the ‘demands’ criterion) to the Wikipedia article cited above tries to do.

But if one wants to retain the demands criterion, they (I am intentionally using ‘they’ as a genderless singular pronoun) can assert that two different predicates, each with a different number of parameters, may get invoked when someone utters  ‘eats’ in a stretch of discourse.  Sometimes the one-place predicate _ eats is invoked, sometimes the two-place predicate _eats_.   Which predicate one uses is optional, depending upon what they feel is called for by the situation and what they want to do with the predicate.  Sometimes the context forces one to use, for example, the two-placed predicate (for example, in answer to the question ‘Joe is eating what?’; sometimes which predicate one invokes is purely a matter of choice.

If all of the predicates demand a certain argument (for example, ‘Joe’ in ‘Joe eats’), what is so demanded is an argument that is not also an adjunct.  If not all of the predicates demand a given argument (‘fried egg’, ‘in the kitchen’), that argument is an adjunct.  In this way, the demands criterion is rescued.

I picture the relations formed by these predicates as follows:

One-place relation formed by _eats:

EATS
PERSON_EATING
PERSON( NAME(‘Joe’) )
PERSON( NAME(‘Khadija’) )
PERSON( NAME(‘Juan’) )
PERSON( NAME(‘Kha’) )
PERSON( NAME(‘Cliff’) )

Here the key is, of course, PERSON_EATING.  The ellipses ‘…’ indicate all the further tuples needed to make this relation satisfy the Closed World Assumption.  (The Closed World Assumption states that a relation contains all and only those tuples expressing the true propositions generated by completing the predicate with the relevant argument(s).)

Two-place relation formed by _eats_:

EATS
PERSON_EATING FOOD_ITEM_BEING_EATEN
PERSON( NAME(‘Joe’) ) FOOD_ITEM( NAME(‘This fried egg’) )
PERSON( NAME(‘Khadija’) ) FOOD_ITEM( NAME(‘This souffle’) )
PERSON( NAME(‘Juan’) ) FOOD_ITEM( NAME(‘This fajita’) )
PERSON( NAME(‘Kha’) ) FOOD_ITEM( NAME(‘This bowl of Pho’) )
PERSON( NAME(‘Cliff’) ) FOOD_ITEM( NAME(‘This plate of Thai food with a 5-star Thai-spicy rating’) )

Here the relation formed by _eats_ is a subtype of the supertype formed by _eats.  That is to say, PERSON_EATING is a unique key in this relation, but it is also a foreign key to the PERSON_EATING attribute of the relation formed by _eats.

This means of, course, that in each tuple there is just one thing that the person is eating.  This constraint would be natural enough if one restricts the now of the present tense eats enough so that only one thing could possibly be getting eaten, for example, the egg one piece of which Joe is now bringing to his mouth via a spoon.  But, of course, if one stretches out this now enough so that our hypothetical author could write:   “Joe goes into the kitchen.  Joe is ravenous.  Joe eats a fried egg, an apple, and a salad,” one could not treat the one-place relation as a subtype of the two-place relation.  I think the solution in this case would be to treat what gets eaten as a meal, a meal comprising one or more items.  The meal then could be treated relationally the way an order and its order-items get treated, the orders going into one relation, and orders and order-items going into another, with the orders and order-items together comprising a unique key.

The predicate _eats_ _ (as in ‘Joe eats the fried egg in the kitchen’) can be treated the same way.  And so on for any number of possible adjuncts that a predicate might accept.

If I can get away with this move, then, an adjunct would be any argument that is 1) accepted by a predicate in which the corresponding relation is a subtype of another relation, and 2) the parameter which takes that argument corresponds to an attribute in the subtype relation which is not a foreign key of the supertype relation.  An adjunct then is one kind of argument.  Non-adjunct arguments (arguments that are just arguments, arguments simpliciter) correspond to a unique key in a supertype relation; adjuncts in turn are arguments not corresponding to any attributes in the subtype relations that are foreign keys to that unique key in the supertype relation.

Notice how this treatment of arguments vs. adjuncts (that is to say, arguments that are just arguments and arguments that are also adjuncts) corresponds to the way “optional (nullable) columns” in SQL tables get turned into actual relations, which cannot contain “null values”:

SQL Table (what is eaten is an optional or “nullable value”):

EATS
PERSON_EATING FOOD_ITEM_BEING_EATEN
Joe  Fried egg
Khadija
Juan
Kha Bowl of Pho
Cliff
 …

Here PERSON_EATING is a not-null column, and FOOD_ITEM_BEING_EATEN is a “nullable” column.

This looks like a single relation with an optional parameter (FOOD_ITEM_BEING_EATEN).  So if one both accepts the demands criterion and takes the  SQL table as their cue, PERSON_EATING would be an argument because it is not optional, i.e., always demanded and FOOD_ITEM_BEING_EATEN would be an adjunct because it is optional.  But then one has no way of accounting for when FOOD_ITEM_BEING_EATEN isn’t optional — for example in answering the question ‘what is Joe eating’?  (Compare with the COMMISSION column in the EMP table of Oracle’s sample SCOTT schema when the employee is a salesman.)  One would either have to try to explain away — an impossible task? — the times when eats surely seems to demand not one, but two arguments, or they would have to give up the demands criterion as the way to distinguish between arguments and adjuncts.

But of course SQL is confused.  The SQL table above is mushing together two different relations, the relation formed by _eats and the relation formed by _eats_.  Disentangle the two relations, and you get a two-fer.  You get rid of the nulls, and you also rescue the demands criterion for distinguishing between arguments simpliciter and arguments that are adjuncts.

When you disentangle the relations, you can see that what is optional, when one is talking about adjuncts, is not the attribute value (e.g., fried egg), but which predicate one invokes when they say eats.  To put it a different way, the attribute value is optional only because the predicate is.

I submit, then, that treating a verb as invoking different predicates whose corresponding relations are involved in subtype/supertype relationships does away with the confusing situation that challenges the demands criterion:  i.e., the initially confusing fact that sometimes an argument seems to be demanded for the verb, and sometimes it seems not to be.

Today’s homage to Plato’s SYMPOSIUM is Channing Tatum (aka Magic Mike) again, as in the previous post.

Channing_Tatum_BlackAndWhite

How can anyone get anything done with such beauty walking the earth?


Semantic Arguments Vs. Adjuncts

The Wikipedia article Argument (linguistics) starts its discussion of the argument/adjunct distinction by asserting that an argument is what is demanded by a predicate to complete its meaning, while an adjunct is not so demanded.  For example, if someone asks me “What is Joe eating?” my answer would be drastically incomplete if I replied “eats.”  My answer would still be drastically incomplete if I supplied just one argument, ‘Joe’, to say ‘Joe eats.’  Only when I supply a second argument, say, ‘a fried egg’, would my reply not create a sense of a question ludicrously left hanging and an answer simply not given.  The predicate _eats_ demands two arguments, such as  ‘Joe’ and ‘a fried egg’ for my reply to make any sense.

( This example, of course, is my own; I am offering it (maybe tendentiously?) in order to make drawing certain conclusions more natural. )

‘[I]n the kitchen’, however, is an adjunct, since nothing would be left ludicrously left hanging in the air were I to leave that argument out of the proposition “Joe eats a fried egg in the kitchen.”  The predicate eats does not demand that argument.

This criterion — i.e., what is demanded by a predicate to complete its meaning … henceforth I will call this the ‘demands criterion’ — runs into trouble when one notices that sometimes eats demands two predicates, but sometimes demands just one.  One might say:  “Joe goes into the kitchen.  Joe eats.”  ( Imagine a novelist or short-story writer working in a certain style.)  Although one could just as well say “Joe goes into the kitchen.  Joe eats a fried egg”, the argument ‘a fried egg’ is not demanded in this particular piece of discourse.

So if one wants to maintain that the predicate eats takes two arguments, they would  have to abandon the ‘what is demanded by a predicate to complete its meaning’ criterion and find another criterion for what is to count as an argument and what is to count as an adjunct.  This a contributor (doubtlessly not the same person who put forward the ‘demands’ criterion) to the Wikipedia article cited above tries to do.

But if one wants to retain the demands criterion, they can assert that two different predicates may get invoked, depending upon the context, depending upon the circumstances, when someone utters the word ‘eats’ in a stretch of discourse.  ( I am not clearly distinguishing between predicate and word here; perhaps I don’t necessarily need to just right here.)  When one invokes the predicate in order to answer the question ‘What is Joe eating?’, invoking the predicate creates a proposition, or tuple, in a 2-place relation.  In circumstances in which nothing is left ludicrously hanging in the air when one says ‘Joe eats’, the predicate creates a proposition, or tuple, in a 1-place relation.  There are two different predicates that may get invoked when one utters ‘eats’.  And depending upon which predicate gets invoked, ‘a fried egg’ is either an argument or an adjunct.

Two-place relation (demands what is eaten to complete the meaning):

EATS
PERSON_EATING FOOD_ITEM_BEING_EATEN
PERSON( NAME(‘Joe’) ) FOOD_ITEM( NAME(‘This fried egg’) )
PERSON( NAME(‘Khadija’) ) FOOD_ITEM( NAME(‘This souffle’) )
PERSON( NAME(‘Juan’) ) FOOD_ITEM( NAME(‘This fajita’) )
PERSON( NAME(‘Kha’) ) FOOD_ITEM( NAME(‘This bowl of Pho’) )
PERSON( NAME(‘Cliff’) ) FOOD_ITEM( NAME(‘This plate of Thai food with a 5-star Thai-spicy rating’) )
PERSON( NAME(‘Cliff’) ) FOOD_ITEM( NAME(‘This strip of bacon’) )

Here the key is composite, comprising both PERSON_EATING and FOOD_ITEM_BEING_EATEN, since we would may want to answer the question “What is Cliff eating?’ with “Cliff eats a fried egg and Cliff eats a strip of bacon.”

One-place relation (does not demand what is eaten to complete the meaning):

EATS
PERSON_EATING
PERSON( NAME(‘Joe’) )
PERSON( NAME(‘Khadija’) )
PERSON( NAME(‘Juan’) )
PERSON( NAME(‘Kha’) )
PERSON( NAME(‘Cliff’) )

Here the key is, of course, PERSON_EATING.

Sometimes what Joe eats is a ‘core element of the situation’, sometimes it is not.  In a possible world there exists a tribe for whom the amount of  energy pounded into the ground by John’s running is a core element of the situation runs, such that something is left ludicrously hanging in the air when one simply says ‘John runs’ and not (to invent a new syntactic marker, ‘tha’, which expresses ‘the energy absorbed by the ground when John runs”’, just as ‘to’ expresses ‘the place to which John ran’ ) ‘John runs tha 1,000 <<some unit of energy>>’.

When what is eaten is an adjunct, not an argument, one can, I think, treat the attribute PERSON_EATING in the two-place relation as a foreign key dependent upon the  PERSON_EATING attribute in the one-place relation.   would be both a unique key in that relation and a foreign key to the one-place relation.  This kind of design is, of course, how one would avoids “nulls” or “optional values” in a SQL table like the following:

SQL Table (what is eaten is an optional or “nullable value”):

EATS
PERSON_EATING FOOD_ITEM_BEING_EATEN
Joe  Fried egg
Khadija
Juan
Kha Bowl of Pho
Cliff
Cliff

Yes — there is a certain oddness, a certain ugliness, to having Cliff suffer from two “null values”.  Maybe there is something fishy about the SQL idea of a “null value”?  But the SQL table does convey the idea that an adjunct is an optional value, while an argument is required.  After conveying this idea, we can get rid of the SQL table with its dubious nulls and replace it with the two-place relation EATS whose PERSON_EATING attribute is a foreign key to the one-place relation.

Once can of course add other adjuncts by creating new relations.

EATS
PERSON_EATING FOOD_ITEM_BEING_EATEN IN ORDER TO
PERSON( NAME(‘Joe’) ) FOOD_ITEM( NAME(‘This fried egg’) ) REASON( NAME(‘Gain Nutrition’) )
PERSON( NAME(‘Khadija’) ) FOOD_ITEM( NAME(‘This souffle’) ) REASON( NAME(‘Gain Nutrition’) )
PERSON( NAME(‘Juan’) ) FOOD_ITEM( NAME(‘This fajita’) ) REASON( NAME(‘Gain Nutrition’) )
PERSON( NAME(‘Kha’) ) FOOD_ITEM( NAME(‘This bowl of Pho’) ) REASON( NAME(‘Gain Nutrition’) )
PERSON( NAME(‘Cliff’) ) FOOD_ITEM( NAME(‘This plate of Thai food with a 5-star Thai-spicy rating’) ) REASON( NAME(‘Show how macho he is’) )
PERSON( NAME(‘Cliff’) ) FOOD_ITEM( NAME(‘This plate of Thai food with a 5-star Thai-spicy rating’) ) REASON( NAME(‘Show how much pain and suffering he can endure’) )
PERSON( NAME(‘Cliff’) ) FOOD_ITEM( NAME(‘This strip of bacon’) ) REASON( NAME(‘Indulge in a guilty pleasure’) )

Here of course, the key is PERSON_EATING, FOOD_ITEM_BEING_EATEN, and IN_ORDER_TO.

This is the way of treating the argument/adjunct distinction that I prefer at the moment, possibly with no good argument for preferring this way to the alternative. The alternative that is at the back of my mind as I write this is something like the following:  there is only one predicate eats, which is a two-place relation.  Or rather, there is only one primary, non-derived predicate eats.  In those cases in which the what-is-eaten argument is optional (so we are giving up the demands criterion for what is to count as an argument), we are projecting on the relation EATS on the PERSON_EATING attribute, to generate propositions such as “Joe eats something.”

EATS(1)
PERSON_EATING SOME ATTRIBUTE
PERSON( NAME(‘Joe’) ) Some thing or things
PERSON( NAME(‘Khadija’) ) Some thing or things
PERSON( NAME(‘Juan’) ) Some thing or things
PERSON( NAME(‘Kha’) ) Some thing or things
PERSON( NAME(‘Cliff’) ) Some thing or things

Here I envisage the demi-urge performing the needed projection by ignoring the FOOD_ITEM_EATEN attribute (perhaps even forgetting there is such an attribute in the relation), then, in order to avoid duplicates (we don’t want our demi-urge to be seeing double!), collapsing what had been two appearances of Cliff into just a single appearance.

The picture of relations above may be pretty (forget the picture of the SQL table — that is definitely not pretty…nothing connected to SQL ever is), but even prettier is  Channing Tatum aka Magic Mike, who is today’s homage to Plato’s SYMPOSIUM:

Channing_Tatum_237

Notwithstanding all of my rapturous sighs at the moment, my sole interest in Magic Mike is, of course, as a stepping stone first, to the Relational Algebra, and then, ultimately, to the Platonic Form of Beauty.


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:

mattdamon2a

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