Category Archives: Syntactic Arguments

Some Clean-Up Work: Why A Name Needs A Selector If One Is To Be Fully Explicit

Let me unpack a bit the NAME() selectors I have been using.  A selector such as NAME(‘Tom’) takes as an argument the string ‘Tom’ and returns the name Tom.(Tom is being mentioned here, not used.  The arguments surely have to be syntactic arguments.)  A string comprises 0 or more written characters (henceforth  just ‘characters’).  A character is an abstract object:  the character ‘e’, for example, can be instantiated by a blob of ink, a pencil mark, a set of pixels….  So a string is an abstract object comprising other abstract objects, and exists at one level-of-abstraction higher than they.

A string of characters is not itself a name, since a name can also be instantiated by a zero or more sounds.  I say “0 or more” because I can imagine a language that uses the glottal stop as a name, whatever the merely practical difficulties might be in doing so.  (A name that could never be pronounced by itself, but only within a stream of other sounds?)

(Perhaps — to jump back to characters for a moment — this language could write the name as ”.  So a name could be instantiated by strings comprising 0 or more characters. )

(Perhaps — to jump back to sounds for a moment — if I tried hard enough I could turn a sound into an abstract object (perhaps one sound can be instantiated by any number of configurations of sound waves?), but I will not try this at the moment. )

Instantiated, as I was saying, by either strings or sounds, a name is an abstract object, one existing at one level of abstraction higher than the abstract object STRING, which itself is one level of abstraction higher than the abstract object CHARACTER.   Not identical with either a sound or a string, a name is best represented not by, for example, ‘Tom’ or <<some sound>>, but by NAME(‘Tom’) or NAME(<<some representation of a string of sounds>>).

This, then, is why, when I am trying to be fully explicit, I refer to a name not as, e.g., ‘Tom’, but as NAME(‘Tom’).

Today’s homage to Plato’s SYMPOSIUM is Ashton Kutcher:

Ashton_Kutcher

There is too much beauty in the world.  How can one concentrate on anything at all with gods like this walking the earth?

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Semantic vs. Syntactic Arguments

In a previous post, playing the role of a would-be ordinary-language philosopher working in Tagalog (which language, to the the total consternation and perplexity of the Spanish grammarians during the 1600s, lacks the verb ‘to be’), I tried to provoke the suspicion that there is no single relation IS that could be pictured as follows:

IS (0)
THING PROPERTY
NUMBER( NAME(‘3’) ) PROPERTY( NAME(‘Prime’) )
CAR( NAME(‘Car With Serial Number 1235813’) ) PROPERTY( NAME(‘Red’) )
FLOWER( NAME (‘Rose With Barcode 3185321’) ) PROPERTY( NAME(‘Beautiful’) )
MINERAL_ITEM( NAME(‘Grain Of Salt Mentioned By Hegel’) ) PROPERTY( NAME(‘Cubical’) )
MINERAL_ITEM( NAME(‘Grain Of Salt Mentioned By Hegel’) ) PROPERTY( NAME(‘White’) )

Contra John Duns Scotus, for example, there is no single relation ‘contracts’ holding between a universal existing as always-already contracted into a particular. (To back up for a moment, the property denoted by NAME(‘three-sided’)is the universal denoted by NAME(‘three-sidedness’)existing as already contracted into a particular triangle.) Nor is there any other single relation which we can identify with the verb ‘is’. Or … letting my Tagalog ordinary-language suspicions run wild for the moment … so I will suppose.

There is no semantic relation (we are supposing) between the particular thing and the particular property.  But there is a syntactic relation between two names, pictured as follows;

IS (0)
THING PROPERTY
NAME(‘3’) NAME(‘Prime’)
NAME(‘Car With Serial Number 1235813’) NAME(‘Red’)
NAME(‘Rose With Barcode 3185321’) NAME(‘Beautiful’)
NAME(‘Grain Of Salt Mentioned By Hegel’) NAME(‘Cubical’)
NAME(‘Grain Of Salt Mentioned By Hegel’) NAME(‘White’)

Voila:  here is the distinction between semantic vs. syntactical arguments to a verb aka predicate that puzzled me in an earlier post.  NAME(‘3’) and NAME(‘Prime’) are syntactic predicates to the verb/predicate ‘is’.  NUMBER( NAME(‘3’) ) and PROPERTY( NAME(‘Prime’) ) are the semantic predicates to the verb ‘is’ — or would be if there were such a verb ‘is’ that took semantic arguments.

In the spirit of ‘let’s see how long I can get away with this’, let me propose the following chain of events for verbs such as eats that do take semantic arguments.  Consider a relation like the one pictured here:

EATS (0)
NAME_OF_PERSON_EATING NAME_OF_FOOD_ITEM_BEING_EATEN
NAME(‘Joe’) NAME(‘This egg’)
NAME(‘Khadija’) NAME(‘This souffle’)
NAME(‘Juan’) NAME(‘This fajita’)
NAME(‘Kha’) NAME(‘This bowl of Pho’)
NAME(‘Cliff’) NAME(‘This plate of Thai food with a 5-star Thai-spicy rating’)

When used in ordinary discourse, rather than mentioned as sentences with whatever syntactic properties, these tuples with their syntactic arguments get transformed into the following tuples with their semantic arguments:

EATS (0)
PERSON_EATING FOOD_ITEM_BEING_EATEN
PERSON( NAME(‘Joe’) ) FOOD_ITEM( NAME(‘This 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’) )

If we think of the intransitive and transitive verbs ‘eats’ as really being the same verb on the semantic level (though it is not clear to me that they are the same), ‘Joe eats’ would be ‘Joe eats something’.  We can derive the corresponding tuple from  the EATS relation first by projecting on the attribute PERSON_EATING:

EATS(1)
PERSON_EATING FOOD_ITEM_EATEN
PERSON( NAME(‘Joe’) ) FOOD_ITEM( NAME(‘This 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’) )

Then by doing a RESTRICT on Joe:

EATS(2)
PERSON_EATING FOOD_ITEM_EATEN
PERSON( NAME(‘Joe’) ) FOOD_ITEM( NAME(‘This 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’) )

The existence of verbs that are sometimes transitive, sometimes intransitive  is what motivated Santorini’s distinction between semantic and syntactic arguments to a verb.

Although I have labored over making this distinction for an embarrassing amount of time, it becomes quite easy to make once one has the notion of a SELECTOR available as a conceptual tool.

I’d like to mention as a final note that possibly we should think of the arguments of eats as always already nested inside the selectors PERSON and FOOD_ITEM; in other words, the names are always transparent, so to speak, letting us see through them the persons and food items, the semantic arguments, named.  It is only under special circumstances — say when the transparent denoting function of the sentence breaks down … maybe one has been staring at the sentence for too long — that the selectors PERSON and FOOD_ITEM get stripped away and we see the names, the syntactic arguments, doing the denoting.  (The sentences always seem to be breaking down this way for C.J. Date in his article “SOME OPERATORS ARE MORE EQUAL THAN OTHERS” in his LOGIC AND DATABASES:  THE ROOTS OF RELATIONAL THEORY.  I get the funny feeling that for him a sentence or expression functions normally at first, but when he stares at it too long it suddenly loses its transparency and becomes an opaque relation between names.  See pages 42 and 45, and see if you get the same impression.)  This final note has been brought to you by the balefully compromised spirit of Martin Heidegger, which was nagging me as I wrote the above.

And now, in the spirit of Plato’s SYMPOSIUM, I would like to picture something a little less dry than the pictures of Relations shown above.  Today it is Kellan Lutz who is serving as my stepping stone, first, to the Relational Algebra, then, finally, to the form of Beauty itself:

Kellan_Lutz

(Rapturous sigh.  How can one live in this world when there is so much beauty in it?)

Update 12/16/2012:  Corrected some errors in the names of some of the Relations; tried to improve the flow of the writing.


Selectors And Semantic vs. Syntactic Arguments

In case anyone wonders (“feel free to come to the point when you finally decide what it is”), the point of the following ramblings is to arrive at a place where I can make a distinction between semantic arguments and syntactic arguments.  The point of making this distinction will become clear (or not) in a later post.  Making the distinction is part of my attempting to put in my own words the argument that Tagalog lacks a subject.

In the previous post, I argued (or claimed, or made the completely unsupported, nay, spurious assertion, as the case may be) that the semantics of Maganda si Robert Pattinson can also be given by the following statement in the database language Tutorial D:

GORGEOUS_EQUALS_GORGEOUS{THIS_ONE, THAT_ONE} where THIS_ONE = PERSON(NAME(‘Robert Pattinson’))

This statement includes the Selector PERSON(NAME(‘Robert Pattinson’)).  Let me unpack a bit what this is. Before I start, I’d like to point out that I THINK that it is  legal in Tutorial D to nest one selector inside another…

NAME(‘Robert Pattinson’) is a operator or function that takes the string ‘Robert Pattinson’ and selects one and only one name.  I will take the concept ‘selects’ as primitive here.  Any implementation of this selector in a physical computer would involve shuffling around ones and zeros until the computer spits out, i.e., returns, one member of the set NAME.  NAME would include strings, but subject to certain limitations.  For example, I assume a  name would have to be, at least, less than 1 billion characters long.  NAME would also include more than strings (that is, representations of text):  a name can be selected by a sound.  So NAME(<<some representation of a sound>>) could also select the name Robert Pattinson. (The reader will notice that I have not yet decided on how to represent, in the absence of a formal selector, a name as opposed to a string as opposed to the person himself…)

PERSON(NAME(Robert Pattinson)) would take the name selected by NAME(‘Robert Pattinson’) and return a member of the set PERSONS, i.e., Robert Pattinson himself.  I don’t know how a computer would implement this operator, but a human being would be implementing that operator in the following type of circumstance:  say, I am sitting in a restaurant.  Someone in the table next to me says:

 I hereby officially declare myself to belong to Team Edward because Robert Pattinson is just too gorgeous.

One part of that utterance, the part that I hear as the word ‘Robert Pattinson’, is the end point of a long causal chain that begins, say, when the parents of Robert Pattinson, after endless wrangling and indecision, finally agree to call their baby ‘Robert’; the doctor in the Maternity Ward crosses out the ‘baby boy’ in ‘baby boy Pattinson’ and writes in  ‘Robert’ on the birth certificate (call this the ‘baptismal event’) … endless events … a director or producer chooses the person named by ‘Robert Pattinson’ to play Edward Cullen in TWILIGHT … endless events…the person sitting at the table next to me sees TWILIGHT…he reads in a magazine he buys at the supermarket that Robert Pattinson played the part of Edward Cullen…he emits a set of soundwaves at the table next to me, which in turn trigger God-only-knows what processes in my brain, until I hear ‘…Robert Pattinson….’  That entire causal chain, ending up in the wetware of my brain, selects the person Robert Pattinson.  THAT’s the implementation of the selector PERSON(NAME(<<some representation of certain sound waves>>)).  Speaking metaphorically and a bit picturesquely, the selector spits out, or returns, Robert Pattinson himself, the flesh-and-blood Robert Pattinson who lives in (I would say ‘Valencia, California’, but that is where Taylor Lautner lives)…. Speaking literally, the selector selects Robert Pattinson himself.

(See Saul Kripke, who apparently never explicitly endorsed this causal theory of reference aka selection.  Gareth Evans would apparently deem this theory, as stated by me, to be naive, but it seems perfectly intuitive to me.)

Invocations of selectors produce literals (more accurately, I guess, are literals).  So whatever else Robert Pattinson himself may be, he is a literal value.

Let me take the liberty of allowing selector invocations as arguments supplied to the parameters of functions, so that we can replace x with the argument PERSON(NAME(‘Robert Pattinson’)) in the function x EQUALS x to produce a true proposition.  Below, I have identified, ala Chisholm, propositions with states of affairs in the world:  here, with Robert Pattinson being identical with Robert Pattinson.  This proposition gives us the semantics of the utterance “Robert Pattinson equals Robert Pattinson.”

I will therefore call the invocation of PERSON(NAME(‘Robert Pattinson’)) a semantic argument.  By contrast, the invocation of NAME(‘Robert Pattinson’), occuring inside an utterance, spoken or written, is a syntactic argument.  In this way, I make sense of the semantic arguments vs. syntactic arguments distinction I puzzled over in a previous post.

I do not know, of course, whether this is the distinction that Beatrice Santorini wanted to make.

I will end by making another homage to Plato’s SYMPOSIUM, according to which interest in Robert Pattinson, Taylor Lautner, Kellan Lutz et al ultimately leads to interest in the Relational Algebra, and from there, to the Form of Beauty itself:

Robert_Pattinson_2

Wow, I love that slightly-unshaven look…(the reader may  hear a rapturous sigh…)

Now, having briefly lapsed into a lower form of eros, I will go back to eros for the Relational Algebra in connection with Semantics….

Update:  After hitting the publish button, I saw this quote from the first Jewish Prime Minister of Great Britain:

The best way to become acquainted with a subject is to write a book about it.

Benjamin Disraeli

Or blog about it at length.