Category Archives: John Duns Scotus

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.

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The Mystery Of The Missing IS: Or, Had John Duns Scotus Been An Ordinary-Language Philosopher Working In Tagalog


Below, I have tried to start incubating the suspicion that there is something fishy about treating ‘is’ as a predicate with two parameters accepting one argument each, i.e., a two-place relation.


Tagalog doesn’t have a verb ‘is’, no verb ‘to be’.  Given that more literal translations of Tagalog sentences often display the phrase ang noun phrase structure as:

 

phrase [is] ang noun phrase


For example:

Titser ang babae.

Maganda ang lalaki.

Umalis ang babae.

gets rendered as:

Teacher [is] the woman.

Beautiful [is] the man.

Having left [is] the woman.

or as I prefer (see my attempt below at eliciting the ‘aha erlebniss’):

Some teacher one  [is] the woman.

Some beautiful one [is] the man.

Some having left one [is] the woman.

…given that, one might think that, always, the suspect verb aka predicate aka relation is implicitly in effect in sentences with that structure.  The lack of a verb ‘to be’, of an ‘is’ in Tagalog that so perplexed the first Spanish grammarians of the language (so that, in their total confusion and lack of understanding, they tried to interpret the Tagalog inversion marker ‘ay‘ as the verb ‘is’, a confusion and misinterpretation that has had hilarious consequences lasting to this day), is always there, just unpronounced (or unwritten).  The space between ‘maganda‘ and ‘ang lalaki‘ in the written sentence, or the lack of interruption in the string of sounds (if that is how maganda ang lalaki gets pronounced — I am not strong enough presently in Tagalog to know) or the glottal interruption (if one exists between the ‘maganda‘ and ‘ang lalaki‘)  … the space, or lack of interruption in the continuous stream of sound, or the glottal, these are, as the case may be, an implicit sign of the two-place relation ‘is’.

Following Naylor, Schachter, and my own intuition, I have been treating the space, the lack of interruption in the continuous stream of sound, the glottal as an implicit equals.  For example, I prefer to translate the above three Tagalog sentences as:

Some teacher one  = the woman.

Some beautiful one = the man.

Some having left one = the woman.

Unlike ‘is’, however, which is (if there is such a critter) a two-place relation, ‘equals’ (alternatively, ‘=’ ) is, as I am about to show, a one place relation.  It is not just that the sign corresponding to ‘is’ is lacking in Tagalog:  the (real or putative) semantics of ‘is’ is lacking in Tagalog as well.  Tagalog is working with something completely different.

Clearly the ‘equals’ that is in play here is not given by the ‘equals’ in the following two-place relation:

 

THISTHAT

EQUALS (0)
Morning Star Evening Star
3 3
Rose With Barcode 3185321 Rose With Barcode 3185321
Clifford Wirt Clifford Wirt
The murderer of Jones The butler

…because in sentences such as Maganda si Taylor Lautner, the word ‘Maganda’  does not, at the moment of its utterance, specify, identify, locate, expose, or pick out any one particular thing.   ‘Maganda’ is equivalent to ‘Some beautiful one’, or the part of the formal sentence below that occurs before the ‘=’:

∃x ∈ MAGANDA: x = si Taylor Lautner.

The x that belongs to the set MAGANDA is left unspecified, unidentified, unlocated, unexposed, un-picked-out at the start:  Maganda … though it does get specified at the end:  …si Taylor Lautner.  But a two-place relation requires two identified, specified arguments for its two attributes.

Let me try to capture in D the sentence ‘∃x ∈ MAGANDA: x = si Taylor Lautner’.  Let me posit the following 1-place relation:


MAGANDA (0)
MAGANDANG_BAGAY
Taylor Lautner
Sunset at time t and place p
Rose With Barcode 3185321
Wine Red
The Taj Mahal
Haendel’s Umbra Mai Fu

Taking this relation as my springboard, I capture ∃x ∈ MAGANDA as MAGANDA{} (which gives us TABLE_DEE, or TRUE, or YES), then do a CARTESIAN PRODUCT of that with a restriction of MAGANDA:

with
MAGANDA{} as t_sub_0,
MAGANDA{MAGANDANG_BAGAY} where   MAGANDANG_BAGAY= ‘Taylor    Lautner’ as t_sub_1:
t_sub_0 X t_sub_1

CARTESIAN PRODUCT is a special case of JOIN.  TABLE_DEE JOIN r, where r is any relation, yields r.  So the D statement above yields:

MAGANDA (1)
MAGANDANG_BAGAY
Taylor Lautner

which expresses the semantics of the sentence ‘Maganda si Taylor Lautner’.  In this way, we get rid of the doubtful (I think) verb aka two-place relation ‘is’.

To sum up, a bit impishly:  the semantics of ‘is’ is different in Tagalog than in English because Tagalog really doesn’t have an ‘is’.  Later, I will try to develop this into part of an argument that Tagalog lacks a subject.  Tagalog’s lacking a verb ‘to be’ is related to its lacking a subject.

To stray back for a moment to philosophy:  were Duns Scotus an ordinary-language philosopher working in Tagalog, it may never have occurred to him to try to find a single relation (e.g. ‘contracts’ ) between the entity Beauty, as the argument on one side of the predicate ‘is’, and Taylor Lautner as the argument on the other side of the predicate, and so on for every other proposition formed by supplying arguments to the parameters x and y in the predicate x is y.

11/10/2012:  Updated to make a point a bit more clearly.

11/10/2012:  Updated to parenthetically add some snark about the first Spanish grammarians of the Tagalog language in the 1600’s.

 

Update:  11/25/2012:  Post grayed-out because I am dissatisfied with it.


That Strange Predicate/Relation IS

The predicate IS has two parameters.  Placing arguments in those parameters produces something like the following Relation:

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

This is a SINGLE relation, one may note, just as INVITES and TO_THE_LEFT_OF are. But while the relations INVITES and TO_THE_LEFT_OF are fairly easy to get one’s mind around, IS is a more difficult case. What is the relation between a property and the thing of which it is the property? Should we say that the property “inheres” in the thing? (Whatever “inheres” means.) Should we follow Plato and think of the relation between thing and property as analogous to the relation between reflection in the mirror and the thing or person reflected? So that the thing is a wholly relational entity wholly dependent upon something more real that exists independently, i.e., the property existing as a Platonic Form? Should we be more Aristotlean and think that, while yes, a given property (e.g. RED, e.g. PRIME) is one thing, not many, it is always already “contracted” (the ‘contracted’ business always makes me think of the old freeze-dried instance coffee commercials … the property gets “sucked” into the thing accompanied by the corresponding sound) ala John Duns Scotus into (but where does the ‘into’ come from? Does this mean ‘inhere’?) the thing so that it never exists independently of the thing? So that it has a “unity less than numerical?” (Source of the ‘unity less than numerical’ thing comes from some writing of Duns Scotus which I do not remember.) Should we think, along with William of Ockham, that it is nonsense to think of a single thing, e.g., the property RED, as existing in several places at the same time, so that we have to think of the red of the car and the red of the rose petal as in fact two different properties, even if they exactly match the same color sample held by the Interior Decorator? (So that ‘Red’ in the Relation above would always have to be marked by a number serving as an index?)

Or maybe the Relation IS is not a real Relation at all, but an artifact of a Word. Given the Word ‘is’, we think there is a corresponding Predicate generating Propositions which, when true, form a Relation. But in reality there is no such Relation. Perhaps?