Semantics: Notes 8

Emmon Bach, SOAS, UMass(Amherst)
Oxford: 4 March, 2008
contact: ebach@linguist.umass.edu
Copyright Emmon Bach 2008. All rights reserved.
Link to Notes:                                            
"http://www.people.umass.edu/ebach/courses/ox08-pl.htm"

(4 March) Structuring the Domain II; Quick Bus Tour

Our guide in ontology has to be language itself, it seems to me.
Godehard Link 1983

Today, we want to leave room for some general wrap-up and discussion ranging over our whole set of sessions. I've listed a number of topics to take up. Unfortunately, to do justice to them would take at least one session for each and that would just be touching the surface.

More on Plurals

Last time (Notes 7) we were left in the middle of Schwarzschild's discussion of "sets theories" and "union theories." The score at that point was that some sentences seemed to favour one theory over the other and others the other way around. Schwarzschild started with the sets theory and added stipulative conditions to accomodate all the judgments, ending up with a theory that looked like it just captured what was given by the union theory. The upshot was that the union theory won, but then we are left to explain facts that seemed to be favouring the sets theory. Here are some crucial examples (Schwarzschild op.cit.: 80: Exx. 104a-b):

1. a. The animals filled the barn to capacity.
   b. The cows and the pigs filled the barn to capacity.
   c. The young animals and the old animals filled the barn to capacity.

Assume as in all these examples that the animals are all and only the pigs and the cows. (1a) seems to entail (1b) and (1c). On the other hand (1b) and (1c) each entail (1a). These facts are captured by two constraints, Lift and Lower that ensure that the following hold:

• Upward closure:
An English predicate that is true of a first order plurality G (non-singleton set of individuals) is true as well of all higher oder pluralities formed using all the members of G. (op. cit.: p. 71)
• Downward closure:
If a predicate is true of a plurality G of any order, then it will be true of that first order plurality G' which is composed of the individuals used to form G. (op. cit., p. 79).

The two constraints on sets theories ensure that the following is true:

(p. 77: 110):

Mereological generalization

a. There are no predicates of English that have higher order pluralities in their extension but that cannot also have first order pluralities in their extension.
b. If a predicate of English is true of a plurality G of any order, it will also be true of that first order plurality G' which is composed of the individuals used to generate G.

If these constraints hold, then the sets theory comes out making the same claims as the union theory does directly. Schwarzschild spends a good bit of the second half of his thesis giving an account of sentences that seem to favour a difference in meaning that comes from different groupings of the same plurality but can be explained on other grounds than different denotations for the different groupings. His explanation relies on an analysis of distributivity, with an appeal to context.

The debate about plurals and groups continues. Some other authors who have maintained various positions on the issues are: Scha, Link, Lasersohn, Landman, Hoeksema.

Stuff and Plurals

A closely related domain of issues is in the analysis of mass terms and count terms, brought into discussion especially by Godehard Link (1983, 1998). The parallels between plurals and mass terms have long been noted. Among the semantic properties relevant to the discussion are these, given in slogan form:

1. Cumulative reference: mud + mud = mud; horses + horses = horses
2. (Anti-)Divisibility: mud divided is mud; a horse divided ≠ a horse

In Link's theory these differences are captured by associating two kinds of lattice-structures with mass and count domains. Only the latter is atomic: that is there is a lower bound of things that have no smaller parts to which their predicate (horse etc.) is applicable. Related to both is a basic domain of "stuff," the material counterpart of the quantities of mass domains and the individuals and groups of the count domains. Link insists on not identifying objects with their constitutive stuff. Thus, Terry's ring can be old and the gold making it up even older. The domain of interpretation contains various lattice structures. The main method of interpretation is not based on sets but on algebraic structures. Link has especially pushed the algebraic approach to semantics (see Link 1998, passim, and Landman 1991 for discussion of algebraic approaches). It is worth noting that the non-atomic structure is the more general, in the sense that you have to add a condition to the general structure to ensure atomicity. In other words in a non-atomic structure it is not a condition that the domain not be atomic. Rather it is just not the case that it is atomic. (Compare this usage of "non-" in technical terms like "symmetric, asymmetric, anti-symmetric, non-symmetric.")

It is evident that this whole domain of discussion is very relevant to the question of the interpretation of nominals in various languages that differ on such matters as obligatory or optional or entirely absent number in nouns, requirement of classifiers with number expressions, requirements on inflectional number or its absence when counting things, and so on. Let's take a look at an especially interesting language in this respect.

Kiowa Number.

The Tanoan languages offer a fascinating system of number in the nominal and pronominal systems. You can find a short introduction in Mithun, 1999: 81-82 (data Jemez). Watkins (1984) gives an extended description of Kiowa (not to be confused with Kiowa Apache, an Athapaskan language). I will cite Kiowa here from Laurel Watkins' work (Watkins 1984).

The most notable feature of the system is inverse number. Nouns are divided into four classes. There are three number categories: singular, dual, plural. According to its class membership, each noun has basic or inherent number or numbers.

1. singular/dual inverse: plural primarily animate
2. dual/plural inverse: singular
3. dual inverse: singular/plural
4. (nouns in this class do not use the inverse suffix
(I omit discussion of the Class IV nouns.) As you can see, the inverse picks the complement meaning with respect to plurality. Disambiguation of the choices (e.g. dual/plural) comes about by combinatorics with number marking in pronominal affixes on verbs and other elements.

Examples:

2. tógúl `young man, two young men'
3. tógúlgɔ̀ `(more than two) young men'

But in combination with an Intransitive Prefix èͅ- on a predoicate, the first word must be interpreted as dual. This prefix marks intransitives as predicates over pairs of entities.

4. gú: ribs (dual/plural)
5. gú:gò rib

In combination with an Intransitive Prefix -èͅ, the first word must be interpreted as dual, the second as singular, while to get the plural the instransitive prefix gyà- is required. You are invited to consult the sources for more details of this complex system.

Now a question: is there any way to assign a uniform semantic value to the inverse suffix?

Here's a try. Let's adopt the kind of structured domain proposed by Link and others. For any common noun we have the set of all groups formed from the atoms or basic atoms of the domain. For languages like the Tanoan languages, for any noun N we have D(N) = the union of the singletons (or atoms) I(N), the pairs II(N), and the pluralities III+(N). The denotation of an uninflected Class I noun is just the union of the singletons and the pairs, for Class II just the union of the pairs and the plurals, for Class III the pairs. Now the inverse can be interpreted as an operation that takes the denotation of the bare noun and delivers the complement of that denotation within the whole domain of the common noun. This treatment requires that we have available a denotation that is not directly associated with any of the various forms of the noun itself. The effect of the various inflections on other elements that disambiguate the expressions then can be achieved by intersecting the denotation of the nominal expression with cardinality sets, as in the example above.

Kinds

Quite a few years ago, Greg Carlson initiated a discussion of generic sentences and related problems with his UMass dissertation (1977). Among the phenomena that are dealt with there and in the vigorous continuing discussion since are these:

6. Dutchmen make good sailors.
7. Chickens lay eggs
8. The armadillo is far from extinction.
9. There were three people absent today.
10. ?There were three people intelligent today.
11. You are really sick!
(Two meanings.)
12. Sally is intelligent.
13. Sally is being intelligent.

Discussion of examples like (7) and (8) go back at least to Arnauld's Logic or the Art of Thinking (1683: this is the socalled Port Royal Logic). They clearly do not involve universal quantification over the Dutchmen or chickens. Rather they seem to be saying something about a typical Dutchman or chicken (appropriately delimited by sex and age). Carlson's idea was to bite the bullet and posit a special kind of individual: the Kind. Similarly, interpretation of sentences like (10) - (14) led him to a distinction between (ordinary) Individuals or Objects and Stages of those individuals. Unfortunately, we don't have leisure here to go into the many interesting questions that are raised in Carlson's work and in the vigorous discussion that has gone on since 1977. (A good update that takes us a little closer to now is Carlson and Pelletier 1995.)

For our purposes here, the main point to make is that Carlson's move, like Link's, was to introduce more structure into the domain of individuals. In his view the domain A should be divided into three Sorts: Kinds, Objects, and Stages, with appropriate relations tying them together: an (ordinary) Object can instantiate a Kind, a Stage is a manifestation of an Object, and predicates as well as constructions can be limited in applicability to these various sorts.

Properties

Chierchia's original work around the time of his doctoral thesis revolved around the issue of intensionality: does the classical setup of Montagovian model structures give us meanings that are fine-grained enough to account for all our judgments. Montague's reonstruction of the concept of a property allowed us to distinguish unicorns from chimaeras, even though extensionally identical. But that seems insufficient for other kinds of examples. One of Chierchia's arguments goes like this: in any world the set of objects that are sold must be the same as the set of objects that are bought, but if we try to do a compositional interpretation of the structure of a passive phrase with an agent we can derive the absurd result that whatever is sold by Oswald must be bought by Oswald as well. So Chierchia investigated models in which properties are not just functions from worlds to sets, but full-fledged members of an independent set in the model structure. (References: Chierchia 1984, Chierchia and Turner 1988.)

Situations

Think of a situation as something of the same logical type as a possible world, but "smaller." A possible world is "a way things could be." A situation is "a way a limited set of things could be." There are two ways to think about this: one is to take a situation as a limited set of conditions or predicates and a "small" domain of individuals (this is more or less in the spirit of Kamp's DRT amd Heim's File Change Semantics); the other is to think of a situation as a small part of an entire world, with all the "thickness" of a world. One approach (in the former class) is the Situation Semantics of Barwise and Perry (1983), which has had a subdued but permanent influence on the whole field.

One set of data that has played a role in situation theory and related matters is the question of the semantic value of the object clause in sentences like (15) to be compared with (16):

14. John saw Bill fill the bathtub.
15. John saw that Bill had filled the bathtub.

(14) entails that John saw Bill (at the relevant time), while (15) does not, in fact (15) could be verified by a story in which John has very indirect evidence for the fact that Bill had filled the bathtub -- perhaps by careful measurement of the remaining water in a hotwater tank.

Events and Eventualities

Discussion of situations leads naturally to questions about events and like. There are two springs for these questions: one is the issues raised by Donald Davidson quite a few years ago about events as independent ingredients for the semantics of natural languages (originally in the sixties of the last century: Davidson 1967, 1980), the other is the classification of predicates and sentences according to Aristotle-Kenny-Vendler distinctions among states, activities, accomplishment, achievements, etc.) and spinoffs into characterizing acceptability and interpretations of sentences like these:

16. Sally knows the answer.
17. ?Sally is knowing the answer.
18. Hilda is running.
19. Hilda has run.
20. Hilda runs.
21. John is dying.
22. Hilda ran three times.
23. ?Pat looked for the book in three hours.
24. Pat found the book in three hours.
25. Pat looked for the book for three hours.
26. ?Pat looked for the book in three hours.

Donald Davidson, like Montague, initiated a programme for using philosophical and logical tools for analysing natural language and took as its main task a Tarski-type definition of Truth. His work on events and adverb interpretation took off from sentences like (27) and (28):

27. Brutus stabbed Caesar in the forum.
28. Jones buttered the toast in the kitchen at midnight with a knife.
29. ∃e[stabbing'(b, j, e) ∧ in-the-forum'(e)]

Note that (29) just by the normal interpretation of conjunction will allow the inference in (30). And (28), by the same reasoning allows a whole range of implications

:

30. Brutus stabbed Caesar.
31. Jones buttered the toast.
32. Jones buttered the toast in the kitchen.
33. Jones buttered the toast with a knife.
34. Jones buttered the toast at midnight.
35. Jones buttered the toast at midnight with a knife.
36. Jones buttered the toast in the kitchen with a knife.
etc.

Other authors have developed Davidson's ideas in various ways, for example, Terry Parsons (1990).

Morphosemantics: the Internal Semantics of Words

By "Morphosemantics" I mean the semantics of morphemes. The point of the term is to highlight questions about the meanings of different kinds of linguistic elements and especially to ask questions about whether the semantic values and semantic relations the we find in phrasal syntax -- roughly: "at and above the word" -- are appropriate and adequate for understanding the meaning of individual morphemes and items "smaller" than words.

I follow di Sciullo and Williams, 1987, in recognizing several different meanings for the word "word." What we mean by word will make a big difference in the questions and answers that we consider here.

These need to be distinguished:

1. phonological word
2. morphological word
3. syntactic word
4. lexical word (lexeme, "listeme")

A full discussion of the issues of word meaning is way beyond our space and time here. We will confine attention to questions about the last sense of word; that which is invoked in a constructive view of language, the base from which we start when we specify a generative theory about how pieces of language are constructed and what they mean. To get into the question we might start from a look at what would be listed in any relatively detailed dictionary of a language. Start with an example:

1. run (1)
2. intransitive verb
3. principal parts: run, ran, run
4. /r∧n/ (Am: /rən/), /ræn/, /r∧n/ (Am: /rən/)
5. to move by means of the legs in such away that both feet lose contact with the ground, floor, or deck periodically,....
6. synonyms and related items: gallop, dash,...

A dictionary entry like this is supposed to give enough information to users to allow them to use the word properly. Some additional information is given of a sort that might help users or help sell the dictionary.

1. orthographic form plus distinguishing mark (number), together these are unique identifier for item
2. syntactic category
3. morphological properties, paradigmatic information
4. phonological representation (including dialect information)
5. denotation or semantic value (by definition)
6. reference to other items in dictionary related (here) by synonymy

We might compare this with some examples from various authors who have dealt with the issue of lexical entries.

Note: I will be giving a course on morphosemantics at Ohio State University for three weeks, starting 31 March. If you want to follow this course online, there will be a link here "http://www.people.umass.edu/ebach/courses/OSU08-pl.htm" .

Final Word

Precisely constructed models for linguistic structure can play an important role, both negative and positive, in the process of discovery itself. By pushing a precise but inadequate formulation to an unacceptable conclusion, we can often expose the exact source of this inadequacy, and consequently, gain a deeper understanding of the linguistic data....I think that some of those linguists who have questioned the value of precise and technical development in linguist theory have failed to recognize the productive potential in the method in rigorously stating a proposed theory and applying it to strictly linguistic material with no attempt to avoid unacceptable conclusions by ad hoc adjustments or loose formulations.

N. Chomsky, Syntactic Structures: p.5.

That's the end of our bus-tour for this term. We do hope that you have enjoyed it. If we have roused your interest enough to convince you that you should return for a closer inspection of some of the sites we have visited then we will be content. Please do tell your friends about us! Cheers!