V61.0004 Introduction to Semantics: Spring 2006


V61.0004 Introduction to Semantics

Prof. Anna Szabolcsi

Spring 2006

Lecture TR 9:30—10:45, Recitation section R 12:30—1:45

Anna Szabolcsi
719 Broadway, Rm. 423
Eytan Zweig
719 Broadway, Rm. 415


In the first half of the semester, the section’s main goal will be to provide extra help if necessary; later it will serve as a forum for more in-depth discussion and perhaps further readings.


Allwood et al., Logic in Linguistics, Cambridge University Press.
Course reader obtainable from New University Copy & Graphics, 11 Waverly Place.

See course overview on the next page; please refer to it throughout the semester.

Tentative Calendar

Week Tuesday Thursday
1 introduction set theory
2 set theory mental lexicon: Aitchison
3 inferences Word/world: Bowerman+Talmy
4 propositional logic syntax
5 propositional logic syntax
6 predicate logic count/mass: Fromkin, ed.
7 MIDTERM telic/atelic: Fromkin, ed.
8 predicate logic predicate logic
Spring Break    
9 tense: Reichenbach modality
10 intensionality tenses and pronouns: Partee
11 determiners: Fromkin, ed. determiners cont’d
12 scope: Reinhart adverbs: Lewis
13 presupposition: Keenan, focus adverbs: Fromkin, ed.
14 pragmatics: Grice review

There will be 9 or 10 written assignments, a midterm, and a final exam. The assignments typically combine logic problems and linguistics questions, graded on a 4-point scale (0-1-2-3), and are worth 30% of the final grade. They will be assigned on Thursday and due at the beginning of class on the following Tuesday. Late assignments will not be accepted. The skills practiced in the assignments will be needed for the exams; it is in your best interest to do all the assignments conscientiously. -- In class we discuss only the main ideas of the assigned readings, but please always read them in full.

The midterm is worth 30% of the final grade and covers the material of the first 5 weeks. The final exam will be cumulative with more emphasis on material not covered in the midterm; it is worth 40% of the final grade. If a student misses either exam without a written excuse acceptable to the
instructor (e.g. a doctor’s note), they receive zero points for that exam.


Language is a system of symbolic signs, in which form and meaning are linked by convention. Meaning is distinct from the entities referred to. Semantics is the study of meaning. Semantics is often divided into word semantics and sentence semantics, although there is no sharp demarcation line between the two. This course will start from word semantics and gradually move on to sentence semantics, concluding with some issues of language use, i.e. pragmatics.

The relation between form and meaning in complex expressions (phrases or sentences) is governed by the principle of compositionality. Compositionality says that the meaning of a complex expression is determined by the meanings of its parts and how they are put together. If you know what the words the, mailman, dog, bit, and bought mean and you are in command of the grammar of English, you automatically know how the meaning of the sentence The mailman bit the dog differs from that of The dog bit the mailman or The mailman bought the dog. Syntax is the study of how the parts of complex expressions are put together. Some people in the class have had syntax (in Linguistic Perspectives, Language, Intro to Linguistics, Language and Mind, or Grammatical Analysis) and some others have not. For two lectures the class will split into two sections, one getting introduced to syntax and the other exploring an additional topic in semantics (one that is not in the calendar).

Building a syntax and a compositional semantics for a natural language like English is a huge task. This course will not actually undertake it but can be regarded as making serious preparations for it. It will follow two parallel tracks. The “Tuesday track” introduces an amount of set theory, propositional logic, predicate logic, modal and intensional logic that form a necessary background for the study of sentence meanings. A logic is a formal language plus an inference system (a calculus). This course focuses on how the languages of the above logics work, not on their calculi. Formal languages are strictly compositional; in this way the logic track will also illustrate the working of compositionality in an artificial, and thus simplified, environment. The “Thursday track” will study a set of linguistic semantic phenomena that we need to understand if we want to build a compositional semantics for English. It will draw on the results of the logic track, and around week 10 linguistic semantics completely takes over. Throughout the course we use logic as a tool for studying natural language and keep an eye on the ways in which English differs from the logical languages.


Two central questions for word semantics are, How are meanings represented in the mind? and How do meanings compare with "the world out there"? Some questions and hypotheses related to the representation of word meanings in the mind are reviewed by Aitchison. Do words have a fixed meaning with sharp edges, or is word meaning fuzzy? Can word meanings be represented as snapshots or checklists? Do we need experts to tell us what words really mean? What roles do squishy distinctions and family resemblances play? What are prototypes good for? Is meaning represented in the form scenarios/frames? Are meanings decomposable into atoms? Do meanings form fields? None of these hypotheses solve the representation problem in general, but each is useful in explaining some empirical phenomenon observed by psycholinguists.

The comparison of what semantic distinctions different languages make reveals that languages have considerable freedom in carving up reality. Bowerman compares the spatial distinctions English makes using in and on with those in Spanish, German, Dutch, and Korean, and examines the role of language versus cognition in first language acquisition. Studying the expression of the components of motion events, Talmy examines how different languages conflate motion with manner, motion with path, or motion with figure.

Another distinction languages typically make is between count nouns like dog and mass nouns like water. One test: only count nouns can be pluralized (dogs, but *waters, unless kinds of water are meant). Mass nouns pose a problem for set theory, which is built on the element-of relation: even if water molecules can be regarded as minimal parts of water, they are not linguistically relevant. A part-whole semantics will be proposed for mass expressions. What has been called natural language metaphysics then asks how the distinctions observed in this nominal, entity domain carry over to the verbal, event domain.

Aspect has to do with the internal structure of the event. States (e.g., be good, know) and activities (run) are atelic: they have no inherent end point. Achievements (recognize Bill) and accomplishments (build a house) are telic: they have an inherent end point. Atelic events are like masses. Every part of water is water, and every part of a running event is a running event. Telic events are like discrete objects that count nouns refer to: they have a built-in articulation.

Telic/atelic aspect is a property of verb phrases, not just individual verbs. With this, we are in the domain of sentence semantics. Next we turn to tense. Tense has to do with the time of an event (E) relative to speech time (S) and -- Reichenbach's innovation -- reference time (R). R is introduced for the sake of perfect tenses but then proves useful across the board. Adverbial modification is then constrained so that it has to preserve the S, R, E relations (whence we cannot have *I left tomorrow.)

Classical logic interprets expressions with reference to just one “world” (situation). Modal auxiliaries and adverbs (must and can, necessarily and possibly) force us to look at a set of possible worlds in addition. The fact that The Semantics class is necessarily in Waverly is judged to be false but The Semantics class is necessarily concerned with interpretation is judged to be true cannot be accounted for by simply looking at the Spring 2006 “world”. Having a set of possible worlds at our disposal also enables us to address a fundamental distinction between sense (meaning) and reference and between extensional and intensional contexts (find a unicorn vs. seek a unicorn, and many others).

Logicians had assumed that present, past, and future tenses are very similar to modal adverbs and auxiliaries. Partee points out a variety of systematic similarities between tenses and pronouns, utilizing core notions of predicate logic like free and bound variables.

The language of predicate logic has fairly articulated sentence structures. One of its central concerns is the semantic contribution of quantifiers like everyone and someone. The study of English makes it necessary to generalize the investigation to determiners like five, more than five, most, etc. and to point out that linguistic quantifiers differ from their predicate logic kin in being restricted to a particular set in the universe of discourse: the one denoted by the common noun they combine with (e.g. most men). Another important question whose study was initiated by Reinhart is how the scope interpretation of quantifiers depends on their position in syntactic structure.

Issues in the entity domain and the event domain converge again in the study of adverbs of quantification like always, sometimes, and usually, initiated by Lewis. Interesting questions arise in connection with what constitutes the restriction of those adverbs. Presuppositions, as studied by Keenan, and focus will be invoked to deal with some of the cases. With this, we reach the borderline between semantics and pragmatics, and conclude with examining Grice’s principles of co-operative conversation. Time permitting, we get back to the first language acquisition of meaning.

In sum, some of the main ideas of the course will be these:

  • Logic offers essential tools for the study of natural language semantics, but the two are not identical.
  • The interpretation of complex expressions is compositional and so it depends on syntactic structure.
  • There exist deep semantic parallelisms between the verbal and nominal domains.
  • Pragmatics shoulders some of the burden of interpreting linguistic expressions.

Updated on 04/14/2011
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