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Formal Semantics G Chierchia, Universita Degli Studi Di Milano-Bicocca, Workings Through a Couple of Examples, with No Milan, Italy Pretence of Completeness

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Formal Semantics G Chierchia, Universita Degli Studi Di Milano-Bicocca, Workings Through a Couple of Examples, with No Milan, Italy Pretence of Completeness Encyclopedia of Language & Linguistics (Second Edition), 2006, Pages 564-579 564 Formal Models and Language Acquisition Jain S, Osherson D N, Royer J S & Kumar Sharma A Osherson D N, Stob M & Weinstein S (1985). Systems that (1999). Systems that learn (2nd edn.). Cambridge, MA: learn. Cambridge, MA: MIT Press. MIT Press. Solomonoff R J (1978). ‘Complexity-based induction sys- Lightfoot D (1991). How to set parameters: arguments tems: comparisons and convergence theorems.’ IEEE from language change. Cambridge, MA: MIT Press. Transactions on Information Theory 24, 422–432. Morgan J L (1986). From simple input to complex gram- Wexler K & Culicover P (1980). Formal principles of lan- mar. Cambridge, MA: MIT Press. guage acquisition. Cambridge, MA: MIT Press. Formal Semantics G Chierchia, Universita degli Studi di Milano-Bicocca, workings through a couple of examples, with no Milan, Italy pretence of completeness. 2006 Elsevier Ltd. All rights reserved. ß Semantics vs. Lexicography One of the traditional ideas about semantics is that it Introduction deals with the meaning of words. The main task of Semantics, in its most general form, is the study of semantics is perceived as the compilation of diction- how a system of signs or symbols (i.e., a language of aries (semantics as lexicography). To this, people some sort) carries information about the world. One often add the task of investigating the history of can think of a language as constituted by a lexicon (an words. Such a history can teach us about cultural inventory of morphemes or words) and a combinato- development. One might even hope to arrive at the rial apparatus according to which complex expres- true meaning of a word through its history. Compil- sions, including, in particular, sentences, can be built ing dictionaries or reconstructing how particular up. Semantics deals with the procedures that enable words have changed over time are worthy tasks; but users of a language to attach an interpretation to its they are not what formal semantics is about. Lexicog- arrays of symbols. Formal semantics studies such raphy, philology, and related disciplines vs. semantics procedures through formally explicit mathematical as conceived here constitute complementary enter- means. prises. They all, of course, deal with language. But The history of semantics is nearly as long and com- the main goal of semantics is to investigate how we plex as the history of human thought; witness, e.g., can effortlessly understand a potential infinity of the early debates on the natural vs. conventional expressions (words, phrases, sentences). To do that, character of language among the pre-Socratic philo- we have to go beyond the level of single words. sophers. The history of formal semantics is nearly as It may be of use to point to the kind of considera- daunting as it is intertwined with the development of tions that have led semantics to move the main focus logic. In its modern incarnation, it is customary to of investigation away from single word meanings and locate its inception in the work of logicians such as their development. For one thing, it can be doubted Frege, Russell, and Tarski. A particularly important that word histories shed light on how words are and relatively recent turning point is constituted by synchronically (i.e., at a given point in time) under- the encounter of this logico-philosophical tradition stood and used. People use words effectively in total with structural and generative approaches to the ignorance of their history (a point forcefully made by study of human languages, especially (though by no one of the founding fathers of modern linguistics, means exclusively) those influenced by N. Chomsky. namely F. de Saussure). To make this point more The merger of these two lines of research (one brew- vividly, take the word money. An important word ing within logic, the other within linguistics), has led indeed; where does it come from? What does its formal semantics to become a central protagonist in history reveal about the true meaning of money? It the empirical study of natural language. The research comes from Latin moneta, the past participle femi- paradigm that has emerged has proven to be quite nine of the verb moneo ‘to warn/to advise.’ Moneta fruitful, both in terms of breadth and depth of results was one of the canonical attributes of the Roman and in terms of the role it is playing in the investiga- goddess Juno; Juno moneta is ‘the one who advises.’ tion of human cognition. The present work reviews What has Juno to do with money? Is it perhaps that some of the basic assumptions of modern formal her capacity to advise extends to finances? No. It so semantics of natural language and illustrates its happens that in ancient Rome, the mint was right Encyclopedia of Language & Linguistics (Second Edition), 2006, Pages 564-579 Formal Semantics 565 next to the temple of Juno. So people metonymically sentence meaning is somehow more readily accessible transferred Juno’s attribute to what was coming out (being, as it were, more complete) than the meaning of the mint. A fascinating historical fact that tells us of words in isolation. something as to how word meanings may evolve; but These are some reasons, then, why the perspective it reveals no deep link between money and the capac- of modern semantics is so different from and comple- ity to advise. This example is not meant to downplay mentary to lexicography and philology; such perspec- the interest of historical investigations on word tive is much more directly tied to the investigation of meanings; it is just an illustration of how linguistic the universal laws of language (language universals) history affects only marginally the way in which a and of the psychological mechanisms underlying such community actually understands its lexicon. laws. Understanding the function, use, etc., of a single There is a second kind of consideration suggesting word presupposes a whole, complex cognitive appa- that the scope of semantics cannot be confined to the ratus. It is, therefore, an arrival point more than a study of word meanings. Do words in isolation have starting point. It seems thus reasonable to start by clearly identifiable meanings? Take any simple word, asking what it is to understand a sentence. say the concrete, singular, common noun dog. What The main thesis we wish to put forth is that to does it mean? Some possible candidates are: the dog- understand a sentence involves understanding its rela- kind, the concept of dog, the class of individual dogs. tions to the other sentences of the language. Each ...And the list can go on. How do we choose among sentence carries information. Such information will these possibilities? Note, moreover, that all these be related to that of other sentences while being unre- hypotheses attempt to analyze the meaning of the lated to that of yet others. In communicating, we rely word dog by tacking onto it notions (kind, concept, on our spontaneous (and unconscious) knowledge of class ...) that are in and of themselves in need of these relations. explication. If we left it at that, we wouldn’t go far. The Notion of Synonymy and Its Problems Looking at dictionary definitions is no big help either. If we look up the entry for dog, typically we will find Imagine watching a Batman movie in which the caped something like: hero fights the Riddler, one of his eternal foes. The Riddler has scattered around five riddles with clues to (1) A highly variable carnivorous domesticated mammal (Canis familiaris) prob. descended his evil plans. Batman has managed to find and solve from the common wolf. four of them. We could report this situation in any of the following ways: Indeed, if someone doesn’t know the meaning of the word dog and knows what carnivorous and mammal (2a) Batman has found all of the five clues but one. mean, then (1) may be of some practical help. But (2b) Batman has found four out of the five clues. clearly to understand (1), we must rely on our under- (2c) Four of the five clues have been found by Batman. standing of whole phrases and the words occurring in them. Words which, in turn, need a definition to be These sentences are good paraphrases of each other. understood. And so on, in a loop. This problem is One might say that they have roughly the same infor- sometimes called the problem of the circularity of the mation content; or that they describe the same state of lexicon. To put it differently, (1) is of help only if the affairs; or that they are (nearly) synonymous. (I will capacity to use and interpret language is already be using these modes of speaking interchangeably.) taken for granted. But it is precisely such capacity To put it differently, English speakers know that there that we want to study. is a tight connection between what the sentences in The limitation of a purely word-based perspective (2a), (2b), and (2c) mean. This is a kind of knowledge on the investigation of meaning is now widely recog- they have a priori, i.e., regardless of what actually nized. Frege summarized it in a nice motto: ‘‘only in goes on. Just by looking at (2a) vs., say, (2b) and the context of a sentence do words have meaning.’’ grasping what they convey, we immediately see that His insight is that complete sentences are linguistic they have roughly the same informational content. units that can sort of stand on their own (more so This is what we mean when we say that under- than any other linguistic units). They can, as it were, standing a sentence involves understanding which express self-contained thoughts.
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