Page 340 - Encyclopedia of Philosophy of Language

Formal Semantics
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Formal semantics of natural language is the study of the meaning of natural language expressions using the tools of formal or symbolic logic. The ultimate aim of the discipline is commonly taken to include the following: to give an explication of the concept of meaning and to use this explication to provide an account of the role of language in the activity of draw- ing inferences (the individual processing of infor- mation), and of the role of language in the activity of sharing or communicating information (the collective processing of information).
This article provides an introduction to formal the- ories of meaning and to the logical analysis of language in the footsteps of Gottlob Frege, the founding father of the enterprise. The process of com- position of meaning and the relations between the concepts of meaning, inference, and truth are presented, and contextual aspects of meaning are dis- cussed. The article ends with a sketch of the emerging perspective of a dynamic theory of meaning.
1. The Composition of Meaning
Introductory logic textbooks usually include a selec- tion of exercises for translating natural language sen- tences into first-order logic. Invariably, these exercises assume that the student already has a firm grasp of what the sentences mean. The aim of such exercises is to expand the student's awareness of the expressive power of predicate logic by inviting him/her to express an (intuitively) well-understood message in the new medium. Because of this presupposed understanding of the original message, such translations cannot count as explications of the concept of meaning for natural language.
It is necessary to ask under what conditions a trans- lation procedure from natural language into some kind of logical representation language can count as an explication of the concept of meaning.Obviously,
the procedure should not presuppose knowledge of the meaning of complete natural language sentences, but rather should specify how sentence meanings are derived from the meanings of smaller building blocks. Thus, the meanings of complex expressions are deriv- able in a systematic fashion from the meanings of the smallest building blocks occurring in those expressions. The meaning of these smallest building blocks is taken as given. It has been argued that the real mystery of semantics lies in the way human beings grasp the meaning of single words; see, for example, Percy (1954), or Plato's dialogue Cratylus.
Formal semantics has little or nothing to say about the interpretation of semantic atoms. It has rather a lot to say, however, about the process of composing complex meanings out of smaller building blocks. The intuition that this is always possible can be stated somewhat more precisely; it is called the Principle of Compositionality and defined as follows:
The meaning of an expression is a function of the mean- ings of its immediate syntactic components plus their syntactic mode of composition.
The principle of compositional!ty is implicit in Gott- lob Frege's writings on philosophy of language; it is made fully explicit in Richard Montague's approach to natural language semantics. Rather than indulge in philosophical reflections on the meaning of com- positionality, the principle will be illustrated here by showing how Alfred Tarski's definition of the sem- antics of 'first-order predicate logic' complies with it.
From the end of the nineteenth century until the 1960s the main tool of semantics was the language of first-order predicate logic, so-called because it is a tool for describing properties of objects of the first order in Bertrand Russell's hierarchy of 'things,' 'properties of things,' 'properties of properties of things,' etc. Essentially, predicate logic was first presented in 1879
by Frege.
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Formal Semantics J. van Eijck