Semantics in context

Linguistic items

: singular/general terms (names, indexicals, descriptions, etc.), quantifiers, connectives, sentences

Semantics is the study of meaning: it seeks to connect our linguistic expressions to things in the world.

Matters of human language may seem quite remote from an endeavour like the bestiary of abstract entities we’re building in this section. Why introduce this topic now? As I will try to illuminate, semantics finds itself at the nexus of metaphysics, logic and epistemology. Does this entail that new abstract entities are needed? As always, there are three main options at hand: eliminativists would say there’s no such thing as semantic entities (only the sounds we make or the symbols we write) and that philosophy has nothing to say about meaning; alternately, we might feel able to build up objects relevant to semantics using existing abstract objects, like properties or sets; lastly, one may have it that sui generis semantic entities are required.

To examine these cases, we will need to go on a brief historical tour. Let’s first rewind towards linguistics and its various branches, to clarify what we’ll be dealing with. For instance, even the colloquial use of word is ambiguous with regards to types and tokens, a concept we’ve introduced above. Sentences like "a five-minute speech should have less than 700 words" clearly refer to word-tokens — in this case utterances spoken by a human being. In contrast: "he uses the word ’like’ a lot" refers to a word-type, and not to one specific utterance. "Low-level" branches of linguistics deal with tokens, be they uttered (phonology), written (graphology), or thought (psycholinguistics). Morphology, on the other hand, deals with word-types and their internal structure.

Beyond morphology, syntax studies the structure of well-formed clauses and sentences. The basic units in syntactic analysis, called constituents, may be composed of one or several word-types: "Paris" and "New York City" play the exact same syntactic role despite the difference in word count.

Natural language formalized

The joint development, over centuries, of philosophical logic and of mathematical notations gave form to ideas such as Leibniz’s characteristica universalis: an ideal language representing the alphabet of human thought, to be used not only for international communication but also to express mathematical, scientific and metaphysical concepts. The idea was revived in a rigorous way by Gottlob Frege with his Begriffsschrift ("concept-script"), which was an inspiration to Russell, Wittgenstein, Church and Turing. That throughline towards informatics and computer science made the notion of formal language almost as natural in our modern world as that of speech or script.

Whilst phonology and morphology are integral to the study of natural languages, a formal language can be solely defined by its syntax, together with a set of symbols. A syntax can be defined directly as the set of well-formed phrases, or via a grammar (a set of formation rules). But in this section, we’ll be looking at the semantics of natural languages or of a hypothetical mental language — why go into a discussion of formal syntaxes?

First, let’s highlight the mundane fact that in daily use, our languages are chock-full of ambiguities, be they lexical ("I am renting this flat", "British left waffles on Falklands"), or grammatical ("the chicken is ready to eat", "they are flying planes"). The atoms of natural language semantics are neither speech acts nor sentence-types but uniquely parseable syntactic forms. Semantics is thus working over a controlled form of natural language whose syntax can be formalized. The meaning of the sentence "a boy climbed every tree" can hardly be examined until we’ve decided which syntactic form we’re talking about, i.e. whether there is one persistent boy who’s climbed every tree, or whether every tree has been climbed by a boy once.

This formalization is equally implicit in the field of logic. Today, a formal logic is defined as the combination of a formal syntax with a set of axioms and rules of inference. Equipped with this schema, we can prove theorems, the conclusions of inferential chains whose sole premises are axioms. Since ancient times, logical inferences have been applied to statements expressed in natural language — this can only work for unambiguous, uniquely parseable ones.

The objects of semantics

With the playing field hopefully a little clearer, we can move to our current interest: semantics. It is an inseparable part of our natural languages: surely, our prehistoric ancestors used language to convey meaning, not to deploy interesting syntactic schemata. Artificially constructed languages themselves are reliant on semantic interpretation, except in metalinguistic contexts, where symbols may just be symbols.

Semantics is commonly defined as the theory of meaning, but we shall distinguish between reference, truth, and meaning proper.