Basic Semantic Concepts Carl Pollard Department of Linguistics Ohio State University September 1, 2016 Carl Pollard Basic Semantic Concepts
Expressions The grammar of each human language recursively specifies what the language’s expressions are, including: what they sound like ( phenogrammatics , roughly similar to what is traditionally called phonology) what they mean ( semantics ) their potential for combining with other expressions to form larger expressions ( tectogrammatics , roughly similar to what is traditionally called syntax , e.g. S, NP, N, etc.) An expression is said to express its meaning. To do linguistic semantics, it’s not enough just to say what some sentences mean; you also have to show how the grammar determines the meaning of each sentence (or other complex expression) from the meanings of the smaller expressions that were combined to form it ( compositionality ). Carl Pollard Basic Semantic Concepts
Static vs. Dynamic Theories of Meaning In reality, what an expression expresses depends in part on the context in which it is uttered. And part of the meaning of an expression is the way that uttering it changes the context for subsequent utterances. Semantic theories that take into account the interaction between context and utterance interpretation are called dynamic . To have a dynamic theory, you have to model contexts. Semantic theories which ignore the role of context are called static . We’ll start out static and ramp things up to dynamic in due course. Carl Pollard Basic Semantic Concepts
Senses Following Frege, we call (static) linguistic meanings senses . Senses are external to language and to the minds of language users (though perhaps there are mental representations of them). Following Montague, we assume different syntactic categories of expressions express different kinds of senses. For example: senses of declarative sentences are propositions . (We’ll discuss these in detail soon.) senses of proper nouns are individuals , also called entities . (This assumption is not uncontroversial, but we’ll adopt it for now.) senses of intransitive verbs, common nouns, and predicative adjectives are unary properties . senses of transitive verbs are binary properties . Properties are understood to be functions that map their arguments to propositions. Carl Pollard Basic Semantic Concepts
Senses and their Extensions We distinguish between a sense and its extension . With Frege, we assume the extension of a proposition is its truth value (so propositions are the kind of thing that have a truth value). With (roughly) Kripke, we assume the extension of an individual is the individual itself. We take the extension of a unary property to be the set of things that have that property. There’s a system to this, which we’ll come to soon. What extension a sense has in general depends on contingent fact , or, informally, on how things are, whereas senses themselves are independent of contingent fact. Carl Pollard Basic Semantic Concepts
Sense and Reference The reference of an expression is the extension of its sense, so this too can depend on how things are. For example: The reference of a declarative sentence is whatever the truth value of the proposition that it expresses happens to be. the reference of an intransitive verb (or common noun or predicative adjective) is the set of individuals that happen to have the property it expresses. the reference of a proper noun is the same as the individual it expresses, and therefore is independent of how things are. (This is a simplification, but we need a dynamic theory to fix it.) Carl Pollard Basic Semantic Concepts
Possible Worlds Most (not all) semantic theories take explicit account of the way that extensions (and therefore reference) can depend on how things are, or might be. Ways that things are or might be are called (possible) worlds , or just worlds . So a semantic theory that take these into account is called a possible worlds semantics , and the model-theoretic interpretation of the theory explicitly represents them. By a world, we understand not just a snapshot at a particular time, but a whole history, stretching as far back and as far forward as things go. One of the worlds, called the actual world, or just actuality , is the way things really are (again, stretching as far back and as far forward as things go). Carl Pollard Basic Semantic Concepts
Different Ways of Conceptualizing Worlds In tractarian theories (named after Wittgenstein’s (1918) Tractatus Logico-Philosophicus ), worlds are certain sets of propositions, namely the maximal consistent ones . (Examples: Wittgenstein, C.I. Lewis, Robert Adams, Alvin Plantinga, William Lycan) In kripkean theories (based on Kripke’s (1963) semantics of modal logic), worlds are taken to be theoretical primitives. This remains the prevalent view in modal logic. Montagovian theories are kripkean theories in which propositions are taken to be sets of worlds. (Examples: Richard Montague, David Kaplan, David Lewis, Robert Stalnaker, inter multa alia ) Usually when linguists speak of possible worlds semantics, they have the Montagovian conception in mind and aren’t aware of the other (and older) options. Carl Pollard Basic Semantic Concepts
Agnostic Possible Worlds Semantics Agnostic possible worlds semantics is a logically weak version that is neutral among all these positions: it could be strengthened into either a tractarian or a kripkean (including montagovian) theory. Carl Pollard Basic Semantic Concepts
The Extension of a Sense at a World We don’t speak of a sense as simply having an extension, but rather as having that extension at a given world . In particular, we don’t speak of a proposition as simply being true or false, but rather as being true or false at a given world . In other words, we assume there is a relation between propositions and worlds, called being true at , and we say p is true at w (written p @ w ) if the ordered pair � p, w � is in this relation. As we’ll see in due course, for any sense s (not just propositions), the extension of s at a world w can be defined in terms of the @ relation. Some versions of possible worlds semantics (e.g. tractarian and montagovian) specify what the @ relation is, while the agnostic version does not (but asserts axioms about it). Carl Pollard Basic Semantic Concepts
The Reference of an Expression at a World When we say that an expression has reference r at a world w , we mean that the sense it expresses has the extension r at w . In particular, when we say that a sentence is true (or false) at w , we mean that the proposition it expresses is true (or false) at w . Carl Pollard Basic Semantic Concepts
Entailment (1/2) For two propositions p and q , we say p entails q provided, no matter how things are, if p is true when things are that way, then so is q . In terms of possible worlds: p entails q if and only if, for every world w , if p @ w , then also q @ w . Obviously entailment is a preorder (relexive and transitive). Two propositions are called ( truth-conditionally ) equivalent if they entail each other. Equivalence is obviously an equivalence relation (reflexive, transitive, and symmetric). Carl Pollard Basic Semantic Concepts
Entailment (2/2) As with truth (at a world), the use of the term ‘entailment’ is extended from propositions to the declarative sentences that express them. (And likewise for ‘equivalent’.) So ‘S 1 entails S 2 ’ means that the proposition expressed by S 1 entails the proposition expressed by S 2 . Native speaker judgments about entailments between sentences (or better, in-context utterances of sentences) are important (some would say, the most important) data in testing semantic hypotheses. Carl Pollard Basic Semantic Concepts
Bolzano’s Notion of Proposition (1/2) Something similar to the notion of proposition used here seems to have first been suggested by the mathematician/philosopher Bernard Bolzano ( Wissenschaftslehre , 1837)—his term was Satz an sich ‘proposition in itself’: They are expressed by declarative sentences. They are the ‘primary bearers of truth and falsity’. (A sentence is only secondarily, or derivatively, true or false, depending on what proposition it expresses.) They are the the ‘objects of the attitudes’, i.e. they are the things that are known, believed, doubted, etc. Carl Pollard Basic Semantic Concepts
Bolzano’s Notion of Proposition (2/2) They are nonlinguistic. They are nonmental. They are not located in space and time. Sentences in different languages, or different sentences in the same language, can express the same proposition. Two distinct propositions can entail each other. Carl Pollard Basic Semantic Concepts
Kinds of Propositions A proposition p is called: a necessary truth , or a necessity , iff it is true at every world. a possibility iff it is true at some world. a truth iff it is true at the actual world. contingent iff it is true at some world and false at some world. a falsehood iff it is false at the actual world. a necessary falsehood , or an impossibility , or a contradiction , iff it is true at no world. a fact of w iff it is true at w . Carl Pollard Basic Semantic Concepts
Recommend
More recommend
