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NLP: Introduction to Semantics
Introduction to Semantics: the Sense/Reference distinction
For those in the logical tradition of semantics, modern semantics begins with Frege. In 'On Sense and Reference' Frege asked a deceptively simple question: how is it that a statement of the form 'a = b' can be informative, whereas a statement of the form 'a = a', being a truth of logic, can be known a priori? Examples:
1) Hesperus = Phosphorus
or 'The Morning Star = the Evening Star', or 'Lewis Carroll = Charles Dodgson', or 'Thira = Santorini', etc. Frege considered two possible explanations, to both of which he gave fairly decisive objections.
i) A 'Referential' Account - can be paraphrased like this: the semantical role or function of a proper name is to stand for, or refer to, a particular object. Frege argued that reference cannot provide the complete account of what is going on. The whole account can
not remain at the level of reference, or what is referred to - i.e. at the level of the objects in the world. For if 'a = b' is true, there is only one object involved:
So at the level of objects, there is nothing to distinguish 'a = b' (if true) and 'a = a'.
ii) A Meta-linguistic, or Quotational, Account - the explanation is simply that the 2 names in question refer to the same thing. This is an intuitively appealing account, since it accords with the kind of thing we o
rdinarily tend to say about these cases, and Frege himself had subscribed to it earlier. So as a proposed analysis of 1) we have
2) (Ex) 'Hesperus' refers to x & 'Phosphorus' refers to x.
What is not in dispute is that this is true - but that is not the point. The point is that - as with the previous account, the truth it emphasizes does not serve to provide a proper analysis of the problem. (1) and (2) are different propositions - (1) is a significant fact about the world - it is a fact abo
ut Venus, not about language. Plausibly, it is a necessary truth - a posteriori but necessary. (2) is contingent ('arbitrary' Frege says) - a fact about language. Since they are different propositions, (2) cannot serve as an analysis of (1). There is no more reason to suppose the names in are not referring to Venus in (1), than in say,
3) Hesperus is pretty
where it is clear that this is about the planet, not the name. To suppose the name functions differently in (1) and (3) is to postu
late an unwarranted ambiguity.
Frege's solution was to distinguish sense (Sinn) from reference (Bedeutung). The two names involved in a true identity statement have the same reference, but they differ in sense. Sense is an objective, or at least inter-subjective, feature of a word or phrase - its literal or communicable content. The sense of an expression is the content which you grasp, in thought, when you understand it. There are many further theses about sense which Frege asserted,
some of which are more contentious than others. He maintained that for proper names, their sense was their "mode of presentation" of their reference - the way of presenting an object. Both 'Hesperus' and 'Phosphorus' have the same reference, but one presents - or describes - it as the first star to appear in the evening, whereas the other presents/describes it as the last star to disappear in the morning.
The sense of a complete sentence, for Frege, was the proposition or Thought expressed by it. '
Thought' here is not something private or psychological, but essentially communicable. Speakers of the same natural language communicate with each other - they trade contents, not uninterpreted strings of symbols - i.e. there must be communicable content which is conveyed in discourse. The proposition expressed by a sentence, Frege maintained, is explicable in terms of the conditions under which it is true - its truth conditions. To grasp the literal content of a sentence I must know under what condition
s it is or would be true.
It is important to be clear on the difference between truth conditions and truth value. Knowing the truth value of a sentence is neither necessary nor sufficient for understanding it. Consider: the following biconditional spells out the truth conditions of a certain English sentence:
true('Interest rates will rise in 1994 & there will be an election in 1995')
interest rates will rise in 1994 & there will be an election in 1995.
But my knowing that fact - i.e. understanding that conjunction, knowing the conditions under which it is or would be true, does not suffice for me to know whether it is actually true or false. Conversely, I may know the truth value of some foreign sentence (having been told it by a trustworthy authority), but that does not mean I understand it. For Frege, the truth value was the reference of a sentence.
What is important is the basic idea of the sense/reference distinction; similar distinctions
have been made both before and after Frege (with differing supplementary theses - different theorists have come to different conclusions about various aspects of the distinction). Roughly speaking, the following distinctions are equivalent:
Sense/Reference - Frege
Connotation/Denotation - John Stuart Mill
Intension/Extension - cf. Extensional logic (e.g. 1st order predicate
logic; Set theory), vs. Intensional logic (modal & tense logics, etc.).
To give you a rough idea o
f how these distinctions apply to the most important logical categories of expression, here are some of the standard ways of accounting for them:
Proper Names
Sense: [do they have a sense? If so:] description of referent
Reference: object
Predicates
Sense: Concept [alternatively: Property]
Reference: Set of objects
Sentences
Sense: Proposition, or Thought expressed; Truth conditions
Reference: Truth Value [alternatively: Situation]
(Different overall theories of mean
ing fill these out in different ways - for instance, situation semantics rejects Frege's view that sentences refer to their truth values, arguing instead that they refer to situations.) But an important principle which guides most theories is compositionality. Frege maintained a version of compositionality both for reference and for sense.
Reference: the reference of a complex (e.g. a sentence) is determined by the references of its parts, and its structure (the way those parts are
put together). Since the reference of a sentence is its truth value, compositionality of reference for sentences is essentially truth-functionality: the truth value of a complex sentence is wholly determined by - i.e. is a function of - the truth values of its parts. But of course not all language is truth functional - most obviously, propositional attitude contexts - e.g. 'John believes that X'. Each one of us believes many truths, but some falsehoods as well; there are many truths tha
t each of us does not know about, and so does not believe. In short, from the truth value of X, you cannot tell whether John believes it or not (contrast the context 'Not X') - and that is just to say that the context 'John believes that X' is not truth functional. Of course, Frege knew this, so he introduced a complication into the thesis. But in any case what is more plausible is compositionality for sense:
Sense: the sense of a complex is wholly determined by its structure and the senses of its p
arts. A standard argument for compositionality of sense is productivity. Productivity of language use is a general argument for structure, systematicity in language (e.g. syntax). But productivity also applies to understanding: our ability to comprehend novel sentences. But there are different ways to work out the thesis of compositionality of sense. Consider: what structure? Syntactic structure? This is one version of semantic compositionality - in effect, the rule-to-rule hypothesis adopted by Mont
ague. It's oversimplified for natural language in general, since e.g. there can be syntactic structure where there is no semantic structure. E.g. idiomatic phrases, such as 'red herring'. The meaning of this is not a function of its parts, its meaning has to be learnt as a unit. Perfect harmony between syntactic and semantic composition (rules) is an ideal which is perhaps only found in artificial languages. But the rule-to-rule hypothesis is a useful working assumption. It has this consequence: we ca
n add an extra layer to a phrase structure tree:
Word or phrase/ syntactic classification/ semantic contribution
So a compositional theory of meaning will have a representation of the contribution of each word and sub-phrase towards the meaning of the whole.
The sense of a component is what it contributes to the sense of any complete sentence in which it could be a part. This can be seen most obviously in the logical expressions - we don't assign a meaning to E, the existential quantifier,
on its own, but in context
'(Ex)P(x)' is true ....
-------------------------------
giving conditions under which sentence in which E dominates is true
If we follow Frege in saying that the sense of a sentence is given by its truth conditions, then the meaning of a part is given by its effect on (or contribution to) the truth conditions of any complex in which it could occur. A simple example is conjunction:
Any sentence of the form (A & B) is true just un
der these conditions:
both A is true, and B is true.
This is a general rule which enables us to derive such specific attributions of truth conditions as the one given earlier. This rule is in fact a re-presentation of what the truth table for & states. That is, a truth table, by stating the effect of on the truth conditions of any sentence in which it could be part of, gives the sense of '&'. (We know what the symbol means: the truth table gives it clear semantics. It sometimes happ
ens that a student hedges their answer to a logic exercise with a vague squiggle. One way to resolve what that means is to get them to give its truth table.)
It is relatively clear what semantics should do for the artificial languages of logic and mathematics. The paradigm is the branch of mathematical logic known as model theory. It is a formal version of truth conditional semantics - indeed, truth tables are the most simple incarnation of model theory. One of the most important semantic
traditions within Linguistics is that deriving from Richard Montague, who advocated treating English as a Formal Language - treating natural language as a language whose semantics can be given through model theory, in just the way a formal language can. Situation semantics inherits that approach. But model theory is essentially structural semantics; it does not really address lexical semantics. It is therefore not the whole story, especially as far as AI is concerned. Some of the interesting aspects of
interpreting natural language depend on word meanings. Compare
John saw a man who beat a donkey with a telescope
which is 3-way ambiguous, with an example which has only two plausible readings,
John shot a man who beat a donkey with a telescope
So lexical semantics very important to natural language processing - how to represent word meanings in a way that will provide information to help resolve such ambiguities.
Reading
Some of the classics:
Gottlob Frege: 'On Sense a
nd Reference', in Peter Geach and Max Black (eds.) Translations from the Philosophical Writings of Gottlob Frege.
Richmond Thomason (ed.) Formal Philosophy - Selected Papers of Richard Montague
Jon Barwise and John Perry: Situations and Attitudes
More introductory:
James Allen: Understanding Natural Language.
Emmon Bach: Informal Lectures on Formal Semantics.
[ UP to Index | ON to A Theory of Reference ]
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