Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 1 An Introduction to Intensional Semantics 1 1. The Inadequacies of a Purely Extensional Semantics (1) Our Current System: A Purely Extensional Semantics The extension of a complex phrase is (always) derived by computing the extensions (and only the extensions) of its component parts. (2) The Insufficiency of This System As powerful as this system is, it is still not sufficient for doing natural language semantics (3) Acute Empirical Problem: Some Semantic Arguments Can’t be Extensions Consider the verb “believe”; from sentences like the following, it seems to have a meaning that combines with the meaning of a sentence (its complement clause). a. Rush believes [ that Barack smokes ]. In our extensional semantics, the ‘meaning’ (semantic value) of a sentence is its T-value. b. [[ Barack smokes ]] = T Thus, in our purely extensional semantics, we would have to view [[ believes ]] as a function of type < t, <e, t>>. But, now consider the fact that the extension of (3a) is T. c. [[ Rush believes [that Barack smokes] ]] = T Given that “believes” is of type <t, <e, t>>, it of course follows that the equation in (d) holds. But, given the values of the extensions in question, it follows that (e) holds, too. d. [[ believes ]]( [[that Barack smokes]] ) ( [[ Rush ]]) = T. e. [[ believes ]] ( T ) ( Rush ) = T But, now consider that the sentence in (f) is also T, and thus has T as its extension. f. [[ Barack is a natural-born citizen ]] = T From (f) and (e), the equation in (g) now follows. g. [[ believes ]]( [[that Barack is a natural-born citizen ]] ) ( [[ Rush ]]) = T. Thus, under a purely extensional semantics, the truth of (c) entails the truth of (h). h. [[ Rush believes [that Barack is a natural-born citizen] ]] = T 1 These notes are based upon material in Heim & Kratzer (1998: Chapter 12).Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 2 Epic Fail: Our putative extensional semantics for “believe” makes the obviously false prediction that if X believes one true/false sentence, then X believes all true/false sentences! …But this obviously false prediction is a necessary consequence of two core assumptions of our purely extensional semantic system: (i) The semantic value of a structure is (always) its extension (ii) The extension of a sentence is its truth value. (5) The Key Conclusion: A Purely Extensional Semantics is Not Enough For words like “believe”, their extension does not combine with the extension of their sentential complement (unlike purely extensional ‘logical connectives’ like and, or, not). • Thus, in this structural context, our ‘semantic interpretation’ function “[[ ]]” has to provide something other than the extension of the complement clause. • Thus, for sentences containing the verb “believes”, their extension (T-value) is not determined purely by computing the extensions of their component parts. • Thus the core assumptions of our purely extensional semantics in (1) are wrong! 2. Towards a Solution: Intensions? Interim Conclusion: The T-conditions of sentences containing believes suggests that believes has a meaning that doesn’t take the extension of its sentential complement as argument… Question: • What, then, does the meaning of believes take as its first argument? • What is the semantic contribution of the sentential complement of believes, if not its extension?Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 3 (6) Recap: The Distinction Between ‘Intension’ and ‘Extension’ a. The extension of a phrase is the thing ‘out in the world’ that it ‘picks out’. (i) The extension of a definite description is the thing it refers to EXTENSION(the president) = Barack Obama (ii) The extension of a sentence is its T-value EXTENSION(the president smokes) = TRUE b. The intension of a phrase is (vaguely put) the ‘general concept’ behind the phrase, which determines (for a given time/situation) what the extension of the phrase is. (i) The intension of a definite description is (vaguely) the ‘conceptual content’ of the description. (ii) The intension of a sentence is (vaguely) its T-Conditions Observation: Within our formal theory of extensional semantics, we have a rather more precise picture of what the extension of a phrase is than what its intension is. (7) Key Observation Sentences with the same extension (truth value) can nevertheless have two different intensions (truth conditions) • “Barack smokes” is T iff Barack smokes • “Barack is a natural-born citizen” is T iff Barack is a natural-born citizen. (8) One Line of Thought… Given the observation in (7), if believes took the intension of its sentential complement as argument (rather than its extension), we could avoid the false prediction in (3)! • Since the intension of “Barack smokes” is distinct from that of “Barack is a natural-born citizen”, Rush could stand in the ‘believes’-relation to the former, but not the latter!Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 4 (9) Some Independent Motivation Question: What kind of relation does the verb “believes” represent? a. Not a Relation Between an Entity and Truth Value See reasoning above in (3)… b. Not a Relation Between an Entity and a Sentence o The following seems true: “Julius Caesar believed that Gaul surrendered.” o But, what kind of possible relation could Julius Caesar have had to the Modern English sentence “Gaul surrendered” ? … he never said it, he never thought it, he never assented to it… c. Relation Between an Entity and a Sentential Intension (T-Conditions, Proposition) o Even though Julius Caesar never uttered or assented to the English sentence “Gaul surrendered”, he did utter and assent to a Latin sentence that had the same T-conditions / intension. o So really, believes seems to denote a relation between an individual and some sentential intension, which we could label a ‘proposition’… (10) Conclusion • From the considerations in (8) and (9),