Ambiguity and Compositionality

Philosophy of Language » Lecture 7

Syntactic Structure

Syntactic Structures

Simplistic
Every sentence (expression of type S) is constituted of a noun phrase (expression of type NP) followed by a verb phrase (expression of type VP).

Evidence for syntactic structure: Ellipsis

  1. Alice will ace the test, and Bob will ace the test.
  2. Alice will ace the test, and Bob will.
  3. Alice will ace the test, and Bob.
  4. *Alice will ace the test, and Bob will ace.
  5. *Alice will ace the test, and Bob will ace the.
  6. *Alice will ace the test, and Bob will the test.
  7. *Alice will ace the test, and Bob will test.

Syntactic Trees

Syntactic Trees For Elided Constituents

A syntactic tree for (2) – note the common structure with (1), which supports the judgment that they are synonymous.

(Diagram omitted in `html` version)

The permissible elided constituent is the verb phrase ace the test, coloured purple to mark its absence; this is thus called verb-phrase ellipsis (Johnson 2001).

Structural Ambiguity

Structural Ambiguity

Ambiguity as Further Evidence for Syntactic Structure

Structural Ambiguity of (9)

The Other Reading of (9)

(Diagram omitted in `html` version)

Ambiguity Due to Preposition Phrases

Ambiguity and Quantifiers

Quantifier Phrases

  1. Exactly half the boys kissed some girl. (Elbourne 2011: 83)

Ambiguity and Entailment

Ambiguity in a Logical Language

Syntactic Structures for Quantified Sentences

Mismatched Determiner Phrases

Quantifier Raising

Quantifier Raising: Leaving a Trace

First, identify the overt structure of the sentence:

(Diagram omitted in `html` version)

Second, remove the determiner phrase and replace it by a trace – the trace will be something like a covert pronoun them.

(Diagram omitted in `html` version)

I.e., John offended them. (Now problematic, because them is indeterminate in reference.)

Quantifier Raising: Binding a Trace

Reading Every man admires some woman

Another Reading of (16)

Meaning From Syntactic Ambiguity

Compositionality

Ambiguity and Meaning

Compositionality

Productivity

Compositionality as Explanation for Productivity

Since competent speakers can understand a complex expression \(e\) they never encountered before, it must be that they (perhaps tacitly) know something on the basis of which they can figure out … what \(e\) means. If this is so, something they already know must determine what \(e\) means. And this knowledge cannot plausibly be anything but knowledge of the structure of \(e\) and knowledge of the individual meanings of the simple constituents of \(e\). (Szabó 2022: §3.1)

The Argument From Systematicity

Anyone who understands a complex expression \(e\) and \(e'\) built up through the syntactic operation \(F\) from constituents \(e_{1},…,e_{n}\) and \(e_{1}',…,e_{n}'\) respectively, can also understand any other meaningful complex expression \(e''\) built up through \(F\) from expressions among \(e_{1},…,e_{n}, e_{1}',…,e_{n}'\). So, it must be that anyone who knows what \(e\) and \(e'\) mean is in the position to figure out, without any additional information, what \(e''\) means. If this is so, the meaning of \(e\) and \(e'\) must jointly determine the meaning of \(e''\). But the only plausible way this could be true is if the meaning of \(e\) determines \(F\) and the meanings of \(e_{1},…,e_{n}\), the meaning of \(e'\) determines \(F\) and the meanings of \(e_{1}',…,e_{n}'\), and \(F\) and the meanings of \(e_{1},…,e_{n}, e_{1}',…,e_{n}'\) determine the meaning of \(e''\). …

[E.g.,] it seems reasonable that anyone who can understand ‘The dog is asleep’ and ‘The cat is awake’ can also understand ‘The dog is awake’ and ‘The cat is asleep’, and that anyone who can understand ‘black dog’ and ‘white cat’ can also understand ‘black cat’ and ‘white dog’. (Szabó 2022: §3.2)

Worries About Systematicity

Challenges to Compositionality

What Might Challenge Compositionality?

Belief Revisited

  1. Carla believes that eye doctors are rich.
  2. Carla believes that ophthalmologists are rich.
  3. Rudolph believes that \(1+1=2\).
  4. Rudolph believes that no consistent finitely axiomatisable formal theory containing arithmetic is complete.

The Aspiration of Compositionality

How Compositionality Works

The Mathematical Implementation of Compositionality

Frege on Unsaturated Meanings

The question now arises how the construction of the thought proceeds, and by what means the parts are put together so that the whole is something more than the isolated parts. In my essay ‘Negation’, I considered the case of a thought that appears to be composed of one part which is in need of completion or, as one might say, unsaturated, and whose linguistic correlate is the negative particle, and another part which is a thought. We cannot negate without negating something, and this something is a thought. Because this thought saturates the unsaturated part or, as one might say, completes what is in need of completion, the whole hangs together. And it is a natural conjecture that logical combination of parts into a whole is always a matter of saturating something unsaturated. (Frege 1923: 1–2; translation follows Heim and Kratzer 1998: 3)

Saturation and Functions

Statements in general, just like equations or inequalities or expressions in Analysis, can be imagined to be split up into two parts; one complete in itself, and the other in need of supplementation, or unsaturated. Thus, e.g., we split up the sentence

Caesar conquered Gaul

into ‘Caesar’ and ‘conquered Gaul’. The second part is unsaturated – it contains an empty place; only when this place is filled up with a proper name, or with an expression that replaces a proper name, does a complete sense appear. Here too I give the name ‘function’ to the referent of this unsaturated part. In this case the argument is Caesar. (Frege 1891: 139)

Functions

What Sort of Function?

Extensions of NPs, VPs, and Sentences

Lambda notation for functions

Multiple Lambdas

Sylvester walks: From Extensions to Intensions

Transitive Verbs

The extension of admires

References

Elbourne, Paul (2011) Meaning: A Slim Guide to Semantics. Oxford University Press.
Fodor, Jerry A (1998) Concepts. Oxford University Press.
Frege, Gottlob (1891/1997) ‘Function and Concept’, in Michael Beaney, ed., The Frege Reader: 130–48. Blackwell.
Frege, Gottlob (1923/1963) ‘Compound Thoughts’, Mind 72: 1–17. doi:10.1093/mind/lxxii.285.1.
Heim, Irene and Angelika Kratzer (1998) Semantics in Generative Grammar. Blackwell.
Hodges, Wilfrid (2001) Logic. Penguin.
Johnson, Kyle (2001) ‘What VP Ellipsis Can Do, and What It Can’t, but Not Why’, in Mark Baltin and Chris Collins, eds., The Handbook of Contemporary Syntactic Theory: 439–79. Blackwell.
Larson, Richard K and Peter Ludlow (1993) ‘Interpreted Logical Forms’, Synthese 95: 305–55. doi:10.1007/bf01063877.
Nunberg, Geoffrey, Ivan A Sag, and Thomas Wasow (1994) Idioms, Language 70: 491–538.
Salmon, Nathan (1986) Frege’s Puzzle. MIT Press.
Segal, Gabriel (1989) ‘A Preference for Sense and Reference’, The Journal of Philosophy 86: 73. doi:10.2307/2027077.
Stalnaker, Robert C (1984) Inquiry, A Bradford Book. MIT Press.
Szabó, Zoltán Gendler (2022) Compositionality, in Edward N Zalta and Uri Nodelman, eds., The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/fall2022/entries/compositionality/.