Metonymy

This chapter addresses metonymy, an operation that is used to refer to an entity by means of an expression that has a particular semantic or conceptual relation to that entity (e.g. ‘the ham sandwich’ referring to a customer at a restaurant or ‘the wooden turtle’ referring to an object on a shelf). It discusses different types and communicative functions of metonymy and delineates it from other referential ambiguities such as homonymy and polysemy. The chapter reviews experimental evidence from real-time processing, acquisition, and language disorder and illustrates that discrete cognitive processes are involved in the constitution of extended meanings. It presents a classification of referential ambiguities based on neurocognitive profiles and suggests that the different types of ambiguities may be linked to the diachronic development of meaning alternations.

What’s really going on with the ham sandwich?

Working within the framework of Relevance Theory, I investigate the nature of referential metonymy (specifically, metonymically-used definite descriptions), aiming to elucidate (i) the pragmatic mechanisms involved in referential metonymy comprehension, and (ii) the contribution of a metonymically-used definite description to the explicitly communicated content of an utterance. I propose that, while the interpretation of referential metonymy is properly inferential in nature, it cannot be explained in terms of ‘meaning modulation’ (narrowing and broadening); rather, the literal meaning of a metonymically-used referring expression remains intact, and is used as evidence of the speaker’s target referent. In addition, I argue that the referential/attributive distinction proposed by Donnellan (1966) for literally-used definite descriptions also applies to metonymically-used definite descriptions. Thus, the contribution of a metonymically-used definite description to explicit utterance content differs according to whether the definite description is used ‘referentially’ or ‘attributively’.

Applications of the ‘Ham Sandwich Theorem’ to Eigenvalues of the Laplacian

We apply Gromov’s ham sandwich method to get: (1) domain monotonicity (up to a multiplicative constant factor); (2) reverse domain monotonicity (up to a multiplicative constant factor); and (3) universal inequalities for Neumann eigenvalues of the Laplacian on bounded convex domains in Euclidean space.