The geometric roots of semantics

By developing the concept of the geometric space of conceptualization, this paper seeks to establish common ground between the perceptual and logical structures expressed in language. The author’s overall thesis is that the logical status of language is a projection of geometric and topological patterns, and that these can be described. Although highly technical, the essay has several points in common with other contributions in the book. Like those by Violi and Geeraerts, for example, it analyses natural kinds and prototypes, and the problem of conceptual universals. It shares with Violi the idea that, since there is no fixed constant in a word’s field of variation, there is no stable membership in a kind, and no real motivation for type-judgements. The paper also discusses topics addressed by Wildgen’s essay (semantic fields and the relation between concepts and their contextual extension) and Albertazzi’s (the origin of spatio-temporal patterns). In its treatment of specific issues — the impact of the ‘linguistic turn’, the critique of compositionality, of the model-theoretic approach to semantics, and of generative grammar — Peruzzi’s analysis supports the theses developed in the Introduction by Albertazzi. It shares with the latter a phenomenological approach to the analysis of schemes which in turn relates to the theories set out in the essays by Langacker, Croft and Wood, and Kövecses.