, Volume 190, Issue 12, pp 2165–2193 | Cite as

Semantics, conceptual spaces, and the meeting of minds

  • Massimo Warglien
  • Peter GärdenforsEmail author


We present an account of semantics that is not construed as a mapping of language to the world but rather as a mapping between individual meaning spaces. The meanings of linguistic entities are established via a “meeting of minds.” The concepts in the minds of communicating individuals are modeled as convex regions in conceptual spaces. We outline a mathematical framework, based on fixpoints in continuous mappings between conceptual spaces, that can be used to model such a semantics. If concepts are convex, it will in general be possible for interactors to agree on joint meaning even if they start out from different representational spaces. Language is discrete, while mental representations tend to be continuous—posing a seeming paradox. We show that the convexity assumption allows us to address this problem. Using examples, we further show that our approach helps explain the semantic processes involved in the composition of expressions.


Conceptual spaces Fixpoint semantics Meeting of minds Compositionality Cognitive semantics 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Management, Advanced School of EconomicsUniversità Ca’ Foscari VeneziaVeneziaItaly
  2. 2.Laboratory for Experimental Economics / Fondazione Ca’ FoscariVeneziaItaly
  3. 3.Department of PhilosophyLundSweden

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