Abstract
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.
Similar content being viewed by others
References
Bates, E. (Ed.) (1976) Language and context. The acquisition of pragmatics. Academic Press, New York
Berge C. (1997) Topological spaces. Dover, Mineola
Boroditsky L. (2000) Metaphoric structuring: Understanding time through spatial metaphors. Cognition 75(1): 1–28
Brinck I. (2004) The pragmatics of imperative and declarative pointing. Cognitive Science Quarterly 3: 255–272
Brinck I., Gärdenfors P. (2003) Co-operation and communication in apes and humans. Mind and Language 18: 484–501
Brouwer L. E. J. (1910) Über ein eindeutige, stetige Transformation von Flächen in sich. Mathematische Annalen 69: 176–180
Cameron P., Hogkin J. G., Naimpally S. A. (1974) Nearness: A better approach to continuity and limits. The American Mathematical Monthly 81(7): 739–745
Clark H. (1992) Arenas of language use. University of Chicago Press, Chicago
Clark H., Schaefer E.F. (1989) Contributing to discourse. Cognitive Science 13: 259–294
Croft W., Cruse D. A. (2004) Cognitive linguistics. Cambridge University Press, Cambridge
Dekker P., van Rooij R. (2000) Bi-directional optimality theory: An application of game theory. Journal of Semantics 17: 217–242
Evans V. (2006) Lexical concepts, cognitive models and meaning-construction. Cognitive Linguistics 17: 491–534
Fauconnier G., Turner R. (1998) Conceptual integration networks. Cognitive Science 22(2): 133–187
Fitting M. (2002) Fixpoint semantics for logic programming: A survey. Theoretical Computer Science 278: 25–51
Galantucci B. (2005) An experimental study of the emergence of human communication systems. Cognitive Science 29: 737–767
Gärdenfors, P. (1997). Does semantics need reality? In Does representation need reality? (pp. 113–120). Austrian Society of Cognitive Science Technical Report 97-01, Vienna.
Gärdenfors P. (2000) Conceptual spaces: The geometry of thought. MIT Press, Cambridge, MA
Gärdenfors P. (2003) How homo became sapiens: On the evolution of thinking. Oxford University Press, Oxford
Gärdenfors, P. (2007). Representing actions and functional properties in conceptual spaces. In T. Ziemke, J. Zlatev, & R. M. Frank (Eds.), Body, language and mind: Embodiment (Vol. 1, pp. 167–195). Berlin: Mouton de Gruyter.
Gärdenfors P., Osvath M. (2010) The evolution of anticipatory cognition as a precursor to symbolic communication. In: Larson R. et al (eds) Evolution of language: Biolinguistic approaches. Cambridge University Press, Cambridge, pp 103–114
Gärdenfors, P., & Warglien, M. (to appear a). The development of semantic space for pointing and verbal communication. In J. Hudson, U. Magnusson & C. Paradis (Eds.), Conceptual spaces and the construal of spatial meaning: Empirical evidence from human communication. Oxford: Oxford University Press.
Gärdenfors, P., & Warglien, M. (to appear b). Using conceptual spaces to model actions and events, to appear in Journal of Semantics.
Garrod S., Anderson A. (1987) Saying what you mean in dialogue: A study in conceptual and semantic coordination. Cognition 27(2): 181–218
Goldin-Meadow S. (2007) Pointing sets the stage for learning language and creating language. Child Development 78: 741–745
Grice, P. (1975). Logic and conversation. In Peter Cole & Jerry L. Morgan (Eds.), Syntax and semantics: Speech acts (Vol. 3, pp. 41–58). New York: Academic Press.
Harnad S. (1990) The symbol grounding problem. Physica D 42: 335–346
Heim, I. (1983). On the projection problem for presuppositions. In Proceedings of the west coast conference on formal linguistics (Vol. II, pp. 114–125). Stanford, CA.
Holyoak K. J., Thagard P. (1996) Mental leaps. MIT Press, Cambridge, MA
Hopfield J. J. (1982) Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences of the United States 79: 2554–2558
Holmqvist, K. (1993). Implementing cognitive semantics. Lund University Cognitive Studies 17, Lund.
Jackendoff R. (2002) Foundations of language: Brain, meaning, grammar, evolution. Oxford University Press, Oxford
Jäger G. (2007) The evolution of convex categories. Linguistics and Philosophy 30: 551–564
Jäger, G. (2010). Natural color categories are convex sets. In Logic, language and meaning, LNCS 6042 (pp. 11–20). Berlin: Springer.
Jäger G., van Rooij R. (2007) Language structure: Psychological and social constraints. Synthese 159: 99–130
Johannesson, M. (2002). Geometric models of similarity. Lund University Cognitive Studies 87, Lund.
Kripke S. (1975) Outline of a theory of truth. Journal of Philosophy 72: 690–716
Lakoff G. (1987) Women, fire, and dangerous things. The University of Chicago Press, Chicago, IL
Lakoff G., Johnson M. (1980) Metaphors we live by. The University of Chicago Press, Chicago, IL
Langacker R. W. (1986) An introduction to cognitive grammar. Cognitive Science 10: 1–40
Langacker, R. W. (1987). Foundations of cognitive grammar (Vol. 1). Stanford, CA: Stanford University Press.
Lewis D. (1969) Convention. Harvard University Press, Cambridge, MA
Lewis D. (1970) General semantics. Synthese 22: 18–67
Lewis D. (1979) Scorekeeping in a language game. Journal of Philosophical Logic 8: 339–359
Maunder C. R. F. (1980) Algebraic topology. Cambridge University Press, Cambridge
Mervis C., Rosch E. (1981) Categorization of natural objects. Annual Review of Psychology 32: 89–115
Nosofsky R. M. (1988) Similarity, frequency, and category representations. Journal of Experimental Psychology: Learning, Memory and Cognition 14: 54–65
Okabe A., Boots B., Sugihara K. (1992) Spatial tessellations: Concepts and applications of Voronoi diagrams. John Wiley & Sons, New York
Parikh P. (2000) Communication, meaning and interpretation. Linguistics and Philosophy 23: 185–212
Parikh P. (2010) Language and equilibrium. MIT Press, Cambridge, MA
Pickering M. J., Garrod S. (2004) Toward a mechanistic psychology of dialogue. Behavioral and Brain Sciences 27: 169–190
Putnam H. (1975) The meaning of ’meaning’. In: Gunderson K. (Ed.) Language, mind and knowledge. University of Minnesota Press, Minneapolis, pp 131–193
Rosch E. (1975) Cognitive representations of semantic categories. Journal of Experimental Psychology: General 104: 192–233
Rosch E. (1978) Prototype classification and logical classification: The two systems. In: Scholnik E. (Ed.) New trends in cognitive representation: Challenges to Piagets theory. Lawrence Erlbaum Associates, Hillsdale, NJ, pp 73–86
Schelling T. (1960) The strategy of conflict. Harvard University Pres, Cambridge, MA
Selten R., Warglien M. (2007) The emergence of simple languages in an experimental coordination game. Proceedings of the National Academy of Sciences 104(18): 7361–7366
Shepard R. N. (1987) Toward a universal law of generalization for psychological science. Science 237: 1317–1323
Skyrms B. (1998) Salience and symmetry-breaking in the evolution of convention. Law and Philosophy 17: 411–418
Stalnaker R. (1979) Assertion. Syntax and Semantics 9: 315–332
Tomasello M. (1999) The cultural origins of human cognition. Harvard University Press, Cambridge, MA
Tourangeau R., Sternberg R. J. (1982) Understanding and appreciating metaphors. Cognition 11: 203–244
van Benthem J. (2008) Games that make sense: Logic, language and multi-agent interaction. In: Apt K., van Rooij R. (eds) New perspectives on games and interaction. Amsterdam University Press, Amsterdam, pp 197–209
Varzi, A., & Warglien, M. (manuscript). Indeterminate contracts and semantic indeterminacy.
Warglien, M. (2001). Playing conversation games. Paper presented at the 2001 Wittgenstein society symposium, Kirchberg.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Warglien, M., Gärdenfors, P. Semantics, conceptual spaces, and the meeting of minds. Synthese 190, 2165–2193 (2013). https://doi.org/10.1007/s11229-011-9963-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-011-9963-z