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Article published In:
Pragmatics & Cognition
Vol. 29:1 (2022) ► pp.59–81

Mathematics, relevance theory and the situated cognition paradigm

| University of Brighton,
Mathematics is a highly specialised arena of human endeavour, one in which complex notations are invented and are subjected to complex and involved manipulations in the course of everyday work. What part do these writing practices play in mathematical communication, and how can we understand their use in the mathematical world in relation to theories of communication and cognition? To answer this, I examine in detail an excerpt from a research meeting in which communicative board-writing practices can be observed, and attempt to explain the observed exchanges with reference to relevance theory (a cognitivist theory of pragmatics), in combination with the situated cognition paradigm. Successful communication in the excerpt appears well described by the notion of metacognitive acquaintance, as described in Sperber & Wilson (2015), especially when a situated view of cognition is adopted. Though this example is taken from a relatively informal face-to-face communicative situation, characteristics of such situations extend even into formal written mathematics, since even the technical terminology developed in the course of the meeting includes details that may provide readers with a kind of access to the mathematicians’ cognitive processes.
Keywords: cognitivism, situated cognition, relevance theory, pragmatics of mathematics, inferential model
Article outline
  • 1.Introduction
  • 2.A very brief introduction to relevance theory
  • 3.An example, metacognitively explained
  • 4.Getting acquainted with cognition
  • 5.Terminology, and the richness of a mental state
  • 6.Conclusion
  • Notes
  • References
Published online: 2 February 2023
DOI logo
https://doi.org/10.1075/pc.21005.mcc
References (35)
References
Barany, Michael J. 2010. Mathematical research in context. Edinburgh: University of Edinburgh. MSc dissertation.Google Scholar
Bringsjord, Selmer. 1998. Computationalism is dead; now what? Journal of Experimental & Theoretical Artificial Intelligence 10(4). 393–402. DOI logoGoogle Scholar
Carston, Robyn. 2002. Thoughts and utterances: The pragmatics of explicit communication. Oxford: Blackwell Publishing. DOI logoGoogle Scholar
Cave, Terence & Deirdre Wilson. 2018. Reading beyond the code: Literature and relevance theory. Oxford: Oxford University Press. DOI logoGoogle Scholar
Clark, Andy. 2010. Supersizing the mind: Embodiment, action, and cognitive extension. Oxford: Oxford University Press.Google Scholar
Clark, Andy & David Chalmers. 1998. The extended mind. Analysis 58(1). 7–19. DOI logoGoogle Scholar
Clark, Billy. 2013. Relevance theory (Cambridge Textbooks in Linguistics). Cambridge: Cambridge University Press. DOI logoGoogle Scholar
de Saussure, Louis & Tim Wharton. 2020. Relevance, effects and affect. International Review of Pragmatics 12(2). 183–205. DOI logoGoogle Scholar
Dreyfus, Hubert L. 1978. What computers can’t do: The limits of artificial intelligence. New York: Harper Collins.Google Scholar
Forceville, Charles. 2014. Relevance theory as model for analysing visual and multimodal communication. In David Machin (ed.), Visual communication, 51–70. Belrin: Mouton de Gruyter. DOI logoGoogle Scholar
Greiffenhagen, Christian. 2014. The materiality of mathematics: Presenting mathematics at the blackboard. The British Journal of Sociology 65(3). 502–528. DOI logoGoogle Scholar
Grice, H. Paul. 1989. Studies in the way of words. Cambridge, MA: Harvard University Press.Google Scholar
Hutchins, Edwin. 1995. Cognition in the wild. Cambridge, MA: MIT Press.Google Scholar
. 2010. Cognitive ecology. Topics in Cognitive Science 2(4). 705–715. DOI logoGoogle Scholar
Kolaiti, Patricia. 2019. The limits of expression: Language, literature, mind. Cambridge: Cambridge University Press. DOI logoGoogle Scholar
. 2020. Perceptual relevance and art: Some tentative suggestions. Journal of Literary Semantics 49(2). 99–117. DOI logoGoogle Scholar
Lakatos, Imre. 1976. Proofs and refutations: The logic of mathematical discovery. Cambridge: Cambridge University Press. DOI logoGoogle Scholar
Lane, Lorenzo. 2016. The bridge between worlds: Relating position and disposition in the mathematical field. Edinburgh: University of Edinburgh.Google Scholar
McCallum, Kate. 2020. Situating mathematical communication: The settings, interactions and material practices of contemporary mathematical research. Brighton: University of Brighton PhD dissertation.Google Scholar
Noë, Alva. 2009. Out of our heads: Why you are not your brain, and other lessons from the biology of consciousness. New York: Hill and Wang.Google Scholar
Pignocchi, Alessandro. 2018. The continuity between art and everyday communication. In Florian Cova & Sébastien Réhault (eds.), Advances in experimental philosophy of aesthetics, 241–264. London: Bloomsbury.Google Scholar
Putnam, Hilary. 1991. Representation and reality. Cambridge, MA: MIT Press. DOI logoGoogle Scholar
Searle, John R. 1980. Minds, brains, and programs. Behavioral and Brain Sciences 3(3). 417–424. DOI logoGoogle Scholar
1992. The rediscovery of the mind. Cambridge, MA: MIT Press. DOI logoGoogle Scholar
Shannon, Claude E. & Warren Weaver. 1949. The mathematical theory of communication. Urbana, IL: University of Illinois Press.Google Scholar
Sperber, Dan. 1982. Apparently irrational beliefs. In Martin Hollis & Steven Lukes (eds.), Rationality and relativism, 149–180. MIT Press. Cambridge, MA: MIT Press.Google Scholar
. 1997. Intuitive and reflective beliefs. Mind & Language 12(1). 67–83. DOI logoGoogle Scholar
Sperber, Dan & Deirdre Wilson. 1986/1995. Relevance: Communication and cognition. Cambridge, MA: Harvard University Press.Google Scholar
. 2015. Beyond speaker’s meaning. Croatian Journal of Philosophy 15(2). 117–149.Google Scholar
Wharton, Tim. 2008. “MeaningNN” and “showing”: Gricean intentions and relevance-theoretic intentions. Intercultural Pragmatics 5(2). 131–152. DOI logoGoogle Scholar
Wharton, Tim & Claudia Strey. 2019. Slave to the passions: Making emotions relevant. In Kate Scott, Billy Clark & Robyn Carston (eds.), Relevance, pragmatics and interpretation, 253–267. Cambridge: Cambridge University Press. DOI logoGoogle Scholar
Wilson, Deirdre. 2017. Communication, comprehension and ‘non-propositional effects’. Paper presented at the Beyond meaning conference, National and Kapodistrian University of Athens.
. 2018. Relevance theory and literary interpretation. In Terence Cave & Deirdre Wilson (eds.), Reading beyond the code: Literature and relevance theory, 185–204. New York: Oxford University Press.Google Scholar
Wilson, Deirdre & Robyn Carston. 2019. Pragmatics and the challenge of ‘non-propositional’ effects. Journal of Pragmatics 1451. 31–38. DOI logoGoogle Scholar
Wilson, Deirdre & Dan Sperber. 2004. Relevance theory. In Laurence R. Horn & Gregory Ward (eds.), The handbook of pragmatics, 607–632. Oxford: Wiley-Blackwell.Google Scholar