A fresh look at the foundations of mathematics: Gesture and the psychological reality of conceptual metaphor
-
Rafael Núñez
Abstract
The study of speech-gesture-thought co-production serves multiple purposes, providing deep insight into many areas of investigation that go from psycholinguistics and cognitive linguistics to discourse analysis, and to the neuroscience of motor action and language. In this piece, building on my previous work (with George Lakoff) on the cognitive science of mathematics (Lakoff & Núñez, 1997, 2000; Núñez & Lakoff, 1998, 2005), I focus on the study of gesture production in order to address the question of the nature of mathematics and its foundations. I analyze (gestural) convergent evidence of the psychological reality of fundamental conceptual metaphors that we claim make infinitesimal calculus possible (in particular, what concerns limits and continuity). These conceptual metaphors, which are analyzed in detail in Where mathematics comes from (Lakoff & Núñez, 2000), emerge from fundamental mechanisms of everyday human imagination, language, and cognition, and structure the inferential organization of mathematical concepts and ideas. In this chapter, I show how the study of the gesture production of professional mathematicians turns out to be crucial in characterizing (in real-time) fundamental metaphorical contents that, while making the very mathematical ideas possible, are not captured by the standard well-accepted formalisms that are taken to “define” what mathematical concepts really are.
Abstract
The study of speech-gesture-thought co-production serves multiple purposes, providing deep insight into many areas of investigation that go from psycholinguistics and cognitive linguistics to discourse analysis, and to the neuroscience of motor action and language. In this piece, building on my previous work (with George Lakoff) on the cognitive science of mathematics (Lakoff & Núñez, 1997, 2000; Núñez & Lakoff, 1998, 2005), I focus on the study of gesture production in order to address the question of the nature of mathematics and its foundations. I analyze (gestural) convergent evidence of the psychological reality of fundamental conceptual metaphors that we claim make infinitesimal calculus possible (in particular, what concerns limits and continuity). These conceptual metaphors, which are analyzed in detail in Where mathematics comes from (Lakoff & Núñez, 2000), emerge from fundamental mechanisms of everyday human imagination, language, and cognition, and structure the inferential organization of mathematical concepts and ideas. In this chapter, I show how the study of the gesture production of professional mathematicians turns out to be crucial in characterizing (in real-time) fundamental metaphorical contents that, while making the very mathematical ideas possible, are not captured by the standard well-accepted formalisms that are taken to “define” what mathematical concepts really are.
Chapters in this book
- Prelim pages i
- Table of contents v
- Contributors vii
- Acknowledgements ix
- Introduction 1
- Why study metaphor and gesture? 5
- From left to right...: Coverbal gestures and their symbolic use of space 27
- Gesture as a conceptual mapping tool 55
- A fresh look at the foundations of mathematics: Gesture and the psychological reality of conceptual metaphor 93
- Peircean semiotics meets conceptual metaphor: Iconic modes in gestural representations of grammar 115
- Unexpected metaphors 155
- Catchment, growth point and spatial metaphor: Analysing Derrida's oral discourse on deconstruction 171
- Form, meaning, and convention: A comparison of a metaphoric gesture with an emblem 195
- What gestures reveal about the nature of metaphor 219
-
Commentaries on the value of studying metaphor and gesture from the perspectives of different disciplines
- Metaphoric gesture and cognitive linguistics 249
- Metaphoric gestures and cultural analysis 253
- Metaphor and gesture: A view from the microanalysis of interaction 259
- Implications of cognitive metaphor and gesture studies for Ethnomethodology and Conversation Analysis and vice versa 265
- Sign and gesture: Towards a new paradigm 273
- The study of metaphor and gesture: A critique from the perspective of semiotics 277
- The neuroscience of metaphoric gestures: Why they exist 283
- Metaphor and gesture: Some implications for psychology 291
- Index 303
Chapters in this book
- Prelim pages i
- Table of contents v
- Contributors vii
- Acknowledgements ix
- Introduction 1
- Why study metaphor and gesture? 5
- From left to right...: Coverbal gestures and their symbolic use of space 27
- Gesture as a conceptual mapping tool 55
- A fresh look at the foundations of mathematics: Gesture and the psychological reality of conceptual metaphor 93
- Peircean semiotics meets conceptual metaphor: Iconic modes in gestural representations of grammar 115
- Unexpected metaphors 155
- Catchment, growth point and spatial metaphor: Analysing Derrida's oral discourse on deconstruction 171
- Form, meaning, and convention: A comparison of a metaphoric gesture with an emblem 195
- What gestures reveal about the nature of metaphor 219
-
Commentaries on the value of studying metaphor and gesture from the perspectives of different disciplines
- Metaphoric gesture and cognitive linguistics 249
- Metaphoric gestures and cultural analysis 253
- Metaphor and gesture: A view from the microanalysis of interaction 259
- Implications of cognitive metaphor and gesture studies for Ethnomethodology and Conversation Analysis and vice versa 265
- Sign and gesture: Towards a new paradigm 273
- The study of metaphor and gesture: A critique from the perspective of semiotics 277
- The neuroscience of metaphoric gestures: Why they exist 283
- Metaphor and gesture: Some implications for psychology 291
- Index 303
