Through a mind darkly An empirically-informed philosophical perspective on systematic knowledge acquisition and cognitive limitations Helen De Cruz c Copyright by Helen De Cruz, 2011. All rights reserved. PhD-dissertation of University of Groningen Title: Through a mind darkly. An empirically-informed philosophical perspective on systematic knowledge acquisition and cognitive limita- tions. Author: H. L. De Cruz ISBN 978-90-367-5182-7 (ISBN print version: 978-90-367-5181-0) Publisher: University of Groningen, The Netherlands Printed by: Reproduct, Ghent, Belgium Cover illustration: The externalized thinker. This image is based on Au- gust Rodin’s bronze sculpture, The Thinker (Le Penseur, 1880). It il- lustrates one of the main theses of this dissertation: cognition is not a solitary and internalized process, but a collective, distributed and exter- nalized activity. RIJKSUNIVERSITEIT GRONINGEN Through a mind darkly An empirically-informed philosophical perspective on systematic knowledge acquisition and cognitive limitations Proefschrift ter verkrijging van het doctoraat in de Wijsbegeerte aan de Rijksuniversiteit Groningen op gezag van de Rector Magnificus, dr. E. Sterken in het openbaar te verdedigen op donderdag 27 oktober 2011 om 16.15 uur door Helen Lucretia De Cruz geboren op 1 september 1978 te Gent Promotor: Prof. dr. mr. I. E. Douven Beoordelingscommissie: Prof. dr. M. Muntersbjorn Prof. dr. J. Peijnenburg Prof. dr. L. Horsten CONTENTS List of figures ix List of tables xi List of papers xiii Acknowledgments xv Preface xvii 1 Introduction 1 1.1 Two puzzles on scientific knowledge ............ 1 1.1.1 Naturalism and knowledge acquisition ....... 1 1.1.2 Puzzle 1: The boundedness of human reasoning .. 3 1.1.3 Puzzle 2: Scientific reasoning ............ 8 1.2 The nature of scientific beliefs ................ 11 1.2.1 Core knowledge .................... 12 1.2.2 Intuitive and reflective beliefs ............ 15 1.2.3 Explanatory depth .................. 18 1.2.4 The role of testimony ................ 19 1.3 Discontinuity or continuity? ................. 26 1.3.1 Science as the result of deliberate practice ..... 27 1.3.2 Children as scientists ................. 31 1.3.3 Cognitive development as conceptual change ... 33 iii iv CONTENTS 1.3.4 Cognition in the wild ................ 38 I Mathematics 45 2 Innateness and mathematical concepts 47 2.1 Nativism and mathematical knowledge ........... 48 2.1.1 Historical claims ................... 48 2.1.2 Current positions in philosophy of mathematics .. 50 2.2 The case of arithmetic .................... 51 2.2.1 Premise 1: Infants’ looking time di↵ers between correct and incorrect arithmetical operations ... 55 2.2.2 Premise 2: This success is best explained by the infants’ conceptual knowledge of number ...... 56 2.2.3 Premise 3: Because the capacity arises early in de- velopment, it cannot have been learned through ex- perience ........................ 58 2.2.4 Conclusion: The property in question is probably innate ......................... 59 2.3 From intuitive to formal mathematical knowledge ..... 60 2.3.1 Characterizing intuitive numbers formally ..... 61 2.3.2 Learning natural numbers through axiomatic systems 65 2.4 Innate skills and mathematical practice .......... 67 2.5 Concluding remarks ..................... 71 3 Evolutionary perspective on number concepts 73 3.1 The cultural evolution of numerical concepts ....... 74 3.2 Cognitive modularity and culture .............. 75 3.2.1 Cognitive modularity ................. 75 3.2.2 Epidemiological approaches to culture ....... 81 3.3 Number as the proper domain of a conceptual module .. 85 3.3.1 Numerical competence in nonhuman animals, hu- man infants, and adults ............... 85 3.3.2 The neural architecture underlying numerical com- petence ........................ 88 3.4 The epidemiology of numerical concepts .......... 92 3.4.1 The positive integers ................. 92 3.4.2 Zero .......................... 96 CONTENTS v 3.4.3 Negative numbers .................. 101 3.5 Conclusion .......................... 103 4 The extended mind and natural numbers 105 4.1 The bounds of cognition ................... 106 4.2 Domain-specificity in numerical representations ...... 108 4.3 Two cognitive routes for number words ........... 112 4.3.1 Counting ....................... 112 4.3.2 Approximate number words ............. 113 4.4 External media and cognitive processes .......... 115 4.4.1 Number words and language ............ 116 4.4.2 Body parts ...................... 120 4.4.3 Tallies and tokens .................. 122 4.4.4 Numerical notation systems ............. 125 4.4.5 Gestures ........................ 127 4.5 Discussion and concluding remarks ............. 128 5 Mathematical symbols as epistemic actions 131 5.1 Introduction .......................... 132 5.2 How we acquire mathematical knowledge ......... 132 5.3 Elementary numerical knowledge .............. 134 5.4 Symbols and mathematical cognition ............ 136 5.4.1 External media in mathematical cognition ..... 136 5.4.2 Costs and benefits of symbol use .......... 140 5.5 Specific properties of mathematical symbols ........ 143 5.5.1 Negative numbers .................. 145 5.5.2 Algebra ........................ 146 5.6 The opacity of mathematical symbols ........... 151 II Science 153 6 Intuitive ontologies in scientific understanding 155 6.1 Introduction .......................... 156 6.2 Intuitive ontologies ...................... 157 6.2.1 What are intuitive ontologies? ........... 157 6.2.2 Neural underpinnings of intuitive ontologies .... 163 6.3 Intuitive ontologies and folk theories ............ 165 6.4 Epistemological limitations to intuitive ontologies ..... 166 vi CONTENTS 6.5 Intuitive ontologies and scientific understanding ...... 167 6.6 Theories on human evolution ................ 170 6.6.1 Pruning and straightening the bushy tree of human evolution ....................... 171 6.6.2 Essentialism and humanized apes .......... 175 6.7 Concluding reflections .................... 179 7 Science as structured imagination 181 7.1 Introduction .......................... 182 7.2 Structured imagination .................... 182 7.2.1 Creativity is structured ............... 182 7.2.2 Analogies in everyday creative thought ....... 184 7.3 Intuitive ontologies and scientific reasoning ........ 185 7.3.1 Intelligibility ..................... 185 7.3.2 Analogies and scientific creativity .......... 186 7.4 Distant analogies as a source of creativity ......... 189 7.4.1 Early modern physiology .............. 190 7.4.2 Early evolutionary biology .............. 193 7.4.3 The evolution of the human mind ......... 195 7.5 Concluding reflections .................... 199 8 The epistemic status of scientific beliefs 201 8.1 Introduction .......................... 202 8.2 Cognitive biases and the perception of reality ....... 203 8.3 Evolutionary arguments ................... 207 8.4 Evolutionary debunking arguments ............. 209 8.5 Cultural transmission of scientific knowledge ........ 213 8.6 18th- and 19th-century transmutation theories ...... 218 9 Evolution and justification 225 9.1 The evolved mind and epistemic justification ....... 226 9.2 Cartesian God or Cartesian demon ............. 227 9.2.1 Evolutionary arguments generalized ........ 229 9.2.2 Evolutionary debunking arguments generalized .. 230 9.3 Responses to the circularity charge ............. 236 9.3.1 Dodging the bullet .................. 236 9.3.2 Biting the bullet ................... 237 9.4 Extended cognition and evolved cognitive biases ..... 241 CONTENTS vii 9.5 Conclusion: A defeasible evolutionary account ...... 245 10 Conclusion 247 10.1 General conclusion ...................... 247 10.2 Normative implications ................... 248 10.3 Metaphysical implications .................. 253 10.4 Naturalism as philosophy of the gaps? ........... 254 Summary 261 Samenvatting 263 Bibliography 267 LIST OF FIGURES 1.1 Dual Earth .......................... 35 2.1 Simple addition and subtraction tasks ........... 54 2.2 Two views of intuitive numerosity ............. 65 3.1 Patterns of brain activity involved in calculation ..... 91 3.2 Linguistic representation of numbers ............ 96 3.3 Historical spread of the number zero with its symbolic rep- resentations throughout the Old World. .......... 99 4.1 The Oksapmin counting system ............... 121 4.2 Notched bone from Ishango, Congo ............. 123 4.3 Brain areas involved in calculation in Chinese and English speakers ............................ 124 5.1 Representing simultaneous equations with counting rods . 148 7.1 Anatomical drawing ..................... 191 8.1 Common yellow wood-sorrel (Oxalis stricta) under normal lighting conditions and photographed using an ultraviolet- sensitive camera ....................... 205 8.2 Relationship between values of N and the complexity of biological theory that can be maintained .......... 221 ix LIST OF TABLES 4.1 The Greek alphabetic system of numerals ......... 126 5.1 Number of operations required to solve a system of n equa- tions with n unknowns .................... 150 8.1 Costs and benefits of agency detection ........... 210 9.1 Generalized forms of EA and EDA. ............. 228 xi LIST OF PAPERS INCORPORATED IN THE TEXT De Cruz, H. & De Smedt, J. (2010a). The innateness hypothesis and mathematical concepts. Topoi, 29, 3–13. De Cruz, H. (2006). Why are some numerical concepts more successful than others? An evolutionary perspective on the history of number concepts. Evolution and Human Behavior, 27,