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Published online by Cambridge University Press:  15 March 2024

Markus Pantsar
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Aachen University of Technology
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References

Adamson, L. B. & Bakeman, R. (1991). The development of shared attention during infancy. In Vasta, R. (Ed.). Annals of Child Development, Vol. 8. (pp. 141). Jessica Kingsley.Google Scholar
Agrillo, C. (2015). Numerical and arithmetic abilities in non-primate species. In Cohen Kadosh, R. C. & Dowker, A. (Eds.), The Oxford Handbook of Numerical Cognition (pp. 214236). Oxford University Press.Google Scholar
Amalric, M. & Dehaene, S. (2016). Origins of the brain networks for advanced mathematics in expert mathematicians. Proceedings of the National Academy of Sciences, 113(18), 49094917.CrossRefGoogle ScholarPubMed
Amalric, M., Denghien, I. & Dehaene, S. (2018). On the role of visual experience in mathematical development: Evidence from blind mathematicians. Developmental Cognitive Neuroscience, 30, 314323. https://doi.org/10.1016/j.dcn.2017.09.007.CrossRefGoogle ScholarPubMed
Anderson, M. L. (2010). Neural reuse: A fundamental organizational principle of the brain. Behavioral and Brain Sciences, 33(4), 245266.CrossRefGoogle ScholarPubMed
Anderson, M. L. (2015). After Phrenology: Neural Reuse and the Interactive Brain. MIT Press.Google ScholarPubMed
Anderson, M. L. (2016). Précis of after phrenology: Neural reuse and the interactive brain. Behavioral and Brain Sciences, 39, e120. https://doi.org/10.1017/S0140525X15000631.CrossRefGoogle ScholarPubMed
Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9(4), 278291.CrossRefGoogle ScholarPubMed
Ansari, D. (2012). Culture and education: New frontiers in brain plasticity. Trends in Cognitive Sciences, 16(2), 9395.CrossRefGoogle ScholarPubMed
Ashkenazi, S., Henik, A., Ifergane, G. & Shelef, I. (2008). Basic numerical processing in left intraparietal sulcus (IPS) acalculia. Cortex; a Journal Devoted to the Study of the Nervous System and Behavior, 44(4), 439448. https://doi.org/10.1016/j.cortex.2007.08.008.CrossRefGoogle ScholarPubMed
Assadian, B. & Buijsman, S. (2019). Are the natural numbers fundamentally ordinals? Philosophy and Phenomenological Research, 99(3), 564580. https://doi.org/10.1111/phpr.12499.CrossRefGoogle Scholar
Ayer, A. J. (1970). Language, Truth and Logic, 2nd ed. Dover.Google Scholar
Aziz, T. A., Pramudiani, P. & Purnomo, Y. W. (2017). How do college students solve logarithm questions? International Journal on Emerging Mathematics Education, 1(1), 2540.CrossRefGoogle Scholar
Balaguer, M. (2016). Platonism in metaphysics. In Zalta, E. N. (Ed.), The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/spr2016/entries/platonism/.Google Scholar
Barrocas, R., Roesch, S., Gawrilow, C. & Moeller, K. (2020). Putting a finger on numerical development: Reviewing the contributions of kindergarten finger gnosis and fine motor skills to numerical abilities. Frontiers in Psychology, 11, 1012. https://doi.org/10.3389/fpsyg.2020.01012.CrossRefGoogle ScholarPubMed
Beck, J. (2017). Can bootstrapping explain concept learning? Cognition, 158, 110121.CrossRefGoogle ScholarPubMed
Benacerraf, P. (1965). What numbers could not be. The Philosophical Review, 74(1), 4773. https://doi.org/10.2307/2183530.CrossRefGoogle Scholar
Benacerraf, P. (1973). Mathematical truth. Journal of Philosophy, 70, 661679.CrossRefGoogle Scholar
Bender, A. & Beller, S. (2012). Nature and culture of finger counting: Diversity and representational effects of an embodied cognitive tool. Cognition, 124(2), 156182. https://doi.org/10.1016/j.cognition.2012.05.005.CrossRefGoogle ScholarPubMed
Ben-Menahem, Y. (1998). Explanation and description: Wittgenstein on convention. Synthese, 115(1), 99130.CrossRefGoogle Scholar
Bennett, M. R. & Hacker, P. M. S. (2003). Philosophical Foundations of Neuroscience. Blackwell.Google Scholar
Beran, M. J., Evans, T. A., Leighty, K. A., Harris, E. H. & Rice, D. (2008). Summation and quantity judgments of sequentially presented sets by capuchin monkeys (Cebus apella). American Journal of Primatology, 70(2), 191194. https://doi.org/10.1002/ajp.20474.CrossRefGoogle ScholarPubMed
Berlyne, D. E. (1966). Curiosity and exploration. Science, 153(3731), 2533. https://doi.org/10.1126/science.153.3731.25.CrossRefGoogle ScholarPubMed
Bigelow, J. (1988). The Reality of Numbers: A Physicalist’s Philosophy of Mathematics. Oxford University Press.Google Scholar
Biro, D. & Matsuzawa, T. (2001). Use of numerical symbols by the chimpanzee (Pan troglodytes): Cardinals, ordinals, and the introduction of zero. Animal Cognition, 4(3–4), 193199. https://doi.org/10.1007/s100710100086.CrossRefGoogle ScholarPubMed
Bock, A. S., Binda, P., Benson, N. C., Bridge, H., Watkins, K. E. & Fine, I. (2015). Resting-state retinotopic organization in the absence of retinal input and visual experience. Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 35(36), 1236612382. https://doi.org/10.1523/JNEUROSCI.4715-14.2015.CrossRefGoogle ScholarPubMed
Boghossian, P. A. (1997). Analyticity. In Hale, B. & Wright, C. (Eds.), A Companion to the Philosophy of Language (pp. 331368). Blackwell.Google Scholar
Bogoshi, J., Naidoo, K. & Webb, J. (1987). The oldest mathematical artefact. The Mathematical Gazette, 71(458), 294. https://doi.org/10.2307/3617049.CrossRefGoogle Scholar
Boolos, G. (1998). Logic, Logic and Logic (Jeffrey, R. & Burgess, J. P., Eds.). Harvard University Press.Google Scholar
Bouhali, F., Thiebaut de Schotten, M., Pinel, P., Poupon, C., Mangin, J.-F., Dehaene, S. & Cohen, L. (2014). Anatomical connections of the visual word form area. Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 34(46), 1540215414. https://doi.org/10.1523/JNEUROSCI.4918-13.2014.CrossRefGoogle ScholarPubMed
Boyd, R. & Richerson, P. J. (1985). Culture and the Evolutionary Process. University of Chicago Press.Google Scholar
Boyd, R. & Richerson, P. J. (1996). Why culture is common, but cultural evolution is rare. In Runciman, W. G., Smith, J. M. & Dunbar, R. I. M. (Eds.). Evolution of Social Behaviour Patterns in Primates and Man (pp. 7793). Oxford University Press.Google Scholar
Boyd, R. & Richerson, P. J. (2005). Not by Genes Alone. University of Chicago Press.Google Scholar
Boyer, C. (1991). A History of Mathematics, 2nd ed. John Wiley & Sons.Google Scholar
Boysen, S. T. & Berntson, G. G. (1989). Numerical competence in a chimpanzee (Pan troglodytes). Journal of Comparative Psychology (Washington, D.C.: 1983), 103(1), 2331. https://doi.org/10.1037/0735-7036.103.1.23.CrossRefGoogle Scholar
Brannon, E. M. & Van de Walle, G. A. (2001). The development of ordinal numerical competence in young children. Cognitive Psychology, 43(1), 5381. https://doi.org/10.1006/cogp.2001.0756.CrossRefGoogle ScholarPubMed
Bremner, J. G., Slater, A. M., Hayes, R. A., Mason, U. C., Murphy, C., Spring, J., Draper, L., Gaskell, D. & Johnson, S. P. (2017). Young infants’ visual fixation patterns in addition and subtraction tasks support an object tracking account. Journal of Experimental Child Psychology, 162, 199208. https://doi.org/10.1016/j.jecp.2017.05.007.CrossRefGoogle ScholarPubMed
Brown, J. R. (2008). Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures, 2nd ed. Routledge.Google Scholar
Buijsman, S. (2019). Learning the natural numbers as a child. Noûs, 53(1), 322.CrossRefGoogle Scholar
Buijsman, S. (2021). How do we semantically individuate natural numbers? Philosophia Mathematica, 29(2), 214233. https://doi.org/10.1093/philmat/nkab001.Google Scholar
Buijsman, S. & Pantsar, M. (2020). Complexity of mental integer addition. Journal of Numerical Cognition, 6(1), 148163.CrossRefGoogle Scholar
Butterworth, B. (1999). What Counts: How Every Brain Is Hardwired for Math. Free Press.Google Scholar
Butterworth, B. (2005). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry, and Allied Disciplines, 46(1), 318. https://doi.org/10.1111/j.1469-7610.2004.00374.x.CrossRefGoogle ScholarPubMed
Butterworth, B. (2010). Foundational numerical capacities and the origins of dyscalculia. Trends in Cognitive Sciences, 14(12), 534541. https://doi.org/10.1016/j.tics.2010.09.007.CrossRefGoogle ScholarPubMed
Campbell, J. I. D. (1994). Architectures for numerical cognition. Cognition, 53(1), 144. https://doi.org/10.1016/0010-0277(94)90075-2.CrossRefGoogle ScholarPubMed
Campbell, J. I. D. & Epp, L. J. (2004). An encoding-complex approach to numerical cognition in Chinese–English bilinguals. Canadian Journal of Experimental Psychology = Revue Canadienne De Psychologie Experimentale, 58(4), 229244. https://doi.org/10.1037/h0087447.CrossRefGoogle ScholarPubMed
Cantlon, J. F. & Brannon, E. M. (2007). Basic math in monkeys and college students. PLoS Biology, 5(12), e328. https://doi.org/10.1371/journal.pbio.0050328.CrossRefGoogle ScholarPubMed
Cantlon, J. F., Merritt, D. J. & Brannon, E. M. (2016). Monkeys display classic signatures of human symbolic arithmetic. Animal Cognition, 19(2), 405415. https://doi.org/10.1007/s10071–015-0942-5.CrossRefGoogle ScholarPubMed
Cantor, G. (1883). Über unendliche, lineare Punktmannigfaltigkeiten, 5. Mathematische Annalen, 21, 545586.CrossRefGoogle Scholar
Cantrell, L. & Smith, L. B. (2013). Open questions and a proposal: A critical review of the evidence on infant numerical abilities. Cognition, 128(3), 331352. https://doi.org/10.1016/j.cognition.2013.04.008.CrossRefGoogle Scholar
Carey, S. (2009). The Origin of Concepts. Oxford University Press.CrossRefGoogle Scholar
Carnap, R. (1937). The Logical Syntax of Language. Open Court.Google Scholar
Carruthers, P. (2006). The Architecture of the Mind. Clarendon Press.CrossRefGoogle Scholar
Casasanto, D. & Boroditsky, L. (2008). Time in the mind: Using space to think about time. Cognition, 106(2), 579593. https://doi.org/10.1016/j.cognition.2007.03.004.CrossRefGoogle ScholarPubMed
Castaldi, E., Pomè, A., Cicchini, G. M., Burr, D. & Binda, P. (2021). The pupil responds spontaneously to perceived numerosity. Nature Communications, 12(1), 5944. https://doi.org/10.1038/s41467–021-26261-4.CrossRefGoogle ScholarPubMed
Casullo, A. (2003). A Priori Justification. Oxford University Press.CrossRefGoogle Scholar
Chalmers, D. J. (1997). The Conscious Mind: In Search of a Fundamental Theory, revised ed. Oxford University Press.Google Scholar
Chang, Y. (2014). Reorganization and plastic changes of the human brain associated with skill learning and expertise. Frontiers in Human Neuroscience, 8, 35. https://doi.org/10.3389/fnhum.2014.00035.CrossRefGoogle ScholarPubMed
Charette, F. (2012). The logical Greek versus the imaginative Oriental: On the historiography of ‘non-Western’ mathematics during the period 1820–1920. In Chemla, K. (Ed.), The History of Mathematical Proof in Ancient Traditions (pp. 274293). Cambridge University Press.Google Scholar
Chemla, K. (Ed.). (2015). The History of Mathematical Proof in Ancient Traditions, reprint ed. Cambridge University Press.Google Scholar
Cheung, P. & Le Corre, M. (2018). Parallel individuation supports numerical comparisons in preschoolers. Journal of Numerical Cognition, 4(2), 380409.CrossRefGoogle Scholar
Cheyette, S. J. & Piantadosi, S. T. (2020). A unified account of numerosity perception. Nature Human Behaviour, 4(12), 12651272. https://doi.org/10.1038/s41562–020-00946-0.CrossRefGoogle ScholarPubMed
Chihara, C. (1973). Ontology and the Vicious Circle Principle. Cornell University Press.Google Scholar
Chihara, C. (1990). Constructibility and Mathematical Existence. Oxford University Press.Google Scholar
Chihara, C. (2005). Nominalism. In Shapiro, S. (Ed.), The Oxford Handbook of Philosophy of Mathematics and Logic (pp. 483514). Oxford University Press.CrossRefGoogle Scholar
Chomsky, N. (2006). Language and Mind, 3rd ed. Cambridge University Press.CrossRefGoogle Scholar
Chrisomalis, S. (2010). Numerical Notation: A Comparative History. Cambridge University Press.CrossRefGoogle Scholar
Christodoulou, J., Lac, A. & Moore, D. S. (2017). Babies and math: A meta-analysis of infants’ simple arithmetic competence. Developmental Psychology, 53(8), 14051417. https://doi.org/10.1037/dev0000330.CrossRefGoogle Scholar
Cisek, P. & Kalaska, J. F. (2010). Neural mechanisms for interacting with a world full of action choices. Annual Review of Neuroscience, 33, 269298. https://doi.org/10.1146/annurev.neuro.051508.135409.CrossRefGoogle ScholarPubMed
Clark, A. & Chalmers, D. (1998). The extended mind. Analysis, 58(1), 719.CrossRefGoogle Scholar
Clark, C., Pritchard, V. E. & Woodward, L. J. (2010). Preschool executive functioning abilities predict early mathematics achievement. Developmental Psychology, 46(5), 11761191. https://doi.org/10.1037/a0019672.CrossRefGoogle ScholarPubMed
Clarke, S. & Beck, J. (2021). The number sense represents (rational) numbers. Behavioral and Brain Sciences, 44, e178. https://doi.org/10.1017/S0140525X21000571.CrossRefGoogle ScholarPubMed
Cole, J. C. (2009). Creativity, freedom, and authority: A new perspective on the metaphysics of mathematics. Australasian Journal of Philosophy, 87(4), 589608. https://doi.org/10.1080/00048400802598629.CrossRefGoogle Scholar
Cole, J. C. (2013). Towards an institutional account of the objectivity, necessity, and atemporality of mathematics. Philosophia Mathematica, 21(1), 936. https://doi.org/10.1093/philmat/nks019.CrossRefGoogle Scholar
Cole, J. C. (2015). Social construction, mathematics, and the collective imposition of function onto reality. Erkenntnis, 80(6), 11011124. https://doi.org/10.1007/s10670–014-9708-8.CrossRefGoogle Scholar
Colyvan, M. (2001). The Indispensability of Mathematics. Oxford University Press.CrossRefGoogle Scholar
Conde-Valverde, M., Martínez, I., Quam, R. M., Rosa, M., Velez, A. D., Lorenzo, C., Jarabo, P., Bermúdez de Castro, J. M., Carbonell, E. & Arsuaga, J. L. (2021). Neanderthals and Homo sapiens had similar auditory and speech capacities. Nature Ecology & Evolution, 5(5), Article 5. https://doi.org/10.1038/s41559–021-01391-6.CrossRefGoogle ScholarPubMed
Confer, J. C., Easton, J. A., Fleischman, D. S., Goetz, C. D., Lewis, D. M. G., Perilloux, C. & Buss, D. M. (2010). Evolutionary psychology: Controversies, questions, prospects, and limitations. American Psychologist, 65(2), 110126. https://doi.org/10.1037/a0018413.CrossRefGoogle ScholarPubMed
Cutini, S., Scatturin, P., Moro, S. B. & Zorzi, M. (2014). Are the neural correlates of subitizing and estimation dissociable? An FNIRS investigation. Neuroimage, 85, 391399.CrossRefGoogle ScholarPubMed
Davidson, K., Eng, K. & Barner, D. (2012). Does learning to count involve a semantic induction? Cognition, 123, 162173.CrossRefGoogle ScholarPubMed
Davis, H. & Pérusse, R. (1988). Numerical competence in animals: Definitional issues, current evidence, and a new research agenda. Behavioral and Brain Sciences, 11(4), 561579. https://doi.org/10.1017/S0140525X00053437.CrossRefGoogle Scholar
Dawkins, R. (2016). The Extended Selfish Gene, 40th anniversary ed. Oxford University Press.Google Scholar
De Bruin, L., Newen, A. & Gallagher, S. (Eds.). (2018). The Oxford Handbook of 4E Cognition. Oxford University Press.Google Scholar
De Cruz, H. (2016). Numerical cognition and mathematical realism. Philosopher’s Imprint, 16, 113.Google Scholar
De Cruz, H. & De Smedt, J. (2010). The innateness hypothesis and mathematical concepts. Topoi, 29(1), 313.CrossRefGoogle Scholar
De Cruz, H., Neth, H. & Schlimm, D. (2010). The cognitive basis of arithmetic. In Löwe, B. & Müller, T. (Eds.), PhiMSAMP. Philosophy of Mathematics: Sociological Aspects and Mathematical Practice (pp. 59106). College Publications.Google Scholar
Decock, L. (2008). The conceptual basis of numerical abilities: One-to-one correspondence versus the successor relation. Philosophical Psychology, 21(4), 459473. https://doi.org/10.1080/09515080802285255.CrossRefGoogle Scholar
Dedekind, R. (1888). Was sind und was sollen die Zahlen?: Stetigkeit und irrationale Zahlen (Müller-Stach, S., Ed.; 1. Auflage). Springer Spektrum. https://doi.org/10.1007/978-3-662-54339-9.Google Scholar
Dehaene, S. (1997). The Number Sense: How the Mind Creates Mathematics, 1st ed. Oxford University Press.Google Scholar
Dehaene, S. (2001a). Précis of the number sense. Mind & Language, 16(1), 1636.CrossRefGoogle Scholar
Dehaene, S. (2001b). Subtracting pigeons: Logarithmic or linear? Psychological Science, 12(3), 244246.CrossRefGoogle ScholarPubMed
Dehaene, S. (2003). The neural basis of the Weber–Fechner law: A logarithmic mental number line. Trends in Cognitive Sciences, 7(4), 145147.CrossRefGoogle ScholarPubMed
Dehaene, S. (2005). Evolution of human cortical circuits for reading and arithmetic: The “neuronal recycling” hypothesis. In Dehaene, S., Duhamel, J. R., Hauser, M. & Rizzolatti, G. (Eds.), From Monkey Brain to Human Brain (pp. 133157). MIT Press.CrossRefGoogle Scholar
Dehaene, S. (2007). Symbols and quantities in parietal cortex: Elements of a mathematical theory of number representation and manipulation. Sensorimotor Foundations of Higher Cognition, 22, 527574.Google Scholar
Dehaene, S. (2009). Reading in the Brain: The New Science of How We Read. Penguin.Google Scholar
Dehaene, S. (2011). The Number Sense: How the Mind Creates Mathematics, revised and updated ed. Oxford University Press.Google Scholar
Dehaene, S. (2020). How We Learn: Why Brains Learn Better Than Any Machine … for Now. Viking.Google Scholar
Dehaene, S. & Akhavein, R. (1995). Attention, automaticity, and levels of representation in number processing. Journal of Experimental Psychology: Learning, Memory, and Cognition, 21(2), 314.Google ScholarPubMed
Dehaene, S., Bossini, S. & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122(3), 371396. https://doi.org/10.1037/0096-3445.122.3.371.CrossRefGoogle Scholar
Dehaene, S. & Changeux, J. P. (1993). Development of elementary numerical abilities: A neuronal model. Journal of Cognitive Neuroscience, 5(4), 390407.CrossRefGoogle ScholarPubMed
Dehaene, S. & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1(1), 83120.Google Scholar
Dehaene, S., Izard, V., Spelke, E. & Pica, P. (2008). Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures. Science, 320, 12171220.CrossRefGoogle ScholarPubMed
Dehaene-Lambertz, G. & Spelke, E. S. (2015). The infancy of the human brain. Neuron, 88(1), 93109. https://doi.org/10.1016/j.neuron.2015.09.026.CrossRefGoogle ScholarPubMed
Detlefsen, M., Erlandson, D. K., Heston, J. C. & Young, C. M. (1976). Computation with Roman numerals. Archive for History of Exact Sciences, 15(2), 141148.CrossRefGoogle Scholar
Dos Santos, C. F. (2021). Enculturation and the historical origins of number words and concepts. Synthese, 199, 92579287. https://doi.org/10.1007/s11229–021-03202-8.CrossRefGoogle Scholar
Dos Santos, C. F. (2022). Re-establishing the distinction between numerosity, numerousness, and number in numerical cognition. Philosophical Psychology, 35(8), 11521180. https://doi.org/10.1080/09515089.2022.2029387.CrossRefGoogle Scholar
Dostoevsky, F. (1864). Notes from Underground (R. Pevear & L. Volokhonsky, trans.). Vintage Classics.Google Scholar
Dummett, M. (1959). Wittgenstein’s philosophy of mathematics. The Philosophical Review, 68(3), 324348. https://doi.org/10.2307/2182566.CrossRefGoogle Scholar
Dummett, M. (1978). Truth and Other Enigmas. Harvard University Press.Google Scholar
Dummett, M. (2006). Thought and Reality. Oxford University Press.CrossRefGoogle Scholar
Dutilh Novaes, C. (2012). Formal Languages in Logic: A Philosophical and Cognitive Analysis. Cambridge University Press.CrossRefGoogle Scholar
Dutilh Novaes, C. & dos Santos, C. F. (2021). Numerosities are not ersatz numbers. Behavioral and Brain Sciences, 44, e198. https://doi.org/10.1017/S0140525X21000984.CrossRefGoogle Scholar
Enderton, H. B. (1977). Elements of Set Theory. Academic Press.Google Scholar
Epps, P. (2006). Growing a numeral system: The historical development of numerals in an Amazonian language family. Diachronica, 23(2), 259288. https://doi.org/10.1075/dia.23.2.03epp.CrossRefGoogle Scholar
Euclid, . (1956). The Thirteen Books of Euclid’s Elements. Vol. 1: Introduction and Books I, II, 2nd ed. revised with additions, Vol. 1. Dover Publications.Google Scholar
Everett, C. (2017). Numbers and the Making of Us: Counting and the Course of Human Cultures. Harvard University Press.CrossRefGoogle Scholar
Everett, C. & Madora, K. (2012). Quantity recognition among speakers of an anumeric language. Cognitive Science, 36(1), 130141. https://doi.org/10.1111/j.1551-6709.2011.01209.x.CrossRefGoogle ScholarPubMed
Fabry, R. E. (2017). Cognitive innovation, cumulative cultural evolution, and enculturation. Journal of Cognition and Culture, 17(5), 375395.CrossRefGoogle Scholar
Fabry, R. E. (2018). Betwixt and between: The enculturated predictive processing approach to cognition. Synthese, 195(6), 24832518.CrossRefGoogle Scholar
Fabry, R. E. (2020). The cerebral, extra-cerebral bodily, and socio-cultural dimensions of enculturated arithmetical cognition. Synthese, 197, 36853720.CrossRefGoogle Scholar
Fabry, R. E. & Pantsar, M. (2021). A fresh look at research strategies in computational cognitive science: The case of enculturated mathematical problem solving. Synthese, 198(4), 32213263. https://doi.org/10.1007/s11229–019-02276-9.CrossRefGoogle Scholar
Feferman, S. (2009). Conceptions of the continuum. Intellectica, 51(1), 169189.Google Scholar
Feigenson, L., Dehaene, S. & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307314.CrossRefGoogle ScholarPubMed
Fechner, G. T. (1860). Elements of psychophysics. In Dennis, W. (Ed.), Readings in the History of Psychology (pp. 206213). Appleton-Century-Crofts.Google Scholar
Ferreirós, J. (2016). Mathematical Knowledge and the Interplay of Practices. Princeton.CrossRefGoogle Scholar
Field, H. (1980). Science without Numbers. Oxford University Press.Google Scholar
Field, H. (1989). Realism, Mathematics, and Modality. Blackwell.Google Scholar
Field, H. (2022). Conventionalism about mathematics and logic. Noûs, 57(4), 815831. https://doi.org/10.1111/nous.12428.CrossRefGoogle Scholar
FitzSimons, G. E. & Godden, G. L. (2000). Review of research on adults learning mathematics. In Coben, D., O’Donoghue, J. & Fitzsimons, G. E. (Eds.), Perspectives on Adults Learning Mathematics, Mathematics Education Library, Vol. 21 (pp. 1345). Springer.Google Scholar
Fodor, J. (1980). Fixation of belief and concept acquisition. In Piattelli-Palmarini, M. (Ed.), Language and Learning: The Debate between Jean Piaget and Noam Chomsky (pp. 142149). Harvard University Press.Google Scholar
Fodor, J. (1983). The Modularity of Mind: An Essay on Faculty Psychology. MIT Press.CrossRefGoogle Scholar
Fodor, J. (2010). Woof, woof. Times Literary Supplement, October 8, 7–8.Google Scholar
Frank, M. C., Everett, D., Fedorenko, E. & Gibson, E. (2008). Number as a cognitive technology. Cognition, 108, 819824.CrossRefGoogle ScholarPubMed
Frankopan, P. (2016). The Silk Roads: A New History of the World. Bloomsbury.Google Scholar
Freed, W. J., de Medinaceli, L., & Wyatt, R. J. (1985). Promoting functional plasticity in the damaged nervous system. Science, 227, 15441553.CrossRefGoogle ScholarPubMed
Frege, G. (1879). Begriffsschift. In Heijenoort, J. (Ed.), From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 (pp. 182). Harvard University PressGoogle Scholar
Frege, G. (1884). Foundations of Arithmetic (J. L. Austin, trans.). Blackwell.Google Scholar
Frege, G. (1892). Über Begriff und Gegenstand. Vierteljahresschrift Für Wissenschaftliche Philosophie, 16, 192205.Google Scholar
Fuson, K. C. (1987). Children’s Counting and Concepts of Number. Springer.Google Scholar
Fuson, K. C. & Secada, W. G. (1986). Teaching children to add by counting-on with one-handed finger patterns. Cognition and Instruction, 3(3), 229260.CrossRefGoogle Scholar
Gallagher, S. (2017). Enactivist Interventions: Rethinking the Mind. Oxford University Press.CrossRefGoogle Scholar
Gallistel, C. R. (2017). Numbers and brains. Learning & Behaviour, 45(4), 327328.CrossRefGoogle ScholarPubMed
Gallistel, C. R. (2018). Finding numbers in the brain. Philosophical Transactions of the Royal Society B: Biological Sciences, 373(1740), 20170119. https://doi.org/10.1098/rstb.2017.0119.CrossRefGoogle Scholar
Gallistel, C. R. & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44(1–2), 4374. https://doi.org/10.1016/0010-0277(92)90050-r.CrossRefGoogle ScholarPubMed
Gallistel, C. R., Gelman, R. & Cordes, S. (2006). The cultural and evolutionary history of the real numbers. In Levinson, S. & Jaisson, P. (Eds.), Evolution and Culture: A Fyssen Foundation Symposium (pp. 247274). MIT Press.Google Scholar
Garland, A. & Low, J. (2014). Addition and subtraction in wild New Zealand robins. Behavioural Processes, 109, 103110. https://doi.org/10.1016/j.beproc.2014.08.022.CrossRefGoogle ScholarPubMed
Geary, D. (2011). Cognitive predictors of achievement growth in mathematics: A five year longitudinal study. Developmental Psychology, 47(6), 15391552. https://doi.org/10.1037/a0025510.CrossRefGoogle Scholar
Geary, D., Berch, D. & Mann Koepke, K. (Eds.). (2014). Evolutionary Origins and Early Development of Number Processing. Elsevier.Google Scholar
Gebuis, T., Cohen Kadosh, R. & Gevers, W. (2016). Sensory-integration system rather than approximate number system underlies numerosity processing: A critical review. Acta Psychologica, 171, 1735. https://doi.org/10.1016/j.actpsy.2016.09.003.CrossRefGoogle ScholarPubMed
Gelman, R. & Butterworth, B. (2005). Number and language: How are they related? Trends in Cognitive Sciences, 9(1), 610.CrossRefGoogle ScholarPubMed
Gelman, R. & Gallistel, C. (1978). The Child’s Understanding of Number. Harvard University Press.Google Scholar
Gelman, R. & Gallistel, C. (2004). Language and the origin of numerical concepts. Science, 306, 441443.CrossRefGoogle ScholarPubMed
Gibson, J. J. (1979). The Ecological Approach to Visual Perception: Classic Edition. Psychology Press.Google Scholar
Gödel, K. (1931). On formally undecidable propositions. In Feferman, S., Dawson, J., Kleene, S., Moore, G., Solovay, R. & van Heijenoort, J. (Eds.), Collected Works: Vol. I: Publications 1929–1936 (pp. 145195). Oxford University Press.Google Scholar
Gödel, K. (1983). What is Cantor’s continuum problem. In Benacerraf, P. & Putnam, H. (Eds.), Philosophy of Mathematics (pp. 470485). Prentice-Hall.Google Scholar
Goldman, A. I. (1967). A causal theory of knowing. Journal of Philosophy, 64(12), 357372. https://doi.org/10.2307/2024268.CrossRefGoogle Scholar
Goodman, N. (1955). Fact, Fiction, and Forecast, 2nd ed. Harvard University Press.Google Scholar
Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science, 306(5695), 496499.CrossRefGoogle ScholarPubMed
Gould, S. J. & Vrba, E. S. (1982). Exaptation: A missing term in the science of form. Paleobiology, 8(1), 415. https://doi.org/10.1017/S0094837300004310.CrossRefGoogle Scholar
Greenfieldboyce, N. (2018). Math bee: Honeybees seem to understand the notion of zero. NPR. www.npr.org/2018/06/07/617863467/math-bee-honeybees-seem-to-understand-the-notion-of-zero.Google Scholar
Griffiths, P. E. (2001). What is innateness? The Monist, 85(1), 7085. https://doi.org/10.5840/monist20028518.CrossRefGoogle Scholar
Hadamard, J. (1954). The Psychology of Invention in the Mathematical Field. Dover Publications.Google Scholar
Halberda, J., Ly, R., Wilmer, J. B., Naiman, D. Q. & Germine, L. (2012). Number sense across the lifespan as revealed by a massive Internet-based sample. Proceedings of the National Academy of Sciences, 109(28), 1111611120. https://doi.org/10.1073/pnas.1200196109.CrossRefGoogle ScholarPubMed
Halberda, J., Mazzocco, M. M. M. & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455(7213), 665668. https://doi.org/10.1038/nature07246.CrossRefGoogle ScholarPubMed
Hale, B., & Wright, C. (2001). Reasons Proper Study. Clarendon Press.CrossRefGoogle Scholar
Hale, B., & Wright, C. (2009). The metaontology of abstraction. In Chalmers, D., Manley, D. & Wasserman, R. (Eds.), Metametaphysics: New Essays on the Foundations of Ontology (pp. 178212). Oxford University Press.CrossRefGoogle Scholar
Hallett, M. (1988). Cantorian Set Theory and Limitation of Size. Clarendon Press.Google Scholar
Hauser, M. D., MacNeilage, P. & Ware, M. (1996). Numerical representations in primates. Proceedings of the National Academy of Sciences, 93(4), 15141517.CrossRefGoogle ScholarPubMed
Heath, T. L. (1921). A History of Greek Mathematics. Dover Publications.Google Scholar
Hebbeler, J. (2015). Kant on necessity, insight, and a priori knowledge. Archiv Für Geschichte Der Philosophie, 97(1), 3465. https://doi.org/10.1515/agph-2015-0002.CrossRefGoogle Scholar
Heck, R. K. (2000). Cardinality, counting, and equinumerosity. Notre Dame Journal of Formal Logic, 41, 187209.CrossRefGoogle Scholar
Hellman, G. (1989). Mathematics without Numbers. Oxford University Press.Google Scholar
Hempel, C. G. (1945). On the nature of mathematical truth. The American Mathematical Monthly, 52(10), 543556. https://doi.org/10.2307/2306103.CrossRefGoogle Scholar
Henik, A. & Tzelgov, J. (1982). Is three greater than five: The relation between physical and semantic size in comparison tasks. Memory & Cognition, 10(4), 389395. https://doi.org/10.3758/BF03202431.CrossRefGoogle ScholarPubMed
Henrich, J. (2015). The Secret of Our Success: How Culture is Driving Human Evolution, Domesticating our Species, and Making Us Smarter. Princeton University Press.CrossRefGoogle Scholar
Heyes, C. (2012). Grist and mills: On the cultural origins of cultural learning. Philosophical Transactions of the Royal Society B: Biological Sciences, 367(1599), 21812191. https://doi.org/10.1098/rstb.2012.0120.CrossRefGoogle ScholarPubMed
Heyes, C. (2018). Cognitive Gadgets: The Cultural Evolution of Thinking. Harvard University Press.Google Scholar
Hilbert, D. (1902). The Foundations of Geometry. Open Court.Google Scholar
Hinrichs, J. V., Yurko, D. S. & Hu, J. M. (1981). Two-digit number comparison: Use of place information. Journal of Experimental Psychology: Human Perception and Performance, 7(4), 890901.Google Scholar
Hintikka, J. (1996). Principles of Mathematics Revisited. Cambridge University Press.CrossRefGoogle Scholar
Hohol, M. (2019). Foundations of Geometric Cognition. Routledge.CrossRefGoogle Scholar
Hohol, M., Wołoszyn, K., Nuerk, H.-C. & Cipora, K. (2018). A large-scale survey on finger counting routines, their temporal stability and flexibility in educated adults. PeerJ, 6, e5878. https://doi.org/10.7717/peerj.5878.CrossRefGoogle ScholarPubMed
Howard, S. R., Avarguès-Weber, A., Garcia, J. E., Greentree, A. D. & Dyer, A. G. (2018). Numerical ordering of zero in honey bees. Science, 360(6393), 11241126. https://doi.org/10.1126/science.aar4975.CrossRefGoogle ScholarPubMed
Hutchins, E. (1994). Cognition in the Wild. MIT Press.Google Scholar
Hutto, D. D. (2019). Re-doing the math: Making enactivism add up. Philosophical Studies, 176, 827837.CrossRefGoogle Scholar
Hutto, D. D. & Myin, E. (2013). Radicalizing Enactivism. Basic Minds without Content. MIT Press.Google Scholar
Hutto, D. D., & Myin, E. (2017). Evolving Enactivism. Basic Minds Meet Content. MIT Press.CrossRefGoogle Scholar
Hyde, D. C. (2011). Two systems of non-symbolic numerical cognition. Frontiers in Human Neuroscience, 5, 150.CrossRefGoogle ScholarPubMed
Hyde, D. C. & Ansari, D. (2018). Advances in understanding the development of the mathematical brain. Developmental Cognitive Neuroscience, 30, 236.CrossRefGoogle ScholarPubMed
Ifrah, G. (1998). The Universal History of Numbers: From Prehistory to the Invention of the Computer. Harville Press.Google Scholar
Imbo, I., Duverne, S. & Lemaire, P. (2007). Working memory, strategy execution, and strategy selection in mental arithmetic. Quarterly Journal of Experimental Psychology, 60(9), 12461264. https://doi.org/10.1080/17470210600943419.CrossRefGoogle ScholarPubMed
Irvine, A. D. (1989). Physicalism in Mathematics. Kluwer Academic Publishers.Google Scholar
Izard, V., Sann, C., Spelke, E. S. & Streri, A. (2009). Newborn infants perceive abstract numbers. Proceedings of the National Academy of Sciences, 106(25), 1038210385. https://doi.org/10.1073/pnas.0812142106.CrossRefGoogle ScholarPubMed
Izard, V., Streri, A. & Spelke, E. (2014). Toward exact number: Young children use one-to-one correspondence to measure set identity but not numerical equality. Cognitive Psychology, 72, 2753.CrossRefGoogle Scholar
Jones, M. (2020). Numerals and neural reuse. Synthese, 197, 36573681.CrossRefGoogle Scholar
Kahneman, D., Treisman, A. & Gibbs, B. J. (1992). The reviewing of object files: Object-specific integration of information. Cognitive Psychology, 24(2), 175219. https://doi.org/10.1016/0010-0285(92)90007-O.CrossRefGoogle ScholarPubMed
Kallen, S. A. (2001). The Mayans. Lucent Books.Google Scholar
Kanjlia, S., Lane, C., Feigenson, L. & Bedny, M. (2016). Absence of visual experience modifies the neural basis of numerical thinking. Proceedings of the National Academy of Sciences, 113(40), 1117211177. https://doi.org/10.1073/pnas.1524982113.CrossRefGoogle ScholarPubMed
Kant, I. (1787). Critique of Pure Reason. Cambridge University Press.Google Scholar
Kaufman, E. L., Lord, M. W., Reese, T. W. & Volkmann, J. (1949). The discrimination of visual number. The American Journal of Psychology, 62, 498525. https://doi.org/10.2307/1418556.CrossRefGoogle ScholarPubMed
Kawai, M. (1965). Newly-acquired pre-cultural behavior of the natural troop of Japanese monkeys on Koshima islet. Primates, 6(1), 130. https://doi.org/10.1007/BF01794457.CrossRefGoogle Scholar
Kitcher, P. (1983). The Nature of Mathematical Knowledge. Oxford University Press.Google Scholar
Kitcher, P. (1992). The naturalists return. The Philosophical Review, 101(1), 53114. https://doi.org/10.2307/2185044.CrossRefGoogle Scholar
Kline, M. (1973). Why Johnny Can’t Add: The Failure of the New Math. St. Martin’s Press.Google Scholar
Knops, A. (2020). Numerical Cognition. The Basics. Routledge.Google Scholar
Kövecses, Z. & Benczes, R. (2010). Metaphor: A Practical Introduction, 2nd ed. Oxford University Press.Google Scholar
Kripke, S. A. (1963). Semantical considerations on modal logic. Acta Philosophica Fennica, 16, 8394.Google Scholar
Kripke, S. A. (1980). Naming and Necessity. Blackwell Publishers.Google Scholar
Kripke, S. A. (1982). Wittgenstein on Rules and Private Language: An Elementary Exposition. Harvard University Press.Google Scholar
Kuhn, T. S. (1993). Afterwords. In Horwich, P. (Ed.), Educational Theory (pp. 311341). MIT Press.Google Scholar
Kummer, H., Goodall, J. & Weiskrantz, L. (1985). Conditions of innovative behaviour in primates. Philosophical Transactions of the Royal Society of London. B, Biological Sciences, 308(1135), 203214. https://doi.org/10.1098/rstb.1985.0020.Google Scholar
Lakoff, G. & Johnson, M. (2003). Metaphors We Live by. University of Chicago Press.CrossRefGoogle Scholar
Lakoff, G. & Núñez, R. (2000). Where Mathematics Comes from. Basic Books.Google Scholar
Laland, K. N. (2017). Darwin’s Unfinished Symphony: How Culture Made the Human Mind. Princeton University Press.CrossRefGoogle Scholar
Landry, E. (2023). Plato was Not a Mathematical Platonist. Elements in the Philosophy of Mathematics. Cambridge University Press. https://doi.org/10.1017/9781009313797.CrossRefGoogle Scholar
Lane, D. A. (2016). Innovation cascades: Artefacts, organization and attributions. Philosophical Transactions of the Royal Society B: Biological Sciences, 371(1690), 20150194. https://doi.org/10.1098/rstb.2015.0194.CrossRefGoogle ScholarPubMed
Lange, M. (2017). Because without Cause: Non-causal Explanations in Science and Mathematics. Oxford University Press.Google Scholar
Lee, M. D. & Sarnecka, B. W. (2010). A model of knower-level behavior in number concept development. Cognitive Science, 34(1), 5167.CrossRefGoogle Scholar
Lee, M. D., & Sarnecka, B. W. (2011). Number-knower levels in young children: Insights from Bayesian modeling. Cognition, 120(3), 391402.CrossRefGoogle ScholarPubMed
Leibovich, T., Katzin, N., Harel, M. & Henik, A. (2017). From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition. The Behavioral and Brain Sciences, 40, e164. https://doi.org/10.1017/S0140525X16000960.CrossRefGoogle Scholar
Leitgeb, H. (2020). Why pure mathematical truths are metaphysically necessary: A set-theoretic explanation. Synthese, 197(7), 31133120. https://doi.org/10.1007/s11229–018-1873-x.CrossRefGoogle Scholar
Lemer, C., Dehaene, S., Spelke, E. & Cohen, L. (2003). Approximate quantities and exact number words: Dissociable systems. Neuropsychologia, 41(14), 19421958. https://doi.org/10.1016/S0028–3932(03)00123-4.CrossRefGoogle ScholarPubMed
Leslie, A. M., Gelman, R. & Gallistel, C. R. (2008). The generative basis of natural number concepts. Trends in Cognitive Sciences, 12(6), 213218. https://doi.org/10.1016/j.tics.2008.03.004.CrossRefGoogle ScholarPubMed
Lewis, D. (1970). General semantics. Synthese, 22(1/2), 1867.CrossRefGoogle Scholar
Linnebo, Ø. (2018a). Platonism in the philosophy of mathematics. In Zalta, E. (Ed.), The Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/archives/spr2018/entries/platonism-mathematics.Google Scholar
Linnebo, Ø. (2018b). Thin Objects. Oxford University Press.CrossRefGoogle Scholar
Lipton, J. S. & Spelke, E. S. (2003). Origins of number sense. Large-number discrimination in human infants. Psychological Science, 14(5), 396401. https://doi.org/10.1111/1467-9280.01453.CrossRefGoogle ScholarPubMed
Lumsden, C. & Wilson, E. (1981). Genes, Mind, and Culture: The Coevolutionary Process. Harvard University Press.Google Scholar
Maddy, P. (2014). A second philosophy of arithmetic. The Review of Symbolic Logic, 7(2), 222249.CrossRefGoogle Scholar
Maguire, E. A., Gadian, D. G., Johnsrude, I. S., Good, C. D., Ashburner, J., Frackowiak, R. S. J. & Frith, C. D. (2000). Navigation-related structural change in the hippocampi of taxi drivers. Proceedings of the National Academy of Sciences, 97(8), 43984403. https://doi.org/10.1073/pnas.070039597.CrossRefGoogle ScholarPubMed
Maguire, E. A., Spiers, H. J., Good, C. D., Hartley, T., Frackowiak, R. S. J. & Burgess, N. (2003). Navigation expertise and the human hippocampus: A structural brain imaging analysis. Hippocampus, 13(2), 250259. https://doi.org/10.1002/hipo.10087.CrossRefGoogle ScholarPubMed
Malafouris, L. (2013). How Things Shape the Mind: A Theory of Material Engagement. MIT Press.CrossRefGoogle Scholar
Manders, K. (2008). The Euclidean diagram. In Mancosu, P. (Ed.), The Philosophy of Mathematical Practice (pp. 80133). Oxford University Press.CrossRefGoogle Scholar
Margolis, E. & Laurence, S. (2008). How to learn the natural numbers: Inductive inference and the acquisition of number concepts. Cognition, 106, 924939.CrossRefGoogle ScholarPubMed
Mateos-Aparicio, P. & Rodríguez-Moreno, A. (2019). The impact of studying brain plasticity. Frontiers in Cellular Neuroscience, 13, 66. www.frontiersin.org/articles/10.3389/fncel.2019.00066.CrossRefGoogle ScholarPubMed
McCloskey, M. (1992). Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia. Cognition, 44(1–2), 107157. https://doi.org/10.1016/0010-0277(92)90052-j.CrossRefGoogle ScholarPubMed
McCloskey, M. & Macaruso, P. (1995). Representing and using numerical information. The American Psychologist, 50(5), 351363. https://doi.org/10.1037//0003-066x.50.5.351.CrossRefGoogle ScholarPubMed
McCrink, K. (2015). Intuitive nonsymbolic arithmetic. In Geary, D., Herch, D. & Koepke, K. (Eds.), Evolutionary Origins and Early Development of Number Processing (pp. 201223). Elsevier Academic Press. https://doi.org/10.1016/B978–0-12-420133-0.00008-9.CrossRefGoogle Scholar
McCrink, K. & Wynn, K. (2004). Large-number addition and subtraction by 9-month-old infants. Psychological Science, 15(11), 776781. https://doi.org/10.1111/j.0956-7976.2004.00755.x.CrossRefGoogle ScholarPubMed
McGarrigle, J. & Donaldson, M. (1974). Conservation accidents. Cognition, 3(4), 341350. https://doi.org/10.1016/0010-0277(74)90003-1.CrossRefGoogle Scholar
Meck, W. H. & Church, R. M. (1983). A mode control model of counting and timing processes. Journal of Experimental Psychology: Animal Behavior Processes, 9(3), 320.Google ScholarPubMed
Menary, R. (2014). Neuronal recycling, neural plasticity and niche construction. Mind and Language, 29(3), 286303.CrossRefGoogle Scholar
Menary, R. (2015). Mathematical Cognition: A Case of Enculturation. MIND Group.Google Scholar
Menary, R. & Gillett, A. (2022). The tools of enculturation. Topics in Cognitive Science, 14(2), 363387. https://doi.org/10.1111/tops.12604.CrossRefGoogle ScholarPubMed
Merzbach, U. C. & Boyer, C. B. (2011). A History of Mathematics, 3rd ed. John Wiley.Google Scholar
Mesoudi, A. & Thornton, A. (2018). What is cumulative cultural evolution? Proceedings of the Royal Society B: Biological Sciences, 285(1880), 20180712. https://doi.org/10.1098/rspb.2018.0712.CrossRefGoogle ScholarPubMed
Metzinger, T. (2013). The myth of cognitive agency: Subpersonal thinking as a cyclically recurring loss of mental autonomy. Frontiers in Psychology, 4, 931. www.frontiersin.org/article/10.3389/fpsyg.2013.00931.CrossRefGoogle ScholarPubMed
Michaelson, E. & Reimer, M. (2022). Reference. In Zalta, E. N. (Ed.), The Stanford Encyclopedia of Philosophy (Summer 2022). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/sum2022/entries/reference/.Google Scholar
Mill, J. S. (1843). A system of logic. In Robson, J. M. (Ed.), Collected Works of John Stuart Mill: Vols. 7 & 8. University of Toronto Press.Google Scholar
Miller, K. F., Smith, C. M., Zhu, J. & Zhang, H. (1995). Preschool origins of cross-national differences in mathematical competence: The role of number-naming systems. Psychological Science, 6(1), 5660.CrossRefGoogle Scholar
Morgan, C. L. (1894). An Introduction to Comparative Psychology. Palala Press.CrossRefGoogle Scholar
Müller-Hill, E. (2009). Formalizability and knowledge ascriptions in mathematical practice. Philosophia Scientiae, 13(2), 2143.CrossRefGoogle Scholar
Muthukrishna, M. & Henrich, J. (2016). Innovation in the collective brain. Philosophical Transactions of the Royal Society B: Biological Sciences, 371(1690), 20150192. https://doi.org/10.1098/rstb.2015.0192.CrossRefGoogle ScholarPubMed
Needham, J. & Wang, L. (1995). Science and Civilisation in China. Cambridge University Press.Google Scholar
Nelson, E. (2020). What Frege asked Alex the parrot: Inferentialism, number concepts, and animal cognition. Philosophical Psychology, 33(2), 206227. https://doi.org/10.1080/09515089.2019.1688777.CrossRefGoogle Scholar
Netz, R. (1999). The Shaping of Deduction in Greek Mathematics. Cambridge University Press.CrossRefGoogle Scholar
Netz, R. (2004). Eudemus of Rhodes, Hippocrates of Chios and the earliest form of a Greek mathematical text. Centaurus, 46(4), 243286.CrossRefGoogle Scholar
Nieder, A. (2006). Temporal and spatial enumeration processes in the primate parietal cortex. Science, 313, 14311435.CrossRefGoogle ScholarPubMed
Nieder, A. (2016). The neuronal code for number. Nature Reviews Neuroscience, 17(6), 366.CrossRefGoogle ScholarPubMed
Nieder, A. (2019). A Brain for Numbers: The Biology of the Number Instinct, illustrated ed. The MIT Press.CrossRefGoogle Scholar
Nieder, A. & Dehaene, S. (2009). Representation of number in the brain. Annual Review of Neuroscience, 32, 185208.CrossRefGoogle ScholarPubMed
Nieder, A. & Miller, E. K. (2003). Coding of cognitive magnitude: Compressed scaling of numerical information in the primate prefrontal cortex. Neuron, 37(1), 149157. https://doi.org/10.1016/s0896–6273(02)01144-3.CrossRefGoogle ScholarPubMed
Nissen, H. J., Damerow, P. & Englund, R. K. (1994). Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East (Larsen, P., Trans.; 1st ed). University of Chicago Press.Google Scholar
Noël, M.-P. (2005). Finger gnosia: A predictor of numerical abilities in children? Child Neuropsychology, 11(5), 413430. https://doi.org/10.1080/09297040590951550.CrossRefGoogle ScholarPubMed
Noles, N. S., Scholl, B. J. & Mitroff, S. R. (2005). The persistence of object file representations. Perception & Psychophysics, 67(2), 324334. https://doi.org/10.3758/BF03206495.CrossRefGoogle ScholarPubMed
Núñez, R. E. (2009). Numbers and arithmetic: Neither hardwired nor out there. Biological Theory, 4(1), 6883. https://doi.org/10.1162/biot.2009.4.1.68.CrossRefGoogle Scholar
Núñez, R. E. (2011). No innate number line in the human brain. Journal of Cross-Cultural Psychology, 42(4), 651668.CrossRefGoogle Scholar
Núñez, R. E. (2017). Is there really an evolved capacity for number? Trends in Cognitive Science, 21, 409424.CrossRefGoogle ScholarPubMed
Núñez, R. E., d’Errico, F., Gray, R. D. & Bender, A. (2021). The perception of quantity ain’t number: Missing the primacy of symbolic reference. Behavioral and Brain Sciences, 44, e199. https://doi.org/10.1017/S0140525X21001023.CrossRefGoogle ScholarPubMed
Obayashi, S., Suhara, T., Kawabe, K., Okauchi, T., Maeda, J., Akine, Y., Onoe, H. & Iriki, A. (2001). Functional brain mapping of monkey tool use. NeuroImage, 14(4), 853861. https://doi.org/10.1006/nimg.2001.0878.CrossRefGoogle ScholarPubMed
Ojose, B. (2008). Applying Piaget’s theory of cognitive development to mathematics instruction. Mathematics Educator, 18(1), 2630.Google Scholar
Orwell, G. (1961). 1984. Signet Classic.Google Scholar
Overmann, K. A. (2016). The role of materiality in numerical cognition. Quaternary International, 405, 4251.CrossRefGoogle Scholar
Overmann, K. A. (2018). Constructing a concept of number. Journal of Numerical Cognition, 4(2), 464493.CrossRefGoogle Scholar
Overmann, K. A. (2021a). Finger-counting in the Upper Palaeolithic. Rock Art Research, 31(1), 6380.Google Scholar
Overmann, K. A. (2021b). Updating the abstract–concrete distinction in Ancient Near Eastern numbers. Cuneiform Digital Library Journal, 2018(1), 122. https://cdli.mpiwg-berlin.mpg.de/articles/cdlj/2018-1.Google Scholar
Pantsar, M. (2009). Truth, Proof and Gödelian Arguments: A Defence of Tarskian Truth in Mathematics. PhD Thesis. University of Helsinki.Google Scholar
Pantsar, M. (2014). An empirically feasible approach to the epistemology of arithmetic. Synthese, 191(17), 42014229. https://doi.org/10.1007/s11229–014-0526-y.CrossRefGoogle Scholar
Pantsar, M. (2015a). Assessing the empirical philosophy of mathematics. Discipline filosofiche, XXV, 111130. https://doi.org/10.1400/236780.Google Scholar
Pantsar, M. (2015b). In search of aleph-null: How infinity can be created. Synthese, 192(8), 24892511.CrossRefGoogle Scholar
Pantsar, M. (2016a). Frege, dedekind, and the modern epistemology of arithmetic. Acta Analytica, 31, 297318. doi: 10.1007/s12136-015-0280-x.CrossRefGoogle Scholar
Pantsar, M. (2016b). The modal status of contextually a priori arithmetical truths. In Boccuni, F. & Sereni, A. (Eds.), Objectivity, Realism, and Proof (pp. 6779). Springer.CrossRefGoogle Scholar
Pantsar, M. (2018a). Early numerical cognition and mathematical processes. THEORIA. Revista de Teoría, Historia y Fundamentos de La Ciencia, 33(2), 285304.Google Scholar
Pantsar, M. (2018b). Mathematical explanations and mathematical applications. In Handbook of the Mathematics of the Arts and Sciences (pp. 116). Springer.Google Scholar
Pantsar, M. (2019a). Cognitive and computational complexity: Considerations from mathematical problem solving. Erkenntnis, 86, 961997.CrossRefGoogle Scholar
Pantsar, M. (2019b). The enculturated move from proto-arithmetic to arithmetic. Frontiers in Psychology, 10, 1454.CrossRefGoogle ScholarPubMed
Pantsar, M. (2020). Mathematical cognition and enculturation: Introduction to the Synthese special issue. Synthese, 197, 36473655. https://doi.org/10.1007/s11229–019-.CrossRefGoogle Scholar
Pantsar, M. (2021a). Bootstrapping of integer concepts: The stronger deviant-interpretation challenge. Synthese, 199, 57915814. https://doi.org/10.1007/s11229–021-03046-2.CrossRefGoogle Scholar
Pantsar, M. (2021b). Descriptive complexity, computational tractability, and the logical and cognitive foundations of mathematics. Minds and Machines, 31(1), 7598.CrossRefGoogle Scholar
Pantsar, M. (2021c). Objectivity in mathematics, without mathematical objects. Philosophia Mathematica, 29(3), 318352. https://doi.org/10.1093/philmat/nkab010.Google Scholar
Pantsar, M. (2021d). On the development of geometric cognition: Beyond nature vs. nurture. Philosophical Psychology, 35, 595616. https://doi.org/10.1080/09515089.2021.2014441.CrossRefGoogle Scholar
Pantsar, M. (2023a). Developing artificial human-like arithmetical intelligence (and why). Minds and Machines, 33, 379396. https://doi.org/10.1007/s11023–023-09636-y.CrossRefGoogle Scholar
Pantsar, M. (2023b). From maximal intersubjectivity to objectivity: An argument from the development of arithmetical cognition. Topoi, 42(1), 271281. https://doi.org/10.1007/s11245–022-09842-w.CrossRefGoogle Scholar
Pantsar, M. (2023c). On radical enactivist accounts of arithmetical cognition. Ergo, 9, 57. https://doi.org/doi.org/10.3998/ergo.3120.Google Scholar
Pantsar, M. (2023d). On what ground do thin objects exist? In search of the cognitive foundation of number concepts. Theoria, 89(3), 298313. https://doi.org/10.1111/theo.12366.CrossRefGoogle Scholar
Parker, F. W. (1879). Quincy Course in Arithmetic. Andesite Press.Google Scholar
Peano, G. (1889). The principles of arithmetic, presented by a new method. In Kennedy, H. (Ed.), Selected Works of Giuseppe Peano (pp. 101134). University of Toronto Press.Google Scholar
Pelland, J.-C. (2018). Which came first, the number or the numeral? In Bangu, S. (Ed.), Naturalizing Logico-Mathematical Knowledge (pp. 179194). Routledge.CrossRefGoogle Scholar
Pelland, J.-C. (2020). What’s new: Innovation and enculturation of arithmetical practices. Synthese, 197, 37973822. https://doi.org/10.1007/s11229–018-02060-1.CrossRefGoogle Scholar
Penner-Wilger, M. & Anderson, M. L. (2013). The relation between finger gnosis and mathematical ability: Why redeployment of neural circuits best explains the finding. Frontiers in Psychology, 4, 877. https://doi.org/10.3389/fpsyg.2013.00877.CrossRefGoogle ScholarPubMed
Penner-Wilger, M., Waring, R. J. & Newton, A. T. (2014). Subitizing and finger gnosis predict calculation fluency in adults. Proceedings of the Annual Meeting of the Cognitive Science Society, 36(36), 11501155. https://escholarship.org/uc/item/4vv725r4.Google Scholar
Penrose, R. (1989). The Emperor’s New Mind: Concerning Computers, Minds and the Laws of Physics. Oxford University Press.CrossRefGoogle Scholar
Penrose, R. (1994). Shadows of the Mind: A Search for the Missing Science of Consciousness. Oxford University Press.Google Scholar
Pepperberg, I. M. (2006). Grey parrot numerical competence: A review. Animal Cognition, 9(4), 377391. https://doi.org/10.1007/s10071–006-0034-7.CrossRefGoogle ScholarPubMed
Pepperberg, I. M. (2012). Further evidence for addition and numerical competence by a grey parrot (Psittacus erithacus). Animal Cognition, 15(4), 711717.CrossRefGoogle ScholarPubMed
Pepperberg, I. M. & Gordon, J. D. (2005). Number comprehension by a grey parrot (Psittacus erithacus), including a zero-like concept. Journal of Comparative Psychology, 119(2), 197209. https://doi.org/10.1037/0735-7036.119.2.197.CrossRefGoogle ScholarPubMed
Petersen, S. E. & Sporns, O. (2015). Brain networks and cognitive architectures. Neuron, 88(1), 207219. https://doi.org/10.1016/j.neuron.2015.09.027.CrossRefGoogle ScholarPubMed
Piaget, J. (1965). Child’s Conception of Number. Norton.Google Scholar
Piaget, J. (1970). Science of Education and the Psychology of the Child. Viking Press.Google Scholar
Piazza, M. (2010). Neurocognitive start-up tools for symbolic number representations. Trends in Cognitive Sciences, 14(12), 542551. https://doi.org/10.1016/j.tics.2010.09.008.CrossRefGoogle ScholarPubMed
Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., Dehaene, S. & Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 3341. https://doi.org/10.1016/j.cognition.2010.03.012.CrossRefGoogle ScholarPubMed
Piazza, M., Pinel, P., Le Bihan, D. & Dehaene, S. (2007). A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron, 53, 293305.CrossRefGoogle ScholarPubMed
Pica, P., Lemer, C., Izard, V. & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306(5695), 499503.CrossRefGoogle Scholar
Pinel, P., Dehaene, S., Riviere, D. & LeBihan, D. (2001). Modulation of parietal activation by semantic distance in a number comparison task. Neuroimage, 14(5), 10131026.CrossRefGoogle Scholar
Plato, . (1992). The Republic (G. M. A. Grube, trans.). Hackett Publishing Company.Google Scholar
Popper, K. R. (1972). Objective Knowledge: An Evolutionary Approach, revised ed. Oxford University Press.Google Scholar
Posth, C., Nakatsuka, N., Lazaridis, I., Skoglund, P., Mallick, S., Lamnidis, T. C., Rohland, N., Nägele, K., Adamski, N., Bertolini, E., Broomandkhoshbacht, N., Cooper, A., Culleton, B. J., Ferraz, T., Ferry, M., Furtwängler, A., Haak, W., Harkins, K., Harper, T. K., … Reich, D. (2018). Reconstructing the deep population history of Central and South America. Cell, 175(5), 11851197.e22. https://doi.org/10.1016/j.cell.2018.10.027.CrossRefGoogle ScholarPubMed
Power, T. G. (2013). Play and Exploration in Children and Animals. Psychology Press.Google Scholar
Prado, J., Mutreja, R., Zhang, H., Mehta, R., Desroches, A. S., Minas, J. E. & Booth, J. R. (2011). Distinct representations of subtraction and multiplication in the neural systems for numerosity and language. Human Brain Mapping, 32(11), 19321947. https://doi.org/10.1002/hbm.21159.CrossRefGoogle ScholarPubMed
Putnam, H. (1967). Mathematics without foundations. Journal of Philosophy, 64(1), 522. https://doi.org/10.2307/2024603.CrossRefGoogle Scholar
Putnam, H. (Ed.). (1979). Mathematics, Matter and Method, 2nd ed. Cambridge University Press.CrossRefGoogle Scholar
Putnam, H. (Ed.). (1983). ‘Two dogmas’ revisited. In Philosophical Papers: Volume 3: Realism and Reason (pp. 8797). Cambridge University Press. https://doi.org/10.1017/CBO9780511625275.007.CrossRefGoogle Scholar
Quine, W. V. (1951). Two dogmas of empiricism. Philosophical Review, 60(1), 2043. https://doi.org/10.2307/2266637.CrossRefGoogle Scholar
Quine, W. V. (1966). The scope of language of science. In The Ways of Paradox and Other Essays (pp. 215232). Random House.Google Scholar
Quinon, P. (2021). Cognitive structuralism: Explaining the regularity of the natural numbers progression. Review of Philosophy and Psychology, 13, 127149. https://link.springer.com/article/10.1007/s13164–021-00524-x.CrossRefGoogle Scholar
Rafi, Z. & Greenland, S. (2020). Semantic and cognitive tools to aid statistical science: Replace confidence and significance by compatibility and surprise. BMC Medical Research Methodology, 20, 244. https://doi.org/10.1186/s12874–020-01105-9.CrossRefGoogle ScholarPubMed
Rayo, A. (2013). The Construction of Logical Space. Oxford University Press.CrossRefGoogle Scholar
Rayo, A. (2015). Nominalism, trivialism, logicism. Philosophia Mathematica, 23(1), 6586.CrossRefGoogle Scholar
Reck, E. & Schiemer, G. (2023). Structuralism in the philosophy of mathematics. In Zalta, E. N. & Nodelman, U. (Eds.), The Stanford Encyclopedia of Philosophy. Stanford University Press. https://plato.stanford.edu/archives/spr2023/entries/structuralism-mathematics/.Google Scholar
Reeve, R. & Humberstone, J. (2011). Five- to 7-year-olds’ finger gnosia and calculation abilities. Frontiers in Psychology, 2, 359. https://doi.org/10.3389/fpsyg.2011.00359.CrossRefGoogle ScholarPubMed
Revkin, S. K., Piazza, M., Izard, V., Cohen, L. & Dehaene, S. (2008). Does subitizing reflect numerical estimation? Psychological Science, 19(6), 607614.CrossRefGoogle ScholarPubMed
Rey, G. (2014). Innate and learned: Carey, mad dog nativism, and the poverty of stimuli and analogies (yet again). Mind & Language, 29, 109132.CrossRefGoogle Scholar
Rips, L. J., Asmuth, J. & Bloomfield, A. (2006). Giving the boot to the bootstrap: How not to learn the natural numbers. Cognition, 101(3), 5160.CrossRefGoogle Scholar
Rips, L. J., Bloomfield, A. & Asmuth, J. (2008). From numerical concepts to concepts of number. Behavioral and Brain Sciences, 31(6), 623642. https://doi.org/10.1017/S0140525X08005566.CrossRefGoogle ScholarPubMed
Rosen, G. (2020). Abstract objects. In Zalta, E. N. (Ed.), The Stanford Encyclopedia of Philosophy. Stanford University Press. https://plato.stanford.edu/archives/spr2020/entries/abstract-objects/.Google Scholar
Rugani, R., Fontanari, L., Simoni, E., Regolin, L. & Vallortigara, G. (2009). Arithmetic in newborn chicks. Proceedings of the Royal Society B: Biological Sciences, 276(1666), 24512460.CrossRefGoogle ScholarPubMed
Rugani, R., Vallortigara, G., Priftis, K. & Regolin, L. (2015). Number-space mapping in the newborn chick resembles humans’ mental number line. Science, 347(6221), 534536. https://doi.org/10.1126/science.aaa1379.CrossRefGoogle ScholarPubMed
Sarnecka, B. W. & Carey, S. (2008). How counting represents number: What children must learn and when they learn it. Cognition, 108(3), 662674.CrossRefGoogle Scholar
Sarnecka, B. W. & Gelman, S. (2004). Six does not just mean a lot: Preschoolers see number words as specific. Cognition, 92, 329352.CrossRefGoogle ScholarPubMed
Sarnecka, B. W. & Wright, C. (2013). The idea of an exact number: Children’s understanding of cardinality and equinumerosity. Cognitive Science, 37(8), 14931506.CrossRefGoogle ScholarPubMed
Sarrazin, J.-C., Giraudo, M.-D., Pailhous, J., Bootsma, R. J., & Giraudo, M.-D. (2004). Dynamics of balancing space and time in memory: Tau and kappa effects revisited. Journal of Experimental Psychology. Human Perception and Performance, 30(3), 411430. https://doi.org/10.1037/0096-1523.30.3.411.CrossRefGoogle Scholar
Saxe, G. B. (1982). Developing forms of arithmetical thought among the Oksapmin of Papua New Guinea. Developmental Psychology, 18(4), 583594. https://doi.org/10.1037/0012-1649.18.4.583.CrossRefGoogle Scholar
Schlaug, G., Jäncke, L., Huang, Y., Staiger, J. F. & Steinmetz, H. (1995). Increased corpus callosum size in musicians. Neuropsychologia, 33(8), 10471055. https://doi.org/10.1016/0028-3932(95)00045-5.CrossRefGoogle ScholarPubMed
Schlimm, D. (2018). Numbers through numerals: The constitutive role of external representations. In Bangu, S. (Ed.), Naturalizing Logico-Mathematical Knowledge (pp. 195217). Routledge.CrossRefGoogle Scholar
Schlimm, D. & Neth, H. (2008). Modeling ancient and modern arithmetic practices: Addition and multiplication with Arabic and Roman numerals. In Love, B. C., McRae, K. & Sloutsky, V. M. (Eds.), Proceedings of the 30th Annual Conference of the Cognitive Science Society (pp. 20972102). Cognitive Science Society.Google Scholar
Schmandt-Besserat, D. (1996). How Writing Came About. University of Texas Press.Google Scholar
Schneider, R. M., Brockbank, E., Feiman, R. & Barner, D. (2022). Counting and the ontogenetic origins of exact equality. Cognition, 218, 104952. https://doi.org/10.1016/j.cognition.2021.104952.CrossRefGoogle ScholarPubMed
Schröder, E. (1873). Lehrbuch der Arithmetik und Algebra für Lehrer und Studirende I. Teubner.Google Scholar
Searle, J. R. (1997). The Construction of Social Reality, illustrated ed. Free Press.Google Scholar
Searle, J. R. (2010). Making the Social World: The Structure of Human Civilization. Oxford University Press.CrossRefGoogle Scholar
Sfard, A. (2008). Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing. Cambridge University Press.CrossRefGoogle Scholar
Shapiro, L. & Spaulding, S. (2021). Embodied cognition. In Zalta, E. N. (Ed.), The Stanford Encyclopedia of Philosophy. Stanford University Press. https://plato.stanford.edu/archives/fall2021/entries/embodied-cognition/.Google Scholar
Shapiro, S. (1996). Mathematical structuralism. Philosophia Mathematica, 4(2), 8182. https://doi.org/10.1093/philmat/4.2.81.CrossRefGoogle Scholar
Shapiro, S. (1997). Philosophy of Mathematics: Structure and Ontology. Oxford University Press.Google Scholar
Shapiro, S. (2000). Thinking about Mathematics. Oxford University Press.Google Scholar
Shum, J., Hermes, D., Foster, B. L., Dastjerdi, M., Rangarajan, V., Winawer, J., Miller, K. J. & Parvizi, J. (2013). A brain area for visual numerals. Journal of Neuroscience, 33(16), 67096715. https://doi.org/10.1523/JNEUROSCI.4558-12.2013.CrossRefGoogle ScholarPubMed
Simon, T. J., Hespos, S. J. & Rochat, P. (1995). Do infants understand simple arithmetic? A replication of Wynn (1992). Cognitive Development, 10, 253269.CrossRefGoogle Scholar
Skemp, R. R. (1987). The Psychology of Learning Mathematics, expanded American ed. Routledge.Google Scholar
Smart, J. J. C. (2017). The mind/brain identity theory. In Zalta, E. N. (Ed.), The Stanford Encyclopedia of Philosophy. Stanford University Press. https://plato.stanford.edu/archives/spr2017/entries/mind-identity/.Google Scholar
Spelke, E. S. (2000). Core knowledge. American Psychologist, 55(11), 12331243. https://doi.org/10.1037/0003-066X.55.11.1233.CrossRefGoogle ScholarPubMed
Spelke, E. S. (2011). Natural number and natural geometry. In Dehaene, S. & Brannon, E. (Eds.), Space, Time and Number in the Brain (pp. 287318). Academic Press.CrossRefGoogle Scholar
Spelke, E. S. & Kinzler, K. D. (2007). Core knowledge. Developmental Science, 10(1), 8996. https://doi.org/10.1111/j.1467-7687.2007.00569.x.CrossRefGoogle ScholarPubMed
Srihasam, K., Mandeville, J. B., Morocz, I. A., Sullivan, K. J. & Livingstone, M. S. (2012). Behavioral and anatomical consequences of early versus late symbol training in macaques. Neuron, 73(3), 608619. https://doi.org/10.1016/j.neuron.2011.12.022.CrossRefGoogle ScholarPubMed
Stalnaker, R. C. (2003). Reference and necessity. In Stalnaker, R. C. (Ed.), Ways a World Might Be: Metaphysical and Anti-metaphysical Essays (pp. 165187). Oxford University Press. https://doi.org/10.1093/0199251487.003.0010.CrossRefGoogle Scholar
Starkey, P. & Cooper, R. G. (1980). Perception of numbers by human infants. Science, 210(4473), 10331035.CrossRefGoogle ScholarPubMed
Sterelny, K. (2003). Thought in a Hostile World: The Evolution of Human Cognition. Blackwell.Google Scholar
Sterelny, K. (2012). The Evolved Apprentice: How Evolution Made Humans Unique. MIT Press.CrossRefGoogle Scholar
Stevens, S. S. (1939). On the problem of scales for the measurement of psychological magnitudes. Journal of Unified Science (Erkenntnis), 9, 9499.Google Scholar
Stewart, I. (2006). Letters to a Young Mathematician. Basic Books.Google Scholar
Stjernfelt, F. & Pantsar, M. (2023). Peirce’s philosophy of notations and the trade-offs in comparing numeral symbol systems. Cognitive Semiotics. https://doi.org/10.1515/cogsem-2023-2007.CrossRefGoogle Scholar
Stoianov, I. & Zorzi, M. (2012). Emergence of a ‘visual number sense’ in hierarchical generative models. Nature Neuroscience, 15(2), 194196.CrossRefGoogle ScholarPubMed
Stoljar, D. (2022). Physicalism. In Zalta, E. N. (Ed.), The Stanford Encyclopedia of Philosophy. Stanford University Press. https://plato.stanford.edu/archives/sum2022/entries/physicalism/.Google Scholar
Strawson, P. F. (1992). Analysis and Metaphysics: An Introduction to Philosophy. Oxford University Press.CrossRefGoogle Scholar
Stroud, B. (1965). Wittgenstein and logical necessity. The Philosophical Review, 74(4), 504518. https://doi.org/10.2307/2183126.CrossRefGoogle Scholar
Sur, M., Garraghty, P. E. & Roe, A. W. (1988). Experimentally induced visual projections into auditory thalamus and cortex. Science, 242(4884), 14371441. https://doi.org/10.1126/science.2462279.CrossRefGoogle ScholarPubMed
Syrett, K., Musolino, J. & Gelman, R. (2012). How can syntax support number word acquisition? Language Learning and Development, 8(2), 146176. https://doi.org/10.1080/15475441.2011.583900.CrossRefGoogle Scholar
Tait, W. W. (2001). Beyond the axioms: The question of objectivity in mathematics. Philosophia Mathematica, 9(1), 2136.CrossRefGoogle Scholar
Tang, Y., Zhang, W., Chen, K., Feng, S., Ji, Y., Shen, J. & Liu, Y. (2006). Arithmetic processing in the brain shaped by cultures. Proceedings of the National Academy of Sciences, 103(28), 1077510780.CrossRefGoogle ScholarPubMed
Tedlock, B. (1992). Time and the Highland Maya. University of New Mexico Press.Google Scholar
Testolin, A., Zou, W. Y. & McClelland, J. L. (2020). Numerosity discrimination in deep neural networks: Initial competence, developmental refinement and experience statistics. Developmental Science, 23(5), e12940.CrossRefGoogle ScholarPubMed
de Toffoli, S. (2023). Who’s afraid of mathematical diagrams? Philosopher’s Imprint, 23, 9. https://doi.org/10.3998/phimp.1348.Google Scholar
Tomasello, M. (1999). The Cultural Origins of Human Cognition. Harvard University Press.Google Scholar
Tomasello, M., Kruger, A. C. & Ratner, H. H. (1993). Cultural learning. Behavioral and Brain Sciences, 16(3), 495552. https://doi.org/10.1017/S0140525X0003123X.CrossRefGoogle Scholar
Trick, L. & Pylyshyn, Z. W. (1994). Why are small and large numbers enumerated differently? A limited capacity preattentive stage in vision. Psychological Review, 101, 80102.CrossRefGoogle ScholarPubMed
Trivett, J. (1980). The multiplication table: To be memorized or mastered? For the Learning of Mathematics, 1(1), 2125.Google Scholar
Uller, C., Carey, S., Huntley-Fenner, G. & Klatt, L. (1999). What representations might underlie infant numerical knowledge? Cognitive Development, 14(1), 136.CrossRefGoogle Scholar
Valério, M. & Ferrara, S. (2022). Numeracy at the dawn of writing: Mesopotamia and beyond. Historia Mathematica, 59, 3553. https://doi.org/10.1016/j.hm.2020.08.002.CrossRefGoogle Scholar
Vandervert, L. R. (2021). A brain for numbers: The biology of the number instinct by Andreas Nieder. The Mathematical Intelligencer, 43(1), 123127. https://doi.org/10.1007/s00283–020-10017-x.CrossRefGoogle Scholar
Varela, F. J., Thompson, E. & Rosch, E. (1991). The Embodied Mind: Cognitive Science and Human Experience. MIT Press.CrossRefGoogle Scholar
Varela, F. J., Thompson, E. & Rosch, E. (2017). The Embodied Mind: Cognitive Science and Human Experience, revised ed. MIT Press.CrossRefGoogle Scholar
Varga, S. (2019). Scaffolded Minds: Integration and Disintegration. MIT Press.CrossRefGoogle Scholar
Varshney, L. R., Chen, B. L., Paniagua, E., Hall, D. H. & Chklovskii, D. B. (2011). Structural properties of the Caenorhabditis elegans neuronal network. PLoS Computational Biology, 7(2), e1001066. https://doi.org/10.1371/journal.pcbi.1001066.CrossRefGoogle ScholarPubMed
Verdine, B. N., Golinkoff, R. M., Hirsh-Pasek, K., Newcombe, N. S., Filipowicz, A. T. & Chang, A. (2014). Deconstructing building blocks: Preschoolers’ spatial assembly performance relates to early mathematics skills. Child Development, 85(3), 10621076. https://doi.org/10.1111/cdev.12165.CrossRefGoogle Scholar
de Waal, F. B. M. (2017). Are We Smart Enough to Know How Smart Animals Are? Norton.Google Scholar
Warren, J. (2020). Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism. Oxford University Press.CrossRefGoogle Scholar
Warren, M. (2018). Bees understand the concept of zero. Science. www.science.org/content/article/bees-understand-concept-zero.CrossRefGoogle Scholar
Wasner, M., Nuerk, H.-C., Martignon, L., Roesch, S. & Moeller, K. (2016). Finger gnosis predicts a unique but small part of variance in initial arithmetic performance. Journal of Experimental Child Psychology, 146, 116.CrossRefGoogle ScholarPubMed
Way, E. C. (1991). Knowledge Representation and Metaphor. Kluwer Academic Publishers.CrossRefGoogle Scholar
Whitehead, A. N. & Russell, B. (1910). Principia Mathematica: Volumes 1–3. Cambridge University Press.Google Scholar
Wiese, H. (2007). The co-evolution of number concepts and counting words. Lingua, 117, 758772.CrossRefGoogle Scholar
Wilder, J. D., Kowler, E., Schnitzer, B. S., Gersch, T. M. & Dosher, B. A. (2009). Attention during active visual tasks: Counting, pointing, or simply looking. Vision Research, 49(9), 10171031. https://doi.org/10.1016/j.visres.2008.04.032.CrossRefGoogle ScholarPubMed
Wilson, J. & Clarke, D. (2004). Towards the modelling of mathematical metacognition. Mathematics Education Research Journal, 16(2), 2548. https://doi.org/10.1007/BF03217394.CrossRefGoogle Scholar
Wittgenstein, L. (1972). Philosophical Investigations (Anscombe, G. E. M., Trans.; 3rd ed). Prentice Hall.Google Scholar
Wittgenstein, L. (1974). Philosophical Grammar: Part I, The Proposition, and Its Sense, Part II, on Logic and Mathematics. University of California Press.Google Scholar
Wittgenstein, L. (1976). Lectures on the Foundations of Mathematics, Cambridge 1939 (Diamond, C., Ed.). University of Chicago Press.Google Scholar
Wittgenstein, L. (1978). Remarks on the Foundations of Mathematics (G. H. von Wright, Trans.; revised ed). MIT Press.Google Scholar
Wright, C. (1992). Truth and Objectivity. Harvard University Press.CrossRefGoogle Scholar
Wynn, K. (1990). Children’s understanding of counting. Cognition, 36(2), 155193.CrossRefGoogle ScholarPubMed
Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358, 749751.CrossRefGoogle ScholarPubMed
Xu, F. & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74(1), B1B11. https://doi.org/10.1016/S0010–0277(99)00066-9.CrossRefGoogle Scholar
Xuan, B., Zhang, D., He, S. & Chen, X. (2007). Larger stimuli are judged to last longer. Journal of Vision, 7(10), 2. https://doi.org/10.1167/7.10.2.CrossRefGoogle ScholarPubMed
Yablo, S. (2002). Abstract objects: A case study. In Bottani, A., Carrara, M. & Giaretta, P. (Eds.), Individuals, Essence and Identity: Themes of Analytic Metaphysics (pp. 163188). Springer Netherlands. https://doi.org/10.1007/978-94-017-1866-0_7.CrossRefGoogle Scholar
Zach, R. (2019). Hilbert’s program. In Zalta, E. N. (Ed.), The Stanford Encyclopedia of Philosophy. Stanford University Press. https://plato.stanford.edu/entries/hilbert-program/.Google Scholar
Zahidi, K. (2021). Radicalizing numerical cognition. Synthese, 198(Suppl 1), 529545.CrossRefGoogle Scholar
Zahidi, K. & Myin, E. (2016). Radically enactive numerical cognition. In Etzelmüller, G. & Christian, C. (Eds.), Embodiment in Evolution and Culture (pp. 5772). Mohr Siebeck.Google Scholar
Zahidi, K. & Myin, E. (2018). Making sense of numbers without a number sense. In Bangu, S. (Ed.), Naturalizing Logico Mathematical Knowledge (pp. 218233). Routledge.CrossRefGoogle Scholar
Zebian, S. (2005). Linkages between number concepts, spatial thinking, and directionality of writing: The SNARC effect and the REVERSE SNARC effect in English and Arabic monoliterates, biliterates, and illiterate Arabic speakers. Journal of Cognition and Culture, 5, 165190. https://doi.org/10.1163/1568537054068660.CrossRefGoogle Scholar
Zhang, J., & Norman, D. A. (1994). Representations in distributed cognitive tasks. Cognitive Science, 18(1), 87122. https://doi.org/10.1207/s15516709cog1801_3.CrossRefGoogle Scholar

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  • Bibliography
  • Markus Pantsar, Aachen University of Technology
  • Book: Numerical Cognition and the Epistemology of Arithmetic
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