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References

Published online by Cambridge University Press:  10 December 2020

Catarina Dutilh Novaes
Affiliation:
Vrije Universiteit, Amsterdam
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The Dialogical Roots of Deduction
Historical, Cognitive, and Philosophical Perspectives on Reasoning
, pp. 238 - 260
Publisher: Cambridge University Press
Print publication year: 2020

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References

Aberdein, A. (2009). Mathematics and argumentation. Foundations of Science, 14, 18.Google Scholar
Aberdein, A., & Dove, I. (2013). The Argument of Mathematics. Dordrecht: Springer.Google Scholar
Achourioti, T., Fugard, A. J., & Stenning, K. (2014). The empirical study of norms is just what we are missing. Frontiers in Psychology, 5, 1159.Google Scholar
Adler, J. E. (1984). Abstraction is uncooperative. Journal for the Theory of Social Behaviour, 14, 165181.Google Scholar
Aigner, M., & Ziegler, G. (1999). Proofs from THE BOOK. Berlin: Springer.Google Scholar
Alderson-Day, B., & Fernyhough, C. (2015). Inner speech: Development, cognitive functions, phenomenology, and neurobiology. Psychological Bulletin, 141, 931965.Google Scholar
Alibert, D., & Thomas, M. (1991). Research on mathematical proof. In Tall, D. (ed.), Advanced Mathematical Thinking (pp. 215230). New York, NY: Kluwer.Google Scholar
Allen, C. (2006). Transitive inference in animals: Reasoning or conditioned associations? In Hurley, S. & Nudds, M. (eds.), Rational Animals? (pp. 175186). Oxford: Oxford University Press.Google Scholar
Andersen, L. E. (2018). Acceptable gaps in mathematical proofs. Synthese, 197, 233247.Google Scholar
Andersen, L. E. (2017). On the nature and role of peer review in mathematics. Accountability in Research, 24, 177192.Google Scholar
Andersen, L. E. (2017). Social Epistemology and Mathematical Practice: Dependence, Peer Review, and Joint Commitments. Ph.D. thesis, University of Aarhus.Google Scholar
Anderson, M. L. (2010). Neural reuse: A fundamental organizational principle of the brain. Behavioral and Brain Sciences, 33, 245313.Google Scholar
Andrade-Lotero, A., & Dutilh Novaes, C. (2012). Validity, the squeezing argument and alternative semantic systems. Journal of Philosophical Logic, 41, 387418.Google Scholar
Andrews, G. (2010). Belief-based and analytic processing in transitive inference depends on premise integration difficulty. Memory and Cognition, 38, 928940.Google Scholar
Andrews, K. (2015). The Animal Mind. London: Routledge.Google Scholar
Antonini, S., & Mariotti, M. A. (2008). Indirect proof: What is specific to this way of proving? ZDM – The International Journal on Mathematics Education, 40, 401412.Google Scholar
Aristotle, . (2009). Prior Analytics I (translated by G. Striker). Oxford: Clarendon Press.Google Scholar
Arora, A., Weiss, B., Schurz, M., Aichhorn, M., Wieshofer, R., & Perner, J. (2015). Left inferior-parietal lobe activity in perspective tasks: Identity statements. Frontiers in Human Neuroscience, 9, 360.Google Scholar
Aschbacher, M. (2004). The status of the classification of the finite simple groups. Notices of the American Mathematical Society, 51, 736740.Google Scholar
Ashworth, E. (2016). The post-medieval period. In Dutilh Novaes, C. & Read, S. (eds.), The Cambridge Companion to Medieval Logic (pp. 166191). Cambridge: Cambridge University Press.Google Scholar
Ashworth, E. (2011). The scope of logic: Soto and Fonseca on dialectic and informal arguments. In Cameron, M. & Marenbon, J. (eds.), Methods and Methodologies: Aristotelian Logic East and West, 500–1500 (pp. 127145). Leiden: Brill.Google Scholar
Atiyah, M. (2007). Commentary: Bourbaki, A Secret Society of Mathematicians and The Artist and the Mathematician – A book review. Notices of the AMS, 54, 11501152.Google Scholar
Atiyah, M. (1994). Responses to: A. Jaffe and F. Quinn, “Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics.Bulletin of the American Mathematical Society, 30, 178207.Google Scholar
Auslander, J. (2008). On the roles of proof in mathematics. In Gold, B. & Simons, R. (eds.), Proof and Other Dilemmas: Mathematics and Philosophy (pp. 6177). Washington, DC: Mathematical Association of America.Google Scholar
Awodey, S., & Reck, E. (2002). Completeness and categoricity. Part I: Nineteenth-century axiomatics to twentieth-century metalogic. History and Philosophy of Logic, 23, 130.Google Scholar
Azzouni, J. (2004). The derivation-indicator view of mathematical practice. Philosophia Mathematica, 12, 81106.Google Scholar
Bakhurst, D. (2007). Vygotsky’s demons. In Daniels, H., Cole, M., & Wertsch, J. (eds.), The Cambridge Companion to Vygotsky (pp. 5076). Cambridge: Cambridge University Press.Google Scholar
Balacheff, N. (1991). The benefits and limits of social interaction: The case of mathematical proof. In Bishop, A. (ed.), Mathematical Knowledge: Its Growth through Teaching (pp. 175192). Dordrecht: Kluwer.Google Scholar
Ball, L., & Thompson, V. (2018). Belief bias and reasoning. In Ball, L. & Thompson, V. (eds.), International Handbook of Thinking and Reasoning (pp. 1636). New York, NY: Routledge.Google Scholar
Barnes, J. (2008). Introduction: Logic and language. In Algra, K., Barnes, J., Mansveld, J., & Schofield, M. (eds.), The Cambridge History of Hellenistic Philosophy (pp. 6576). Cambridge: Cambridge University Press.Google Scholar
Barnes, J. (2007). Truth, Etc. Oxford: Oxford University Press.Google Scholar
Barnes, J. (1969). Aristotle’s theory of demonstration. Phronesis, 14, 123152.Google Scholar
Bazán, B., Wippel, J., Fransen, G., & Jacquart, D. (1985). Les questions disputées et les questions quodlibétiques dans les facultés de théologie, de droit et de médecine. Turnhout: Brepols.Google Scholar
Beall, J. (2007). Truth and paradox: A philosophical sketch. In Jacquette, D. (ed.), Philosophy of Logic (pp. 325410). Amsterdam: Elsevier.Google Scholar
Beall, J., & Restall, G. (2006). Logical Pluralism. Oxford: Oxford University Press.Google Scholar
Beatty, E. L., & Thompson, V. (2012). Effects of perspective and belief on analytic reasoning in a scientific reasoning task. Thinking & Reasoning, 18, 441460.CrossRefGoogle Scholar
Beiser, F. (2011). The German Historicist Tradition. Oxford: Oxford University Press.Google Scholar
Benson, H. (1995). The dissolution of the problem of the elenchus. Oxford Studies in Ancient Philosophy, 13, 45112.Google Scholar
Bermúdez, J. (2006). Animal reasoning and proto-logic. In Hurley, S. & Nudds, M. (eds.), Rational Animals? (pp. 127138). Oxford: Oxford University Press.Google Scholar
Betti, A., & van den Berg, H. (2014). Modelling the history of ideas. British Journal for the History of Philosophy, 22, 812835.CrossRefGoogle Scholar
Bex, F., & Verheij, B. (2013). Legal stories and the process of proof. Artificial Intelligence and Law, 21, 253278.Google Scholar
Bocheński, J. (1961). A History of Formal Logic. South Bend, IN: University of Notre Dame Press.Google Scholar
Boghossian, P. (2008). Content and Justification: Philosophical Papers. Oxford: Oxford University Press.Google Scholar
Bassler, O. B. (2006). The surveyability of mathematical proof: A historical perspective. Synthese, 148, 99133.CrossRefGoogle Scholar
Brandenburger, A., & Nalebuff, B. (1996). Co-Opetition: A Revolution Mindset that Combines Competition and Cooperation. New York, NY: Crown.Google Scholar
Brandom, R. (1994). Making It Explicit: Reasoning, Representing, and Discursive Commitment. Cambridge, MA: Harvard University Press.Google Scholar
Brown, P. (2015). How math’s most famous proof nearly broke. Nautilus, May 28, https://medium.com/nautilus-magazine/how-maths-most-famous-proof-nearly-broke-f05cef973cb1Google Scholar
Bueno, O., & Shalkowski, S. A. (2009). Modalism and logical pluralism. Mind, 118, 295321.Google Scholar
Buridan, J. (2001). Summulae de dialectica (translated by G. Klima). New Haven, CT: Yale University Press.Google Scholar
Burnyeat, M. F. (2000). Plato on why mathematics is good for the soul. In Smiley, T. (ed.), Mathematics and Necessity: Essays in the History of Philosophy (pp. 181). Oxford: Oxford University Press.Google Scholar
Buroker, J. (2014). Port-Royal logic. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/port-royal-logic/Google Scholar
Burris, S., & Legris, J. (2015). The algebra of logic tradition. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/algebra-logic-tradition/Google Scholar
Butchart, S., Handfield, T., & Restall, G. (2009). Using peer instruction to teach philosophy, logic and critical thinking. Teaching Philosophy, 32, 140.Google Scholar
Butterfill, S., & Apperly, I. (2013). How to construct a minimal theory of mind. Mind & Language, 28, 606637.Google Scholar
Byrne, R. (2018). Counterfactual reasoning and imagination. In Ball, L., & Thompson, V. (eds.), The Routledge International Handbook of Thinking and Reasoning (pp. 7187). New York, NY: Routledge.Google Scholar
Byrne, R. (1989). Suppressing valid inferences with conditionals. Cognition, 31, 6183.CrossRefGoogle ScholarPubMed
CadwalladerOlsker, T. (2011). What do we mean by mathematical proof? Journal of Humanistic Mathematics, 1, 3360.Google Scholar
Caret, C., & Hjortland, O. (2015). Logical consequence: Its nature, structure, and application. In Caret, C. & Hjortland, O. (eds.), Foundations of Logical Consequence (pp. 329). Oxford: Oxford University Press.Google Scholar
Carroll, L. (1895). What the Tortoise said to Achilles. Mind, 104, 691693.Google Scholar
Carter, J. (2019). Exploring the fruitfulness of diagrams in mathematics. Synthese, 196, 40114032.Google Scholar
Carus, A. (2008). Carnap and Twentieth-Century Thought: Explication as Enlightenment. Cambridge: Cambridge University Press.Google Scholar
Castagnoli, L. (2010). Ancient Self-Refutation: The Logic and History of the Self-Refutation Argument from Democritus to Augustine. Cambridge: Cambridge University Press.Google Scholar
Castelnérac, B. (2015). Impossibility in the Prior Analytics and Plato’s dialectic. History and Philosophy of Logic, 36, 303320.Google Scholar
Castelnérac, B., & Marion, M. (2013). Antilogic. The Baltic International Yearbook of Cognition, Logic and Communication, 8, 131.Google Scholar
Castelnérac, B., & Marion, M. (2009). Arguing for inconsistency: Dialectical games in the academy. In Primiero, G. (ed.), Acts of Knowledge: History, Philosophy and Logic (pp. 3776). London: College Publications.Google Scholar
Castelvecchi, D. (2020). Mathematical proof that rocked number theory will be published. Nature, 580, 177.Google Scholar
Castelvecchi, D. (2015). The impenetrable proof. Nature, 526, 178181.Google Scholar
Chang, K. (2004). In math, computers don’t lie. Or do they? New York Times, April 6, www.nytimes.com/2004/04/06/science/in-math-computers-don-t-lie-or-do-they.htmlGoogle Scholar
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. 274292). Cambridge: Cambridge University Press.Google Scholar
Chemla, K. (2012). The History of Mathematical Proof in Ancient Traditions. Cambridge: Cambridge University Press.Google Scholar
Chemla, K. (2012a). Reading proofs in Chinese commentaries: Algebraic proofs in an algorithmic context. In Chemla, K. (ed.), The History of Mathematical Proof in Ancient Traditions (pp. 423486). Cambridge: Cambridge University Press.Google Scholar
Clerbout, N., Gorisse, M., & Rahman, S. (2011). Context-sensitivity in Jain philosophy: A dialogical study of Siddharṣigaṇi’s Commentary on the Handbook of Logic. Journal of Philosophical Logic, 40, 633662.Google Scholar
Cohen, D. H. (2016). Argumentative virtues as conduits for reason’s causal efficacy: Why the practice of giving reasons requires that we practice hearing reasons. Topoi, 38, 711718.Google Scholar
Cohen, M. R., & Nagel, E. (1934). An Introduction to Logic and Scientific Method. London: Routledge and Kegan.Google Scholar
Cole, M., Gay, J., Glick, J. A., & Sharp, D. W. (1971). The Cultural Context of Learning and Thinking. New York, NY: Basic Books.Google Scholar
Cole, J. C. (2015). Social construction, mathematics, and the collective imposition of function onto reality. Erkenntnis, 80, 11011124.Google Scholar
Colyvan, M. (2010). There is no easy road to nominalism. Mind, 119, 285306.Google Scholar
Cooper, W. S. (2003). The Evolution of Reason: Logic as a Branch of Biology. Cambridge: Cambridge University Press.Google Scholar
Corcoran, J. (2003). Aristotle’s Prior Analytics and Boole’s Laws of Thought. History and Philosophy of Logic, 24, 261288.Google Scholar
Corneli, J., Martin, U., Murray-Rust, D., & Pease, A. (2017). Towards mathematical AI via a model of the content and process of mathematical question and answer dialogues. In Geuvers, H., England, M., Hasan, O., Rabe, F., & Teschke, O. (eds.), CICM 2017: Intelligent Computer Mathematics (pp. 132146). New York, NY: Springer.Google Scholar
Counihan, M. (2008). Looking for Logic in All the Wrong Places: An Investigation of Language, Literacy and Logic in Reasoning. Ph.D. dissertation, ILLC-University of Amsterdam.Google Scholar
D’Agostino, M., & Floridi, L. (2009). The enduring scandal of deduction. Synthese, 167, 271315.Google Scholar
Dawson, Jr, J. W. (2006). Why do mathematicians re-prove theorems? Philosophia Mathematica, 14, 269286.Google Scholar
De Jong, W., & Betti, A. (2010). The classical model of science: A millennia-old model of scientific rationality. Synthese, 174, 185203.Google Scholar
De Neys, W. (2014). Conflict detection, dual processes, and logical intuitions: Some clarifications. Thinking & Reasoning, 20, 169187.CrossRefGoogle Scholar
De Strycker, E. (1932). Le syllogisme chez Platon (suite et fin). Revue néo-scolastique de philosophie, 34, 218239.Google Scholar
De Villiers, M. D. (1999). Rethinking Proof with the Geometer’s Sketch-Pad. Emeryville, CA: Key Curriculum Press.Google Scholar
Dehaene, S. (2009). Reading in the Brain: The Science and Evolution of a Human Invention. New York, NY: Viking.Google Scholar
Descartes, R. (1988). Rules for the direction of our native intelligence. In Selected Philosophical Writings (pp. 119). Cambridge: Cambridge University Press.Google Scholar
Descartes, R. (1985). Principles of philosophy. In The Philosophical Writings of Descartes, Vol. 1 (pp. 177292). Cambridge: Cambridge University Press.Google Scholar
Detlefsen, M. (2008). Proof: Its nature and significance. In Gold, B. & Simons, R. (eds.), Proof and Other Dilemmas: Mathematics and Philosophy (pp. 332). Washington, DC: Mathematical Association of America.Google Scholar
Devlin, K. (2003). When is a proof? Devlin’s Angle, Mathematical Association of America, www.maa.org/external_archive/devlin/devlin_06_03.htmlGoogle Scholar
Dias, M., & Harris, P. (1990). The influence of the imagination on reasoning by young children. British Journal of Developmental Psychology, 8, 305318.Google Scholar
Dias, M., & Harris, P. (1988). The effect of make-believe play on deductive reasoning. British Journal of Developmental Psychology, 6, 207221.Google Scholar
Dias, M., Roazzi, A., & Harris, P. L. (2005). Reasoning from unfamiliar premises: A study with unschooled adults. Psychological Science, 16, 550554.Google Scholar
Dod, B. (1982). Aristoteles Latinus. In Kretzmann, N., Kenny, A., & Pinborg, J. (eds.), The Cambridge History of Later Medieval Philosophy (pp. 4579). Cambridge: Cambridge University Press.Google Scholar
Dogramaci, S. (2015). Communist conventions for deductive reasoning. Nous, 49, 776799.Google Scholar
Douven, I. (2011). Abduction. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/abduction/Google Scholar
Dufour, M. (2013). Arguing around mathematical proofs. In Aberdein, A. & Dove, I. J. (eds.), The Argument of Mathematics (pp. 6176). Dordrecht: Springer.Google Scholar
Dummett, M. (1978). The justification of deduction. In Truth and Other Enigmas (pp. 290318). Cambridge, MA: Harvard University Press.Google Scholar
Duncombe, M. (2016). Thought as internal speech in Plato and Aristotle. Logical Analysis and History of Philosophy, 19, 105125.Google Scholar
Duncombe, M. (2014). Irreflexivity and Aristotle’s syllogismos. Philosophical Quarterly, 64, 434452.Google Scholar
Duncombe, M., & Dutilh Novaes, C. (2016). Dialectic and logic in Aristotle and his tradition. History and Philosophy of Logic, 37, 18.Google Scholar
Dutilh Novaes, C. (2019). The beauty (?) of mathematical proofs. In Aberdein, A. & Inglis, M. (eds.), Advances in Experimental Philosophy of Logic and Mathematics (pp. 6393). London: Bloomsbury Academic.Google Scholar
Dutilh Novaes, C. (2018a). A dialogical conception of explanation in mathematical proofs. In Ernest, P. (ed.), The Philosophy of Mathematics Education Today (pp. 8198). Cham: Springer.Google Scholar
Dutilh Novaes, C. (2018b). The enduring enigma of reasoning. Mind & Language, 33, 513524.Google Scholar
Dutilh Novaes, C. (2017a). The syllogism as defined by Aristotle, Ockham, and Buridan. In Pelletier, J. & Roques, M. (eds.), The Language of Thought in Late Medieval Philosophy (pp. 217231). Berlin: Springer.Google Scholar
Dutilh Novaes, C. (2017b). What is logic? Aeon, January 12, https://aeon.co/essays/the-rise-and-fall-and-rise-of-logicGoogle Scholar
Dutilh Novaes, C. (2016a). Medieval theories of consequence. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/consequence-medieval/Google Scholar
Dutilh Novaes, C. (2016b). Reductio ad absurdum from a dialogical perspective. Philosophical Studies, 173, 26052628.Google Scholar
Dutilh Novaes, C. (2015a). A dialogical, multi‐agent account of the normativity of logic. Dialectica 69, 587609.Google Scholar
Dutilh Novaes, C. (2015b). Conceptual genealogy for analytic philosophy. In Bell, J., Cutrofello, A., & Livingston, P. (eds.), Beyond the Analytic–Continental Divide: Pluralist Philosophy in the Twenty-First Century. London: Routledge.Google Scholar
Dutilh Novaes, C. (2015c). The formal and the formalized: The cases of syllogistic and supposition theory. Kriterion, 131, 253270.Google Scholar
Dutilh Novaes, C. (2013a). The Ockham–Burley dispute. In Conti, A. (ed.), A Companion to Walter Burley (pp. 4986). Leiden: Brill.Google Scholar
Dutilh Novaes, C. (2013b). A dialogical account of deductive reasoning as a case study for how culture shapes cognition. Journal of Cognition and Culture, 13, 459482.Google Scholar
Dutilh Novaes, C. (2012a). Formal Languages in Logic: A Philosophical and Cognitive Analysis. Cambridge: Cambridge University Press.Google Scholar
Dutilh Novaes, C. (2012b). Reassessing logical hylomorphism and the demarcation of logical constants. Synthese, 185, 387410.Google Scholar
Dutilh Novaes, C. (2012c). Form and matter in later Latin medieval logic: The cases of suppositio and consequentia. Journal of the History of Philosophy, 50, 339364.Google Scholar
Dutilh Novaes, C., & French, R. (2018). Paradoxes and structural rules from a dialogical perspective. Philosophical Issues, 28, 29158.Google Scholar
Dutilh Novaes, C., & Read, S. (2016). The Cambridge Companion to Medieval Logic. Cambridge: Cambridge University Press.Google Scholar
Dutilh Novaes, C., & Veluwenkamp, H. (2017). Reasoning biases, non-monotonic logics, and belief revision. Theoria, 83, 2952.Google Scholar
Easwaran, K. (2015). Rebutting and undercutting in mathematics. Philosophical Perspectives, 29, 146162.Google Scholar
Easwaran, K. (2009). Probabilistic proofs and transferability. Philosophia Mathematica, 17, 341362.Google Scholar
Egan, K. (1997). The Educated Mind. Chicago, IL: University of Chicago Press.Google Scholar
Einarson, B. (1936). On certain mathematical terms in Aristotle’s logic: Part I. American Journal of Philology, 57, 3354.Google Scholar
Elio, R. (2002). Common Sense, Reasoning, and Rationality. Oxford: Oxford University Press.Google Scholar
Elqayam, S. (2018). The new paradigm in psychology of reasoning. In Ball, L. & Thompson, V. (eds.), The Routledge International Handbook of Thinking and Reasoning (pp. 130150). New York, NY: Routledge.Google Scholar
El-Rouayheb, K. (2016). Arabic logic after Avicenna. In Dutilh Novaes, C. & Read, S. (eds.), The Cambridge Companion to Medieval Logic (pp. 6793). Cambridge: Cambridge University Press.Google Scholar
Empiricus, Sextus (1966). Outlines of Pyrrhonism. In Saunders, J. (ed.), Greek and Roman Philosophy after Aristotle (pp. 152182). New York, NY: The Free Press.Google Scholar
Erdőhegyi, Á., Topál, J., Vrányi, Z., & Miklósi, Á. (2007). Dog-logic: Inferential reasoning in a two-way choice task and its restricted use. Animal Behavior, 74, 725737.Google Scholar
Ernest, P. (1997). Social Constructivism as a Philosophy of Mathematics. New York, NY: State University of New York Press.Google Scholar
Ernest, P. (1994). The dialogical nature of mathematics. In Mathematics, Education and Philosophy: An International Perspective (pp. 3348). London: Falmer Press.Google Scholar
Etchemendy, J. (1990). The Concept of Logical Consequence. Cambridge, MA: Harvard University Press.Google Scholar
Etchemendy, J. (1983). The doctrine of logic as form. Linguistics and Philosophy, 6, 319–34.Google Scholar
Evans, J. S. (2016). Belief bias in deductive reasoning. In Pohl, R. F. (ed.), Cognitive Illusions: Intriguing Phenomena in Judgement, Thinking and Memory, 2nd edn. (pp. 165184). London: Routledge.Google Scholar
Evans, J. S. (2002). Logic and human reasoning: An assessment of the deduction paradigm. Psychological Bulletin, 128, 978996.Google Scholar
Evans, J. S. (1989). Bias in Human Reasoning: Causes and Consequences. Hillsdale, NJ: Erlbaum.Google Scholar
Evans, J. S., & Curtis-Holmes, J. (2005). Rapid responding increases belief bias: Evidence for the dual-process theory of reasoning. Thinking & Reasoning, 11, 382389.Google Scholar
Evans, J. S., & Stanovich, K. E. (2013). Dual-process theories of higher cognition: Advancing the debate. Perspectives on Psychological Science, 8, 223241.Google Scholar
Evans, J. S., Barston, J. L., & Pollard, P. (1983). On the conflict between logic and belief in syllogistic reasoning. Memory & Cognition, 11, 295306.Google Scholar
Evans, J. S., Handley, S. J., & Harper, C. N. (2001). Necessity, possibility and belief: A study of syllogistic reasoning. Quarterly Journal of Experimental Psychology, 54, 935958.Google Scholar
Evans, J. S., Handley, S. J., Harper, C. N., & Johnson-Laird, P. (1999). Reasoning about necessity and possibility: A test of the mental model theory of deduction. Journal of Experimental Psychology: Learning, Memory, & Cognition, 25, 14951513.Google Scholar
Evans, J. S., Newstead, S., Allen, J., & Pollard, P. (1994). Debiasing by instruction: The case of belief-bias. European Journal of Cognitive Psychology, 6, 263285.Google Scholar
Fabry, R. (2018). Enculturation and narrative practices. Phenomenology and the Cognitive Sciences, 17, 911937.Google Scholar
Fallis, D. (2003). Intentional gaps in mathematical proofs. Synthese, 134, 4569.Google Scholar
Fallis, D. (2002). What do mathematicians want? Probabilistic proofs and the epistemic goals of mathematicians. Logique et analyse, 45, 116.Google Scholar
Fallis, D. (1997). The epistemic status of probabilistic proof. The Journal of Philosophy, 94, 165186.Google Scholar
Fantl, J., & McGrath, M. (2009). Knowledge in an Uncertain World. Oxford: Oxford University Press.Google Scholar
Field, H. (2008). Saving Truth from Paradox. Oxford: Oxford University Press.Google Scholar
Fink, J. (2012). Introduction. In The Development of Dialectic from Plato to Aristotle (pp. 123). Cambridge: Cambridge University Press.Google Scholar
Fisher, M. A. (1989). Phases and phase diagrams: Gibbs’ legacy today. In Mostow, G. & Caldi, D. (eds.), Proceedings of the Gibbs Symposium: Yale University, May 15–17. Providence, RI: American Mathematical Society.Google Scholar
Fjellstad, A. (2016). Naive modus ponens and failure of transitivity. Journal of Philosophical Logic, 45, 6572.Google Scholar
Frankish, K. (2010). Dual-process and dual-system theories of reasoning. Philosophy Compass, 5, 914926.Google Scholar
Frans, J., & Kosolosky, L. (2014). Revisiting the reliability of published mathematical proofs: Where do we go next? Theoria, 29, 345–60.Google Scholar
Fraser, C. (2018). Mohist canons. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/mohist-canons/Google Scholar
Fraser, C. (2015). School of names. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/school-names/Google Scholar
Fraser, C. (2013). Distinctions, judgment, and reasoning in Classical Chinese thought. History and Philosophy of Logic, 34, 124.Google Scholar
Frederick, S. (2005). Cognitive reflection and decision making. Journal of Economic Perspectives, 19, 2542.Google Scholar
Frege, G. (1967). Basic Laws of Arithmetic. Berkeley, CA: University of California Press.Google Scholar
Frege, G. (1967). Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought. In van Heijenoort, J. (ed.), From Frege to Gödel: A Source Book in Mathematical Logic (pp. 182). Cambridge, MA: Harvard University Press.Google Scholar
French, R. (2019). A dialogical route to logical pluralism. Synthese, 2019, 121.Google Scholar
French, R. (2015). Prover–Skeptic games and logical pluralism. In Brochhagen, T., Roelofsen, F., & Theiler, N. (eds.), Proceedings of the 20th Amsterdam Colloquium (pp. 128136). Amsterdam: ILLC.Google Scholar
Ganeri, J. (2003). Ancient Indian logic as a theory of case-based reasoning. Journal of Indian Philosophy, 31, 3345.Google Scholar
Ganeri, J. (2001). Introduction: Indian Logic and the Colonization of Reason. In Ganeri, J. (ed.), Indian Logic: A Reader (pp. 125). London: Routledge.Google Scholar
Garfield, J. L. (1990). The dog: Relevance and rationality. In Dunn, J. & Gupta, A. (eds.), Truth or Consequences: Essays in Honour of Nuel Belnap (pp. 97109). Dordrecht: Kluwer Academic Publishers.Google Scholar
Geist, C., Löwe, B., & van Kerkhove, B. (2010). Peer review and knowledge by testimony in mathematics. In Löwe, B., & Müller, T. (eds.), PhiMSAMP. Philosophy of Mathematics: Sociological Aspects and Mathematical Practice (pp. 155178). London: College Publications.Google Scholar
Gentzen, G. (1969). Investigations into logical deduction. In The Collected Papers of Gerhard Gentzen (pp. 68131). Amsterdam: North-Holland.Google Scholar
Geuss, R. (1994). Nietzsche and genealogy. European Journal of Philosophy, 2, 274292.Google Scholar
Gigerenzer, G. (1996). On narrow norms and vague heuristics: A reply to Kahneman and Tversky. Psychological Review, 103, 592596.Google Scholar
Gillon, B. (2016). Indian logic. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/logic-india/Google Scholar
Gilmore, C., Gobel, S., & Inglis, M. (2018). An Introduction to Mathematical Cognition. New York, NY: Routledge.Google Scholar
Ginzburg, J. (2016). The semantics of dialogue. In Aloni, M. & Dekker, P. (eds.), The Cambridge Handbook of Formal Semantics (pp. 130172). Cambridge: Cambridge University Press.Google Scholar
Glivický, P., & Kala, V. (2017). Fermat’s last theorem and Catalan’s conjecture in weak exponential arithmetics. Mathematical Logic Quarterly, 63, 162174.Google Scholar
Goel, V. (2007). Anatomy of deductive reasoning. Trends in Cognitive Science, 11, 435441.Google Scholar
Goel, V., & Waechter, R. (2018). Inductive and deductive reasoning Integrating insights from philosophy, psychology, and neuroscience. In Ball, L. & Thompson, V. (eds.), The Routledge International Handbook of Thinking and Reasoning. London: Routledge.Google Scholar
Goldfeld, D. (1996). Beyond the last theorem. Math Horizons, 4, 2634.Google Scholar
Goldwasser, S., Micali, S., & Rackoff, C. (1989). The knowledge complexity of interactive proof systems. SIAM Journal on Computing, 18, 186208.Google Scholar
Gould, S. J. (1977). Ontogeny and Phylogeny. Cambridge, MA: Harvard University Press.Google Scholar
Gowers, T., & Nielsen, M. (2009). Massively collaborative mathematics. Nature, 461, 879881.Google Scholar
Greiffenhagen, C. (2008). Video analysis of mathematical practice? Different attempts to ‘open up’ mathematics for sociological investigation. Forum: Qualitative Social Research, 9, 32.Google Scholar
Grimm, S., Baumberger, C., & Ammon, S. (2017). Explaining Understanding: New Perspectives from Epistemology and Philosophy of Science. London: Routledge.Google Scholar
Haberler, Z., Laursen, S. L., & Hayward, C. N. (2018). What’s in a name? Framing struggles of a mathematics education reform community. International Journal of Research in Undergraduate Mathematics Education, 4, 415441.Google Scholar
Hahn, U., & Oaksford, M. (2008). A normative theory of argument strength. Informal Logic, 26, 124.Google Scholar
Halmos, P. R. (1985). I Want to Be A Mathematician: An Automathography. New York, NY: Springer.Google Scholar
Halmos, P. R. (1970). How to write mathematics. L’enseignement mathématique, 16, 123152.Google Scholar
Hanna, G., Jahnke, H. N., & Pulte, H. (2010). Explanation and Proof in Mathematics: Philosophical and Educational Perspectives. Berlin: Springer.Google Scholar
Hansen, M. (1991). The Athenian Democracy in the Age of Demosthenes. Oxford: Blackwell.Google Scholar
Harman, G. (2009). Field on the normative role of logic. Proceedings of the Aristotelian Society, 109, 333335.Google Scholar
Harman, G. (1986). Change in View. Cambridge, MA: MIT Press.Google Scholar
Harris, P. L. (2000). The Work of the Imagination. London: Wiley-Blackwell.Google Scholar
Hasnawi, A., & Hodges, W. (2016). Arabic logic up to Avicenna. In Dutilh Novaes, C. & Read, S. (eds.), The Cambridge Companion to Medieval Logic (pp. 4566). Cambridge: Cambridge University Press.Google Scholar
Hasse, D. (2014). Influence of Arabic and Islamic philosophy on the Latin West. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/arabic-islamic-influence/Google Scholar
Hatfield, G. (1997). The workings of the intellect: Mind and psychology. In Easton, P. (ed.), Logic and the Workings of the Mind: The Logic of Ideas and Faculty Psychology in Early Modern Philosophy (pp. 2145). Atascadero, CA: Ridgeview Publishing.Google Scholar
Heath, T. (1908). The Thirteen Books of Euclid’s Elements. Cambridge: Cambridge University Press.Google Scholar
Hegel, G. (1991). Elements of the Philosophy of Right. Cambridge: Cambridge University Press.Google Scholar
Heinzmann, G. (2006). Naturalizing dialogic pragmatics. In van Benthem, J., Heinzmann, G., Rebushi, M., & Visser, H. (eds.), The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today (pp. 285–279). Berlin: Springer.Google Scholar
Hempel, C., & Oppenheim, P. (1948). Studies in the logic of explanation. Philosophy of Science, 15, 135175.Google Scholar
Henkin, L. (1961). Some remarks on infinitely long formulas. In International Mathematical Union (ed.), Infinitistic Methods (Proceedings of the Symposium on Foundations of Mathematics, Warsaw, 2–9 September 1959) (pp. 167183). Oxford: Pergamon.Google Scholar
Henrich, J. (2015). The Secret of our Success. Princeton, NJ: Princeton University Press.Google Scholar
Henrich, J., Heine, S. J., & Norenzayan, A. (2010). The weirdest people in the world? Behavioral and Brain Sciences, 33, 6183.Google Scholar
Hersh, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics, 24, 389399.Google Scholar
Heyes, C. (2019). Précis of Cognitive Gadgets: The Cultural Evolution of Thinking. Behavioral and Brain Sciences, 42, e169.Google Scholar
Heyes, C. (2018). Cognitive Gadgets: The Cultural Evolution of Thinking. Cambridge, MA: Harvard University Press.Google Scholar
Hilton, D. J. (1995). The social context of reasoning: Conversational inference and rational judgment. Psychological Bulletin, 118, 248271.Google Scholar
Hintikka, J. (1996). The Principles of Mathematics Revisited. Cambridge: Cambridge University Press.Google Scholar
Hintikka, J. (1995). Commentary on Allen. Proceedings of the Boston Area Colloquium of Ancient Philosophy, 11, 206215.Google Scholar
Hintikka, J. (1973). Logic, Language-Games and Information: Kantian Themes in the Philosophy of Logic. Oxford: Clarendon Press.Google Scholar
Hintikka, J., & Sandu, G. (1997). Game-theoretical semantics. In van Benthem, J., & ter Meulen, A. (eds.), Handbook of Logic and Language (pp. 361410). Amsterdam: Elsevier.Google Scholar
Hmelo-Silver, C. E., Duncan, R. G., & Chinn, C. A. (2007). Scaffolding and achievement in problem-based and inquiry learning: A response to Kirschner, Sweller, and Clark (2006). Educational Psychologist, 42, 99107.Google Scholar
Hodds, M., Alcock, L., & Inglis, M. (2014). Self-explanation training improves proof comprehension. Journal for Research in Mathematics Education, 45, 62101.Google Scholar
Hodges, W. (2018). Proofs as cognitive or computational: Ibn Sīnā’s innovations. Philosophy and Technology, 31, 131153.Google Scholar
Hodges, W. (2017). Ibn Sina on reduction ad absurdum. Review of Symbolic Logic, 10, 583601.Google Scholar
Hodges, W. (2013). Logic and games. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/logic-games/Google Scholar
Hodges, W. (2009). Traditional logic, modern logic and natural language. Journal of Philosophical Logic, 38, 589.Google Scholar
Hodges, W. (2001). Dialogue foundations: A sceptical look. Proceedings of the Aristotelian Society, Supp. Vol. 75, 1732.Google Scholar
Hodges, W. (1998). An editor recalls some hopeless papers. Bulletin of Symbolic Logic, 4, 116.Google Scholar
Horgan, J. (1993). The death of proof? Scientific American, 269, 93103.Google Scholar
Horgan, J., Aaronson, S., Woit, P., & Dahlke, K. (2020). OK, maybe proofs aren’t dying after all. Scientific American blog, March 7, https://blogs.scientificamerican.com/cross-check/okay-maybe-proofs-arent-dying-after-all/Google Scholar
Hundleby, C. (forthcoming). Feminist perspectives on argumentation. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy.Google Scholar
Hutchins, E. (2011). Enculturating the supersized mind. Philosophical Studies, 152, 437446.Google Scholar
Hutchins, E. (1980). Culture and Inference: A Trobriand Case Study. Cambridge, MA: Harvard University Press.Google Scholar
Inglis, M. (2018). The negative view of proof. Wiki Mathematics Education, https://maths4maryams.org/mathed/wp-content/uploads/2018/09/WikiLetter-6.pdfGoogle Scholar
Inglis, M., & Mejía-Ramos, J. (2019). Functional explanation in mathematics. Synthese, 2019, 124.Google Scholar
Irani, T. (2017). Plato on the Value of Philosophy. Cambridge: Cambridge University Press.Google Scholar
Jaffe, A., & Quinn, F. (1993). Theoretical mathematics: Towards a cultural synthesis of mathematics and theoretical physics. Bulletin of the American Mathematical Society, 29, 113.Google Scholar
Jago, M. (2013). The content of deduction. Journal of Philosophical Logic, 42, 317334.Google Scholar
Jaskowski, S. (1967). On the rules of supposition in formal logic. In McCall, S. (ed.), Polish Logic 1920–1939 (pp. 232258). Oxford: Oxford University Press.Google Scholar
Johnson-Laird, P. (2008). Mental models and deductive reasoning. In Rips, L. (ed.), Reasoning: Studies in Human Inference and Its Foundations (pp. 206222). Cambridge: Cambridge University Press.Google Scholar
John-Steiner, V. (2007). Vygotsky on thinking and speaking. In Daniels, H., Cole, M., & Wertsch, J. (eds.), The Cambridge Companion to Vygotsky (pp. 136152). Cambridge: Cambridge University press.Google Scholar
Jones, F. (1977). The Moore method. The American Mathematical Monthly, 84, 273278.Google Scholar
Kant, I. (1998). Critique of Pure Reason (edited by Guyer, P. & Wood, A.). Cambridge: Cambridge University Press.Google Scholar
Kapp, E. (1975). Syllogistic. In Barnes, J., Schofield, M., & Sorabji, R. (eds.), Articles on Aristotle (pp. 135). London: Duckworth.Google Scholar
Keefe, R. (2014). What logical pluralism cannot be. Synthese, 191, 13751390.Google Scholar
Keiff, L. (2009). Dialogical logic. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/logic-dialogical/Google Scholar
Khalifa, K. (2010). Social constructivism and the aims of science. Social Epistemology, 24, 4561.Google Scholar
Kirschner, P., Sweller, J., & Clark, R. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41, 7586.Google Scholar
Kitcher, P. (2001). Science, Truth, and Democracy. Oxford: Oxford University Press.Google Scholar
Klarreich, E. (2018). Titans of mathematics clash over epic proof of ABC conjecture. Quanta, September 20, www.quantamagazine.org/titans-of-mathematics-clash-over-epic-proof-of-abc-conjecture-20180920/Google Scholar
Klement, K. (2002). When is genetic reasoning not fallacious? Argumentation, 16, 383400.Google Scholar
Klima, G. (2006). Syncategoremata. In Brown, K. (ed.), Encyclopedia of Language and Linguistics, Vol. xii (pp. 353356). Oxford: Elsevier.Google Scholar
Knorr, W. (1989). The Philonian method of cube duplication. In Knorr, W. (ed.), Textual Studies in Ancient and Medieval Geometry (pp. 4161). Boston, MA: Birkhäuser.Google Scholar
Koetsier, T. (1991). The Philosophy of Mathematics of Imre Lakatos, a Historical Approach. Amsterdam: Elsevier.Google Scholar
Kogan, M., & Laursen, S. L. (2014). Assessing long-term effects of inquiry-based learning: A case study from college mathematics. Innovative Higher Education, 39, 183199.Google Scholar
Kolata, G. (1986). Prime tests and keeping proofs secret. Science, 233, 938939.Google Scholar
Koons, R. (2013). Defeasible reasoning. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/reasoning-defeasible/Google Scholar
Koriat, A. (2012). When are two heads better than one and why? Science, 336, 360362.Google Scholar
Kouri Kissel, T., & Shapiro, S. (2020). Logical pluralism and normativity. Inquiry: An Interdisciplinary Journal of Philosophy, 63, 389410.Google Scholar
Krabbe, E. (2008). Strategic maneuvering in mathematical proofs. Argumentation 22, 453468.Google Scholar
Krabbe, E. (2006). Dialogue logic. In Gabbay, D. & Woods, J. (eds.), Handbook of History of Logic. Volume 7 (pp. 665704). Amsterdam: Elsevier.Google Scholar
Krabbe, E. (2001). Dialogue logic revisited. Proceedings of the Aristotelian Society, Supp. Vol. 75, 3349.Google Scholar
Krämer, S. (2003). Writing, notational iconicity, calculus: On writing as a cultural technique. Modern Languages Notes (German Issue), 118, 518537.Google Scholar
Kranz, S. (2011). The Proof Is in the Pudding: The Changing Nature of Mathematical Proof. New York, NY: Springer.Google Scholar
Kuhn, D., & Crowell, A. (2011). Dialogic argumentation as a vehicle for developing young adolescents’ thinking. Psychological Science, 22, 545552.Google Scholar
Lakatos, I. (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge: Cambridge University Press.Google Scholar
Lakoff, G., & Nunez, R. (2000). Where Mathematics Comes From. New York, NY: Basic Books.Google Scholar
Larvor, B. (2001). What is dialectical philosophy of mathematics? Philosophia Mathematica, 9, 212229.Google Scholar
Latour, B., & Woolgar, S. (1986). Laboratory Life: The Construction of Scientific Facts. Princeton, NJ: Princeton University Press.Google Scholar
Laughlin, P. R. (2011). Group Problem Solving. Princeton, NJ: Princeton University Press.Google Scholar
Lazareva, O. (2012). Transitive inference in nonhuman animals. In Wasserman, E. & Zentall, T. (eds.), The Oxford Handbook of Comparative Cognition (pp. 718735). Oxford: Oxford University Press.Google Scholar
Leron, U. (1985). A direct approach to indirect proofs. Educational Studies in Mathematics, 16, 321325.Google Scholar
Lesher, J. (2002). Parmenidean elenchos. In Scott, G. (ed.), Does Socrates Have a Method? (pp. 1935). University Park, PA: Pennsylvania State University Press.Google Scholar
Levesque, H. J. (1986). Making believers out of computers. Artificial Intelligence, 30, 81108.Google Scholar
Lewens, T. (2009). Seven types of adaptationism. Biology and Philosophy, 24, 161182.Google Scholar
Lewis, D. (1979). Scorekeeping in a language game. Journal of Philosophical Logic, 8, 339359.Google Scholar
Liberman, K. (2007). Dialectical Practice in Tibetan Philosophical Culture: An Ethnomethodological Inquiry into Formal Reasoning. London: Rowman & Littlefield.Google Scholar
Lloyd, G. (2013). Reasoning and culture in a historical perspective. Journal of Cognition and Culture, 13, 437457.Google Scholar
Lloyd, G. (2012). The plurality of Greek ‘mathematics.’ In Chemla, K. (ed.), The History of Mathematical Proof in Ancient Traditions (pp. 294310). Cambridge: Cambridge University Press.Google Scholar
Lloyd, G. (1996). Adversaries and Authorities: Investigations Into Ancient Greek and Chinese Science. Cambridge: Cambridge University Press.Google Scholar
Lloyd, G. (1996). Science in Antiquity: The Greek and Chinese cases and their relevance to the problem of culture and cognition. In Olson, D. & Torrance, N. (eds.), Modes of Thought: Explorations in Culture and Cognition (pp. 1533). Cambridge: Cambridge University Press.Google Scholar
Lloyd, G. (1990). Demystifying Mentalities. Cambridge: Cambridge University Press.Google Scholar
Lorenzen, P. (1960). Logik und agon. International Congress of Philosophy (ed.), Atti del XII Congresso Internazionale di Filosofia, 4 (pp. 187194). Florence: Sansoni Editore.Google Scholar
Lorenzen, P., & Lorenz, K. (1978). Dialogische Logik. Darmstadt: Wissenschafstliche Buchgesellschaft.Google Scholar
Luria, A. R. (1976). Cognitive Development: Its Social and Cultural Foundations. Cambridge, MA: Harvard University Press.Google Scholar
Macbeth, D. (2012). Diagrammatic reasoning in Frege’s Begriffsschrift. Synthese, 186, 289314.Google Scholar
MacFarlane, J. (2004). In what sense (if any) is logic normative for thought? Draft of presentation at Central Division APA 2004, http://johnmacfarlane.net/normativity_of_logic.pdfGoogle Scholar
MacFarlane, J. (2000). What Does It Mean To Say That Logic Is Formal? Ph.D. dissertation, University of Pittsburgh.Google Scholar
MacKenzie, D. (2001). Mechanizing Proof; Computing, Risk, and Trust. Cambridge, MA: MIT Press.Google Scholar
MacKenzie, D. (1999). Slaying the Kraken: The sociohistory of a mathematical proof. Social Studies of Science, 29, 760.Google Scholar
MacKenzie, J. (1989). Reasoning and logic. Synthese, 79, 99117.Google Scholar
Maddy, P. (2002). A naturalistic look at logic. Proceedings and Addresses of the American Philosophical Association, 76, 6190.Google Scholar
Malink, M. (2015). The beginnings of formal logic: Deduction in Aristotle’s Topics vs. Prior Analytics. Phronesis, 60, 267309.Google Scholar
Malink, M. (2014). Deduction in Sophistici Elenchi 6. In Lee, M. (ed.), Strategies of Argument: Essays in Ancient Ethics, Epistemology, and Logic (pp. 149174). Oxford: Oxford University Press.Google Scholar
Mancosu, P. (2011). Explanation in mathematics. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/mathematics-explanation/Google Scholar
Mancosu, P. (2010). Between Vienna and Berlin: The immediate reception of Gödel’s incompleteness theorems. History and Philosophy of Logic, 20, 3345.Google Scholar
Mancosu, P. (2008). The Philosophy of Mathematical Practice. Oxford: Oxford University Press.Google Scholar
Mancosu, P., & Pincock, C. (2012). Mathematical Explanation. Oxford Bibliographies.Oxford: Oxford University Press.Google Scholar
Marion, M. (2011). Wittgenstein on surveyability of proofs. In McGinn, M. & Kuusela, O. (eds.), The Oxford Handbook of Wittgenstein (pp. 138161). Oxford: Oxford University Press.Google Scholar
Marion, M. (2009). Why play logical games? In Majer, O., Pietarinen, A., & Tulenheimo, T. (eds.), Games: Unifying Logic, Language, and Philosophy (pp. 326). Berlin: Springer.Google Scholar
Marion, M. (2006). Hintikka on Wittgenstein: From language-games to game semantics. Acta Philosophica Fennica, 78, 255274.Google Scholar
Marion, M., & Rückert, H. (2016). Aristotle on universal quantification: A study from the point of view of game semantics. History and Philosophy of Logic, 37, 201229.Google Scholar
Markovits, H., & Nantel, G. (1989). The belief-bias effect in the production and evaluation of logical conclusions. Memory and Cognition, 17, 1117.Google Scholar
Markovits, H., Venet, M., Janveau-Brennan, G., Malfait, N., Pion, N., & Vadeboncoeur, I. (1996). Reasoning in young children: Fantasy and information retrieval. Child Development, 67, 28572872.Google Scholar
Martin, U., & Pease, A. (2013). Mathematical practice, crowdsourcing, and social machines. In Carette, J., Aspinall, D., Lange, C., Sojka, P., & Windsteiger, W. (eds.), CICM 2013: Intelligent Computer Mathematics (pp. 98119). New York, NY: Springer.Google Scholar
Matilal, B. (1998). The Character of Logic in India. Albany, NY: State University of New York Press.Google Scholar
Matzke, D., Nieuwenhuis, S., van Rijn, H., Slagter, H. A., van der Molen, M. W., & Wagenmakers, E.-J. (2015). The effect of horizontal eye movements on free recall: A preregistered adversarial collaboration. Journal of Experimental Psychology: General, 144, e1e15.Google Scholar
Mazur, E. (1997). Peer Instruction: A User’s Manual. Upper Saddle River, NJ: Prentice Hall.Google Scholar
Mellers, B., Hertwig, R., & Kahneman, D. (2001). Do frequency representations eliminate conjunction effects? An exercise in adversarial collaboration. Psychological Science, 12, 269275.Google Scholar
Menary, R. (2007). Writing as thinking. Language Sciences, 29, 621632.Google Scholar
Menary, M., & Gillett, A. (2017). Embodying culture. In Kiverstein, J. (ed.), The Routledge Handbook of Philosophy of the Social Mind (pp. 7287). London: Routledge.Google Scholar
Menary, R. (2013). Cognitive integration, enculturated cognition and the socially extended mind. Cognitive Systems Research, 25/26, 2634.Google Scholar
Mercier, H. (2018). Reasoning and argumentation. In Ball, L. & Thompson, V. (eds.), The Routledge International Handbook of Thinking and Reasoning (pp. 401414). New York, NY: Routledge.Google Scholar
Mercier, H., & Sperber, D. (2017). The Enigma of Reason. Cambridge, MA: Harvard University Press.Google Scholar
Mercier, H., & Sperber, D. (2011). Why do humans reason? Arguments for an argumentative theory. Behavioral and Brain Sciences, 34, 5774.Google Scholar
Mercier, H., Trouche, E., Boudry, M., & Paglieri, F. (2016). Natural born arguers: An evolutionary perspective on critical thinking education. Educational Psychologist, 52, 116.Google Scholar
Merton, R. (1942) The Sociology of Science: Theoretical and Empirical Investigations. Chicago, IL: University of Chicago Press.Google Scholar
Mill, J. S. (1999). On Liberty. Peterborough: Broadview Press.Google Scholar
Miller, L. (1984) Islamic Disputation Theory: A Study of the Development of Dialectic in Islam from the Tenth through the Fourteenth Centuries. Ph.D. dissertation, Princeton University.Google Scholar
Millikan, R. G. (2006). Styles of rationality. In Hurley, S. & Nudds, M. (eds.), Rational Animals? (pp. 117126). Oxford: Oxford University Press.Google Scholar
Minio-Paluello, L. (1962). Aristoteles Latinus: Analytica Priora. Leiden: Brill.Google Scholar
Mochizuki, S. (2014). On the verification of inter-universal Teichmüller theory: A progress report (as of December 2014), www.kurims.kyoto-u.ac.jp/~motizuki/IUTeich%20Verification%20Report%202014-12.pdfGoogle Scholar
Mody, S., & Carey, S. (2016). The emergence of reasoning by the disjunctive syllogism in early childhood. Cognition, 154, 4048.Google Scholar
Moore, C., & Mertens, S. (2011). The Nature of Computation. Oxford: Oxford University Press.Google Scholar
Moshman, D., & Geil, M. (1998). Collaborative reasoning: Evidence for collective rationality. Thinking and Reasoning, 4, 231248.Google Scholar
Moss, J. (2007). The doctor and the pastry chef: Pleasure and persuasion in Plato’s Gorgias. Ancient Philosophy, 27, 229249.Google Scholar
Moulton, J. (1983). A paradigm of philosophy: The adversary method. In Harding, S. & Hintikka, M. B. (eds.), Discovering Reality (pp. 149164). Dordrecht: Kluwer.Google Scholar
Mueller, I. (1974). Greek mathematics and Greek logic. In Corcoran, J. (ed.), Ancient Logic and Its Modern Interpretations (pp. 3570). Dordrecht: Reidel.Google Scholar
Mugnai, M. (2010). Logic and mathematics in the seventeenth century. History and Philosophy of Logic, 31, 297314.Google Scholar
Musgrave, A., & Pigden, C. (2016). Imre Lakatos. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/archives/win2016/entries/lakatos/Google Scholar
Nauta, L. (2009). In Defense of Common Sense: Lorenzo Valla’s Humanist Critique of Scholastic Philosophy. Cambridge, MA: Harvard University Press.Google Scholar
Nehamas, A. (1990). Eristic, antilogic, sophistic, dialectic: Plato’s demarcation of philosophy from sophistry. History of Philosophy Quarterly, 7, 316.Google Scholar
Netz, R. (2003). Introduction: The history of early mathematics – ways of re-writing. Science in Context, 16, 275286.Google Scholar
Netz, R. (1999). The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. Cambridge: Cambridge University Press.Google Scholar
Newstead, S., Handley, S. J., & Buck, E. (1999). Falsifying mental models: Testing the predictions of theories of syllogistic reasoning. Memory & Cognition, 27, 344354.Google Scholar
Nichols, M. (2009). Socrates on Friendship and Community: Reflections on Plato’s Symposium, Phaedrus, and Lysis. Cambridge: Cambridge University Press.Google Scholar
Nickerson, R. S. (1998). Confirmation bias: A ubiquitous phenomenon in many guises. Review of General Psychology, 2, 175220.Google Scholar
Nietzsche, F. (2007). On the Genealogy of Morality. Cambridge: Cambridge University Press.Google Scholar
Norman, A. (2016). Why we reason: Intention-alignment and the genesis of human rationality. Biology and Philosophy, 31, 685704.Google Scholar
Normore, C. (1993). The necessity in deduction: Cartesian inference and its medieval background. Synthese, 96, 437454.Google Scholar
Norris, S. P., & Ennis, R. H. (1989). Evaluating Critical Thinking. Pacific Grove, CA: Midwest Publications.Google Scholar
Notomi, N. (2014). The Sophists. In Warren, J., & Sheffield, F. (eds.), The Routledge Companion to Ancient Philosophy (pp. 94110). New York, NY: Routledge.Google Scholar
Novikoff, A. (2013). The Medieval Culture of Disputation: Pedagogy, Practice, and Performance. Philadelphia, PA: University of Pennsylvania Press.Google Scholar
Nussbaum, E. M. (2008). Collaborative discourse, argumentation, and learning: Preface and literature review. Contemporary Educational Psychology, 33, 345359.Google Scholar
Nye, A. (1990). Words of Power. New York, NY: Routledge.Google Scholar
Oakhill, J., & Johnson-Laird, P. (1985). The effect of belief on the production of syllogistic conclusions. Quarterly Journal of Experimental Psychology, 37, 553569.Google Scholar
Oaksford, M., & Chater, N. (2002). Commonsense reasoning, logic and human rationality. In Elio, R. (ed.), Common Sense, Reasoning and Rationality (pp. 174214). Oxford: Oxford University Press.Google Scholar
Oaksford, M., & Chater, N. (1994). A rational analysis of the selection task as optimal data selection. Psychological Review, 101, 608631.Google Scholar
Oaksford, M., & Chater, N. (1991). Against logicist cognitive science. Mind & Language, 6, 138.Google Scholar
Ockham, William of. (1974). Summa logicae. St. Bonaventure, NY: The Franciscan Institute.Google Scholar
Oetke, C. (1996). Ancient Indian logic as a theory of nonmonotonic reasoning. Journal of Indian Philosophy, 24, 447539.Google Scholar
O’Neill, C. (2012). The ABC conjecture has not been proved. Mathbabe blog post, https://mathbabe.org/2012/11/14/the-abc-conjecture-has-not-been-proved/Google Scholar
Paglieri, F., & Castelfranchi, C. (2010). Why argue? Towards a cost–benefit analysis of argumentation. Argument & Computation, 1, 7191.Google Scholar
Panaccio, C. (2004). Ockham on Concepts. Aldershot: Ashgate.Google Scholar
Pascual, E., & Oakley, T. (2017). Fictive interaction. In Dancygier, B. (ed.), The Cambridge Handbook of Cognitive Linguistics (pp. 347360). Cambridge: Cambridge University Press.Google Scholar
Paseau, A. (2016). What’s the point of complete rigour? Mind, 125, 177207.Google Scholar
Paseau, A. (2010). Proofs of the compactness theorem. History and Philosophy of Logic, 31, 7398.Google Scholar
Pease, A., Lawrence, J., Budzynska, K., Corneli, J., & Reed, C. (2017). Lakatos-style collaborative mathematics through dialectical, structured and abstract argumentation. Artificial Intelligence, 246, 181219.Google Scholar
Peckhaus, V. (2009). The mathematical origins of nineteenth-century algebra of logic. In Haaparanta, L. (ed.), The Development of Modern Logic (pp. 159195). Oxford: Oxford University Press.Google Scholar
Pelletier, J. (1999). A brief history of natural deduction. History and Philosophy of Logic, 20, 131.Google Scholar
Perelman, C., & Olbrechts-Tyteca, L. (1969). The New Rhetoric: A Treatise on Argumentation (translated by J. Wilkinson & P. Weaver). Notre Dame, IN: University of Notre Dame Press.Google Scholar
Phillips, S. (2017). Fallacies and defeaters in early Navya Nyaya. In Tuske, J. (ed.), Indian Epistemology and Metaphysics (pp. 3352). London: Bloomsbury Academic.Google Scholar
Piccinini, G. (2003). Epistemic divergence and the publicity of scientific methods. Studies in History and Philosophy of Science Part A, 34, 597612.Google Scholar
Pinker, S. (1994). The Language Instinct. New York, NY: Harper Collins.Google Scholar
Plato, (2010). Meno and Phaedo. Cambridge: Cambridge University Press.Google Scholar
Plumwood, V. (1993). The politics of reason: Towards a feminist logic. Australasian Journal of Philosophy, 71, 436462.Google Scholar
Poincaré, H. (1946). The Foundations of Science. Lancaster: The Science Press.Google Scholar
Pollock, J. (1987). Defeasible reasoning. Cognitive Science, 11, 481518.Google Scholar
Pollock, J. (1974). Knowledge and Justification. Princeton, NJ: Princeton University Press.Google Scholar
Prado, J., Chadha, A., & Booth, J. R. (2011). The brain network for deductive reasoning: A quantitative meta-analysis of 28 neuroimaging studies. Journal of Cognitive Neuroscience, 23, 34833497.Google Scholar
Prawitz, D. (2005). Logical consequence from a constructive point of view. In Shapiro, S. (ed.), The Oxford Handbook of Philosophy of Mathematics and Logic (pp. 671695). Oxford: Oxford University Press.Google Scholar
Priest, G. (2018). The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuskoti. Oxford: Oxford University Press.Google Scholar
Prior, A. (1960). The runabout inference ticket. Analysis, 21, 3839.Google Scholar
Quine, W. V. (1974). The Roots of Reference. Chicago, IL: Open Court.Google Scholar
Rabin, M. (1980). Probabilistic algorithm for testing primality. Journal of Number Theory, 12, 128138.Google Scholar
Rahman, S., Klev, A., McConaughey, Z., & Clerbout, N. (2018). Immanent Reasoning or Equality in Action. Cham: Springer.Google Scholar
Rav, Y. (1999). Why do we prove theorems? Philosophia Mathematica, 7, 541.Google Scholar
Read, S. (1994). Formal and material consequence. Journal of Philosophical Logic, 23, 247265.Google Scholar
Read, S. (1988). Relevant Logic: A Philosophical Examination of Inference. Oxford: Blackwell.Google Scholar
Rescorla, M. (2009). Chrysippus’ dog as a case study in non-linguistic cognition. In Lurz, R. (ed.), The Philosophy of Animal Minds (pp. 5271). Cambridge: Cambridge University Press.Google Scholar
Rescorla, M. (2009). Epistemic and dialectical regress. Australasian Journal of Philosophy, 87, 4360.Google Scholar
Restall, G. (2005). Multiple conclusions. In Hajek, P., Valdez-Villanueva, L., & Westerståhl, D. (eds.), Proceedings of the Twelfth International Congress on Logic, Methodology and Philosophy of Science. London: King’s College Publications.Google Scholar
Restall, G. (2004). Logical pluralism and the preservation of warrant. In Rahman, S., Symons, J., Gabbay, D. M., & van Bendegem, J. P. (eds.), Logic, Epistemology, and the Unity of Science (pp. 163173). Dordrecht: Springer.Google Scholar
Rittberg, C., Tanswell, F., & Van Bendegem, J. (2018). Epistemic injustice in mathematics. Synthese, 2018, 130.Google Scholar
Robert, A., & Schwarzenberger, R. (1991). Research in teaching and learning mathematics at an advanced level. In Tall, D. (ed.), Advanced Mathematical Thinking (pp. 127139). New York, NY: Kluwer.Google Scholar
Roberts, D. (2019). A crisis of identification: On Mochizuki’s proof of the ABC conjecture. Inference: International Review of Science, 4, https://inference-review.com/article/a-crisis-of-identificationGoogle Scholar
Rosenblatt, L. (2017). Naive validity, internalization, and substructural approaches to paradox. Ergo, 4, 93120.Google Scholar
Rota, G. C. (1997). The phenomenology of mathematical proof. Synthese, 111, 183196.Google Scholar
Russell, B., & Whitehead, A. (1910–13). Principia Mathematica. Cambridge: Cambridge University Press.Google Scholar
Russell, G. (2013). Logical pluralism. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/logical-pluralism/Google Scholar
Sørensen, M. H., & Urzyczyn, P. (2006). Lectures on the Curry–Howard Isomorphism. New York, NY: Elsevier.Google Scholar
, W., West, R. F., & Stanovich, K. E. (1999). The domain specificity and generality of belief bias: Searching for a generalizable critical thinking skill. Journal of Educational Psychology, 91, 497510.Google Scholar
Saito, K., & Sidoli, N. (2012). Diagrams and arguments in ancient Greek mathematics: lessons drawn from comparisons of the manuscript diagrams with those in modern critical editions. In Chemla, K. (ed.), The History of Mathematical Proof in Ancient Traditions (pp. 135162). Cambridge: Cambridge University Press.Google Scholar
Schechter, J. (2013). Could evolution explain our reliability about logic? Oxford Studies in Epistemology, 4, 214239.CrossRefGoogle Scholar
Schiller, M. R. (2013). Granularity analysis for mathematical proofs. Topics in Cognitive Science, 5, 251269.Google Scholar
Schliesser, E. (2019). Synthetic philosophy. Biology & Philosophy, 34, 19.Google Scholar
Schmandt-Besserat, D. (1996). How Writing Came About. Austin, TX: University of Texas Press.Google Scholar
Scholze, P., & Stix, J. (2018). Why abc is still a conjecture, www.kurims.kyoto-u.ac.jp/~motizuki/SS2018-08.pdfGoogle Scholar
Schotch, P., Brown, B., & Jennings, R. (2009). On Preserving: Essays on Preservationism and Paraconsistent Logic. Toronto: University of Toronto Press.Google Scholar
Schroeder-Heister, P. (2016). Open problems in proof-theoretic semantics. In Piecha, T. & Schroeder-Heister, P., Advances in Proof-Theoretic Semantics (pp. 253283). Cham: Springer.Google Scholar
Schroeder-Heister, P. (2012). Paradoxes and structural rules. In Dutilh Novaes, C. & Hjortland, O., Insolubles and Consequences (pp. 203211). London: College Publications.Google Scholar
Schroeder-Heister, P. (2012). The categorical and the hypothetical: a critique of some fundamental assumptions of standard semantics. Synthese, 187, 925942.CrossRefGoogle Scholar
Schusterman, R. J., & Kastak, D. (1993). A California sea lion (Zalophus californianus) is capable of forming equivalence relations. Psychological Record, 43, 823839.Google Scholar
Scotto di Luzio, P. (2000). Logical systems and formality. In Anderson, M., Cheng, P., & Haarslev, V., Theory and Application of Diagrams. Diagrams 2000 (pp. 117132). Berlin: Springer.Google Scholar
Scribner, S. (1977). Modes of thinking and ways of speaking: Culture and logic reconsidered. In Johnson-Laird, P. N. & Wason, P. C. (eds.), Thinking: Readings in Cognitive Science (pp. 483500). New York, NY: Cambridge University Press.Google Scholar
Scribner, S., & Cole, M. (1981). The Psychology of Literacy. Cambridge, MA: Harvard University Press.Google Scholar
Sen, A. (2005). The Argumentative Indian. Harmondsworth: Allen Lane.Google Scholar
Sequoyah-Grayson, S. (2008). The scandal of deduction. Journal of Philosophical Logic, 37, 6794.Google Scholar
Shapiro, L. (2016). The very idea of a substructural approach to paradox. Synthese, 2016, 120.Google Scholar
Shapiro, L. (2015). Varieties of Logic. New York, NY: Oxford University Press.Google Scholar
Shapiro, L. (2005). Logical consequence, proof theory, and model theory. In Shapiro, S. (ed.), The Oxford Handbook of Philosophy of Mathematics and Logic (pp. 651670). Oxford: Oxford University Press.Google Scholar
Shoham, Y. (1987). A semantical approach to nonmonotonic logic. In McDermott, J. (ed.), Proceedings of the Tenth International Conference on Artificial Intelligence (pp. 227250). Los Altos, CA: Morgan Kaufmann.Google Scholar
Shorey, P. (1924). The origin of the syllogism. Classical Philology, 19, 119.Google Scholar
Siders, A. (2013). Gentzen’s consistency proof without heightlines. Archive for Mathematical Logic, 52, 449468.Google Scholar
Sidoli, N. (2018). Uses of construction in problems and theorems in Euclid’s Elements I–VI. Archive for History of Exact Sciences, 72, 403452.Google Scholar
Sievers, C., & Gruber, T. (2016). Reference in human and non-human primate communication: What does it take to refer? Animal Cognition, 19, 759768.Google Scholar
Smart, P. (2018). Mandevillian intelligence: From individual vice to collective virtue. In Carter, J., Clark, A., Kallestrup, J., Palermos, S., & Pritchard, D. (eds.), Socially-Extended Epistemology (pp. 253274). Oxford: Oxford University Press.Google Scholar
Smiley, T. (1988). Conceptions of consequence. In Craig, E. (ed.), The Routledge Encyclopedia of Philosophy (pp. 599603). London: Routledge.Google Scholar
Smith, P. (2011). Squeezing arguments. Analysis, 71, 2230.Google Scholar
Smith, R. (1997). Aristotle’s Topics: Books i and viii. Oxford: Oxford University Press.Google Scholar
Smith, R. (1994). Dialectic and the syllogism. Ancient Philosophy, 14, 133151.Google Scholar
Smith, R. (1978). The mathematical origins of Aristotle’s Syllogistic. Archive for History of Exact Sciences, 19, 201209.Google Scholar
Solomon, E. (1976). Indian Dialectics: Methods of Philosophical Discussion. Ahmedabad: B. J. Institute of Learning and Research.Google Scholar
Solomon, M. (2006). Groupthink versus the wisdom of crowds. Southern Journal of Philosophy, 44, 2842.Google Scholar
Sorabji, R. (2004). The Philosophy of the Commentators, 200–600 ad, Vol. 3: Logic and Metaphysic. London: Bloomsbury.Google Scholar
Spaulding, S. (2016). Mind misreading. Philosophical Issues, 26, 422440.Google Scholar
Sperber, D. (1996). Explaining Culture: A Naturalistic Approach. Oxford: Blackwell.Google Scholar
Spinoza, B. (1985). Ethics. In The Collected Writings of Spinoza, Vol. 1 (edited and translated by Curley, E.). Princeton, NJ: Princeton University Press.Google Scholar
Spruyt, J., & Dutilh Novaes, C. (2015). Those funny words: Medieval theories of syncategorematic terms. In Cameron, M. & Stainton, R. (eds.), Linguistic Content: New Essays on the History of Philosophy of Language (pp. 100120). Oxford: Oxford University Press.Google Scholar
Solmsen, F. (1951). Aristotle’s syllogism and its Platonic background. The Philosophical Review, 60, 563571.Google Scholar
Stanovich, K. E. (2012). On the distinction between rationality and intelligence: Implications for understanding individual differences in reasoning. In Holyoak, K. J. & Morrison, R. G. (eds.), The Oxford Handbook of Thinking and Reasoning (pp. 433455). Oxford: Oxford University Press.Google Scholar
Stanovich, K. E. (2003). The fundamental computational biases of human cognition: Heuristics that (sometimes) impair decision making and problem solving. In Davidson, J. & Sternberg, R. J. (eds.), The Psychology of Problem Solving (pp. 291342). Cambridge: Cambridge University Press.Google Scholar
Stanovich, K. E. (1999). Who Is Rational? Studies of Individual Differences in Reasoning. Mahwah, NJ: Erlbaum.Google Scholar
Stanovich, K. E., & West, R. F. (2008). On the relative independence of thinking biases and cognitive ability. Personality Processes and Individual Differences, 94, 672695.Google ScholarPubMed
Steinberger, F. (2017). Frege and Carnap on the normativity of logic. Synthese, 194, 143162.Google Scholar
Steinberger, F. (2017). The normative status of logic. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/logic-normative/Google Scholar
Steinberger, F. (2016). Explosion and the normativity of logic. Mind, 125, 385419.Google Scholar
Steiner, M. (1978). Mathematical explanation. Philosophical Studies, 34, 135151.Google Scholar
Steingart, A. (2012). A group theory of group theory: Collaborative mathematics and the ‘uninvention’ of a 1,000-page proof. Social Studies of Science, 42, 185213.CrossRefGoogle Scholar
Steinkrüger, P. (2015). Aristotle’s assertoric syllogistic and modern relevance logic. Synthese, 192, 14131444.CrossRefGoogle Scholar
Stenning, K. (2002). Seeing Reason: Image and Language in Learning to Think. Oxford: Oxford University Press.CrossRefGoogle Scholar
Stenning, K., & van Lambalgen, M. (2008). Human Reasoning and Cognitive Science. Cambridge, MA: MIT Press.Google Scholar
Stenning, K., & Yule, P. (1997). Image and language in human reasoning: A syllogistic illustration. Cognitive Psychology, 34, 109159.Google Scholar
Sterelny, K. (2012). The Evolved Apprentice. Cambridge, MA: MIT Press.Google Scholar
Street, A. (2013). Arabic and Islamic philosophy of language and logic. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/arabic-islamic-language/Google Scholar
Striker, G. (2009). Aristotle’s Prior Analytics Book I: Translated with an Introduction and Commentary. Oxford: Oxford University Press.Google Scholar
Strobino, R. (2018). Ibn Sina’s logic. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/ibn-sina-logic/Google Scholar
Stupple, E. J., Ball, L. J., Evans, J. S., & Kamal-Smith, E. (2011). When logic and belief collide: Individual differences in reasoning times support a selective processing model. Journal of Cognitive Psychology, 23, 931941.Google Scholar
Sunstein, C. R. (2002). The law of group polarization. Journal of Political Philosophy, 10, 175195.CrossRefGoogle Scholar
Sweeney, E. (2008). Literary forms of medieval philosophy. In E. Zalta (ed.), Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/medieval-literary/Google Scholar
Szabó, A. (1978). The Beginnings of Greek Mathematics. Dordrecht: Reidel.Google Scholar
Taber, J. (2004). Is Indian logic nonmonotonic? Philosophy East and West, 54, 143170.CrossRefGoogle Scholar
Tanswell, F. (2020). Go forth and multiply! On actions, instructions and imperatives in mathematical proofs. Manuscript.Google Scholar
Tanswell, F. (2018). Conceptual engineering for mathematical concepts. Inquiry, 61, 881913.CrossRefGoogle Scholar
Tanswell, F. (2017). Proof, Rigour and Informality: A Virtue Account of Mathematical Knowledge. Ph.D. thesis, University of St Andrews.Google Scholar
Tanswell, F. (2015). A problem with the dependence of informal proofs on formal proofs. Philosophia Mathematica, 23, 295310.Google Scholar
Tarnopolsky, C. (2010). Prudes, Perverts, and Tyrants: Plato’s “Gorgias” and the Politics of Shame. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Tarski, A. (2002). On the concept of following logically. History and Philosophy of Logic, 23, 155196.CrossRefGoogle Scholar
Taylor, R., & Wiles, A. (1995). Ring theoretic properties of certain Hecke algebras. Annals of Mathematics, 141, 553572.Google Scholar
Thom, P. (2016). Robert Kilwardby’s disputational logic. History and Philosophy of Logic, 37, 230243.CrossRefGoogle Scholar
Thom, P. (2016). The syllogism and its transformations. In Dutilh Novaes, C. & Read, S. (eds.), The Cambridge Companion to Medieval Logic (pp. 290315). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Thompson, V., Striemer, C. L., Reikoff, R., Gunter, R. W., & Campbell, J. D. (2003). Syllogistic reasoning time: Disconfirmation disconfirmed. Psychonomic Bulletin & Review, 10, 184189.Google Scholar
Thomsen Thörnqvist, C. (2014). ‘Anonymus Aurelianensis iii’ in Aristotelis Analytica Priora: Critical Edition, Introduction, Notes, and Indexes. Leiden: Brill.Google Scholar
Thurston, W. (1994). On proof and progress in mathematics. Bulletin of the American Mathematical Society, 30, 161177.Google Scholar
Tolley, C. (2012). Bolzano and Kant on the nature of logic. History and Philosophy of Logic, 33, 307327.Google Scholar
Tomasello, M. (2014). A Natural History of Human Thinking. Cambridge, MA: Harvard University Press.CrossRefGoogle Scholar
Tomasello, M. (1999). The Cultural Origins of Human Cognition. Cambridge, MA: Harvard University Press.Google Scholar
Torrens, D., Thompson, V., & Cramer, K. M. (1999). Individual differences and the belief bias effect: Mental models, logical necessity, and abstract reasoning. Thinking & Reasoning, 5, 128.Google Scholar
Trafford, J. (2017). Meaning in Dialogue. Berlin: Springer.Google Scholar
Trippas, D., Thompson, V., & Handley, S. J. (2017). When fast logic meets slow belief: Evidence for a parallel-processing model of belief bias. Memory & Cognition, 45, 539552.Google Scholar
Trouche, E., Sander, E., & Mercier, H. (2014). Arguments, more than confidence, explain the good performance of reasoning groups. Journal of Experimental Psychology: General, 143, 19581971.Google Scholar
Tymoczko, T. (1979). The four-color problem and its philosophical significance. The Journal of Philosophy, 76, 5783.Google Scholar
Uckelman, S. L., Alama, J., & Knoks, A. (2014). A curious dialogical logic and its composition problem. Journal of Philosophical Logic, 43, 10651100.Google Scholar
Unguru, S. (1975). On the need to rewrite the history of Greek mathematics. Archive for History of Exact Sciences, 15, 67114.Google Scholar
Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics. Princeton, NJ: Institute for Advanced Study, https://homotopytypetheory.org/bookGoogle Scholar
Van Bendegem, J. (2018). The who and what of the philosophy of mathematical practices. In Ernest, P. (ed.), The Philosophy of Mathematics Education Today (pp. 3960). Cham: Springer.Google Scholar
Vlastos, G. (1982). The Socratic elenchus. The Journal of Philosophy, 79, 711714.Google Scholar
Vygotsky, L. S. (1978). Mind in Society: The Development of Higher Psychological Processes (edited by Cole, M., John-Steiner, V., Scribner, S., & Souberman, E.). Cambridge, MA: Harvard University Press.Google Scholar
Vygotsky, L. S. (1931). History of the development of the higher mental functions. In The Collected Works of L. S. Vygotsky, Vol. 4 (pp. 1251). New York, NY: Plenum Press.Google Scholar
Walton, D., & Krabbe, E. (1995). Commitment in Dialogue. Albany, NY: State University of New York Press.Google Scholar
Wayner, P. (2009). Disappearing Cryptography: Information Hiding: Steganography and Watermarking, 3rd edn. Burlington, MA: Morgan Kaufmann.Google Scholar
Wendelken, C. (2015). Meta-analysis: how does posterior parietal cortex contribute to reasoning? Frontiers in Human Neuroscience, 8, 1042.Google Scholar
Wilkins, M. C. (1928). The effect of changed material on the ability to do formal syllogistic reasoning. Archives of Psychology, 16, 583.Google Scholar
Wilpert, P. (1956/57). Aristoteles und die Dialektik. Kant-Studien, 48, 247257.Google Scholar
Wilson, D., & Sperber, D. (1981). On Grice’s theory of conversation. In Werth, P. (ed.), Conversation and Discourse (pp. 155178). London: Croom Helm.Google Scholar
Wittgenstein, L. (1978). Remarks on the Foundations of Mathematics, 3rd edn. Oxford: Blackwell.Google Scholar
Wittgenstein, L. (1953). Philosophical Investigations. Oxford: Blackwell.Google Scholar
Wolchover, N. (2017). A long-sought proof, found and almost lost. Quanta Magazine, March 28, www.quantamagazine.org/statistician-proves-gaussian-correlation-inequality-20170328/Google Scholar
Wolfsdorf, D. (2013). Socratic philosophizing. In Bussanich, J. & Smith, N. (eds.), The Bloomsbury Companion to Socrates (pp. 3467). London: Bloomsbury.Google Scholar
Yamazaki, Y. (2004). Logical and illogical behavior in animals. Japanese Psychological Research, 46, 195206.Google Scholar
Zardini, E. (2008). A model of tolerance. Studia Logica, 90, 337368.Google Scholar
Zittoun, T., & Gillespie, A. (2015). Internalization: How culture becomes mind. Culture & Psychology, 21, 477491.Google Scholar
Zollman, K., Bergstrom, C., & Huttegger, S. (2013). Between cheap and costly signals: The evolution of partially honest communication. Proceedings of the Royal Society B, 280, 18.Google Scholar

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  • References
  • Catarina Dutilh Novaes, Vrije Universiteit, Amsterdam
  • Book: The Dialogical Roots of Deduction
  • Online publication: 10 December 2020
  • Chapter DOI: https://doi.org/10.1017/9781108800792.014
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  • References
  • Catarina Dutilh Novaes, Vrije Universiteit, Amsterdam
  • Book: The Dialogical Roots of Deduction
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  • Chapter DOI: https://doi.org/10.1017/9781108800792.014
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  • References
  • Catarina Dutilh Novaes, Vrije Universiteit, Amsterdam
  • Book: The Dialogical Roots of Deduction
  • Online publication: 10 December 2020
  • Chapter DOI: https://doi.org/10.1017/9781108800792.014
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