Sheldon Smith on Newton’s Derivative: Retrospective Assignation, Externalism and the History of Mathematics
Tóm tắt
To illustrate the view that a speaker can have a partial understanding of a concept, Burge uses the example of Leibniz’s and Newton’s understanding of the concept of derivative. In a recent article, Sheldon Smith criticizes this example and maintains that Newton’s and Leibniz’s use of their derivative symbols does not univocally determine their references. The present article aims at challenging Smith’s analysis. It first shows that Smith misconstrues Burge’s position. It second suggests that the philosophical lessons one should draw from the practice of the historians of philosophy are more ambivalent than what Smith thinks.
Tài liệu tham khảo
Bernard A (2003) Sophistic aspects of Pappus’s collection. Arch Hist Exact Sci 57(2):93–150
Blåsjö V (2021) Historiography of mathematics from the mathematician’s point of view. In: Handbook of the History and Philosophy of Mathematical Practice. Springer, Cham
Burge T (2005) Frege on sense and linguistic meaning. In: Truth, Thought, Reason: Essays on Frege. Oxford University Press, Oxford, pp 242–269
Burge T (2007a) Individualism and the mental. In: Foundations of Mind: Philosophical Essays, vol 2. Oxford University Press, Oxford, pp 100–150
Burge T (2007b) Other bodies. In: Foundations of Mind: Philosophical Essays, vol 2. Oxford University Press, Oxford, pp 82–99
Burge T (2013) Concepts, Conceptions, Reflective Understanding: Reply to Peacocke. In: Cognition through understanding, vol 3. Oxford University Press, Oxford, pp. 521–533.
Descartes R (1984). In: Cottingham J et al (eds) The philosophical writings of Descartes, vol 2. Cambridge University Press, Cambridge
Ebbs G (1997) Rule-following and realism. Harvard UP, Cambridge
Ebbs G (2009) Truth and words. Oxford University Press, Oxford
Engelsman S. B (1984) Families of curves and the origins of the partial differentiation. Elsevier, Amsterdam
Field H (1973) Theory change and the indeterminacy of reference. J Philos 70:462–481
Freudenthal H (1977) What is algebra and what has it been in history? Arch Hist Exact Sci 16(3):189–200
Guicciardini N (2009) Isaac Newton on mathematical certainty and method. MIT Press, Cambridge
Guicciardini N (2021) Anachronisms in the history of mathematics. Essays on the historical interpretation of mathematical texts. Cambridge UP, Cambridge
Mansfeld J (1998) Prolegomena mathematica: from Apollonius of Perga to the late Neoplatonism. With an appendix on pappus and the history of Platonism. Brill, Leiden
Netz R (1999) The shaping of deduction in Greek mathematics: a study in cognitive history. Cambridge UP, Cambridge
Peacocke C (2008) Truly understood. Oxford University Press, Oxford
Putnam H (1975a) The analytic and the synthetic. In: Mind, language and reality: philosophical papers. Cambridge University Press, Cambridge, pp 33–69
Putnam H (1975b) The meaning of ‘meaning.’ In: Mind, language and reality: philosophical papers. Cambridge UP, Cambridge, pp 215–271
Quine WVO (1960) Word and object. MIT Press, Boston
Rey G (1998) What implicit conceptions are unlikely to do. In: Villanueva E (ed) Concepts: philosophical issues. Ridgeview Publishing Company, Atascadero, pp 93–104
Smith SR (2015) Incomplete understanding of concepts: the case of the derivative. Mind 124(496):1163–1199
Unguru S (1975) On the need to rewrite the history of Greek mathematics. Arch Hist Exact Sci 15(1):67–114
Unguru S (1979) History of ancient mathematics: some reflections on the state of the art. Isis 70(254):555–565
Weil A (1980) History of mathematics: why and how?. In: Proceedings of the international congress of mathematicians 1978, Helsinki, Academia Scientiarum Fennica, pp 227–236