Symposium: Virtue Epistemology of Mathematical Practice

  • Rittberg, C. J. (Organiser)
  • Fenner Stanley Tanswell (Organiser)
  • Andrew Aberdein (Organiser)

Activiteit: Other


Twenty-first century philosophy of mathematics has exhibited a turn towards issues of mathematical practice [4]. This represents a shift from the field's traditional focus on metaphysical questions to a focus on epistemology, in particular social epistemology. One of the most productive programmes in twenty-first century epistemology has been virtue epistemology. These parallel developments suggest that the time is ripe for avirtue epistemology of mathematics. George Polya, one of the most influential precursors to the practice turn in philosophy of mathematics, identified `intellectual courage, intellectual honesty, and wise restraint' as the `moral qualities of the scientist' that he considered indispensable [6]. However, these virtues are seldom explicitly invoked in his work or that of his followers. Indeed, until recently, discussion of virtues in the philosophy of mathematics has been fleeting and fragmentary at best. In the last few years this has begun to change. Epistemic virtues have attracted attention in the philosophy of science as components of a full account of successful theory choice [5], an argument that readily extends to mathematics. Within the philosophy of mathematical practice itself, attention to virtues has emerged from a variety of disparate sources. For example, Penelope Maddy's work on the justification of axioms appeals to theoretical virtues [3], an aspect of her work developed further by others [7]; Noel Clemente has suggested that aprioricity of axioms could be analysed in terms of a reliabilist epistemic virtue [2]; Fenner Tanswell has proposed virtue epistemology as the correct epistemology for mathematics (and perhaps even as the basis for progress in the metaphysics of mathematics) [9]; Francis Su has advocated an understanding of social utility of mathematical practice grounded in virtue ethics [8]; and Don Berry has put forward an account of the role of proof in terms of theoretical virtues of permanence, reliability, autonomy, and consensus [1]. This panel brings together several researchers who have begun to study mathematical practice from the perspective of virtue epistemology with the intention of consolidating and encouraging this trend. [1] Berry, D. (2018). Proof and the virtues of shared enquiry. Philosophia Mathematica. Forthcoming. [2] Clemente, N. L. (2016). A virtue-based defense of mathematical apriorism. Axiomathes, 26:71–87. [3] Maddy, P. (2011). Defending the Axioms: On the Philosophical Foundations of Set Theory. Oxford University Press, Oxford. [4] Mancosu, P., ed. (2008). The Philosophy of Mathematical Practice. Oxford University Press, Oxford. [5] Paternotte, C. and Ivanova, M. (2017). Virtues and vices in scientific practice. Synthese, 194:1787–1807. [6] Polya, G. (1954). athematics and lausible easoning. wo olumes. Princeton University Press, Princeton, N.J. [7] Rittberg, C. and Tanswell, F. (2016). Mathematical values and set-theoretic pluralism. Presented at Set Theoretic Pluralism Symposium, Aberdeen. [8] Su, F. E. (2017). Mathematics for human flourishing. The American Mathematical Monthly, 124(6):483–493. [9] Tanswell, F. (2016). Proof, Rigour & Informality: A Virtue Account of Mathematical Knowledge. PhD thesis, University of St. Andrews.
Periode1 jul 2018
EvenementstitelSPSP 2018: Society for Philosophy of Science in Practice
LocatieGhent, Belgium
Mate van erkenningInternational