1. Ændr 2. linje i overskriften til AU Passata Light 11 DECEMBER 2015 AARHUS UNIVERSITY AU THE SOCIALITY OF INDIVIDUAL MATHEMATICAL KNOWING Line E. Andersen, PhD student, and Henrik Kragh Sørensen Centre for Science Studies Aarhus University

2. 11 DECEMBER 2015 AARHUS UNIVERSITY AU Overskrift én linje Bold eller Regular “My feeling is that it is unethical for a mathematical researcher to use a result the proof of which he does not ‘understand’ […]. In principle, of course, understanding here means a thorough knowledge of all the arguments involved in the written proof.” ​ René Thom (1994)

3. 11 DECEMBER 2015 AARHUS UNIVERSITY AU Overskrift én linje Bold eller Regular SOCIAL ASPECTS OF INDIVIDUAL MATHEMATICAL KNOWING ​ Aspect 1 The correctness of a proof that p must be checked by more than a couple of mathematicians before anyone can be said to know that p ​ Aspect 2 It is possible for a mathematician to know that p from testimony alone, without knowing a proof of p

4. 11 DECEMBER 2015 AARHUS UNIVERSITY AU Overskrift én linje Bold eller Regular STRUCTURE OF THE TALK ​ 1. How is Aspect 1 supported by mathematicians’ experience as researchers? ​ 2. How is Aspect 2 is supported by mathematicians’ experience as researchers? ​ 3. How could mathematicians’ conception of individual mathematical knowing be developed further so as to be clearer on when a mathematician can rationally rely on others?

5. 11 DECEMBER 2015 AARHUS UNIVERSITY AU Overskrift én linje Bold eller Regular ​ Aspect 1 The correctness of a proof that p must be checked by more than a couple of mathematicians before anyone can be said to know that p ​ How is Aspect 1supported by mathematicians’ experience as researchers?

6. 11 DECEMBER 2015 AARHUS UNIVERSITY AU Overskrift én linje Bold eller Regular ​ Aspect 2 It is possible for a mathematician to know that p from testimony alone, without knowing a proof of p ​ How is Aspect 2 supported by mathematicians’ experience as researchers?

7. 11 DECEMBER 2015 AARHUS UNIVERSITY AU Overskrift én linje Bold eller Regular STRUCTURE OF THE TALK ​ 1. How is Aspect 1 supported by mathematicians’ experience as researchers? ​ 2. How is Aspect 2 is supported by mathematicians’ experience as researchers? ​ 3. How could mathematicians’ conception of individual mathematical knowing be developed further so as to be clearer on when a mathematician can rationally rely on others?

8. 11 DECEMBER 2015 AARHUS UNIVERSITY AU Overskrift én linje Bold eller Regular HARDWIG (1991) ​ A knows p when A knows that B knows p ​ But for A to know that B knows p, A must know that B  is honest  is competent  is conscientious  has ‘adequate epistemic self–assessment’

9. 11 DECEMBER 2015 AARHUS UNIVERSITY AU Overskrift én linje Bold eller Regular Thank you for your attention!

10. 11 DECEMBER 2015 AARHUS UNIVERSITY AU Overskrift én linje Bold eller Regular REFERENCES ​ Fallis, Don (2003). “Intentional Gaps in Mathematical Proofs”. Synthese, vol. 134, no. 1–2, pp. 45–69. ​ Geist, C., Löwe, B., & Van Kerkhove, B. (2010). Peer Review and Knowledge by Testimony in Mathematics. In B. Löwe & T. Müller (Eds.), PhiMSAMP. Philosophy of Mathematics: Sociological Aspects and Mathematical Practice (pp. 155–178). London: College Publications. ​ Hardwig, John (July 1985). “Epistemic Dependence”. Journal of Philosophy, vol. 82, no. 7, pp. 335–349. ​ Hardwig, John (1991). “The role of trust in knowledge”. Journal of Philosophy, vol. 88, pp. 693–708. ​ Löwe, Benedikt, Thomas Müller, and Eva Müller-Hill (2010). “Mathematical Knowledge as a Case Study in Empirical Philosophy of Mathematics”. In: Philosophical Perspectives on Mathematical Practice. Ed. by Bart Van Kerkhove, Jonas De Vuyst, and Jean Paul Van Bendegem. London: College Publications, pp. 185–203. ​ Müller–Hill, E. (2011), Die epistemische Rolle formalisierbarer mathematischer Beweise. Dissertation. ​ Sauvaget, Thomas (2010). Published results: when to take them for granted? MathOverflow. url: http://mathoverflow.net/questions/23758/ (visited on 11/18/2015).