When is a Proof a Proof?

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References

Atiyah, Michael (1984) ‘Interview’ , Mathematical Intelligencer 6(1): 9-19 .

Barnes, Barry, David Bloor & John Henry (1996) Scientific Knowledge. A Sociological Approach ( London: Athlone ).

Bloor, David (1978) ‘Polyhedra and the Abominations of Leviticus’ , British Journal for the History of Science 39(11): 243-272 .

Bloor, David (1991 [1976]) Knowledge and Social Imagery ( Chicago, IL: University of Chicago Press [London: Routledge and Kegan Paul, 1976]).

Collins, H.M. (1985) Changing Order: Replication and Induction in Scientific Practice ( Chicago, IL: University of Chicago Press ).

Connes, Alain, Gerd Faltings, Vaughan Jones, Stephen Smale & René Thom (1992) ‘Round-Table Discussion’, in Carlos Casacuberta & Manuel Castellet (eds), Mathematical Research Today and Tomorrow ( Berlin & New York: Springer ): 87-108.

Daston, Lorraine (1992) ‘Objectivity and the Escape from Perspective’ , Social Studies of Science 22(4): 597-618 .

Daston, Lorraine (1998) ‘Fear and Loathing of the Imagination in Science’ , Daedalus 127(1): 73-95 .

Daston, Lorraine & Peter Galison (1992) ‘The Image of Objectivity’ , Representations 40(1): 81-128 .

10.

DeMillo, Richard, Richard J. Lipton & Alan J. Perlis (1985) ‘Social Processes and Proofs of Theorems and Programs’, in Thomas Tymoczko (ed.) New Directions in the Philosophy of Mathematics ( Boston, MA & Basle: Birkhäuser ): 267-285. (First published 1997.)

11.

Fetzer, James F. (1988) ‘Program Verification: The Very Idea’ , Communications of the ACM 31(9): 1048-1063 .

12.

Frege, Gottlob (1986) Wissenschaftlicher Briefwechsel( Hamburg: Felix Meiner ).

13.

Galison, Peter (1998) ‘Judgement Against Objectivity’, in Caroline A. Jones & Peter Galison (eds), Picturing Science, Producing Art ( London: Routledge ): 327-359.

14.

Gibbons, Michael, Camille Limoges, Helga Nowotny, Simon Schwartzman, Peter Scott & Martin Trow (1994) The New Production of Knowledge ( London: SAGE Publications ).

15.

Goldstein, Catherine (1995) ‘Zahlen als Liebhaberei und Beruf im 17. und 19. Jahrhundert’, in Michel Serres (ed.), Elemente einer Geschichte der Wissenschaften( Frankfurt am Main: Suhrkamp ): 487-525.

16.

Grabiner, Judith V. (1981) ‘Changing Attitudes Toward Mathematical Rigor: Lagrange and Analysis in the Eighteenth and Nineteenth Centuries’, in Hans Niels Jahnke & Michael Otte (eds), Epistemological and Social Problems of the Sciences in the Early Nineteenth Century ( Dordrecht: Reidel ): 311-330.

17.

Grattan-Guiness, Ivor (1992) ‘Charles Babbage as an Algorithmic Thinker’ , Annals of the History of Computing 14(3): 34-48 .

18.

Heintz, Bettina (1993) Die Herrschaft der Regel. Zur Grundlagengeschichte des Computers ( Frankfurt am Main: Campus ).

19.

Heintz, Bettina (1995) ‘Die Gesellschaft in der Maschine. Überlegungen zum Verhältnis von Informatik und Soziologie’, in Hans-Jörg Kreowskiet al. (eds), Realität und Utopien der Informatik ( Münster: Agenda ): 12-31.

20.

Heintz, Bettina (2000) Die Innenwelt der Mathematik. Zur Kultur und Praxis einer beweisenden Disziplin ( Wien & New York: Springer ).

21.

Hilbert, David (1964) ‘Die logischen Grundlagen der Mathematik’, in David Hilbert, Hilbertiana ( Darmstadt: Wissenschaftliche Buchgesellschaft ): 33-48. (First published 1923.)

22.

Hildebrandt, Stephan (1965) Wahrheit und Wert mathematischer Erkenntnis, Carl Friedrich von Siemens Stiftung (ed.) ( Munich: C.F. von Siemens Foundation ).

23.

Hoare, C.A.R. (1993) ‘Mathematics of Programming’, in Timothy Colburn, James Fetzer & Terry Rankin (eds), Program Verification ( Dordrecht: Kluwer ): 135-154.

24.

Krohn, Wolfgang & Johannes Weyer (1989) ‘Gesellschaft als Labor’ , Soziale Welt 40(3): 349-373 .

25.

Lakatos, Imre (1976) Proofs and Refutations: The Logic of Mathematical Discovery ( Cambridge: Cambridge University Press ).

26.

Livingston, Eric (1986) The Ethnomethodological Foundations of Mathematics ( London: Routledge and Kegan Paul ).

27.

Livingston, Eric (1999) ‘Cultures of Proving’ , Social Studies of Science 29(6): 867-888 .

28.

Locher, L. (1938) ‘Die Finslerschen Arbeiten zur Grundlegung der Mathematik’ , Commentarii Mathematici Helvetici 10: 206-207 .

29.

MacKenzie, Donald (1992) ‘Computers, Formal Proofs, and the Law Courts’ , Notices of the American Mathematical Society 39(9): 1066-1069 .

30.

MacKenzie, Donald (1993) ‘Negotiating Arithmetic, Constructing Proof: The Sociology of Mathematics and Information Technology’ , Social Studies of Science 23(1): 37-65 .

31.

Markowitch, Jörg F. (1997) ‘Metaphysik und Mathematik’, PhD thesis, University of Vienna.

32.

Nygaard, Kristen (1986) ‘Program Development as a Social Activity’, in Hans Jürgen Kugler (ed.), Information Processing 86( Amsterdam: North Holland ): 189-198.

33.

Pickering, Andrew (1995) The Mangle of Practice ( Chicago, IL: University of Chicago Press ).

34.

Poincaré, Henri (1914) Wissenschaft und Methode( Leipzig: B.G. Teubner ).

35.

Popper, Karl R. (1950) ‘Indeterminism in Quantum Physics and in Classical Physics, Part II’ , British Journal for the Philosophy of Science 1(3): 173-195 .

36.

Porter, Theodore (1995) Trust in Numbers. The Pursuit of Objectivity in Science and Public Life ( Princeton, NJ: Princeton University Press ).

37.

Post, Emil (1965 [1936]) ‘Finite Combinatory Processes. Formulation I’, in Martin Davis (ed.), The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions ( New York: Lippincott Williams & Wilkins ): 289-291.

38.

Restivo, Sal (1992) Mathematics in Society and History ( Dordrecht: Kluwer ).

39.

Schaffer, Simon (1994) ‘Babbage’s Intelligence: Calculating Engines and the Factory System’ , Critical Inquiry 21(1): 201-228 .

40.

Schütz, Alfred & Thomas Luckmann (1979) Stukturen der Lebenswelt ( Frankfurt am Main: Suhrkamp ).

41.

Shapin, Steven & Simon Schaffer (1985) Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life( Princeton, NJ: Princeton University Press ).

42.

Simon, Herbert A. (1988) The Sciences of the Artificial ( Cambridge, MA: MIT Press ).

43.

Thom, René (1974) ‘Moderne Mathematik - Ein erzieherischer und philosophischer Irrtum?’, in Michael Otte (ed.), Mathematiker ü ber die Mathematik ( Berlin: Springer ): 371-402.

44.

Thurston, William P. (1994) ‘On Proof and Progress in Mathematics’ , Bulletin of the American Mathematical Society 30(2): 161-177 .

45.

Turing, Alan M. (1964 [1950]) ‘Computing Machinery and Intelligence’, in Alan Ross Anderson (ed.), Minds and Machines ( Englewood Cliffs, NJ: Prentice-Hall ): 4-30.

46.

Turing, Alan M. (1965 [1936]) ‘On Computable Numbers, With an Application to the Entscheidungsproblem’, in Martin Davis (ed.), The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions ( New York: Lippincott Williams & Wilkins ): 116-151.