Computers, justification, and mathematical knowledge

Minds and Machines

Volumn 17, Issue 2, 2007, Pages 185-202

  Arkoudas, Konstantine ^a   Bringsjord, Selmer ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

A priori; Certificates; Four color theorem; Justification; Mathematical knowledge; Proofs

Indexed keywords

CODES (SYMBOLS); COMPUTER SOFTWARE; MATHEMATICAL PROGRAMMING; THEOREM PROVING;

FOUR-COLOR THEOREM; JUSTIFICATION; MATHEMATICAL KNOWLEDGE; MECHANICAL PROOF SYSTEM;

KNOWLEDGE ENGINEERING;

EID: 34547837416     PISSN: 09246495     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11023-007-9063-5     Document Type: Article

References (27)

1. Appel, K., & Haken, W. (1977). Every planar map is 4-colorable. Illinois Journal of Mathamatics, 21, 429-567.
2. Arkoudas, K. (2000). Denotational proof languages, PhD thesis, MIT, Department of Computer Science, Cambridge, USA.
3. Arkoudas, K. (2005). Simplifying proofs in Fitch-style natural deduction systems. Journal of Automated Reasoning, 34(3), 239-294.
4. Arkoudas K: n.d., Athena, http://www.pac.csail.mit.edu/athe.na
5. Bonjour, L. (1998). In defense of pure reason, Cambridge University Press.
6. Burge, T. (1993). Content preservation. Philosophical Review, 102, 457-488.
7. Burge, T. (1998). Computer proof, apriori knowledge, and other minds. Noûs, 32, 1-37.
8. Chalmers, D. J. (1996). The conscious mind. Oxford University Press
9. Chisholm, R. (1989). Theory of knowledge (3rd Ed.). Prentice-Hall.
10. Cohen, D. I. A. (1991). The superfluous paradigm. In J. H. Johnson & M. J. Loomes (Eds.), The mathematical revolution inspired by computing (pp. 323-329). Oxford: Clarendon Press.
11. Coquand, T., & Huet, G. (1988). The calculus of constructions. Information and Computation, 76, 95-120.
12. Detlefsen, M., & Luker, M. (1980). The four-color theorem, and mathematical proof. The Journal of Philosophy, 77(12), 803-820.
13. Gonthier, G. (2005). A computer-checked proof of the four colour theorem. http://www.research.microsoft.com/~gonthier/4colproof.pdf
14. Kitcher, P. (1983). The Nature of mathematical knowledge. Oxford University Press.
15. Kitcher, P. (2000). A priori knowledge revisited. In P. Boghossian & C. Peacocke (Eds.), New essays on the a priori. Oxford: Clarendon Press.
16. MacKenzie, D. (1999). Slaying the kraken: The sociohistory of a mathematical proof. Social Studies of Science, 29(1), 7-60.
17. Rapaport, W. J. (1999). Implementation is semantic interpretation. The Monist, 82, 109-130.
18. Reichenbach, H. (1938). Experience and prediction. University of Chicago Press.
19. Reynolds, J. C. (1998). Theories of programming languages. Cambridge University Press.
20. Rota, G. -C. (1997). The phenomenology of mathematical proof. Synthese, 111, 183-196
21. Slaney, J. (1994). The crisis in finite mathematics: Automated reasoning as cause and cure. In A. Bundy (Eds.), Automated Deduction-CADE-12 (pp. 1-13). Springer: Berlin, Heidelberg.
22. Teller, P. (1980). Computer proof. The Journal of Philosophy, 77(12), 797-803.
23. Tymoczko, T. (1979). The four color theorem and its philosophical significance. The Journal of Philosophy, 76(2), 57-83.
24. Voronkov, A. (1995). The anatomy of Vampire: Implementing bottom-up procedures with code trees. Journal of Automated Reasoning 15(2).
25. Weidenbach, C. (2001). Combining superposition, sorts, and splitting, In: A. Robinson & A. Voronkov (Eds.), Handbook of automated reasoning, (Vol. 2). North-Holland.
26. Weizenbaum, J. (1976). Computer power and human reason, Freeman and Company
27. Williams, B. A. O. (1972). Knowledge and reasons. In G. H. V. Wright (Ed.), Problems in the theory of knowledge (pp. 1-11). Springer.