Internal laws of probability, generalized likelihoods and Lewis' infinitesimal chances - A response to Adam Elga

British Journal for the Philosophy of Science

Volumn 58, Issue 1, 2007, Pages 25-43

  Herzberg, Frederik ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33847657591     PISSN: 00070882     EISSN: 14643537     Source Type: Journal    
DOI: 10.1093/bjps/axl028     Document Type: Review

References (25)

1. Albeverio, S. [1987]: 'Some Personal Remarks on Nonstandard Analysis in Probability Theory and Mathematical Physics', in M. Mebkhout, R. Sénéor (eds), VIIIth International Congress on Mathematical Physics-Marseille 1986, Singapore: World Scientific, pp. 409-20.
2. Albeverio, S., Fenstad, J., Høegh-Krohn, R. and Lindstrøm, T. [1986]: Nonstandard Methods in Stochastic Analysis and Mathematical Physics, Orlando: Academic Press.
3. Anderson, R. M. [1976]: 'A Nonstandard Representation for Brownian Motion and Itô integration', Israel Journal of Mathematics, 25, pp. 15-46.
4. Cox, R. D. and Hinkley, D. V. [1974]: Theoretical Statistics, London: Chapman and Hall.
5. Elga, A. [2004]: 'Infinitesimal Chances and the Laws of Nature', Australasian Journal of Philosophy, 82, pp. 67-76.
6. Fajardo S. and Keisler H. J. [2002]: Model Theory of Stochastic Processes, Natick, MA: A. K. Peters.
7. Halmos, P. R. [1974]: Measure Theory, Berlin: Springer.
8. Hoover, D. N. and Perkins, E. [1983]: 'Nonstandard Construction of the Stochastic Integral and Applications to Stochastic Differential Equations I, II', Transactions of the American Mathematical Society, 275, pp. 1-58.
9. Jech, T. [2000]: Set Theory, 3rd edn, Berlin: Springer.
10. Jin, R. and Keisler,H. J. [2000]: 'Maharam Spectra of Loeb Spaces', Journal of Symbolic Logic, 65, pp. 550-66.
11. Kanamori, A. [2003]: The Higher Infinite, 2nd edn, Berlin: Springer.
12. Kanovei, V. and Shelah, S. [2004]: 'A Definable Nonstandard Model of the Reals', Journal of Symbolic Logic, 69, pp. 159-64.
13. Keisler, H. J. [1984]: 'An Infinitesimal Approach to Stochastic Analysis', Memoirs of the American Mathematical Society, 297.
14. Keisler, H. J. [1988]: 'Infinitesimals in Probability Theory', in N. Cutland (ed.), Nonstandard Analysis and Its Applications, Cambridge: Cambridge University Press, pp. 106-39.
15. Lewis, D. [1994]: 'Humean Supervenience Debugged', Mind, 103(412), pp. 473-90.
16. Lindstrøm, T. [1988]: 'An Invitation to Nonstandard Analysis', in N. Cutland (ed.), Nonstandard Analysis and lts Applications, Cambridge: Cambridge University Press, pp. 1-105.
17. Loeb, P. A. [1975]: 'Conversion from Nonstandard to Standard Measure and Applications in Probability Theory', Transactions of the American Mathematical Society, 211, pp. 113-22.
18. Maharam, D. [1942]: 'On Homogeneous Measure Algebras', Proceedings of the National Academy of Sciences, 28, pp. 108-11.
19. Nelson, E. [1987]: Radically Elementary Probability Theory, Princeton, NJ: Princeton University Press.
20. Ng, S.-A. [2003]: Hypermodels in Mathematical Finance. Modelling via Infinitesimal Analysis, Singapore: World Scientific.
21. Perkins, E. [1981]: 'A Global Intrinsic Characterization of Brownian Local Time', Annals of Probability, 9, pp. 800-17.
22. Perkins, E. [1983]: 'Stochastic Processes and Nonstandard Analysis', in A. E. Hurd (ed.), Nonstandard Analysis-Recent Developments, Berlin: Springer, pp. 162-85.
23. Robinson, A. [1966]: Non-Standard Analysis, Amsterdam: North-Holland.
24. Solovay, R. M. [1970]: 'A Model of Set Theory in Which Every Set of Reals is Lebesgue Measurable', Annals of Mathematics, 92(2), pp. 1-56.
25. Stroyan, K. D. and Bayod, J. M. [1986]: Foundations of Infinitesimal Stochastic Analysis, Amsterdam: North-Holland.