What Are My Chances?

 

Physics involves, amongst other things, the half-lives of radioisotopes, and the probability distributions, say |f|², of quantum-mechanical wavefunctions f (such as describe the motions of particles). So the question naturally arises, what is meant by ‘probability’ here?

In the following ten sections I defend the metaphysical view (due to Popper 1983, see §4) that the objective physical probabilities that arise as a result of quantum-mechanical indeterminism (see §1) are single-case propensities. The tenth section is essentially an argument (from 2006) that we cannot have both a propensity interpretation of quantum-mechanical probability and an actually infinite totality of the natural numbers, and it also contains and refers to arguments for a potentially infinite totality of the natural numbers. Feedback welcomed, of course.

 

1: Laplace’s Urn

2: Hájek’s Arguments

3: Von Mises’ Limits

4: Popper’s Propensities

5: Reichenbach’s Limits

6: Mellor’s Personalism

7: Lewis’s Humeanism

8: Humphreys’ Paradox

9: Eagle’s Arguments

10: Levy’s Paradox

References

 

Incidentally, in the interests of clarity I use single quotation marks to make names, so as to refer to the enclosed words (as when I invited you to consider “what is meant by ‘probability’ here”), and double ones for short quotations that, not being indented (as larger quotations will be), merge into the surrounding sentence in a much simpler sort of way (as when I quoted myself just then).