We examine the idea that similar problems should have similar solutions (to paraphrase van Fraassen’s slogan ‘Problems which are essentially the same must receive essentially the same solution’, see van Fraassen in Laws and symmetry, Oxford Univesity Press, Oxford, 1989, p. 236) in the context of symmetries of sentence algebras within Inductive Logic and conclude that by itself this is too generous a notion upon which to found the rational assignment of probabilities. We also argue that within our formulation of symmetry the paradoxes associated with the so called ‘Principle of Indifference’ collapse, but only to be replaced by genuinely irremediable examples of the same phenomenon.
- Bertrand, J. (1898). Calcul des probabilities. Paris: Gauthier-Villars et fils.Google Scholar
- Boolos, G., & Jeffrey, R. (1980). Computability and logic (2nd edn). Cambridge: Cambridge University Press.Google Scholar
- Carnap, R. (1950). Logical foundations of probability. Chicago, Routledge: University of Chicago Press, & Kegan Paul Ltd.Google Scholar
- Carnap, R. (1952). The continuum of inductive methods. Chicago: University of Chicago Press.Google Scholar
- Carnap, R. (1971). A basic system of inductive logic, part 1. In R. Carnap, & R. C. Jeffrey (Eds.), Studies in inductive logic and probability (volume I) (pp. 33–165). Berkeley and Los Angeles: University of California Press.Google Scholar
- Paris, J. B. (1994). The uncertain reasoner’s companion. Cambridge: Cambridge University Press.Google Scholar
- Paris, J. B., & Vencovská, A. (2010). Postscript to “Symmetry’s End”. Available at http://www.maths.manchester.ac.uk/~jeff/.
- Schlipp, P. A. (Ed). (1963). The philosophy of Rudolf Carnap. LaSalle, Illinois: Open Court.Google Scholar