Conclusion
In a short amount of space we have covered a lot of territory in the philosophy of probability. In §2, we considered various formal theories of probability. We saw that not only are there rival theories to Kolmogorov's axioms, but these rivals arguably have desirable features that Kolmogorov's axioms lack.
In §3, we saw some of the various interpretations of probability and some of the issues connected with each interpretation. The discussion of each interpretation was necessarily brief, but each of these interpretations suffers from one problem or another. In fact, the failures of each interpretation have motivated some to take probability as a primitive, undefined concept (e.g., Sober forthcoming). We see, then, that despite the ubiquity of probability in our lives, the mathematical and philosophical foundations of this fruitful theory remain in contentious dispute.[73]
Source:
Allhoff F.. Philosophies of the Sciences: A Guide. N.-Y.: Wiley-Blackwell,2010. — 386 p.. 2010
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