November, Dan D
(2019)
Interpretive Implications of the Sample Space.
[Preprint]
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Abstract
In this paper I claim that Kolmogorov's probability theory has other basic notions in addition to 'probability' and 'event'. These notions are described by the sample space component of his probability space structure. This claim has several interesting consequences, two of which I discuss in this paper. The major consequence is that the main interpretations of probability theory are in fact not interpretations of Kolmogorov's theory, simply because an interpretation of a mathematical theory in a strict sense must explicate all of the theory's basic notions, while the main interpretations of probability do not explicate all of Kolmogorov's theory’s basic notions. In particular, the main interpretations only explicate 'probability' and 'event' and do not explicitly address the additional basic notions which I claim Kolmogorov's theory includes. The other important consequence of my claim concerns the relation between 'probability' and 'event'. Very roughly, contrary to the common conception of 'events' as independent of 'probabilities', I claim that in some cases they do depend on them!
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