Laszlo E. Szabo

Realists, Platonists and intuitionists jointly believe that mathematical concepts and propositions have meanings, and when we formalize the language of mathematics, these meanings are meant to be reflected in a more precise and more concise form. According to the formalist understanding of mathematics (at least, according to the radical version of formalism I am proposing here) the truth, on the contrary, is that a mathematical object has no meaning; we have marks and rules governing how these marks can be combined. That’s all.

I shall argue that there is no such property of an event as its “probability.” This is why standard interpretations cannot give a sound definition in empirical terms of what “probability” is, and this is why empirical sciences like physics can manage without such a definition. “Probability” is a collective term, the meaning of which varies from context to context: it means different — dimensionless [0, 1]-valued — physical quantities characterising the different particular situations. In other words, probability is a reducible concept, supervening on physical quantities characterising the state of affairs corresponding to the event in question. On the other hand, however, these “probability-like” physical quantities correspond to objective features of the physical world, and are objectively related to measurable quantities like relative frequencies of physical events based on finite samples — no matter whether the world is objectively deterministic or indeterministic.