Laszlo E. Szabo

It is widely believed that the principal difference between Einstein's special relativity and its contemporary rival Lorentz-type theories was that while the Lorentz-type theories were also capable of “explaining away” the null result of the Michelson-Morley experiment and other experimental findings by means of the distortions of moving measuring-rods and moving clocks, special relativity revealed more fundamental new facts about the geometry of space-time behind these phenomena. I shall argue that special relativity tells us nothing new about the geometry of space-time, in comparison with the pre-relativistic Galileo-invariant conceptions; it simply calls something else "space-time", and this something else has different properties. All statements of special relativity about those features of reality that correspond to the original meaning of the terms "space" and "time" are identical with the corresponding traditional pre-relativistic statements. It will be also argued that special relativity and Lorentz theory are completely identical in both senses, as theories about space-time and as theories about the behavior of moving physical objects.

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.