Mapping Quantum Reality: What to Do When the Territory Does Not Make Sense?

One of the central goals of science is to find consistent and rational representations of observational data: a map of the world, if you will. How we do this depends on the specific tools, which are often mathematical. When dealing with real-world situations, where the data (or “territory”) has a random component, the mathematical tools most commonly used are those grounded in probability theory, defined in a precise way by the Russian mathematician Andrei Kolmogorov. In this paper we explore how experimental data (the “territory”) can be represented (or “mapped”) consistently in terms of probability theory, and present examples of situations, both in the physical and social sciences, where such representations are impossible. This suggests that some “territories” cannot be “mapped” in a way that is consistent with classical logic and probability theory.

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