Chapter 11 in this book is some of the best writing on this topic that I have come across: https://www.gutenberg.org/files/37157/37157-pdf.pdf …
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Probability is measurement of the degree of uncertainty associated to phenomena, to follow Kelvin: it is only by associating numbers with any scientific concept that the concept can be properly understood. Probability uses mathematics, but it is not mathematics (like Physics).
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Physics is math !
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Leave aside quantum probability
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I do disagree. Kolmogorov's axioms define probability as a mathematical object but say nothing about its meaning - its correspondence to the real world.
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Beyond of Kolomogorov is just words - not reality. If You find better and more precisly def just write it here.
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