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I am interested in reading books and papers regarding the philosophy of probability. I want to know what the correct philosophical interpretation of probability is, and also other topics regarding probability and its philosophy. I have already read math texts on probability, I am looking for texts that treat probability from a philosophical perspective.

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    "Correct" interpretation of probability in philosophy might be a high standard. If you haven't, I'd start with SEP's article "Interpretations of Probability". It's succinct, free, and a click away.
    – J D
    Feb 8, 2022 at 21:49
  • Max Tegmark has an interesting take on this in his book Our Mathematical Universe, though it has a much broader focus.
    – JohnEye
    Feb 9, 2022 at 12:06
  • Would "the philosophy of probability" include points made about probability relevant to the philosophy of science? If so, I recommend this.
    – J.G.
    Feb 9, 2022 at 14:42
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    At @Stef's suggestion, I hereby rewrite my last comment as a new comment (they or anyone else can tell me if an answer would be preferred): Would "the philosophy of probability" include points made about probability relevant to the philosophy of science? If so, I recommend Probability Theory: The Logic of Science by Jaynes and Bretthorst.
    – J.G.
    Feb 9, 2022 at 16:24

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The most self-contained book I am aware of on the subject is Philosophical Theories of Probability by Donald Gillies (Routledge, 2000):

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I believe reading the historical development of ideas is philosophically a very rewarding occupation. So, I would recommend also Ian Hacking's The Emergence of Probability: A Philosophical Study of Early Ideas about Probability, Induction and Statistical Inference (2nd edition, Cambridge University Press, 2006) and Jan von Plato's Creating Modern Probability: Its Mathematics, Physics and Philosophy in Historical Perspective (Cambridge University Press, 1994).

I suppose these books would give a sound basis for further inquiry.

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    It's an excellent book. Very readable. There are few controversial topics in philosophy where I think one side is clearly right, and I can see no value at all in the opposing arguments, but probability is one of them. Probability is obviously a kind of logic. All of the other explanations fail to explain how logic is used. Feb 8, 2022 at 19:25
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In addition to the books mentioned by Tankut, I would suggest also:

Antony Eagle, Philosophy of Probability: Contemporary Readings, (Routledge, 2010). This contains many important papers on the philosophy of probability, particularly

David Lewis, “A Subjectivist’s Guide to Objective Chance” (also in his collection Philosophical Papers volume 2, 1986, 263–294),

Alan Hájek, “‘Mises Redux’ — Redux. Fifteen Arguments Against Finite Frequentism”, also in Erkenntnis, 45: 209–227, 1997.

Alan Hájek, “Fifteen Arguments Against Hypothetical Frequentism”, also in Erkenntnis, 70: 211–235, 2009.

Some other useful papers and books are:

Alan Hájek, “What Conditional Probability Could Not Be”, Synthese, 137: 273–323, 2003.

Kenny Easwaran, "Dr. Truthlove or: How I Learned to Stop Worrying and Love Bayesian Probabilities", Nous 50:4, 816–853, 2016.

Richard Jeffrey, The Logic of Decision (Chicago, 1983).

Ian Hacking, The Logic of Statistical Inference (Cambridge, 1965).

Jon Williamson, In Defence of Objective Bayesianism (Oxford, 2010).

J.R. Lucas, The Concept of Probability (Oxford, 1970).

F.C. Benenson, Probability, Objectivity and Evidence (Routledge, 1984).

Also, there are lots of papers by authors including Henry Kyburg, Patrick Maher, Wesley Salmon, Brian Skyrms, Ellery Eels, Jack Good, Bruno de Finetti, Richard Bradley, Bas van Fraassen, Branden Fitelson, Dennis Lindley.

In reference to your point about "the correct philosophical interpretation of probability", you might want to bear in mind the possibility that there is no unique correct interpretation. An operational approach to understanding probability might be to say that any quantity can be interpreted as a probability if and only if it obeys the probability calculus. Finite frequencies do, quite straightforwardly. De Finetti's work shows that rational degrees of credence obey the probability calculus, at least to a good approximation, subject to a few basic assumptions about rationality.

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There is a book from 2021 called "Bernoulli's Fallacy" by Aubrey Clayton that might fit with what you are looking for. You can find more information and an excerpt here.

Some quotes taken from the linked website:

Ranging across math, philosophy, and culture, Bernoulli’s Fallacy explains why something has gone wrong with how we use data—and how to fix it.

Aubrey Clayton is a mathematician who teaches the philosophy of probability and statistics at the Harvard Extension School.

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I would suggest Ten Great Ideas about Chance by Persi Diaconis and Brian Skyrms, https://press.princeton.edu/books/hardcover/9780691174167/ten-great-ideas-about-chance

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