There are many philosophical interpretations of probability. Is pluralism the correct one? That is, are different interpretations of probability correct for different purposes? In other words, there is no one overarching correct interpretation. Also, what arguments have philosophers given both for and against pluralism? I would like to see some references.
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1Are you using standard language? I haven't heard pluralism used like that. Rather instead, interpretations of probability. Coin flips are just not like quantum processes like radioactive decay, so it's hard to see how to advocate only one at least of the current interpretations, can cover all cases. You might like to read plato.stanford.edu/entries/probability-interpret & clarify your question.– CriglCraglCommented Jul 13 at 18:55
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If you wish to be inclusive in your interpretation of probability, you could say that any quantity that obeys the probability calculus can be regarded as a probability. The question is whether it is useful for a given quantity to be treated as a probability.– BumbleCommented Jul 14 at 16:01
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@CriglCragl it's common in philosophy to use "pluralism" to mean something like "multiple models are true (or true enough) simultaneously"– TKoLCommented Jul 14 at 20:01
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@CriglCragl "In epistemology, pluralism is the position that there is not one consistent means of approaching truths about the world, but rather many." en.m.wikipedia.org/wiki/Pluralism_(philosophy)– TKoLCommented Jul 14 at 20:01
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@TKoL: What I mean is, are there really antipluralists on interpretations of probability? Even a unified approach, will need different regimes, like a hoped for unified field theory is not opposed to different fundamenral forces, just assembles them into a shared picture.– CriglCraglCommented Jul 15 at 11:49
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2 Answers
I would say that it is. Even within Bayesianism there are interpretations of probability that are for different purposes and are not directly exchangeable. In subjectivist Bayesianism, a probability is a measure of your personal belief as to the plausibility of some event or proposition. In subjectivist Bayesianism it is O.K. for your prior to just be a mathematical representation of your belief, whether they could be justified or not. E.g. it is difficult to provide a justification for a mathematical representation of a rational belief in God (and no, zero and one are not rational representations for that question - just rhetoric). In objective Bayesianism, a probability is still a representation of the plausibility of an event or proposition, but the aim is to represent a "state of knowledge" rather than a "belief" (although the two terms are used exchangeably - natural language is very ambiguous - I am using the terms this way for emphasis). In that case priors are often used to represent a state of knowledge that pretty much everybody would agree with, not necessarily as being what they personally believe, but as a reference state of knowledge, often representing ignorance, or encoding invariances etc. The aim there is to provide probabilities relating to reality, rather than reasoning with personal beliefs.
Neither of those is "right", both are useful. The mechanics of the two are basically the same, but you need to be very clear what your probabilities refer to.
Think Bayesianism as an umbrella term is as close as you will get to the right thing (note it is a superset of frequentism - a long run frequency is an excellent basis for a plausability, and frequentism does involve prior beliefs - they just get hidden). That is not to say frequentism is not also a useful and valid approach (to a smaller set of questions due to the more restrictive definition of probability).
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1Good answer, I think some type of pluralism about what probabilities are has to be right.– TKoLCommented Jul 15 at 9:53
Pluralism is accepted by some philosophers while others hope for a unified theory of probability .
However , fundamentally, probability remains defined as the measure of likelihood or chance that a particular event will occur.
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"However , fundamentally, probability remains defined as the measure of likelihood or chance that a particular event will occur." is not true for frequentist probabilities, which cannot attach a probability to the occurrence of a particular event or the truth of a particular hypothesis - neither have a long run frequency.– user6527Commented Jul 15 at 9:35
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1"Probability remains defined as the measure of likelihood or chance that a particular event will occur" - sure, now define "likelihood" and "chance." This is just circular.– causative ♦Commented Jul 15 at 9:37