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When I say subjective probability, I am referring to the notion of defining a probability in relation to a credence of belief. For example, one may say that there’s a very high probability that the sun will rise tomorrow or that there’s a low probability that god exists.

To me, those statements seem meaningless or unnecessary. All one can say is that the sun rose for X number of days or that we haven’t directly confirmed God to exist and that’s it. I am curious as to whether other philosophers or any other philosophies in probability simply outright reject this notion of probability. In my examples, I’m moreso looking for something close to the notion of the god example instead of the sun example since atleast the sun has a history of an actual observable frequency in the rising sense.

I am aware of different interpretations of probability but from what I could find, I didn’t come across specific philosophers who simply rejected the very idea of this outright

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    An insightful observation. Read a good (introductory) book on classical logic (that's what I csll philosophical logic) and be informed. What does it mean to say there's x% chance that the sun will rise tomorrow? A metaphysician's nightmare! Mar 2, 2023 at 6:25
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    You just defined it as credence of belief, so it is perfectly meaningful to you. Whatever bad adjectives can be attached to that definition, "meaningless" is not one of them. Philosophers do not argue for trivial absurdities, so you won't come across it, but see Kyburg for a saner critique:"I shall argue that although the theory appears to be all things to all people, in fact it is a snare and a delusion and is either vacuous and without systematic usefulness, or is simply false."
    – Conifold
    Mar 2, 2023 at 6:50
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    I suppose I could have been more clear and meant to imply what the quote says indeed @Conifold. I meant meaningless in the sense of being superfluous or vacuous. To say that the probability of God is low isn’t really saying much apart from saying your confidence in it is low. And yet, when it comes to positions on any other matter, saying that your confidence is high or low is taken to be irrelevant.
    – user62907
    Mar 2, 2023 at 6:58
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    See Interpretations of Probability: there are several other interpretations, that obviously reject the subjective one. I do not think that they consider it "meaningless"... Mar 2, 2023 at 8:45
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    One can have a very inclusive approach to the interpretation of probability and say that any quantity that obeys the probability calculus can be considered a probability. There are good reasons for supposing that rational degrees of belief do so, at least approximately. So while one can choose to understand probability differently, e.g. as a hypothetical frequency, one can hardly say that subjective or epistemic probability is vacuous. It has its critics, but then so do the other interpretations.
    – Bumble
    Mar 2, 2023 at 14:39

2 Answers 2

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Subjective or belief-based probability is the interpretation behind Bayesian statistics. It has been historically opposed (to the point that my university frequentist statistics teacher would mock Bayesians) to frequentist statistics, which is the interpretation behind your words:

All one can say is that the sun rose for X number of days or that we haven’t directly confirmed God to exist and that’s it.

Frequentist probability is in turn the main interpretation behind what is called Classical Statistics. One of its main features is indeed the narrowing of the set of possible outcomes:

classical statistical procedures share the feature that they only rely on probability assignments over sample spaces [..] an important motivation for this is that those probabilities can be interpreted as frequencies, from which the term of frequentist statistics originates [..] classical procedures employ the data to narrow down a set of hypotheses.

Note however that classical statistics might be too restrictive in some scenarios, as hypotheses are discarded when they render the observed sample too improbable, which of course differs from discarding hypotheses that deem the observed sample impossible. This is really well exemplified in the answers to your previous question, Does every possible event have non-zero probability?. The one you marked said no, and it was a frequentist answer, whereas the next, most voted answer said it could happen, it was Bayesian, more flexible if the scenario requires it.

So if you're looking for a philosophy of statistics opposing the subjective interpretation of probability, the most developed as of today is classical statistics, and you should find plenty of references under Problems with the Bayesian approach. However, beware that Bayesian statistics are growing rapidly in popularity, since their flexibility have made them really useful in Machine Learning and Artificial Intelligence.

Finally, a pretty recent (when compared to the other two) proposal is that of Imprecise Probabilities, which are promising since they too differ from Bayesian statistics and are also more flexible than frequentist. Their counterpart in logic would be fuzzy logic. This might fit in your God example interest.

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    Thank you for your very helpful answer
    – user62907
    Mar 3, 2023 at 7:36
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The existence of God is a single event. Its an inappropriate use of probabilities to reach a conclusion based on a single event. Your sunrise example has millions of years of events to base a probability and is more appropriate for this type of analysis. Subjective probabilty seems to apply to luck like using your favorite numbers in picking a lottery ticket. Subjectively, one feels these numbers are better than others and that's why they are chosen.

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