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  1. More than one hypothesis may fit the data (hypotheses generation is the stock-in-trade of science)

  2. Choosing a scientific hypothesis is not about truth. People have gone on record that inter alia it's about simplicity (Occam's razor)

Ergo,

  1. Scientific hypotheses are not truths. They're best thought of as models that fit with observation.

Bayes' theorem, in the context of science, can be summed up as P(H/E) which, translated into English, means The probability that a hypothesis H is true, given the evidence E.

To cut to the chase, Bayes' theorem is a probabilistic calculation of truth of a scientific hypothesis, but scientific hypotheses are not about truth (vide supra).

How do we explain this incongruence, IF it is one?

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It depends on what you mean by true. Scientific theories such as relativity and quantum mechanics are models of reality. An accepted meaning of 'true' is 'in accord with facts or reality'. Therefore, one might refer to scientific theories as being true if they model reality to an acceptable extent. Your 'incongruity' seems to arise only because you use the words true and truth in different ways.

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  • An interesting obaervation. You, I believe, hit the bullseye mon ami. However, you do admit that there are two very different meanings of truth at play here. What about the fact that all other contender hypotheses are also "in accord" with the facts?
    – Hudjefa
    Commented Jan 8, 2023 at 20:10
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    @AgentSmith I think we should give up on using the word "true". I don't think science really needs it anyway. Science provides "models that fit with observation", as you say. That's enough. It's a mistake to drag science into making it say that some things are "true", except, as Marco says, in the sense that they are "truthful" to observation as far as we know. Again, that's enough. I really think we should not try to find "truth" or use the word "truth".
    – Frank
    Commented Jan 8, 2023 at 23:31
  • Agreed, but then what's the meaning of P(H/E) where H is a scientific hypothesis and E is evidence for that hypothesis? You made a good suggestion - interpret true as being "in accord with the facts" but then, as I brought to yer attention, all hypotheses (there's always more than one) are "in accord with the facts".
    – Hudjefa
    Commented Jan 9, 2023 at 5:40
  • @AgentSmith in that sense of the word true, there are degrees of truth. We used to consider Newton's law of gravitation to be correct until Einstein came up with a truer model.
    – Professor Sushing
    Commented Jan 9, 2023 at 7:20
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    @AgentSmith, In general scientific hypotheses make specific claims about specific phenomena and make measurable claims about outcomes and results of experiments. Non-scientific hypotheses either don't make specific claims, don't make measurable claims, or cannot be applied to experiment.
    – Gerald
    Commented Jan 17, 2023 at 2:58
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I would put pressure on your second assumption. As there many reasons of way and how to choose one scientific hypotheses out of the many that are possible, and parsimony is a leading reason, but for sure no the only one.

Also, you if have problems with the definition of truth, you should use bayes the following way: "The probability that a hypothesis H fits the data better than others, given the evidence E."

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  • Interesting. Are you sure that's an acceptable answer?
    – Hudjefa
    Commented Jan 8, 2023 at 13:43

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