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Philosophy

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  • I largely agree with your position, but just to push on it a bit: How would you feel about the hypotheses “2 + 2 = 5”, “there exists some integer strictly between 2 and 3”, or “there exists some even integer that is not divisible by two”?
    – Peter LeFanu Lumsdaine
    Commented Jul 10, 2023 at 20:16
  • @PeterLeFanuLumsdaine Good question! I added a paragraph addressing mathematical statements.
    – Scott McPeak
    Commented Jul 10, 2023 at 20:54
  • “but the agent is prevented from ever getting away from their zero starting point credence.” No they aren’t. They simply can update their prior once they observe DIRECT evidence of the mechanism of that hypothesis. In other words, what a hypothesis predicts is different from its actual mechanism. This is the fundamental flaw in Bayesian reasoning. There is nothing in the formula that covers this kind of evidence, since Bayesianism only deals with predictions. But arguably, it is the most important form of evidence. It’s the starting point that gets us to assign a prior > 0 in the first place.
    – user62907
    Commented Jul 11, 2023 at 5:18
  • 1
    @thinkingman How would you define "direct" evidence?
    – Scott McPeak
    Commented Jul 11, 2023 at 14:09
  • 2
    @thinkingman Hmm. Let me check my understanding. Imagine you've never seen an ice cube. So you assign a zero prior to the hypothesis (H) "ice cubes exist". Then I show you an ice cube, and you agree it is an ice cube, but you don't know how it came to be (you have not observed a mechanism), so your credence in H is still zero. Then I show you the ice maker I used, and explain how it works. At that point you update your credence in H to be non-zero. Is that right--is that what you consider rational behavior?
    – Scott McPeak
    Commented Jul 11, 2023 at 14:50