Timeline for Can a zero prior probability for some theories be justified?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jul 11, 2023 at 22:36 | comment | added | user62907 | Let us continue this discussion in chat. | |
| Jul 11, 2023 at 16:15 | comment | added | user62907 | The hypothesis we’re evaluating is ice cubes existing in your example, not “the ice cube is created using X and Y”. Directly observing an ice cube is evidence of an ice cube. Knowing that the ice cube forms using an ice maker is a different hypothesis and is unknown until I observe your ice cube machine. Neither of these processes involve Bayesian theory. It is completely useless for this kind of thing. And yes, this is rational, and much more rational than just asserting that something is possible by assigning it a non zero prior | |
| Jul 11, 2023 at 14:50 | comment | added | Scott McPeak | @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? | |
| Jul 11, 2023 at 14:39 | comment | added | user62907 | Observation of a mechanism | |
| Jul 11, 2023 at 14:09 | comment | added | Scott McPeak | @thinkingman How would you define "direct" evidence? | |
| Jul 11, 2023 at 5:19 | comment | added | user62907 | Without an actual mechanism, a non zero prior for a new hypothesis is actually what is irrational. Because this allows you to make the assumption that many theories, including a pink unicorn sitting in front of me, are possible. If you think this is rational, then so be it. | |
| Jul 11, 2023 at 5:18 | comment | added | user62907 | “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. | |
| Jul 10, 2023 at 20:54 | comment | added | Scott McPeak | @PeterLeFanuLumsdaine Good question! I added a paragraph addressing mathematical statements. | |
| Jul 10, 2023 at 20:53 | history | edited | Scott McPeak | CC BY-SA 4.0 |
add note about mathematical statements
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| Jul 10, 2023 at 20:16 | comment | added | Peter LeFanu Lumsdaine | 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”? | |
| Jul 10, 2023 at 16:47 | history | answered | Scott McPeak | CC BY-SA 4.0 |