Great episode ! I would love to have more epistemology episodes like this one.

From a scientific perspective, more immodest hypotheses (i.e., hypotheses that make more and specific claims) are better because there are more opportunities or ways to test them. Vague hypotheses are harder to test, thereby making them less falsifiable or testable, which diminishes their value. But that's just from a scientific view. I suppose we're only focusing on philosophical or metaphysical hypotheses here.

Adding the giraffe as you talk about sticking your neck out is quite fabulous

This particular idea of intrinsic probability seems like it might find a natural home in Jon Williamson's version of objective Bayesianism: coherence being circumscribed by the norm of Probabilism and modesty being embodied by the norm of sufficient Equivocation (in the sense that more humble hypotheses mitigate worst case expected loss). OB holds that the rational set of positions to hold is sufficiently (if not maximally) equivocal while be constrained by empirical evidence and probabilistic coherence. Sans empirical evidence, these two norms are what determine OB's evaluations. They seem to align with Draper's points: the more ways there are for a theory to fail, sans evidence, the more intrinsically improbable it should be; e.g. cleaving between Asian and non-Asian crows introduces additional sources of possible failure (and entropy) into the hypotheses. I've been pursuing OB from a more statistical angle, but being a fan of Draper's in the past, I'm hopeful to see some synergy in other domains. A chief difference here seems to be that Draper seems to want to stop at ordinal (if not just qualitative) evaluation, while OB would assign genuine (though language-dependent) quantities about the contending hypotheses.

Here's a possible objection from a hypothetical critic: how can it be 'probability' at all if it is not numerically quantitative? Every probability theory must include numbers, right? If not, then perhaps we shouldn't even call it 'probability'. Maybe a better term for it is 'plausibility'.

Can't wait!

All of the following is already nicely captured by the Bayesian formalism, but I'll state it nonetheless. Related to what @CosmoPhiloPharmaco wrote, there is an interesting interaction between modesty and evidence. Namely that a less modest hypothesis H supported by some evidential test gains, all else being equal, stronger support than a comparable hypothesis which is more modest. H being immodest gives a test of the same strictness greater opportunity to falsify it. If this doesn't occur, then our belief in H should strengthen more than if it was also confirmed, but more modest a priori. As an example: Background assumption = No crow has any color (all are black, white, or somewhere in between) and there is no reason to favor any particular color distribution for the population over another a priori. H1 = All crows are black. H2 = All crows are exactly midgrey or lighter. H3 = All crows are exactly midgrey or darker. Notice that H1 implies H3, so H3 is less specific (more modest). Note that H2 and H3 are of exactly equal specificity. So, H2 is more modest than H1. Note also that H1 and H2 are incompatible - these are the hypotheses we want to compare by test. Now we magically uniformly sample a crow from the general crow population. Say it is white - this confirms H2. It certainly wins over H1, but since it covered half of the possible color spectrum already, this is not very impressive. Conversely, say the crow is pitchblack. This is the only color acceptable to H1, and yet it predicted precisely that. We should be quite impressed! While its initial immodesty was a mark against it - it had more ways to be wrong - in the event that those ways didn't realize, we must increase our belief in it much more strongly for precisely this reason. Thus, when comparing hypotheses in reality, where we usually ought to consider both the intrinsic probability and the evidence, the two may interact in unexpected ways if we're not careful with our thinking.

Have you heard of Solomonoff induction, in the prior probability of a hypothesis is lower if it requires a longer algorithm to fully specify? (It's essentially a form of Occam's Razor.) How does that compare to Draper's criteria? When Draper argues for "nothing else" beyond his two criteria, writing that "what else could its probability depend on?", an obvious answer is "the number of bits required to specify the theory."

ah yes, it's all very clear to me now

I have a hang-up with the crow example which I think illustrates a deeper question I have with this intrinsic probability, but I'm not sure how well I can word it so I'll try my best. How do asian crows being black inductively support non-asian crows being black? I feel like I kinda understand in that if some crows are black, it seems to set a precedent that crows can be black and so it seems more probable that non-asian crows are black. I think, if I understand properly (and my amorphous intuition is working). However, we can only make that claim because of our extrinsic knowledge of how species are related. Animals closely related share traits, so with that extrinsic knowledge, we can say that situation 1 seems more intrinsically possible than situation 2, but without that, there's no reason to think the two groups are related at all and thus we can't say either is more intrinsically more probable. Maybe it's just an example I have trouble understanding because I think the further discussion of incoherence makes sense. We do something that seems the same in mathematics when we do proof by contradiction. If a mathematical statement leads to internal inconsistence, we know it must be false.

What factors determine whether a hypothesis becomes a certainty? Can you be a Christian even though God will never stop being a hypothesis? In that case, is it moral to convert people into believers?

Great video. Do you have a specific account of how (i) the intrinsic probability of H and (ii) extrinsic considerations on H determine the prior probability of H?

Hypothesis (H)1: god is a brute fact and created the known universe. Hypothesis 2: the universe itself is a brute fact. H1 is less modest than H2. So on intrinsic probability, H2 is more likely. In the event that the extrinsic probability cannot be accurately assessed, or there is no way to distinguish which hypothesis has a higher extrinsic probability, the rational thing to do would be to accept H2. Is this a fair application of this theory?

This sounds like sphistry. The ball is round is more intrinsic possible than a ball is a sphere. Are you saying by adding more information to the arguement makes it less intrinsically possible? I'm just a simpleton but that is how it came across to me.

Is the modesty criterion just the product rule of probability theory? I.e., P(A and B) = P(A) P(B | A) < P(A) (or equal if A implies B).

One of the reasons I bristle so much at Draper's and your refusal to actually assign numbers to hypotheses is that, as I understand it, "intrinsic probability" is supposed to identify a unique rationally acceptable set of priors that would be assigned prior to observing any contingent events whatsoever. If that's the case, then once you compare two theories on modesty and coherence, the "and nothing else" clause says that we have everything logically required to pin down that unique number. So why is this such a huge ask? Carnap's theory did this... you give Carnap a language with atomic propositions and you just calculate the probabilities in half a second by counting state or structure descriptions. But maybe I'm wrong about my interpretation, though? Maybe this stems from a bigger worry I have: There are lots of adjacent concepts in the literature (related to "the uniqueness thesis" or "logical probability"), and it's not clear what Draper's proprietary terminology adds to the discussion. I would have liked the video to situate intrinsic probability in the context of more widely discussed ideas.

I have a huge problem with examples of modesty that use nested hypotheses (e.g., The claim that there is a person behind a door is nested in the claim that a particular person is behind a door). I agree with the relationship you state between the probabilities of the more and less specific events when one is a subset of the other, but these don't support Draper's modesty account because they follow from additivity and are thus true for any probability measure. It's just a total distraction imho.

This all seems rather subjective and toothless. It is fine to pontificate about which ideas we should prefer, but if there is no rigorous logical support for our opinions then how will we convince people who disagree? What if someone's cherished belief turns out to have low intrinsic probability according to our analysis? We have no numbers, no math to show them. We cannot clearly calculate that the intrinsic probability is what we say it is, so they may as well just reject our notion of intrinsic probability. One person says A is more modest than B, while another says that B is more modest than A. Now what?

What? No. A) all Asian crows are black, all non-asian crows are black B) all Asian crows are black, all non-asian crows are white 1) A) is more modest than B). A) has 1 assertion: All crows are black. B) has 2 assertions Asian crows are black. Non Asian crows are right. Else, a longer listing of types of crow that happen to include all crows, stating those are all black individually would be less modest despite being the exact same hypothesis. 2) A) and B) are equally coherent. A) has only one claim and the claims ob B) are independent. The claims of B) are dependent if and only if one would include premises not currently included. Like "a species should share the same color" (which is obviously nonsense). A hypothesis is less coherent if it states a rule but needs to specify opposing rules for certain cases. Like "the brighter a light source, the more energy is statistically has. Energy does warm things up. But the moon has light cooling the surface of earth". That's incoherent.

*Triggered*

Perhaps it is better to think in terms of theoretical virtues than in terms of intrinsic probability. I am not quite sure that more mkdest theories are intrinsically more probable (maybe they are), but I am quite sure that more mdoest theories are at least theoretically objectively better, and as long as they have explanatory power at least eqauk ti that of less modest theories, we should prefer the more modest one. This is just Ockham's razor at work.

Im curious if you interact with Climenhagas objection to drapers theory. Basically the objection is that his theory implies that uniformity is what makes theories more simple but that this runs into counter-examples involving coins and charge. Christian Idealism presents a version of this objection in one of his videos (although its been a while since ive seen it) I actually emailed Kyle what his view is given that he rejects Draper's approach and he said that he takes Ted Postons position of assigning 1/3 to theisms intrinsic probability. Although he said he is not "fully convinced" of Postons argument but thinks its the best we have for determining the initial probability

I didn't understand your presentation about coherence. Is it about uniformity about beliefs?

When you use the word "theory" are you using it in a colloquial sense or in the scientific sense. The race analogy is rather unsatisfying. When you said there was a race, the man on the Clapham omnibus will imagine a "fair race" ie all competitors will run the same difference. When you said they all ran the same speed but one person finished first, one can deduce that runner ran a shorter distance. Because that's how physics works. Not sure what the point of that analogy is.

Also triggered. Sorry but I call Theists out for using this language Im also gonna be upset at ya'll!!!

LOL, methinks someone needs to read some Karl Popper...