There is no faith required to use inductive reasoning, only to believe that it offers surety. And even then, only in the case that you are aware of the foundational limitations of inductive reasoning and still elect to trust in the surety of what it gives you. Otherwise it might just be a habituated belief.

Kitoba, I could be wrong, but I think the author is only saying that those are the only two prior probabilities that must be constrained for Bayesian reasoning to function. I'm not a statistician, but the claim doesn't sound that ridiculous.

Curious what you mean by the last word. Inductive reasoning convinces me that the sun will rise tomorrow with an extremely high level of confidence, though I wouldn't pretend it's like a mathematical proof nothing else could happen. I'm not sure whether surety is supposed to cover that or not.

Yes, that is what I meant by surety.



This is exactly correct. It doesn't sound that ridiculous. But take a closer look at what he actually said:



As the author intended, you focused in on the sentence in the center. That's the one that seems to carry the content. But look at the two sentences sandwiching it instead:

"You only need faith in two things... Anything else worth believing in is a deductive consequence of one or both"

That's the concealed philosophical claim he's making but not proving --that everything worth believing is Bayesian (i.e. within the Bayesian universe of discourse). It's certainly an argument one could make, but he's not making it, he's assuming it.

That's not to say the explicit argument he makes is correct, but whether you accept or deny his explicit claims, you're already conceding his implicit ones.

Would you then define faith as the gap between the results of inductive reasoning and a logical proof (a proof bound by and playing by all the rules of formal logic)?

I think I'd be comfortable calling that an instance or a usage of faith, but not a definition of faith. There could be many instances of faith in situations that were quite different. But yes, if you want to go from 99.9% sure to 100% sure, it's going to take faith to bridge you past that last .1%.

Up until that 0.1%, what is it? Merely a high confidence answer?

______

Also, to add to the fun, Sean Carroll weighed in on a similar question today:
Science, Morality, Possible Worlds, Scientism, and Ways of Knowing

Yes


That article is almost exactly what I've been trying to express --apparently poorly --within this thread. Would you say you agree with it?

One more point. Suppose one does not insist on crossing that 0.1% threshold. Suppose one is content with high confidence answers and stops there.



Is it now so really hard to understand?

______



That article is almost exactly what I've been trying to express --apparently poorly --within this thread. Would you say you agree with it?[/quote]

I agree with the article. I don't necessarily agree it is what you've been arguing.

Is it a difference in content or in emphasis? Or, to ask a more productive question, what have I said that you would view as conflicting with Carroll's views as stated in that article?



I don't believe most of us are truly satisfied with high-confidence answers, no.

This isn't anything different than I expressed before, so it doesn't change anything I previously said. But I'm not sure it's really a productive line of discussion. If your intuition doesn't match mine, it's a dead end. I'm not willing at this point to make any argument along the lines of "you only think you're satisfied with high-confidence answers". After all, Hume called the unwillingness to be satisfied with high-confidence answers a mental illness chiefly afflicting philosophers.

I'd like to point out that there is nontrivial context for the article. A lot of the site is about applying rationality, and one of the main approaches there is Bayesian. The idea that shifting your probability distributions around provides everything you really need to know (taking into account the probability that you screwed up your deductive logic brings that back to probability land, for instance) is probably the starting point for most there - and he's pointing out two exceptions to that.

As for high-confidence answers, well, I'm very sorry for 'most of' you then. As you say, though, not very likely to be fruitfully resolved.

Just to be absolutely clear, you're talking about the "Less Wrong" article, not the Carroll article, correct?



I get that. But he could have started the same article with the words "There are only two things you need to take on faith for Bayesian inference," and for all the people who accept that everything you need to know is Bayesian, the impact would have been exactly the same, and the article would have been more intellectually honest.

And if he absolutely felt he needed to add his judgment that Bayesian is all you need, he could have added a link to somewhere on his site where he had established that as a valid assumption. The danger in doing it this way is that potentially you can have a whole site full of articles that all start with the same assumption, but never support it.

Since you seem to know his site pretty well, is there a good article on it that supports the contention that all meaningful existence is inside the Bayseian universe of discourse? The only thing he really talks about explicitly in this article is mathematics, and even there I can think up several obvious counterexamples.

I would say that keeping in mind, that all you ever will get (about anything that is not a mental construct like mathematics), is high propability answers, is a good safeguard against deluding yourself. I don't think that is really a distinction between believers and non believers, at least many believers allow small propabilities, that they misundersood god, or some similiar formulation.

How much that point, that minimal propabilities of being wrong exist, is stressed seems to a large part depend on how much of a nitpicker you are and on rhetorics tactics (do you want to sway the audience, by declaring things an absolute truth, or do you want to apeare wise and not set in your ways, by admiting the propability, that you are wrong). Being a nitpicker is almost a prerequesite for being a philosopher, so it's not particulary suprising, that they often stress that point.

This is the implicit assumption that undermines this:



The problem here is there is a set of the population that does not fit the first if statement. Nor does it fit the second if statement. And then the entire argument devolves into statements of belief and intuition.

Provision of two or three of the obvious counterexamples would be helpful. I can think of some things that appear like that, but aren't.