Skepticism about Probability

A sufficiently skeptical position is completely immune to criticism, or to any other form of argument. I don't see what anyone could hope to do about that, beyond not bothering arguing with people who profess such extreme skepticism.

(I am reminded of a little fable I think I saw in an old OB post. Human space travellers encounter an alien planet whose inhabitants have adopted an anti-inductive principle, with the unsurprising result that pretty much everything they do is miserably unsuccessful. The humans ask them "So why do you keep on doing this?" and they say "Well, it's never worked for us before...")

1. Are you familiar with Sextus Empiricus? If you like intransigent skepticism, you'll love him. And the SEP just published a new entry on him! While you are at it, you might want to look at this entry on a priori justification.

2. You are trying to answer Descartes' Evil Daemon argument. That is futile, because the whole point of the argument is to be unbeatable. But suppose you did come up with an argument against it; I can always come up with an even stronger "daemon" or whatnot that can defeat the argument. (There's always the classic "How do you know you're not dreaming right now?" also from Descartes.)

3. Perhaps you are not actually searching for something to defeat radical skepticism, but instead are trying to show everyone else the true nakedness of their epistemic pretensions?

This now has 90 comments, including 2 of my own. None of them are particularly enlightening, IMO, but this is still evidence that it's interesting or amusing. As such, I've retracted my downvote.

If the point is we can't derive the validity of probability from nothing, congratulations. You have rediscovered something significantly less useful than the wheel or fire.

So if you can't derive the validity of probability from nothing, what can you do?
1) Walk around in a self-induced fog of feigned ignorance, having slipped the fact that you have put logical derivation on a throne dictating "truth" without ever having questioned that operation. You certainly can't derive from nothing that logical derivation is the only source of truth.
2) Look out at the parking lot to see all the cars, look at the telephone, the cell phone in your pocket, and the computer on which you are typing. Contemplate the apparent facts that these all arise from groups of humans "knowing" things "well enough" to put, ultimately, millions of pieces together to create things with an astonishing level of actual complexity compared to even the most brilliant philosopher's gedanken experiment. Realize that this is either a show put on for you by a demon trying to trick you in to believing that the world is an orderly place who s bits and pieces obey discoverable rules so well that you can discover them and build things that didn't previously exist out of the pieces to do things you want... OR that the world really is like that.

And if you go the skeptical route, at this level, what do you gain? Because if I ignore your skeptical route and instead study engineernig and physics and chemistry, I gain the ability to build cars and bombs and phones and to become sufficiently wealthy that I can have children and pass my mind-numbing credulousness down in to the next generation.

So is the demon who is deluding us all winning? Or have we, by forcing it to up its game to the level of billion-transistor circuits and the beginnings of AI software that it must fake, called its bluff and forced it to create the world it thought it was faking?

If it turns out there really is/was a demon and at the end we spend the rest of eternity being tortured in flames while you stand there in your pit of flames telling us "I told you so," then I owe you a beer.

how are said axioms to be justified?

This is how I'd answer a sceptic:

If I put two apples into a bag that previously had two apples, I can take four apples out of the bag. Thus, I believe that axioms on which basic arithmetic is based are "justified". By the same token I believe axioms of probability and I'm pretty sure you see a close approximation of a "fair coin" on a daily basis, not to mention more complex behaviors which probability theory predicts very well. If after that you're still skeptic of the correlation, I expect you to have strong evidence against the correlation. I predict you'd say that this reasoning is circular because the whole notion of "evidence" is sort of dependent on the axioms (Bayes etc.), in which case I can't help you any more than say that the given axioms are what they are precisely because of empirical observations.

In a huge oversimplification that's how math theories are constructed - you add or remove axioms until the stuff it predicts corresponds to stuff we observe. The correlation is the goal.

Why should I take the skeptic seriously?

I cannot picture how I would live my life without coping with uncertainty. And I know that probability follows from various plausible axiomatizations of uncertainty. (E.g, Cox's theorem)

This makes me suspect strongly that the skeptic is playing terminological games, since there's no actual substantive thing I could do differently if they convinced me.

Belief in the axioms of probability theory is justified by the fact that someone with inconsistent beliefs can be Dutch-booked.

If you're willing to put money on your beliefs (i.e. bet on them), then you ought to believe in the axioms in the first place, otherwise your opponent will always be able to come up with a combination of bets that will cause you to lose money.

This fact was proved by Bruno de Finetti in 1930-ties. See e.g. AI: A Modern Approach for an easily approachable technical discussion.

I think that depends a lot on the specific skepticism you are dealing with.

how you answer a skeptic about ... reality

The standard answer is a punch in the nose. I have yet to meet a claimant to skepticism willing to let me perform this experiment enough times to get a trustworthy result.

Lighter-weight skeptics (those willing to at least tentatively accept some postulates about reality being real, and the validity of predicting future experiences) generally have no problem with "I can't justify these from first principles, but I'm using them until I can think of better".

"the question isn’t how to arrive at the Truth, but rather how to eliminate error. Which sounds kind of obvious, until I meet yet another person who rails to me about how empirical positivism can’t provide its own ultimate justification, and should therefore be replaced by the person’s favorite brand of cringe-inducing ugh." -- Scott Aaronson