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...")
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.
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 d
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) Loo...
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...
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.
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
"Self-evident" in the sense that they don't need any starting assumptions whatsoever.
Have you ever seen such a proposition? I don't think that I have. Not a single sage of recorded history has been able to come up with something whose self-evidence convinced everyone. And if someone is unconvinced, how shall you convince them, if it's "self-evident"?
The point I am making repeatedly because others don't seem to get it is that if there is no way to justify the premise that the world exists without resort to assumptions, then we're no better than the people who believe in God on faith.
What is this? If you have any unjustified belief, you are identical with someone who pays no heed to rationality at all?
And what does this have to do with probability in particular? You originally asked about probability, so I recommended works on the foundations. Even if none of them persuade you that they are a sound basis, at least you will be informed about the arguments and conceptual structures that people have created, at which point you may be able to productively search for something better.
But now you have broadened this to a requirement for a refutation of the Evil Demon/Matrix scenario. I see no possibility of any such refutation, because sufficient powers can always be attributed to the Demon/Skynet/Lizard Overlords/NSA to explain away any putative refutation. If there is a refutation, you will have to find it yourself.
I mentioned John C. Wright earlier, and there is more to say. He finds the ultimate foundation in the uncaused cause that is the Originator of all causation, the Good that needs no justification because it is the Originator of all that is good, proves their existence by the argument against infinite regress, and recognises them in the world as the Christian God, specifically as preached by the Roman Catholic Church. You could work out from that what his self-evident truths might be, for him to build these arguments on, but his actual self-evident truths are the religious visions that he had. He was never argued into any of this by the arguments that he presents (and neither am I, an atheist).
Self-evidence is a subjective property of a belief. The experience of self-evidence is the absence of experience of justification for the thing believed.
I explained my context was the refutation of philosophical scepticism in general- what I was after should have been clear.
1- You assume that the criterion of self-evidence should be based on being universally convincing. Why should this necessarily be so? Self-evidence comes when the contrary proposition simply doesn't make sense, as it were (simplistic example: free will). The question is how to deal with that with regards to demonstrating the validity of probability/induction. 2- Because the fundamental starting assumption is unjustified, we are no more justified in believing we know the truth than the people who believe in God on faith.
I've raised arguments for philosophical scepticism before, which have mostly been argued against in a Popper-esque manner of arguing that even if we don't know anything with certainty, we can have legitimate knowledge on probabilities.
The problem with this, however, is how you answer a sceptic about the notion of probability having a correlation with reality. Probability depends upon axioms of probability- how are said axioms to be justified? It can't be by definition, or it has no correlation to reality.