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Skepticism about Probability
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.
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Comments (129)
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...")
Which means that anti-scepticism is a position taken on faith in the religious sense. It is, after all, the anti-sceptic who claims something can be known.
What I'm looking for is an argument that starts from no assumptions whatsoever but the self-evident, that gets to a justifiable probability theory. That would get around arguments such as the Evil Demon argument.
The sceptic also claims that something can be known: that nothing can be known.
Any conclusion can be reached by choosing the right "self-evident" assumptions; any conclusion can be denied by denying the self-evidence. It is self-evident to John C. Wright that God exists and His angels spoke to him in a vision. It had previously been self-evident to him that no such thing was possible. His rational mind pursues the implications of his latter beliefs as relentlessly as it did his previous beliefs. (His blog makes a fascinating case study in taking ideas seriously.)
What will be self-evident to you? Only you can decide that. You would be better off reading diverse books on the foundations of probability (Jaynes, Feller, Savage, de Finetti, Kolmogorov, ...) and seeing whether their arguments convince you, than asking someone to come up with an argument that you will find compelling.
I highly doubt those authors address the idea of scepticism in the sense of showing from first principles that probability is legitimate, in a way that addresses such things as Descarte's Evil Demon Argument. They are discussing how to implement probability, not whether the entire concept is legitimate.
You are denying the validity of self-evidence here, and admittedly there is a problem with properly establishing self-evident ideas. That's part of my problem, admittedly, and what I am trying to bypass somehow.
Nothing can address the Evil Demon Argument. Descartes thought it was self-evident that he thought, and therefore that he existed, but you can find various modern philosophers, and ancient ones of the Buddhist traditions, who declare that the self does not exist and claim to have none.
As a foundation for knowledge, yes, I am.
Doesn't "self-evident" mean that they don't need establishing?
"Self-evident" in the sense that they don't need any starting assumptions whatsoever. 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.
I am searching for a way to deal with the Evil Demon Argument etc. for that reason. As for said philosophers, they have a different concept of a self from Descartes and so to an extent are talking about different things.
Let us imagine two people. One believes "on faith" that (1) what their senses tell them has some correlation with how things really are, (2) their memory has some correlation with the past, and (3) their reasoning isn't completely random and broken. The other believes "on faith" those three things, and also that every statement in a certain collection of ancient documents is true, that a certain person who lived 2000 years ago was really a god in human form, that our true selves are immortal immaterial entities, and that after our deaths we will be judged and consigned to eternal bliss or eternal torment.
I'm quite happy saying that the first of those people is doing better than the second. S/he needs to assume far less; the things s/he assumes are more obviously true and more obviously unavoidable assumptions; there is less arbitrariness to them.
Both of them, indeed, fail if you judge them according to the following principle: "Everything you believe should be derived from absolutely incontestable axioms with which no one could possibly disagree". But why on earth should we do that?
You really should add a fourth- the principle of induction. You also misinterpret my premise- it is not that nobody could possibly disagree, but that the ideas could not possibly be false, even under an Evil Demon argument.
The problem is the same as the Isolation Objection to Coherentism- that if there is any actual correlation to reality, it is merely by chance rather than through actual evidence. This is because both groups have no basis for their assumptions.
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"?
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.
"Free will" is a concept, not a proposition. What is the proposition about free will that you are claiming to be self-evident, and its opposite "not making sense"?
Such an experiment doesn't exist. It's not self-evident that we don't live in a simulation in which strange things can happen.
I know it's not self-evident that we don't with certainty (and I said argument, not experiment), but I'm not trying to get to the conclusion we don't live in such a simulation- only that it is improbable.
Simple: The fact that we don't see strange things happening is bayesian evidence that we don't live in a world where that is possible.
As I already mentioned, it is probability itself which must be justified in the first place. How do you do that?
What assumptions am I granted? Can't argue anythin' from nuthin'. Even "I think" is an assumption if logic is.
This is the problem which must be dealt with. Rather than assume an assumption must be correct, you must somehow show it will work even if you start from no assumptions.
Your universal propositional calculus might not be able to generate that proposition, but my calculus can easily prove: Yours won't generate any propositions if it has no axioms.
This is precisely the problem. I was posting in the hopes of finding some clever solution to this problem- a self-proving axiom, as it were.
"Self-evident assumptions" sounds suspiciously like "axioms", yet axioms are apparently not what you seek. What exactly are you hoping to find? What would an acceptable "self-evident assumption" be?
Assumptions that can be demonstrated to be true in any possible universe.
As it has been fably noted, the assumption that cannot be verified is the induction (from past into the future). It is well-known in the area of philosophy (something with the words “induction is impossible”) that if something worked well before it won't necessarily work further (unless you assume apriori that induction is possible).
One can freely claim anything (any prediction / hypothesis) if induction is not assumed; the prediction happening to be false would not say anything about the validity of the induction and, thus, of the relevant models.
And the probabilities in particular can be justified from induction (additionally, some of the axioms are relevant to the mathematical representation of the probabilities, not to the notion itself). As well as Ockham's principle, and many other relevant ideas.
You have a point. Then how do you justify induction?
You don't (or “I don't”, if that's what you meant).
You could say something like that: “if induction is impossible then decision-making and communication are futile”.
However, that by itself does not disprove / dejustify claims that induction is possible but in other ways / with exceptions (on the lines of “the induction is possible unless applied to god^W magic”).
If you have no non-circular basis for believing in induction, surely it is irrational?
So, what are you trying to say?
"Better" isn't a function of the real world anyway- I'm appealing to it because most people here want to be rational, not because it is objectively better.
What do you mean by "rational" is not a binary?
“Better” / “preferable” / “utility” / … is necessary for “usefulness” e.g. “usefulness of this communication” (and also for decision-making).
By “not a binary” I mean the division is not into “rational” / “non-rational”, but into “more rational” / “less rational”; where “rational” is relevant to the aforementioned “better” (with regards to efficiency of optimization and also forms of communication).
… vaguely speaking.
On thought, my response is that no circular argument can possibly be rational so the question of if rationality is binary is irrelevant. You are mostly right, though for some purposes rational/irrational is better considered as a binary.
You apparently don't think it's self evident that induction works. Do you think that it's self evident that deduction works (like Descartes did)? If you do, why? If you met someone who was willing to accept the premises of a deductive argument but not the conclusion, like the tortoise in this parable, how would you convince the person they were wrong? The only way to do it would be using deductive arguments, but that's circular! So it seems that deductive arguments are just as "unjustifiable" as inductive arguments.
But if you reject deductive arguments as well, then you can't do anything. Even if you start with self-evident premises, you won't be able to conclude anything from them. Perhaps this is a hint that your standards for justification are so high that they're effectively useless.
A premise isn't self-evident because anybody whatsoever would accept it, but because it must be true in any possible universe.
Deductive arguments aren't self-evident, but for a different reason than you think- the Evil Demon Argument, which shows that even if it looks completely solid it could easily be mistaken. There may be some way to deal with it, but I can't think of any. That's why I came here for ideas.
You claim my standards of justification are too high because you want to rule skepticism out- you are implicitly appealing to the fact skepticism results as a reason for me to lower my standards. Isn't that bias against skepticism, lowering standards specifically so it does not result?
There are all kinds of things that are true in every possible universe that aren't self-evident. Look up "necessary a posteriori" for examples. So no, self-evident is not the same as necessary, at least not according to a very popular philosophical approach to possible worlds (Kripke's). More generally, "necessity" is a metaphysical property, and "self-evidence" is an epistemic property. Just because a proposition has to be true does not mean it is going to be obvious to me that it has to be true. Even Descartes makes this distinction. He doesn't regard all the truths of mathematics to be self-evident (he says he may be mistaken about their derivation), but presumably he does not disagree that they are necessarily true. (Come to think of it, he may disagree that they are necessarily true, given his extreme theological voluntarism, but that's an orthogonal debate.)
As for your question about standards: I think it is a very plausible principle that "ought" implies "can". If I (or anyone else) have an obligation to do something, then it must at least be possible for me to do it. So, in so far as I have a rational obligation to have justified beliefs, it must be possible for me to justify my beliefs. If you're using the word "justification" in a way that renders it impossible for me to justify any belief, then I cannot have any obligation to justify my beliefs in that sense. And if that's the case, then skepticism regarding that kind of justification has no bite. Sure, my beliefs aren't justified in that rigorous sense, but if I have no rational obligation to justify them, why should I care?
So either you're using "justification" in a sense that I should care about, in which case your standards for justification shouldn't be so high as to render it impossible, or you're using "justification" in Descartes's highly rigorous sense, in which case I don't see why I should be worried, since rationality cannot require that impossible standard of justification. Either way, I don't see a skeptical problem.
It seems we're using different definitions of words here. Maybe I should clarify a bit.
The definition of rationality I use (and I needed to think about this a bit) is a set of rules that must, by their nature, correlate with reality. Pragmatic considerations do not correlate with reality, no matter how pressing they may seem.
Rather than a rational obligation, it is a fact that if a person is irrational then they have no reason to believe that their beliefs correlate with the truth, as they do not. It is merely an assumption they have.
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.
Implicit assumptions- not just the senses, but the reliability of memory and the reliability of rules of induction.
I already mentioned that I believe in the world, not because I think it rational, but as an act of religious-style faith. I think it irrational to believe the world exists because it makes so many assumptions that can't be defended in a rational argument.
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 do you know you're not dreaming right now?" also from Descartes.)
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?
If we can have no a priori knowledge, it means skepticism wins because everything is based on faith. Given this, I try to find a means to make a priori knowledge work despite objections, both of this sort and skeptical.
If this is right, then radical skepticism wins entirely. The point is if it can be shown false on probabilities.
Yes and no. I do believe it hopeless, but I search because I'm looking anyway,
What does "skepticism wins" mean?
If what is right--that you can't be sure you're not dreaming? Of course that's right; how would you ever tell? Any method of distinguishing you came up with can't possibly be relied upon, because if you are dreaming, then that method only works in your dreamworld. In other words, it can distinguish between meta-dreams and dreams, but not between dreams and reality. (And there's no real reason to think it can even do the former, because hey, it's a dreamworld after all, and no rules apply.)
You search because you're looking? What does that mean?
Here's a question. I assume you are familiar with the probability-theoretic notion of maximum entropy. By "radical skepticism" do you mean the thesis that the only possible rational belief-state is maximum entropy?
It means we cannot be justified in knowing anything, and are isolated from any objective reality. The basic rules of probability from which we assume the reliability of memory, senses etc are taken on religious style faith.
I've been trying to find a way around this, but you are probably right.
I mean I am checking and and again just in case because I don't like the idea that scepticism is right.
I'm not familiar with that notion.
Justification depends on a function that tells you whether something is justified. I can easily justify a belief with the fact that a teacher taught it to me.
In what sense do you think it can not be justified and why do you think that framework of justification has some sort of reality to it?
Something is epistemically justified if, as you said, it has some sort of reality to it not by coincidence but because the rule reliably shows what is real. I am trying to find a framework with some sort of reality to it, and that requires dealing with scepticism.
If you don't believe in reality in the first place how could you check whether something has reality?
You need to look at reality to check whether something is real. There no way around it. Your idea for justification has no solid basis in reality if you don't believe in it in the first place.
You don't get to be certain about justification and be skeptic about reality. There are certain types of Buddhism who you could call skeptic about reality but they would also not accept the concept of justification in which you happen to believe.
I don't believe in the reality around us, not on a rational level- that does not mean I don't believe there are things which are real(there may be, anyway). I just have no idea what they are.
Justification is DEFINED in a certain manner, and I think the best one to use is the definition I have given. That is how I can be certain about justification (or at least what I am calling justification) and a skeptic about reality.
OK, let's skip to (4), as that might help you formulate your skepticism more precisely. "Maximum entropy" has more than one meaning, but here it basically means a belief-state that assigns an equal probability to all possibilities. In other words, it's the probability distribution you would use if you had zero information. For example, if I ask you whether glappzug is thuxreq or not thuxreq, you can't do better than to just pick an answer randomly. You have no clue to go on, so just get the choice over with and move on.
A thorough-going skeptic, it seems to me, would have to think that all choices are just like that one. Even when we think we have information, we don't really (because we could be dreaming!). Therefore there's no reason to discriminate between any pair of alternatives, or among any set of them.
When you say "skepticism wins," do you mean that for any set of alternative claims, there is never any reason to discriminate among them?
Probability itself being somehow valid is something I do not think rationally legitimate. Therefore, in a sense yes but in a sense no.
In that case, I don't know how to proceed until you formulate your skepticism more precisely. What exactly is it that is not justified, if "skepticism wins"?
Nothing is justified if skepticism wins. Unless we have irrational faith in at least one starting assumption (and it is irrational since we have no basis for making the assumption), it is impossible to determine anything except our lack of knowledge.
So on thought, yes. There is never any valid rational reason to discriminate between possibilities because nothing can demonstrate the Evil Demon Argument false.
OK. I am still not exactly sure what you mean by "justification." Let's put this in more concrete terms. Imagine the following:
What does the Evil Demon Argument (and all in its family) say about the rationality of each choice, compared to the others (assuming it says anything at all)?
What advice would you personally give someone sitting at such a dinner table, and why?
The Evil Demon Argument says that you don't know that it's actually those three things before you. Further, it says that you don't know that eating the rice will actually have the effects you're used to, or that your memories can be used to remember your preferences. Etc etc...
On reason, I would give no advice. On faith, I would say to have the rice.
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".
That idea proves nothing, and you know it.
It proves nothing to the skeptic. To the rest of us, it proves that the skeptic actually believes in reality, at least enough to flinch.
Why are you applying ad hominem selectively? You wouldn't use an ad hominem argument in most things- why is the skeptic an exception?
This isn't ad-hominem. I don't care which skeptic it is. I'm simply pointing out a pretty severe inconsistency between stated beliefs and actions. I use a similar tactic on a lot of topics where I don't have the time or skill to do ground-up research (and to help decide where it's worth the time). If the proponents of an idea behave very inconsistently with the idea, I update more strongly on their behavior than their statements.
The skeptic is making a prediction, that there is no probability or causality (they usually say "there is no basis for" rather than "there is no", but a quick recital of Tarski makes them equivalent). Anything can happen! If observed actions are inconsistent with that belief, that's evidence I should update on.
Note that the skeptic can't use this information, because there's no justification for belief that observation has any information about reality.
Ad hominem represents arguing based not on the evidence but on the character of the person giving it. This is bad because it leads people to instinctively ignore arguments from those they dismiss rather than considering them.
In this case it is also circular, as you presume the existence of the skeptic which you should not be able to know.
Wait. How do you justify any belief in what any statement or action will "lead people to" do?
In reality, I believe non-skepticism on religious faith whilst thinking that rationally speaking skepticism is true. I slip up from time to time.
I should note, however, that a lot of my argument is that the rules of logic themselves suggest problems with beliefs as they currently stand- namely those surrounding circular arguments.
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.
No sceptic familiar with the Evil Demon Argument would agree that 2+2=4, as this assumes the mind remains undistorted which is part of what is under discussion.
My belief is belief on probabilities on faith in the religious sense, rather than on evidence, as I do not believe such evidence exists.
What you have is a giant circular argument, and therefore useless. A skeptic doubts the senses give actual evidence, they doubt math, and they doubt your axioms of probability. It is downright retarded to use one of those to prove the others.
How many skeptics walk off the cliff expecting to continue walking? If you're skepticism is of the purely theoretical kind "sure, I doubt everything, but God (heh) forbid me act on these doubts" then I cannot help you either.
Besides, that's cherry-picking circularities. Let's go meta: don't you doubt your doubts? If you claim you can't calculate or measure the level of anything real because "that's axioms", what makes doubt in math/physics weaker than doubt in doubt in math/physics? And if none is weaker then the other, why don't walk off the cliff?
Part one is ad hominem, and has no relation to the validity of the argument.
As for part 2, the point is not that the world is certainly an illusion but that we don't know either way. Given that, meta-doubts are implied.
For me personally, my posistion is that rationally there is no way out of skepticism but that I believe it false on religious style faith.
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.
Can you clarify here? Starting from no assumptions whatsoever, how do things such as Cox's theorem get to the basic axioms of probability from which it can be inferred that the universe probably exists, that memories are probably accurate, and that induction probably works?
That's not the work Cox's theorem does. Cox's theorem tells you that if you believe in the universe, and you're going to deal with uncertainty, and you believe some (plausible) axioms, you should come out with something mathematically identical to probability.
I've never felt the need to justify my belief in the universe or that the past was roughly as I remember it. I've never seen any viable alternative to those beliefs.
Everybody I've ever met acts as though the universe exists. And you might say "we don't really know it, or even have evidence for it." But this feels like a terminological game. Everybody I've ever met seems to have some mental activity that looks like belief, that's updated in ways that look like induction. The burden is on the skeptic to label these things and construct an ontology that explains how we live our lives. I don't feel any need to justify acting as though the world exists.
Any account which assumes we do live our lives, or proscribes ways to do so, is not sceptical at all.
Besides, your argument is circular as you assume the world's existence. It also involves argument ad populorum, appealing to popular belief rather than evidence. Showing that humans are incapable of believing X does not refute X.
I cheerfully plead guilty on all charges.
I am not a skeptic. I am unbothered by any logical circularity in my belief in objective reality. I see no reason to worry about a belief I am incapable of believing.
Honestly, I can't quite picture what it would be like to worry about such things, let alone believe them. If the universe doesn't exist, there's nothing you can do about it, so why waste energy thinking about the possibility?
Circular arguments have no correlation with reality except by chance- you may as well make something up and believe it. It would make about as much sense.
It is correct that if skepticism is correct then there is nothing we can do. Logically speaking, since probability doesn't exist there is a probability of 100%.
I don't believe this is true. A circular argument is at least internally consistent, and that prunes away a lot of ways to be inconsistent with reality.
This assumes the falsity of skepticism to begin with. Even then, it is possible for a circular argument to be internally inconsistent.
For skepticism to be correct you would need to show that it's possible to be skeptic.
It's certainly possible to pretend to be skeptic but pretending to be skeptic doesn't make you any more of a skeptic than pretending to be a duck makes you a duck.
Not so. There is no logical connection between the feasibility of a human believing something and its truth. Something can be true and impossible to believe simultaneously.
I think that's the category that Wittenstein summarizes as "things you can't talk about".
But we are talking about scepticism. It's an exception to the Wittgensteinian rule.
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 De Finetti's justification is fine as far as it goes, but it doesn't go quite as far as people think it does. Here's a couple dialogues to illustrate my point.
Dialogue 1
A: I have secretly flipped a fair coin and looked at the result. What's your probability that the coin came up heads?
B: I guess it's 50%.
A: Great! Will you accept a bet against me that the coin came up heads, at 1:1 odds?
B: Hmm, no, that doesn't seem fair because you already know the outcome of the coinflip and chose the bet accordingly.
A: So rational agents shouldn't necessarily accept either side of a bet according to their stated beliefs?
B: I suppose so.
Dialogue 2
A: I believe the sky is green with probability 90% and also blue with probability 90%.
B: Great! I can Dutch book you now. Here's a bet I want to make with you.
A: No, I don't wanna accept that bet. The theory doesn't force me to, as we learned in Dialogue 1.
In Dialogue 1 I adjust my probability estimate as the bet is offered, no?
That's a reasonable thing to do, but can you obtain something like De Finetti's justification of probability via Dutch books that way?
The obvious steelman of dialogue participant A would keep the coin hidden but ready to inspect, so that A can offer bets having credible ignorance of the outcomes and B isn't justified in updating on A offering the bet.
Russel & Norvig:
"One common objection to de Finetti’s theorem is that this betting game is rather contrived. For example, what if one refuses to bet? Does that end the argument? The answer is that the betting game is an abstract model for the decision-making situation in which every agent is unavoidably involved at every moment. Every action (including inaction) is a kind of bet, and every outcome can be seen as a payoff of the bet. Refusing to bet is like refusing to allow time to pass."
I think a fair bet presupposes that both opponents will have access to the same amount of information, which is not the case in Dialogue 1. The bets in life are not always fair, but that has nothing to do with belief in probability axioms.
That Russell & Norvig quote doesn't appear to be a very good response to the objection it's addressing. De Finetti's argument is supposed to be a pragmatic argument for probabilism. In response to someone asking "Why should my beliefs obey the probability calculus?", de Finetti says "If you don't, you'll end up getting screwed (by being susceptible to dutch books)."
The response to de Finetti that Russell & Norvig are considering is "There are ways to get around susceptibility to dutch books other than accepting probabilism. For instance, I could formulate a policy of refusing to accept bets. Why is probabilism the right way to deal with susceptibility to dutch books?" Russell & Norvig are saying "Well, this is a thought experiment situation in which you are forced to bet."
OK, but that completely ruins the pragmatic appeal of de Finetti's theorem. I can feel the attraction of probabilism if it's the only way I'm protected against being screwed in reality. But not if it's the only way I'm protected against being screwed in an abstract model that doesn't match reality. Why should I care about getting screwed in a thought experiment?
That people often raise these objections is the reason why I prefer Savage's theorem as a decision-making foundation for probability.
This makes assumptions such as the existence of the world and the existence of bets which a global sceptic would not believe.
If you don't believe in the existence of the external world, then you shouldn't be worrying about the "notion of probability having a correlation with reality" in the first place. The OP presupposes the existence of the world. Do not shift the goalposts.
I never said I disbelieved in it- I'm postulating, not accepting a position. It is also worth noting that in my postulated position I was neither accepting nor rejecting the existence of said external world.
As I mentioned, this argument started out on the basis of trying to figure out if something could be known without assumptions that could not themselves be justified. If assumptions are necessary to know anything, it means that we effectively believe on religious-style faith.
I was arguing against a rhetorical "you", identified with the sceptic, not you personally.
That said, an extreme skepticism is altogether a different game compared to a skepticism about probabilities. The latter is reasonable; the former, although it cannot be falsified, is useless. Reality does not go away when one stops believing into it.
Logical skepticism, on the other hand, is self-defeating. To make a logical argument against the possibility of logical arguments, against the value of reasoning - that is self-contradictory.
The logical sceptic could argue that they are showing that logic is self-defeating- that when logic is taken to its ultimate conclusion it is shown to be false, therefore logically logic should be rejected. This is precisely what I would argue.
As for the matter of reality- if it exists, then of course it doesn't go away when we stop believing it. But how do we know that?
If logic is pennies, and blue is a sock, then why are cats punctuation marks? Yes, because your mask is Maryland, and WiFi smokes bananas.
(This is what happens when you live in a world without logic, and is the only response you should have to someone who is a logic skeptic).
See my below response gedymin.
Logically, "self-defeating" is not equal to "not self-defeating". If the skeptic rejects logic, then he should accept that "self-defeating" is equal to "not self-defeating". Therefore, if logic is self-defeating, then logic is also not self-defeating.
As for the second point - the epistemic perspective is more important than the ontological one. Seriously, read the conclusion of the "Simple truth".
This debate is getting silly, I'm out of here.
On the first point, if you get to a conclusion within logic which marks it as "self-defeating", then from a logical perspective logic doesn't work. Non-logic doesn't matter for those who aren't logical, but for a logical person logic matters.
On the second point, once you start postulating actually viable alternatives to the world not existing, and considering the Evil Demon Argument, there is nothing in there which is actually dealt with.
I think that depends a lot on the specific skepticism you are dealing with.
The scepticism I think is the most problematic is total scepticism. I've already explained the argument against it that scepticism about probability deals with.
"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
Complete elimination of error would logically imply knowing the truth.
Something like empirical positivism is like a castle on air- it makes assumptions with no basis in reality.
Given that it happens within physical brains it obviously does have at least some basis in reality.
Genuine deep skepticism doesn't happen in real brains and therefore has no basis in reality.
Circular argument- You assume a basis in reality which assumes skepticism is wrong.
Either there a reality and then there a basis or there reality in the first place and it's meaningless to speak about things having a basis in reality.
I mean do you believe that reality has a basis in reality?
I think we mean different things by "basis in reality". I use it to refer to something correlating with the real world, and evidence that demonstrates such a connection either probable or certain. Probability, of course, can only work if probability were somehow demonstrated valid.
Circular arguments do not count as a basis in reality, hence your argument, which assumes the existence of physical brains, does not work.