The following claims are incompatible:
Beliefs are never under our direct voluntary control.
Beliefs are high credences.
Credences are defined by corresponding decisional dispositions.
Sometimes, the decisional dispositions that correspond to a high credence are under our direct voluntary control.
Here is a reason to believe 4: We have the power to resolve to act a certain way. When successful, exercising the power of resolution results in a disposition to act in accordance with the resolution. Among the things that in some cases we can resolve to do is to make the decisions that would correspond to a high credence.
So, I think we should reject at least one of 1-3. My inclination is to reject both 1 and 3.
But surely it is plausible that beliefs are not high credences,
ReplyDeletee.g. imagine (as in my previous comments on your excellent blog)
a spherical die with thousands of tiny faces:
You can roll the die around in your hand, surveying all the faces
and thinking, of each face, how unlikely it is to end up on top
when you roll the die, but that it might. So, for each face you have
a very high credence in the proposition that it will not end up on top,
but you do not believe that it will not end up on top.
Or consider almost all of our quotidian beliefs,
e.g. (as in previous comments here) the view from some window:
The chance of any particular arrangement of cars, leaves et cetera is low,
and so your expectation of having that view is low.
Conversely, your expectation of not having that view,
and your credence that you won't have that view, are high.
But it is of course not the case that you tacitly believe
that you won't have that view because on the contrary
you know that you will probably have some such unsurprising view,
and you can hardly distinguish between such views.
You may well say that a high credence of each not being the case
is quite compatible with a high credence of one of them occurring,
but that compatibility is paradoxical; and I just do not believe
that anyone really did tacitly believe, before they looked,
that the view that they have when they look was not going to be there:
they just are not ever that surprised!
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ReplyDeleteI should have justified this line:
ReplyDelete"but you do not believe that [for each of them] it will not end up on top."
The justification is quite simple:
You are not at all surprised when (for one of them) it does end up on top.
I think I do believe about each of the faces -- at least the ones I think about in particular -- that it won't end up on top.
ReplyDeleteAnd I am not surprised when some of my beliefs turn out to be false.
The following seems quite irrational to me: "I believe that p, and I know that q is more probable than p, but I don't believe q." So if I believe that p, I should believe anything more probable than p. In fact, I think I should believe anything at least as probable as p. But I believe that I am sitting now. The probability of that is maybe 1-10^(-10). So if a die has more than 10^10 faces, I should believe of each face that it is not going to be on top.
ReplyDeleteI think that we are using "belief" in different ways,
ReplyDeletebut I think that I am right. Cambridge defines "belief" thus:
"the feeling of being certain that something exists or is true"
and you are surely not certain that for each face it won't end up on top.
And I think that you should be surprised when a belief turns out to be false,
even though it is unsurprising that human beliefs should turn out to be false;
you believe that S is P, and then S is not P, why no surprise?
I suppose that some sort of Lockean assumption informs your reading of "belief,"
ReplyDeleteand so I am not surprised that you find "I believe ... believe q." irrational;
conversely, I think that my reading of "probable" is more nuanced than yours:
Of course you were sitting (or if not, I certainly am now),
and so the probability of that is 1. Now, you may wish to raise skeptical doubts,
but there is a tradition (again from Cambridge) that allows me such certainty ...
If you could show me how you get 1-10^(-10)? But
it does not matter, because insofar as you show me
I only lose my certainty that I am sitting momentarily,
I can always see that I am sitting, and so believe that I am sitting.
I could similarly see the equality of all the faces of the die (in theory)
and so not believe, of each, that it would not end up on top.
Doubts that I am sitting would, I am sure, also make me doubt
that I am seeing the faces of the die, to have beliefs about;
and there would be other nuances hidden in your 1-10^(-10).
The following pair seems quite irrational to me:
ReplyDeleteYou believe that one of the faces will end up on top.
You believe, of each of the faces, that it will not end up on top.
That is because this is contradictory:
One of them will be on top, and none of them will be on top.
So, we are both committed to things that seem irrational.
And of course, you can know that q is slightly more probable than p
but act as though it is only very likely that q is slightly more probable than p,
without loss of rationality.
Another potential problem for you: what about the following?
ReplyDeleteIf I know that p, and if q really is more probable than p,
then I know that q if I believe that q.
You know that you are sitting,
but do you know of each face that it will not end up on top?
To my ears that does sound worse.
Alternatively, of course, you can know that p,
ReplyDeleteand know that q is more probable than p,
but not know that q. (I note the intimacy of
belief and knowledge: Knowledge just is belief
that is indeed true and appropriately justified.)
I asked if you know of each face that it will not end up on top,
ReplyDeletebut of course I meant all the faces that do not end up on top;
still, that is the problem with your position:
You have the same feeling of certainty associated with each face,
but for one face you cannot have had knowledge because it did end up on top.
To call the other beliefs "knowledge" seems wrong, when the difference was pure luck.
But were you to accept that you should not call them "knowledge"
then there would be that challenge to your having such beliefs.
I can believe that I will very probably not win the lottery
ReplyDeletewithout believing that I won't win.
Why would I buy a ticket if I believed that I would not win?
I would buy a ticket if I believed that I might win,
even though I would probably not win, if the prize was big enough.
According to you, I can believe that I won't win
but still rationally buy a ticket (if the prize is big enough).
That seems quite irrational to me (but not to you).
So, there is this pair, your irrationality-for-me:
I believe that p, and I know that q is more probable than p, but I don't believe q
and my irrationality-for-you:
I believe that p, and I know that it can't be p and q, but I believe q anyway
(p is my not winning, q is that I may shortly be rich).
Of course, another route to my irrationality-for-you would be
to define belief to be a credence of over 50%.
Swinburne did that, I think; but perhaps you don't,
in order to avoid that irrationality?
If so, then you would accept that it was irrational.
If certainty is needed for belief, then I believe next to nothing. I bet that at least once per lifetime most of us have a dream that fools us with evidence about as good as I now have for the fact that I am sitting here. Once per lifetime is about 1 in 30,000, which is much worse than the 10^(-10) that I mentioned.
ReplyDeleteOn the large die, I of course don't know of *each* face that it won't turn up, since one cannot know the false. But I believe of each face that it won't turn up, and that belief is knowledge if it is true.
I can believe that I won't win while believing that I might win.
Certainty is not needed for belief, but there is a feeling of certainty associated with having a belief. And I am pretty sure that knowledge stands opposed to epistemic luck. But, you are right too.
ReplyDeleteI am pretty sure that there are several meanings of "belief" in the literature. I move logically from non-luck to not believing that the faces won't turn up, and then get nuanced about the probabilities; you are more Lockean. But there is a lot more being done in the literature too. Is there a right view about belief and knowledge? It seems like we need to have, as a society, a correct view about knowledge. But, it is not as if we have a single logic anymore!
I think that you are this irrational:
ReplyDeleteI believe that p, and I know that q is more probable than p, but I don't believe q.
You believe five propositions, and so you believe the conjunction;
or else you are that irrational, that you do not.
But, that conjunction is less probable than some other proposition that you don't believe.
It certainly can be rational to believe a bunch of propositions but not their conjunction. For instance, obviously, I believe everything I believe. But I also believe that the conjunction of all the things I believe is false, since obviously I know that I've made a mistake about something.
ReplyDeleteIt certainly can, but your example involves more than five propositions; there are almost certainly five propositions that you believe quite strongly and which are as I described: It really would be irrational to go through them one by one and then deny that you believe their conjunction. (It would probably be impossible to know which ones they were, and so actually do this, of course
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ReplyDeleteLet's say I have 125 beliefs, and I believe them all quite strongly but I am confident that I am wrong about at least one.
ReplyDeleteSo I disbelieve the conjunction of the 125 beliefs.
Now, divide up the 125 beliefs into 5 groups of 25. Thus, the conjunction of the 125 beliefs is equivalent to the conjunction of five conjunctions of 25-beliefs each. Either I believe each of the five 25-fold conjunctions or I disbelieve one of them. If I believe them all, then I have a case where I believe five propositions but disbelieve their conjunction.
So, suppose that I disbelieve one of the 25-fold conjunctions. Divide that 25-fold conjunction into a conjunction of five 5-fold conjunctions. I either believe each of the 5-fold conjunctions, or I disbelieve at least one of them. If I believe each of the 5-fold conjunctions, then since I disbelieve the conjunction of them all (since that's obviously equivalent to the 25-fold conjunction), I have a counterexample to your claim.
So, the remaining case is where I have a 5-fold conjunction which I disbelieve but where I believe the conjuncts, again a counterexample.
The argument clearly generalizes to any collection of n beliefs where n is a power of 5. With a little more tweaking, you can make the argument work even if n is not a power of 5.
How are those counterexamples?
ReplyDeleteI only need there to be some 5 propositions that you believe, but whose credences and dependencies are such that their conjunction has a probability less than your standard for belief. Given some such beliefs you would, I think, find it hard to actually go through them one by one (which you did not just do) and then deny that you believed them all, because 5 is such a low number (although high enough for the mathematics of the probability of their conjunction to work as I say).
You clearly misunderstood what I was asserting though, so I am unsure that the above will clarify matters much (I find it as clear as my original assertion); if not, then sorry
And I don't deny that there *are* some such 5 propositions. I can even give you examples:
ReplyDelete1. Simultaneity is relative.
2. Seriously human-harmful global warming will happen if we do nothing about it.
3. The true physics is indeterministic.
4. Angels are immaterial.
5. The ZFC axioms are consistent.
Of each of these, I think that the claim is true. But I don't believe their conjunction--there is enough room for doubt about each one that my confidence in the conjunction is too low for belief.
That clarifies it for me, thanks.
ReplyDeleteStill I want to say "You believe 1, and you believe 2, and you believe 3, and you believe 4, and you believe 5, and that is not what you believe.
I don't know why I thought that that was irrational!"
But seriously, I think that we mean different things by "belief."
You say "I think that the claim is true," and
you say "there is enough room for doubt," and
so I would say "I believe that S is probably P,"
where you might say "I believe that S is P."
I too believe that the ZFC axioms are probably consistent;
if I found out that they were, then I would not say "I knew it!"
I would say "I thought they were; now I know it." By contrast,
I believe that it matters that numbers are not defined by the ZFC axioms;
I think that I already know that.
By the way, I am finding your comments a useful way for me to feel that I have to clarify my own thoughts, as well as occasionally informative (and I am sure that they are more often informative), so many thanks
Incidentally, given your skeptical doubts, you cannot be 100% sure of anything;
ReplyDeleteso I wonder, when you move from knowing something in your sense (your thinking that it very probably is so, for good reason, when it is so),
to knowing it in my sense (e.g. having seen that it is so),
do you have words to describe that rather crucial transition?
For a concrete example, suppose you haven't been in a garden for a while, and it is time for a flower to be in bloom. I say that I know that it is in bloom when I have seen that it is. But you might say that before you see it. And having seen it, you cannot say that you are now sure that it is.
(I guess that my question distorts your actual views,
but at least it shows why I have mine
Martin:
ReplyDeleteI wouldn't say I know 1-5 on my list, but that I believe them. My probabilistic bar for knowledge is higher than for believe. I think 92-95% is pretty much enough for belief, but for knowledge I'd want something like 98% or better, and my beliefs on 1-5 don't reach that level. I could give another list of things I think I know where I don't know their conjunction, but it would be a bit harder.
I can certainly transition from knowing something to knowing it more confidently. Let's say I vividly see a horse in the hallway of my Department. That's enough for knowing it's there. But if a colleague were to say that she sees it, too, that would make me more confident.
The big transition is from high probability to certainty. There are very few things I accept with probability 1. Among these are:
- I exist.
- The truths of faith.
- Some basic logical principles.
- Some things that obviously follow from the above.
- Maybe a little bit more.
I would talk of the transition to certainty as just that--transition to certainty.
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ReplyDeleteThank you Alex, that clarifies it for me even more.
ReplyDeleteMy own thoughts now seem, even to me, to have been all over the place.
You have been very patient!
I see how your saying it isn't irrational,
ReplyDeletebut it is paradoxical (Moore's paradox):
"Simultaneity is relative, and seriously human-harmful global warming will happen if we do nothing about it, and the true physics is indeterministic, and angels are immaterial, and the ZFC axioms are consistent, but I do not believe that simultaneity is relative and seriously human-harmful global warming will happen if we do nothing about it and the true physics is indeterministic and angels are immaterial and the ZFC axioms are consistent."
Technically, I wouldn't say "Simultaneity is relative, and seriously human-harmful global warming will happen if we do nothing about it, and the true physics is indeterministic, and angels are immaterial, and the ZFC axioms are consistent". Instead, I would say each of the clauses as a separate statement.
ReplyDeleteSimilarly, if you took a book I just wrote, and replaced every period with an "and", I wouldn't agree, because although every sentence is sincere, I am quite confident that the conjunction of all the sentences is false.
I get the "technically," I think: We would read the (very short) book with such "and"s, and so it would be as though you said it.
ReplyDeleteI think there must be a difference in quality as well as quantity between the preface paradox and Moore's paradox, though.
Still, I have no idea what ...
Let your credence that p be 94%,
ReplyDeleteand your credence that q be 95%.
Suppose that betting that p is much less risky than betting that q,
in various subtle and not-so-subtle ways,
so that you tend to act as though p, and not q, a lot of the time.
You would seem to be believing that p, and not that q.
Might you not seem to yourself to be believing that p, and not that q?
Indeed, could it be that you were, in fact, believing that p, and not that q?
Or p could be 92% and q 93%, of course.
ReplyDelete