C and not-C
And then there is this fella Andrew Pessin, who says you can be certain and also uncertain and that way all shall win, all shall have prizes. You do it using the Paradox of the Preface.
Imagine an author writing something like this as a preface to her work:
I am certain, of each and every sentence in this work, that it is true, on the basis of various considerations including the careful arguments and use of evidence which led me to it. And yet I recognize that I am a fallible human being, likely to have made some error(s) in the course of this long work. Thus I am also quite certain that I have made some such error somewhere, even if I cannot say where.
I could buy that if he had made it “I am sure, of each and every sentence” and so on. I could buy it if he had made it I am convinced, or I strongly believe, or I really really think. But by making it “I am certain” he turns the whole thing into gibberish. If you are already quite certain that you have made a mistake somewhere, then you can’t also be certain that you haven’t – you can’t be certain that every sentence is true.
Maybe he meant a kind of colloquial version of ‘certain’ which is like the colloquial version of ‘literal’ in that it doesn’t mean what the word means. I have noticed that a lot of people use the word to refer to claims that they can’t possibly be certain of, and wondered if they actually think it is an exact synonym of ‘sure’ or ‘convinced.’ But if he did…that’s kind of stupid, frankly, since the whole piece depends on that word, and he used it sloppily. You can’t be certain that you have made no mistakes and at the same time certain that you have made a mistake.
Anyway, I avoid this kind of tangle by simply never being certain or even sure that I have made no mistakes.
Yes, I read this yesterday, and was quite amazed by the silliness. Clearly, he doesn’t know what a paradox is. What he is describing is a contradiction. A paradox is when something seems obviously true, based on the sheer logic of the thing, logically can’t be true, like the Greek who said that all Greeks are liars. But when you claim that something is absolutely certain, though you’re sure there’s a mistake somewhere, that’s a contradiction. And he thinks peace is going to break out on the strength of it! Astounding! As Grayling says, religion rots the mind!
Professor Pessin is so palpably proud (no alliteration intended) of his big idea. What strange intellectual knots people tie themselves in so they can justify religion. Believe your beliefs are certain! Believe your beliefs are certainly wrong! There’s a mindset that sees paradox as something sophisticated or clever – not something to think through and sort out, but something to wallow in – like a divine mystery. But as E.M Forster said: a mystery is only a high-sounding term for a muddle.
“Clearly, he doesn’t know what a paradox is. What he is describing is a contradiction.”
I’m betting Pessin does know what a paradox is. From the Stanford Encyclopedia of Philosophy: “Most paradoxes — but not all — involve contradictions.” For example, you start out believing there is motion. Zeno has an apparently sound argument that there is no motion. Aha, so there is motion and there is no motion! The contradiction IS the paradox. Now you try to solve it, in the sense of showing either that there really is no motion or that there’s something wrong with Zeno’s argument. But grasping the paradox is contending with a contradiction.
So–of course Pessin makes the paradox of the preface out to involve a contradiction. It seems you can be certain of the conjunction of all the propositions in a book, and also uncertain (since you know you are fallible). That’s the paradox. One “way out” is to be less certain of the conjunction of all the propositions, but is that always possible? It could be that when you go through the propositions, the fact is that you are certain of each one. You’d be pretending if you said otherwise. So the paradox doesn’t immediately vanish with that suggestion.
How all that applies to the issue of religious disagreement is another story, but he’s entirely right to present the paradox of the preface as involving a contradiction. Finding a solution means dissolving the contradiction, but to appreciate the paradox in the first place is to wrestle with a contradiction.
I am both certain and uncertain that this sentence is mistaken.
He should have couched it in terms of probability: I have very high confidence in every claim I make, but chances are some of them are wrong. (e.g. 100 claims, each independently made with 99% confidence, stand a 63% chance of containing at least one error).
The air of paradox arises partly because of the unapt word “certain” and partly because of a failure to appreciate the sort of compound interest effect that happens with the chances of any individual error.
A few months back I had a catholic priest explain to me his view on the advantages of catholic theology over the theology of other religions. His claimed that the major point in favor of catholic thinking was that it allowed for two contradictory views to be maintained at the same time for many important issues (he didn’t exactly use the word “contradictory” but that is clearly what he was describing). He seemed to find this a masterful solution to tricky problems – when a flaw in one of the explanations is used you simply switch to the other and when that is found problematic you jump back to the first. He really didn’t see the very basic error he was making in all of this and thought that simply having an system of thought that gives an answer for every question is ideal (without wondering whether those answers may be true or not).
I’m not sure using “certain” rather than “sure” or “convinced” breaks the idea. If “I am certain of X” meant “There is (literally) probability zero that I am wrong about X” then you could never use it correctly; even for a trivial tautology you have to set aside a tiny non-zero probability for “evil scientists are messing with my thought processes to make think this is a trivial tautology”. So I think “I am certain of X” must mean something more like “I am confident enough of X that I’m prepared to just ignore the possibility of being wrong”.
That these probabilities we treat as zero turn into something we can’t sensibly treat as zero (even get arbitrarily close to 1 ) if we combine to many events is worth noting, I guess. It’s really, really not “the key to religious harmony” though. Pessin doesn’t even seem to bother making an argument that it is. He treats it as if it were the same as “I might be wrong” which he says is the important thing to remember, but constructing the “Paradox of the Preface” adds nothing to that.
Yes, of course, Jean, I should have been more careful. Paradoxes often involve contradictions, when you understand them. When you understand that the seeming truth of Achilles and the Tortoise, halving distances to infinity, contradicts facts about time and distance, you see why what seemed intuitively true is mistaken. But that’s the point about paradoxes. There’s often a contradiction at the heart of them, but it’s often hard to say why something that seems so obvious ends up in a contradiction. Paradoxes are a bit like optical illusions, like the duck-rabbit in Philosophical Investigations – now you see it now you don’t. It seems obvious, looked at one way, but then again, looked at another….
With religion it’s different. It’s not a paradox to say that Jesus is the son of God, on the one hand, or that Mohammed is the last of the prophets, on the other. Intuitively, neither is obvious, and they clearly conflict. But it’s just a straight contradiction, not a paradox. As to the Preface, being certain that you’re right but confident that you’ve made a mistake is not a paradox. If you’re confident that you’ve made a mistake somewhere, you have no right to be certain. That’s the problem with religion. It makes exhorbitant claims that cannot in the nature of the case be made good. It’s just straight, ‘I believe one thing (with certainty), and you believe another (with certainty), and we could both be wrong.’ In what way is this a paradox? In a paradox you have to start with something that seems, intuitively, just true, but as soon as you put pressure on it, it flips into its opposite. This is not the way religious belief behaves under pressure. There’s no way of putting pressure on it and getting its opposite.
Religion is based, as the standard line has it, on belief without adequate evidence. The possibility that any particular religious belief is true is vanishingly small, so no one has a right to be certain. Since there have been so many different religions, and are so many conflicting religious beliefs in the religious market place, people should recognise that the religious project is simply unfulfillable, since religions don’t simply say things like, ‘It’s possible that there is a god, and that that god’s name is Jesus.’ Fundamentalism, as many religious scholars have pointed out, is a modern phenomenon. There’s no longer anywhere to hide from the fact that religions conflict, and that religion and science are also in conflict. Biologos couldn’t get off the ground if there was no conflict. Every self aware person knows this, so, in order to be religious, you have to qualify it away (liberalism), or you have to hold the religion’s fundamental beliefs ex anima (fundamentalism). Pessin thinks you can hold onto religious belief in a third way, being certain, but yet not being certain. This is not, I suggest, paradox. It’s simply confusion.
As for the use of “paradoxical”, there’s another sense of the word which definitely doesn’t involve contradictions – it means roughly: “going strongly against received opinion”. This is actually one of the primary senses of the French cognate, but it is also used in English. (Somewhere Russell mentions it, but I can’t remember where, alas.)
Eric–Phase 1 in “playing with paradoxes” is appreciating the contradiction. Phase 2 is solving it–making it go away. In the best paradoxes, it’s hugely difficult to make it go away (I love the surprise exam paradox). The paradox of the preface doesn’t seem like one of the best, but it’s not really immediately obvious how to solve it.
The analogy he’s making with religious belief is not that there’s some paradox simply in different religions saying different things. It’s much closer than that. I’m actually very certain Jesus is not the son of God, there was no virgin birth, etc., etc. But occasionally I ponder the fact that I do have super smart friends who believe these things. That makes me uncertain about Jesus, etc. So there’s the contradiction: certain and uncertain. It might not be a matter of certain at one time, uncertain at another, either. The two attitudes (arguably) coexist.
What’s irking people (I think!) is that Pessin says I should ‘live with the paradox” instead of trying to solve it. So–no phase 2. I should just be certain and uncertain. That of course also allows my Christian friends to be certain that Jesus was the son of God while also (in deference to me) uncertain. (Which is supposed to lead to peace on earth…) I’m not saying I agree with him about “living with the paradox”–I just don’t think it’s a howlingly stupid thing to say, as many (at Jerry Coyne’s blog) seem to think.
Jean,
Certainty, if unqualified, does not leave room for doubt. It is an absolute. If someone says they are certain that Jesus is the son of god they are either being imprecise and mean they believe with a high degree of, but not total, certainty or they really do mean it, in which case there is no wiggle room open to them.
Matt, It sounds like you are just flat out denying there is any paradox of the preface, but it’s a well-known paradox! There are various possible solutions, and pros and cons to each one.
Jean,
What I am saying is that you are simply not understanding what words mean. I am not sure if you are doing on purpose or through ignorance. Either way it is rather irritating. You did the same at Jerry Coyne’s blog and got called on there.
Is English your first language ?
Jean,
Maybe this will make things clearer for you.
I will assume a basic understanding of probability notation.
To claim certainty is to claim that P = 1.
If P = 1 then P’ = 0.
What you seem to be saying is this:
If P = 1, then P’ > 0.
Which is nonsense.
Matt Heath,
Well I never do use it, at least not reportingly of myself. I never claim to be certain of anything. I just think it’s the wrong word to use, and I don’t use it.
Jean,
That’s not what’s irking me, at any rate; what’s irking me is the insistence on using the word “certain” when it’s the wrong word, coupled with the insistence that it doesn’t mean what it does mean. Judging from what was said on Jerry’s blog, that’s what’s irking a good many other people, too. As Matt Penfold says, the word is an absolute, and you’re treating it as if it isn’t – or rather, you’re treating it as if it is in the paradox and isn’t when you use it of your own degree of belief.
Well, I’m sorry, I still don’t think that he can use the ‘paradox of the preface’ here. I’m not even sure that there is a paradox of the preface, despite the fact that it has been claimed. For instance, I can finish my book, examine everything, and think it must be true. So, I say so in my preface. But then I admit that mine is only one point of view, and I may be mistaken. Of course I may, even if I can’t see it. That’s not a paradox. I may have warrant to think that what I have written is true, because I have examined everything, and I can’t see any mistakes, but it may not be. What’s the problem?
In Makinson’s original short paper on the ‘paradox’, he takes it to be irrational to believe that a set of beliefs is rational if any one of the set is not true, because then it would seem to follow that it is rational to believe both p and ~p. But is that the way rationality works? Rationality is based on warrant, not on apodictic certainty. If I check my beliefs thoroughly, and can detect no errors, then holding those beliefs to be true is rational. So, it is not wrong to claim that so far as I can tell, it is rational to believe the set of beliefs expressed in my book, but it is not silly to claim that I may be wrong. If I am wrong, then I will not believe both p and ~p, because, if it is established that I am wrong, then I should change my beliefs, and if I am rational, I will.
So, while I agree with you that lots of smart people believe stupid things, it doesn’t follow that there is a paradox here either. There is not one religious person I know who could say that they have good reason to accept with certainty all the beliefs that they profess, that they’ve examined them all, and so far as they can see, there’s every reason to believe that each belief is sound. In fact, apologetic theology implies that they can’t, because the point of it is to address difficulties of belief. It’s meant to set doubts at rest. (It seldom does, by the way.) The fact that there are other religious people who reject one’s beliefs entirely and accept another set of beliefs is one of the strongest reasons to question one’s own religious beliefs. To say that there’s a paradox here is, so far as I can see, just silly. We believe things for all sorts of reasons: because we’ve been indoctrinated, because it’s part of the qualifications of membership in a community, because we don’t want to hurt our dearest (cf. Darwin), because we’re afraid of the deep end of the pool, because we want to believe – we really do! – that our loved ones are not gone forever, because we’re afraid of death, and this gives us some comfort on dark nights, because … well, one could go on. Rationality is not the first consideration in the acceptance of religious belief. So the paradox of the preface, even if there is a paradox of the preface, which I doubt, can get no leverage here, because different beliefs, held with equal certainty, just are a reason not to hold one’s religious beliefs.
Something I wonder about. Jean, you said
Is it really Jesus it makes you uncertain about? Does it make you think ‘Hm, maybe Jesus was the son of God’? Or does it make you uncertain about the reasons for belief? Does it make you think something like ‘Hm, maybe there really are sensible reasons for believing Jesus is the son of God’?
If there’s anything I ever do use the word ‘certain’ about, at least inside my own head (I’m really leery of putting it in writing, and surprised that Pessin doesn’t have the same inhibition), it’s that I myself have no reason at all to believe Jesus is the son of God. There is nothing that feels like any kind of reason to believe that. If I try to entertain it I just immediately collide with the fact that I don’t even know what the hell God is, or is supposed to be, or what people mean by it, or how the hell they think they know all these detailed things about this ‘God’ we hear so much about. So I can’t even begin to believe that Jesus is or was the son of this meaningless signifier. (Meaningless to me.) I would still never say ‘I am certain that Jesus was not the son of God,’ but then I don’t feel any need to, because the idea doesn’t have any purchase on me to begin with.
But I can think about reasons for believing that, and what that might be like, and what reasons I might have if I were different, and so on.
Ah – I was typing mine while you were posting yours, Eric. We were thinking along similar lines.
Ophelia, You seem to want him to state the paradox so that there’s really no paradox–not even an apparent contradiction. He actually states it in a couple of ways, but it has to be stated so that there IS an apparent contradiction, or he wouldn’t be capturing the paradox.
At most what you could fault him for is not embracing your favored solution to the version that’s couched in terms of certainty–talking about degrees of certainty. I personally don’t find that immediately compelling, and a quick perusal of the literature shows that some others don’t as well. So I wouldn’t treat Pessin as a cretin for not sorting things out quickly by availing himself of that solution. The “we know better” tone of the thread at WEIT strikes me as naive, as much as that will “irritate” Mr. Penfold.
Ophelia, Call me whatever, but I do feel certain that Jesus was not the son of God. The whole idea is a logical mess. Jesus is God and God’s son–so one thing has to exist before itself. Ugh. I’m certain (100%) it isn’t true. On the face of it, there are also moments of uncertainty, when I contemplate how my super smart friend X believes it. A contradiction can’t be true–one thing (me) can’t really be both certain and uncertain. So… what to say?
It might be helpful to redescribe myself as not really 100% certain, or as not uncertain, despite my smart friend (more likely). Another possibility–I’m certain at some times, uncertain at others. Or maybe one area of my head is certain, another area is uncertain. If one of the least two is the case, should I try to fix myself? I take it Andrew Pessin is saying no, that it’s somehow beneficial to just to leave the two states be. Might not be right, but he certainly isn’t saying anything cretinous or crazy.
I think Eric was right, that there’s nothing paradoxical to the statement. It doesn’t have any entangled entailments that give you an intuitive sense that logic is being followed even though the conclusions are absurd. It’s just two discrete, inconsistent assertions, which have no intuitive force.
Also I don’t think there’s any issue with the use of the word “certain”, which is an unambiguous psychological state. So I think admonitions in favor of talking in terms of probability, not certainty, to be premature.
Why I find the passage unpersuasive is that I don’t think there’s any contradiction in it. In the first part, he talks about “thinking a thing true in virtue of”. I suspect that this is a sexed up way of talking about justification. Then in the second part, he talks about making errors unbeknownst to him, which is what is more characteristic of the sense of “truth” we have come to know and love. Derp. He conflates the two, but that’s his problem, not ours.
Jean, if I don’t think it’s a paradox in the first place, then it’s not that I want him to state the paradox so that there’s really no paradox, it’s that I think he’s doing something odd in using words in such a way that he creates a paradox where there isn’t one. I haven’t treated Pessin as a cretin, so that seems to me to be a red herring.
To follow up –
How is that different from just creating a paradox where there isn’t one? Why are you sure (if you are) that he is capturing a paradox rather than creating one?
Why am I so sure he’s stating a paradox, rather than creating one? I’m just giving him the benefit of the doubt, which makes sense considering that this is a time-honored paradox, recognized and written about by a lot of good philosophers. Also, recognizing a paradox is not a very big deal. It doesn’t mean affirming a contradiction, but just means saying there’s an appearance of contradiction. You can then sally forth and try to solve the problem.
I didn’t say you were so sure – on the contrary, I indicated that I didn’t even know that you were sure at all. Asking why you were so sure would have been rude, and I wasn’t rude.
It doesn’t make sense to me to give people “the benefit of the doubt” when that requires overlooking a sloppy use of words. I’m not an approximationist about language; I think we should be careful to use words precisely and to read them precisely.
Willful equivocation has a long and frankly tedious history in apologetics. I find Pessin’s application of the paradox of the preface to religious belief to be a rather pedestrian example of the genre, unusual only in being even more transparent than most. *yawn*
To Eric @ 16 and others:
Jean’s right that there is a paradox of the preface, even though Pessin’s presentation isn’t apt. The paradox doesn’t normally involve certainty. Here’s the original formulation, from Makinson’s 1965 paper “The Paradox of the Preface” (which you’re familiar with, I see):
Note that certainty doesn’t enter into this formulation, either as a propositional attitude (i.e. “I am certain that p”) or as a property (“It is certain that p”). And the paradox is this: on one hand, it seems like all the subject’s beliefs are warranted. On the other hand, they’re inconsistent and the subject knows they’re inconsistent. We’re inclined to say that warranted beliefs are prima facie rational beliefs. We’re also inclined to say that anyone who knows they have inconsistent beliefs is irrational in continuing to hold them. Put another way, we think it’s irrational to belief in a known contradiction.
Here’s another way of presenting the paradox that might clarify things. Suppose I (as a rational but fallible being) take an inventory of my beliefs. For each of my beliefs, I check and see if it’s true to the best of my ability. I throw out the false ones, since it would be irrational to hold a belief while simultaneously believing it’s false. Now, I’m in this position: for each of my beliefs, I believe it is true. One of the remaining beliefs is this one: that I have at least one false belief. I think this belief is true because I’m aware of my limitations and fallibility. This belief, however, is inconsistent with my other beliefs. But it doesn’t seem like I’ve made a mistake in my reasoning. Again, we have a paradox: it seems like rationality requires that I believe that each of my beliefs is true. It also seems like rationality requires (given my fallibility and past experience) that I belief that some of my beliefs are false.
I want to make it clear that my defense of the paradox of the preface as a genuine paradox does not mean that I think either 1) that Pessin’s presentation is a good one or 2) that the paradox of the preface can be used for apologetic purposes. The paradox of the preface reveals that our intuitive notion of rationality is confused. That doesn’t mean that we can have warranted certainty in p and warranted uncertainty in p simultaneously, as Pessin seems to suggest.
DEQ,
According to your phrasing, both are cases of warranted assertions. But if we look closely, we find that the former happen to be retrospective warrants, while the latter are prospective. And so you are misled into thinking that they are the same concept. They’re not. Retrospective justification comes on the cheap, but prospective justification is expensive.
Prospective warrant, to pragmatists of a certain Peircian sort, might as well be substituted for “truth”. In that case, we don’t have the prospective warrant that we think we have. Instead, we have a retrospective warrant, and a reasonable (but fallible) prospective claim. Or, if you like, the former is optimally justified, and the latter is sub-optimally justified.
Needless to say, there is no inconsistency between believing your claims are warranted (justified, reasonable) and believing that at least one of them might be in error. There are a lot of different ways of saying this: that the person has made an error without making a mistake; that they are justified, but not asserting a true claim; etc.
Benjamin –
I’m not clear which cases you’re talking about or what you mean by prospective and retrospective justification. In the second version of the paradox, at least, all my beliefs are justified by some combination of conceptual analysis and empirical investigation, including the belief that some of my beliefs are false. There doesn’t seem to be any difference in kind there.
There’s also some confusion, I think, about the nature of the paradox. Of course I can believe that all of my beliefs are justified and that some are nonetheless false. That’s not what’s at issue. The issue is instead that I belief of each of my beliefs (to use the second version) that it is true, and I also believe that some of my beliefs are false. This is genuinely inconsistent, and it is this inconsistency (together with some intuitively plausible ideas about rationality) that give rise to the paradox.
I’m happy to clarify. There are two kinds of considerations here. First:
Each has been verified using the usual methods available. Hence, “I am certain, of each and every sentence in this work, that it is true, on the basis of various considerations including the careful arguments and use of evidence which led me to it”. Notice two things. First, the beliefs about the warranted status of each is quite straightforward. We assume, by hypothesis, that he knows each of them because each has passed the tests, which he understands by consulting his memory of going through the motions. Hence, it is retrospective. Second, the standard for justification here is relatively low — each instance has passed stringent conditions under which they have been verified. That’s the sense in which the knowledge is cheap.
And then our second consideration:
Two things again. First, he doesn’t, as a matter of fact, know for certain that he will be shown to be wrong. That’s because of the problem of induction: he is erroneously applying past experience to the future case, which (most of us think) is more difficult to justify than mere retrospective justification. It is never as rational to assert the prospective forecast than to report on past successes. Also, trivially, the application of past knowledge to a future case is an instance of prospective justification. Hence, second: the standard of justification is quite a bit higher, and hence more expensive.
The verifying has been done in the first consideration. Meanwhile, in the second, all the weight rests upon faulty induction. Hence we eliminate the second consideration as a viable candidate, and are left feeling cautiously optimistic in our epistemology. To be perfectly explicit: when you say “The issue is… that I [believe] of each of my beliefs… that it is true, and I also believe that some of my beliefs are false”, you are not rationally entitled to believe that some of your beliefs are false in the same way that you are entitled to believe that each of your beliefs are true.
And needless to say, without any intractable contradiction, there is no paradox.
Also, while I don’t really know what conception of rationality you’re working with, the intuitive conception I’m working with has the following features: (a) it regards the problem of induction as a genuine problem, and hence it is vital for us to distinguish between retrospective v. prospective claims, and (b) it understands epistemic warrant as depending upon contextual standards (e.g., expensive v. cheap) which can’t be used at cross-purposes without producing vacuous puzzles. Of course, if you don’t share that view, then we’re not going to see eye to eye.
Is this clear? If not, please be explicit about what you find worrisome or confusing.
DEQ.
This is the part that I can’t understand. Why would anyone believe, quite simply, that each of their beliefs is true, and nevertheless that at least one is false? This is silly. It’s a contradiction and easily seen to be one. It’s not a paradox. I may believe that each of my beliefs is true – because I’ve checked, and can find nothing wrong – and yet believe that at least one may be false, since I’ve been shown in the past that some things I have taken to be true have been proved false.
I know what Makinson’s paper says, and I think he is wrong. No reasonable person would say something like, [P] “There is no possibility that any of the beliefs in my book is false, and yet it is possible that one or more may be.” But it takes the latter to generate the ‘paradox’. I don’t think there’s one here. And Pessin’s position depends on P. But worse than that, Pessin depends on its being the case that one believes a conjunction of beliefs comprising a religion, knowing that others believe a different and contradictory conjunction of beliefs comprising a different religion, and yet thinks it is perfectly rational to believe in the first conjunction, knowing that it is contradicted by the second. Given that the warrant for believing the first conjunction is questionable, as religious beliefs always are, the existence of the second conjunction should cause him to entertain the first conjunction with less conviction, but he thinks that it doesn’t. Not only that, but he thinks this is a good reason for those believing the first conjunction to get along better with those who hold the second. This is putting far more weight on a supposed paradox than it can bear. (I think all this is roughly also Ben’s point.)
So DEQ, QED.
Eric–I think what you’re saying gets back to the question of what a paradox is. A paradox involves merely apparent contradiction. Paradoxes can have solutions, where the contradiction is explained away. I think you’re mixing up these two stages–rejecting even the appearance of contradiction because you think you have a solution (I think Benjamin is doing the same thing).
So here’s why there’s an appearance of contradiction: (1) I go through my book, examining the sentences one at a time, reviewing the evidence for each one. I believe s1, I believe s2, etc. (2) Presumably it’s fair to say that I believe s1 & s2 & s3 … so I believe there are no errors in the book. (3) I then reflect on my fallibility and concede there must be errors. So on rational grounds, I believe a contradiction (there are no errors, there are errors). It can’t be rational to believe a contradiction, yet the argument seems to show its rational. Paradox!
In your attempt to deny even the appearance of contradiction, I think you’re not taking step 1 seriously enough, but who knows–maybe you have a solution. But lots of people have suggested solutions (since 1965–that’s a lot of people acknowledging an appearance of contradiction!), and when they do, they don’t all say aha, then there’s no paradox.
So Pessin is on solid ground when he says this is a paradox (again, it doesn’t follow there’s no solution). As for the application to the issue of belief (all kinds of belief–he’s clear about that)–I do not actually think he’s saying that every believer is in exactly the same condition as the author in the preface paradox. He’s saying very strong believers can adopt the same combination of confidence and humility (“humble absolutism,” he calls it), not that they are in exactly the same epistemic state. I also don’t think he’s necessarily saying it’s rational for them to adopt it (he says he’s making an absurd suggestion), but it’s nevertheless good.
So there’s a paradox, but whether it teaches us something about how to combine confidence and humility is of course open to debate.
But there again – those are different terms. How to combine confidence and humility is quite a different matter from how to be certain that and certain that not at the same time. And believing there are no errors is different from being certain there are no errors. And so on.
Jean’s comment is very helpful, because it gives possible common ground. I will agree, for the sake of argument, that you can have a merely apparent paradox. (Quine called these falsidical paradoxes).
The problem is that this isn’t one of them. The contradiction had no intuitive force to begin with. I understood the error almost immediately upon reading it. There was no sense of surprise or intractability, just a sense of error.
I’m happy to agree to anything about paradoxes. I’m not at all happy to agree that this one is about belief that and belief that not when the fact that it’s about certain that and certain that not is what I have been objecting to all along.
Right!
If this were just about certainty (the psychological state), then while it would jettison Pessin’s apologetics, DEQ’s formulation of the ”Paradox’ of the Preface’ would still be a live option. And if it were about certainty (the philosophical sense of apodictic certainty), then we might put on our Quine hats and simply say there’s no such thing — ever.
I think, with Eric, that DEQ and Jean are mistaken in thinking that the Preface example is even a falsidical paradox. That is because it is not rational to believe the two contradictory propositions.
Even Pessin, in his way, understood why. He constantly uses this phrase, “in their own right”, without taking seriously what the phrase entails.
To see the problem, let’s consider an analogy. Suppose I say to you, drunkenly;
(3) would be a correct, so far as it goes. But then suppose I said, “This shows that both (1) and (2) are equally rational claims.” That’s misleading at best, false at worst; since (1) is about a fictional character, and we know it, (1) does not have the warrant that (2) has.
Oh wow, that’s an interesting series of nested blockquotes!
Lordy, what is that?!
I don’t know, but I like it. It has a paradoxish, hall of mirrors sort of vibe to it.
Now no one will ever know. Ha!
The crowd disapproves.
☺☺☺☺☺☺☺☺
And lo they did write angry letters to the editor.
✍✍✍✍✍✍✍✍✍✍
Sorry, I fixed it just before you said you liked it. I keep this place tidy, man!
And another Salman Rushdie is born!
Just a quick point–all paradoxes involve apparent contradiction (what other kind could there be? Contradictory claims cannot be true!). That doesn’t mean their apparent paradoxes. In some cases the appearance is really, really compelling, in some less so.
Ophelia, I agree that the paradox of the preface may not shed the least bit of light on “how to combine confidence and humility.” I’m just defending a member of my tribe from accusations of being truly incompetent. Wrong is one thing. Incompetent is another. By the way–the guy’s been on David Letterman! He can’t be all bad. (That’s the classic Argument from David Letterman, just possibly fallacious.)
It is true that all paradoxes involve a certain kind of apparent contradictions. These are contradictions that are somehow intuitively surprising or challenging.
Unfortunately, this “paradox” has no intuitive surprise for some of us, because it is so immediately resolvable. There are no intuitions that persist in its favor, nor were there any troubles in finding out the source of the contradiction in the first place.
I can’t speak for Eric, but don’t have the intuition because I’ve been primed to spot these equivocations by reading Fogelin on the subject of skepticism and contextual standards. So if my remarks so far have not been helpful, and you’re interested in pursuing this, I suggest taking a look at this very short paper:
Fogelin, Robert. “Precis of Pyrrhonian Reflections on Knowledge and Justification.” Philosophy and Phenomenological Research. Vol. LVII, No.2, June 1997
That same volume contains replies by Dretske, Stroud, and Moser, as well as a reply to the replies by Fogelin. The paper is on the Gettier cases, but the manner in which he does the analysis is more important for present purposes.
As an aside, contradictory claims might be true — it depends on your theory of truth. Veridical paradoxes (again, Quine’s term) are so tenacious that we’re tempted to call them true contradictions. At the very least, a story about truth needs to be told — otherwise, it is sheer dogma to just assert that classical logic must hold come what may.
Replying to Benjamin @ 30:
In response to Makinson’s presentation of the paradox, you write:
Here you’re introducing certainty again. Certainty is a red herring. The paradox doesn’t involve certainty in either Makinson’s formulation or in my own preferred version (the second one in my original post). The same issue arises when you write:
Again, you’re introducing certainty, which is irrelevant. The writer may not be certain that he made a mistake. He may not know he made a mistake. But that doesn’t mean it isn’t rational to believe he’s made a mistake. Pessin talked about certainty, and that was a mistake on his part, since the paradox isn’t about certainty and doesn’t require certainty to get going.
That said, your objection to Makinson’s formulation isn’t really about certainty. So let’s examine it. Your claim, as I understand it, is that the justification for statements s1, …, sn is of a different kind then the justification for the claim that –(s1 & … & sn). In particular, the latter claim is justified through inductive methods, and (b/c of the problem of induction) inductive justification is always weaker than deductive justification. Does that sound right?
If this is your claim, then I see at least three significant problems.
1) There are a number of good solutions to the problem(s) of induction. In particular, I like Goodman’s solution; inductive inferences are justified when they conform to the canons of inductive reasoning as given by our best inductive logic. But you can pick your favorite; the important thing is that developments in formal epistemology give us solutions to Hume and Goodman’s riddles. You might not be convinced by any of them, but you can’t simply appeal to the problem of induction without at least addressing them.
2) Whether or not the problem of induction is solved, it’s just not true that inductive justification is always weaker than deductive justification. Here’s one reason why you might think otherwise: one might think that inductive inferences never license certainty in their conclusions, whereas deductive inferences do. But deductive inferences don’t guarantee certainty. I might, for instance, carry out a complex deductive proof, and because I’m not completely confident in my reasoning ability be uncertain of the solution even after the proof is completed. Or I might carry out a deductive inference but be uncertain of the conclusion because I am uncertain of the premises (for instance, when I’m making suppositions and inferring things from them). So deductive inferences don’t guarantee certainty, and so induction and deduction aren’t justified in kind
3) Even if you don’t agree with points 1) and 2), there’s no reason to think that the justificatory process used to establish s1, …, sn is deductive or retrospective, if these are supposed to be different notions. We can stipulate that s1, …, sn are all justified using inductive, prospective methods, in which case the supposed asymmetry disappears.
I don’t have any robust notion of rationality in mind. The problem of induction is a genuine problem insofar as it really does require us to examine closely our notion of inductive justification; it’s not insoluble. And I don’t care about whether or not justification is contextual; I think it is, but it’s irrelevant since we can stipulate that s1, …, sn and –(s1 & … & sn) are justified using the same methods and protocols. Alternately, we can restrict our attention to those beliefs in the set s1, …, sn that are justified using inductive/prospective methods.
———————
Replying to Eric @ 31:
Two points. 1) You’d believe the conjunction you describe because you have good reason to think each conjunct is true. Here’s the conjunction in my preferred formulation: For each of my beliefs b in the set b1, … bn, I believe b is true, AND I believe that there exists some belief c in the set b1, …, bn such that c is false. I believe the first conjunct for two reasons: first, because I’ve checked to the best of my ability, and second, because it’s a requirement of rationality; if I believed I had a false belief, rationality would require me to change my mind. I believe the second conjunct because (despite my best efforts) I have never been able to rid myself of all false beliefs before, and indeed I have no reason to think that any human is capable of that feat.
If I’m justified in believing the second conjunct, I’m also justified in believing the weaker claim that one of my beliefs might be wrong. But that’s irrelevant. I should, cēterīs paribus, believe something if I am justified in believing it (or perhaps only if I believe I’m justified; it makes no difference here). And I am justified in believing that at least one of my beliefs is mistaken. It’s inductive justification, to be sure, but it might not license certainty, but that doesn’t matter.
Pessin’s position might depend on P, but I’ve explicitly rejected Pessin’s formulation of the paradox and his attempts to use it for apologetics. So there’s that. My claim is just that there really is such a thing as the paradox of the preface. It’s not what Pessin describes, but it’s out there.
DEQ, yes you’re right about the certainty bit, I just needed to cover all the bases in order to keep the discussion relevant and on track. But by all means ignore those comments. (And I’m going to ignore your point (2), since it trades on my very same mistake!)
You understand my position exactly right. You go on to argue that there is a solution to the problem of induction. In order for my argument to be defeated, it would require that these “solutions” be so strong that they provide the same level of warrant as other claims we might make (deductive ones, for instance).
(1) I don’t have any favorite solutions to the problem of induction because I doubt that any exist. And so, as far as this is concerned, whether or not formal epistemology has any developments at all remains to be seen. So you’ll have to pick some and present them for me to comment on.
Let’s take your favorite, Goodman. If Goodman’s argument is as you say it is, then it’s not remotely illuminating. As you’ve presented it, we have to just “the canons of inductive reasoning as given by our best inductive logic”. And how do we justify these methods to a point where they have the same level of warrant as deductive inferences? We don’t. Or, if we do, you haven’t suggested how.
(3) The asymmetry arises from two points. a) We suppose from the outset that s1 &…sn are fully justified — it is an assumption by hypothesis. If we don’t make this assumption, then there’s no point of comparison — the paradox cannot arise. For in order for the paradox to even get off the ground, at least one of the declarations has to be held by the agent as true. And no plausible rational agent would hold a thing true when they know it is not justified.
b) Your solution is to stipulate. We are told to imagine a situation in which the epistemic context is the same for s1 &… sn as well as ~(s1 &…sn), such that they both come out equally warranted. Then, the asymmetry is certainly broken. So, for instance, imagine that our agent has a single source, the Inerrant Book of Life, which determines s1 &…sn and ~(s1 &…sn) to be true. In that case, we really would have a genuine paradox, a true contradiction – no doubt! Yet this is also a situation that is implausible.
In any case, it’s a tad unfair of you to start stipulating outside the box. I’m working with the example that has been given, and shown what its imperfections. The burden is now on you to make a variant of the “Preface” that is capable of pumping the intuitions you want to pump, in such a way that it avoids the problems I’ve demonstrated. But then we would not be having a dispute over whether or not “Preface” is a paradox, we’d be arguing over whether or not “DEQ’s Preface Variant X” is a paradox.
Jean, I don’t really like the argument to David Letterman! I think it’s possibly just a bit weak.
DEQ. You said:
I still don’t spot the paradox. What you are essentially saying is this: I have checked all my conclusions, and, so far as I can tell (Pessin’s ‘in their own right’, as Ben points out), they’re all right. So I accept the conjunction of n1,…….nn. So far so good. As I said, I have sufficient warrant to believe it. That makes me rational. I’ve studied the matter. I’ve checked. Now comes the next step. …. But, maybe I missed something. I have before. This doesn’t mean it isn’t rational to accept the conjunction n1,.. nn. And that’s why the next step just doesn’t compute for me. It depends on the ‘so far as I can tell,’ because the next step is: if it turns out that one of the conjuncts is not right, it’s all my fault. (The italicised phrase is important, and it is precisely where Pessin makes his mistake.) None of those who helped me with the book are responsible for it, and I’ll take the blame. But if so, then I can’t accept the conjunction of n1, ….nn, can I? So, I’ll have to go back to work. That’s implicit in the preface, surely, and if it’s not, the person is not being reasonable, whether rational or not.
So, intuitively, there’s no paradox. It’s not just that, to take the Achilles and the Tortoise paradox, you know there’s something wrong, but you’re not sure what. That’s what gives that peculiar ‘feel’ of a paradox, like the paradoxes of self-reference. But, in this case, it doesn’t even seem wrong. And no matter what you or Jean say, I can’t get a paradox out of it, because it’s saying something about belief at two different times. The preface is not saying that there is an error, but that there may be, for the author may, in fact, be right. At the time of writing the preface he has every reason to believe his conclusions are correct, even while he acknowledges that it may turn out that someone finds an error. If it’s paradoxical to say this, then any belief is paradoxical, because, after all, it could be wrong, and it is rational to accept that it could be. As I could be. But right now I can’t see it, and it’s perfectly rational for me to accept that I am right, even though someone may convince me otherwise. But that will be then, not now.
“it’s saying something about belief at two different times.”
Yes. It had occurred to me that this is just a chronological thing rather than a paradox. Yes you believe you’ve written each sentence with care, and, then, yes you’re aware you could have gotten something wrong. It’s also possible simply to oscillate between the two thoughts – which is not the same thing as believing both of them at the same time. Duck-rabbit. Duck, rabbit, duck, rabbit, duck, rabbit.
Yes it is a philosophical paradox in that we are led by apparently impeccable logic to a conclusion we are reluctant to accept viz. flouting the principle of contradiction. An ordinary paradox or lay paradox would be a proposition which we immediately take to be false but which turns out to be true.A possible basis for the paradox is the construal of facts as atomic. They exist as little individual nuggets of rationality, propositions that we hold and that link together to make conceptual schemas. That I think would be the earlier Wittgenstein of the Tractatus; the later would see propositions against a background ‘game’. The total picture of the rational process is to see it as open-ended, fallible and self-correcting. There are no moments that are opposed in this process. It is not a divisible one except in an abstract sense just as time is not really infinitely divisible pace Zeno’s paradox.As for Pessin’s dividend. That’s nonsense. In religious terms faith is more certain than knowledge so if you have faith then the proposition that one could be wrong doesn’t come into it.
No, Michael, it is not a paradox. And there is no flouting of the principle of non-contradiction. I write a book. I have checked everything to the best of my ability, so that I believe that what I have said in my book is true. I acknowledge the possibility of being wrong, but I don’t think I am. Therefore, I do not believe both p and ~p. It would be irrational for me, after having checked my work, and not finding any errors, to believe, I mean, actually to believe, that I got something wrong. The possibility of something’s being wrong is a different matter altogether, and I will face that possibility when someone shows me where I made a mistake, if in fact I have, but I cannot see it right now, so it would be unreasonable for me to believe at that time that I am wrong. It is quite right for me to believe that I may have got something wrong, but I would have no warrant besides the sheer possibility of having made a mistake to believe that I have. There is no paradox. It’s a mistake.
To say that the logic is impeccable is to beg the question. The logic is eminently peccable. The intuitions in its favor are non-existent, the puzzle easily resolvable.
Anyway, I’m willing to say this: for those of you who had some kind of intuitions that have caused you to puzzle over this thing interminably, then I recognise that, for you, it certainly must seem like a paradox, and so for you it must be a paradox. But for many of us, it isn’t even a falsidical paradox, because we have a more efficient epistemic standpoint. And one of the reasons why you might think that one epistemic standpoint is more efficient than another is if it eliminates and/or resolves the greater number of paradoxes in an intelligible and motivated way.
Which is ironic, coming from me, seeing as I’m perfectly happy to admit all kinds of true contradictions willy-nilly. To hell with LEM! Contradictions for all, hooray! …This just isn’t one of them.
Come, come, Benjamin. That is a bit too cavalier. After all, from ‘p.~p’ it is possible to derive any proposition. Every proposition, by this reasoning is true, and you only need to accept one contradiction to do it!
When you call X a paradox, you are only saying the reasoning (that leads to contradiction) initially appears to be impeccable. That’s not really saying much. Two minutes later, the job of the paradox-finder is to show why the reasoning isn’t actually impeccable. That’s exactly what Makinson does in the 1965 paper–first he presents the reasoning about the author as seeming proper, then he shows why it isn’t. (Initial appearance: the author is warranted in having inconsistent beliefs, even though nobody is warranted in having inconsistent beliefs. On further reflection: he’s not warranted, for a subtle reason Makinson identifies.)
So whether this is a paradox or not is really a question of initial appearances. To Benjamin and Eric there isn’t even an initial appearance of impeccable reasoning. To lots of people, there is. That’s why this is standard fare in books about paradoxes, reference works, etc. It’s also why dozens of philosophers have labored over the solution. If this were obviously bad reasoning, we’d all quickly agree on why, but over 45 years, there hasn’t been an agreement on what’s bad about it.
All that being said, the initial appearance of impeccable reasoning leading to contradiction is more striking in some paradoxes, less so in others. For example, in the surprise exam paradox, the appearance is overwhelming. Here, no where near as overwhelming. But you wouldn’t have so many people (well regarded epistemologists, logicians, etc) working on this for 45 years if there were no initial appearance, etc. That’s all it takes to make the paradox of the preface a bonafide paradox. Identifying paradoxes is partly a matter of human psychology, and how things strike at least many people–qualified people, that is. People who know their logic, epistemology, etc.
FYI– My way of thinking about paradox, with its focus on appearances, comes from RM Sainsbury’s very good book on paradoxes. The paradox of the preface is in there, thought it’s not one of the main entries.
http://www.amazon.com/Paradoxes-R-M-Sainsbury/dp/0521720796/ref=sr_1_fkmr1_1?ie=UTF8&qid=1275309877&sr=1-1-fkmr1
I agree with Jean, finally! Maybe this is an indication that the contextualist turn in epistemology is a real development.
Eric, logical explosion can only happen if you have a powerful enough logic, i.e., classical logic. Take out a few inferential rules (double negation elimination and disjunction introduction, for instance) and it doesn’t occur. These slightly less powerful ways of reasoning are called ‘paraconsistent logics’.
For what it’s worth, I see NO paradox. NONE.
There was absolutely *no* initial appearance of any contradiction whatsoever, and I ‘ve had to read 57 comments on this thread, plus several other posts and wikipedia entries, to finally come to the conclusion that there just may be something behind it all, if I try *really* hard.
Some paradox!
Hey now, there’s surely a contradiction there. I just don’t see how it’s a paradox. If there were no contradiction, then it would imply that it’s cogent reasoning (which it isn’t).
But I see exactly what Eric does, and that *is* cogent reasoning:
I mean, I am now starting to see how the imaginary preface-writer is in fact not thinking exactly this – or rather, I am now starting to see how he can be interpreted as thinking something slightly different, and that this can, with a lot of effort, begin to appear a bit contradictory. But why bother?
That’s because when Eric is writing his preface, he is not as confused as the Preface Writer, who asserts a contradiction. Hence, for the latter, there’s a contradiction.
Well, considering how confused this guy is, he shouldn’t be holding C in the first place.
Well, I don’t know, Jean. People have to talking about god and gods for centuries, millennia, and I’d say there are none. Same with fake paradoxes that get an entry in a book on paradoxes! I have any number of books that talk about god (seriously too)! Having said that, I’ll shut up! I checked back, and thought the discussion would have run into the sand by now, but no…., almost ten more posts! I think Tea has the right idea! But then I would say that, wouldn’t I? Thanks Tea! I agree, if the preface writer is so confused, he should be much more careful what he believes!
Just what I’ve been saying all along. :- )
I don’t think it’s out of the question that there’s no paradox here–which would mean: not even an initial appearance of contradiction. But if you wanted to argue for that, I think you’d need an error theory. In other words, you’d need to explain why so many logicians and epistemologists (etc) have been fooled into seeing this as a paradox, and you weren’t! That’s something I think we can probably do when claiming the majority has the wrong view about gods. Personally, I have no idea how you’d make the case here. The people supposedly fooled are awfully smart and well-informed.
I’m not really clear what’s so dumb about the preface author. Here–I’ll pretend to be the author. I believe everything I wrote in my book. I believe there are a few errors. You guys want me to not believe everything, but just be quite certain about everything (I take it). But it seems odd to say that just because of a few likely errors, I should spread a tiny bit of uncertainty over all 10,000 sentences in the book. Or should I direct a tad bit of uncertainty more carefully? But where? I really don’t know where the errors are, so don’t know where to aim.
All in all (considering the last paragraph), it strikes me as reasonable for me to believe everything in my book. At the same time, it’s reasonable for me to believe there are errors. Hence it’s reasonable for me to have contradictory beliefs about my book. But it can’t be reasonable for me to have contradictory beliefs. Hence, the paradox.
Is anybody biting (or have you run off to the Memorial Day parade?) As I say, this all just needs to have an initial appearance of making sense. You can think it has that initial appearance AND think there’s a solution.
The error theory here is the rise of contextualist epistemology in the 80’s or so
The error involves failure to observe how the use of the phrase “rational in its own right” for two separate statements does not allow us to infer that the two statements are equally rational
But belief is inherently tentative, isn’t it? Unless said to be otherwise. Sometimes that’s made obvious – one can say “I believe that’s right” in a tone that makes clear the belief is tentative. One can say “I believe Jill said she was getting the early train” and that means you’re not sure.
So I just don’t see belief that you’ve caught all the mistakes and belief that you could be wrong about that as flatly contradictory. Certainty that, yes; belief that, no.
But for all I know that’s completely tangential to what all these hundreds of baffled philosophers have been wrestling with all this time; for all I know there’s some deeply technical issue that I just can’t recognize.
But at the moment I don’t really believe it.
Eric:Some paradoxes work through misdirection like conjuring tricks. In this case the trick is to use our everday sense of knowledge as being delivered through propositions or as a chain of individual propositions. That seems ok until it’s not because it also rational to hold that we will likely be discovered to be wrong at some point. So we have to think that we are both right and wrong at the same time.The resolution is to be found in the distinction between the members of a set and the set itself. As Makinson states in his final sentence:
Roy Sorensen says something interesting and possibly relevant in his book about paradoxes–
It looks to me like there is that kind of tug of war in the literature about the paradox of the preface. It might take actually watching the spectacle to feel genuinely puzzled.
I don’t know what to say that will validate Michael’s intuitions. In order to retain the point, he’s asking us to pretend to be irrational (use our “everyday sense of knowledge”), and then asks us to appreciate what it would feel like when a person primed to use an irrational method is asked to think rationally. I decline the invitation!
But suppose that it were an effective argument. In that case, this same technique could be used to assert that any contradiction whatsoever is a paradox. Even the most unsurprising, banal inconsistencies become a sort of paradox. In which case, it loses any meaning.
However, the argument is not effective, because it downplays the stuff we already know. Our everyday sense of knowledge is a strange garden has a surprisingly large inventory, many different fruits. Nestled in one corner of the garden of common sense, we find the intuitions that help us understand what has gone wrong. (A stark example: A good burglar is good in his own right. Saint Francis is good in his own right. That doesn’t mean it makes sense to say that the burglar is equally as good as Francis.) If it takes more than a moment to access these intuitions, it probably just means that the path through the garden of everyday knowledge doesn’t extend that far in yet.
Benjamin, your analysis works for me when I think of the apparent paradox of “all Greeks are liars.” I can see how it appears as a paradox, and I thought it was a paradox when I first heard it. I had to think about it for a while before I realized that it can be resolved rather elegantly. But when it comes to the preface paradox, I just don’t see it. No appearance of a paradox whatsoever.
(Although, now that I think about it, this can be because I spent a whole week at a conference on contextualism before I ever heard of the preface paradox. So maybe that explains it, and you’re right. :)
Holy cow! This keeps growing like Topsy! (The internet is a great thing. Now I know where ‘growing like Topsy’ comes from! Asked where she came from Topsy (Uncle Tom’s Cabin), the slave girl, expected to say something about God, said ‘I guess I just growed.’ Great story. Never read the book.)
In order to think of the ‘paradox of the preface’ as a paradox, we need a very unnatural sense of ‘I believe’ — almost a religious sense that affirms that one can’t possibly be wrong. Popes can do this, apparently, but no one else that I know, and, of course, pope’s are wrong. (It gets them into a pickle too, because its so damned hard to say that you’re wrong, and they get stuck affirming things they may not believe, but must be true because said by another pope. Talk about chasing your tail!) Perhaps we need the more tentative German Glauben in place of Denken. But, as Ophelia points out, coming to conclusions is a tentative matter, not an apodictic one. Ich glaude dass ich recht habe, rather than I believe all these propositions to be true. There, as Ben points out, is the error theory. So, Makinson’s theory falls to the ground. It is rational to believe the collection of beliefs, considered as warrantedly asserted, to be true, even though one or more may turn out, on further examination, to be wrong. Rationality does not depend on the truth value of my assertions, it depends on the warrant for my assertions plus my willingness to revise my beliefs on further evidence.
Why there seems to some to be a paradox here may simply depend — I think it does depend — on different conceptions of what rational belief is. Clearly, according to at least one such conception, the paradox of the preface is a paradox, but this is, in my view, a very strange notion of rational belief. Rational belief just is the acceptance of warranted conclusions, and the willingness to revise one’s beliefs on further evidence. That’s probably too telegraphic to bear the whole weight of a philosophical analysis at this point, but I hope the intention is clear. In other words, Ich glaube dass …., but I could be wrong.
Tea, yes, that’s what I’ve been arguing! I only take issue with your claim that there’s no contradiction asserted; as you put it, “There was absolutely *no* initial appearance of any contradiction whatsoever”. There’s surely a contradiction, it’s just an unsurprising one.
Well, OK, saying “I believe everything in this book is true and I believe that something in this same book is false” is an obvious contradiction – but it all falls apart as soon as you learn the person’s reasoning behind his beliefs. And since the guy is explaining his reasons for his beliefs (I’ve checked it all, but I’m also fallible) at the same time as he’s explaining what his beliefs are (it’s all true because I’ve checked, but it’s not all true because I’m fallible), there’s not even a nanosecond left for any wondering.
Eric, But maybe it’s a math book, and as I go through it, I’m as certain as humanly possible before each statement. There’s no uncertainty at all, except with regard to the total collection of statements. It’s ad hoc to “tone down” what belief is, as it pertains to each statement, just so I can make it a little tentative when it comes to the total collection. That’s an ad hoc way to solve the problem.
So bearing in mind that it’s a math book: (1) the author believes S1, the author believes s2, the author believes s3, etc.. (2) Here’s the critical inference: then doesn’t it have to be the case that the author believes s1 & s2 & s3? It’s when we make that step that we get the problem. The literature on this paradox focuses on that inference. In fact, the literature gets technical very fast, because how are you going to block that inference? It looks impeccable.
People have proposed some very fancy logical maneuvers to deal with this. Honesty, I think the literature has to be read before you say it’s all a waste of time.
Jean,
I don’t think there’s anything ad hoc about contextualism. Of course if you believe that S1 is true and that S2 is true and that S3 is true, then you must also believe that “S1 and S2 and S3” is true – but only if you’re still using the same standards of what you consider a sufficient justification for holding a certain belief. The preface writer is cheating by switching between different standards!
What I’m trying to say is that the preface writer’s belief about the sum of his claims is no different than the sum of his beliefs about each of those claims separately: I believe S1 is true based on the evidence, but I’m fallible, so there’s a chance S1 may not be true. When you pile 10.000 of such claims on top of each other and call it a book, of course the chance that I got at least one of them wrong becomes more real. But that’s just all there’s to it, really.
Benjamin:Everything I know is wrong.My view is that this ‘atomic’ theory of knowledge is perfectly fine for most needs but that it buckles when too much load is put on it namely a prediction of fallibility which appears to give the impression of contradiction. Of course the matter is under discussion by keener minds than mine but here it seems to me that you have a simultaneous inside/outside dichotomy in which we are asked to assume two perspectives at one and the same time. The inside is the chain of propositions and the outside is rationality itself. As Makinson suggests in the sentence misquoted (author for other) Reason is dialectical.
Tea, I wasn’t commenting on contextualism, I was responding to something Eric said. Again, let’s suppose it’s a math book, and belief in each statement is very confident. What I said is that it would be ad hoc to pretend that belief is tentative all along the way, just to make it easier to assert that belief in the conjunction of all the statements was tentative.
But getting to your “contextualist” solution–There is something very puzzling about the idea that I need to adjust my standards or bring in new evidence to go from “I believe s1 and I believe s2 and I believe s3” to “I believe s1 and s2 and s3.” Good heavens, if conjunction isn’t simply a matter of logic, then what is? If the paradox of the preface has implications this surprising, it’s well worth paying attention to it. (You said “why bother?” way up.)
For another view of why you can’t make the inference from “x believes s1 and x believes s2…” to “x believes s1 and s2”, there’s this–
http://schwitzsplinters.blogspot.com/2006/07/paradox-of-preface.html
There are lots of competing theories about this.
Jean, you said:
I agree, this is very puzzling, so I’m afraid I wasn’t clear: What I’m saying is that one needs to (and the preface writer obviously does) adjust her standards somewhere on her way from “I believe s1 and I believe s2 etc.” to “But I *don’t* believe s1 AND s2.”
If it’s a math book, that does change things. But then why isn’t it ad hoc to make it a math book?
An ad hoc solution is one that doesn’t have independent credibility, but is just a “fix” designed to solve the problem. Is it credible that book authors generally believe individual statements tentatively? I tried to challenge this by presenting the best counterexample I could think of–the author of a math book. Even if it were the only counterexample, that wouldn’t make it “ad hoc” to mention it.
It’s also worth noting and re-emphasizing the way the Paradox was introduced. “I am certain, of each and every sentence in this work, that it is true, on the basis of various considerations including the careful arguments and use of evidence which led me to it. And yet I recognize that I am a fallible human being, likely to have made some error(s) in the course of this long work.” Those are two very distinct sources of evidence, as a matter of fact. Never mind whether or not we “need to” adopt different standards (in the way that I suggested and Tea emphasized, and not in the way that Jean suggested) — those just are different standards.
Michael, you seem to be barking up the wrong tree, though you have Jean there to keep you company. The atomistic v. holistic concern (or set vs. members of a set, etc.) is a red herring. The prime facie resolution to the problem at the top of the page involves acknowledging the separate sources of evidence, and the separate senses of rationality involved in treating them.
Just so – he lost me with that very sentence. One has no right to be certain that every sentence one has written in a book is true on the basis of standards of that kind. Of a math book, with proofs, yes, but that’s what makes math different.
That sentence itself irritated me – it’s the wrong way to think. It ain’t fallibilist.
Benjamin, You’re way off base. What I said had nothing to do with what Michael said. In any event, Michael’s part-whole intuition is entirely respectable. It’s in the literature in many forms–with lots of formidable proponents. Your “different sources of evidence” line is also in the literature in various forms. There’s a lot out there on this paradox. That’s all I really have to say about it–it’s complicated. I’ve said that about 50 times now, so I’m signing off.
Well Jean, just saying it over and over again doesn’t make it true, and it doesn’t even convince. Saying it’s in the literature doesn’t convince any more than it convinces when believers say that theologians have really compelling arguments. The literature may be complicated and fascinating, but what Pessin said isn’t. My post was about what Pessin said, not the literature.
I do admit to not understanding Michael terribly well, despite having some sympathies with the approaches he endorses. But his comment has a passing resemblance to your comment on the members of the set and the set itself, which is how I interpreted it.
Anyway, it may be that atomism/holism play into the solution, or into somebody else’s solutions, of course. But they do not have a central place in the contextualist line of argument that I’ve suggested, at least not as far as I can see.
I don’t deny that the literature is there; nobody does. But the question has to do with the effectiveness of the literature to deal with what I take to be a promising solution. Before I take the time out to pursue it, I have to trust that I’m not wasting my time with academic puzzle-makers who really are worthy of the scorn directed towards Pessin that we saw at the start of this thread. To get that kind of trust, it requires a token effort on your part to acknowledge the objection, and propose areas of weakness; not just a restatement of a position that we have seen reason to reject.
Deference to the literature in this way is fine, so long as it’s a way of opting out of the conversation due to time constraints, etc. But just to state the obvious, that’s not an actual defence; rather, it’s a demurral.
I haven’t been back to this for almost a day, and, just like Topsy, it growed (again)!
Jean, if you’re still reading, my point goes even for a math book, because even mathematicians make mistakes, and especially ones with my level of skill at it. That was (at least partly) Quine’s point in Two Dogmas, surely, though it’s almost half a century since I read it. You have a right to be pretty sure if you’ve checked all your sums, but it’s easy to make mistakes even in math, so a more modest, I’m sure, but I could be wrong, is in order.
As to there being a lot of literature out there. Well, yes, and there’s a growing literature on atheism vs religion too, but I’m quite prepared to ignore a lot of it, because it seems to me that defences of religion tend, on the whole, to be special pleading. I bought Eric Reitan’s book, because it was being said how penetrating it was, but when you read it, it’s just the same old same old.
I believe that the paradox of the preface is generated by taking a very strange conception of what people generally claim when they write the preface to their books, and an odd conception of what it is to have rational belief. It confuses what I have a warrant to believe, rationally, now, and what it would be rational to believe at another time, if someone shows that, despite my present warrant, what I now believe is untrue. That’s what I think anyway.
I have to admit that I do not understand Michael’s point when he says:
In fact, that seems to me to be wrong. Rationality, so far as I can see, pertains to the way in which we hold and defend our beliefs/propositions, and the way in which we revise them on further evidence, if required. In other words, it really is dialectical, and there is no inside and outside. Its a process, in other words, and it consists in holding our propositions to be true in a tentative way, responsive to evidence. And if that is what it is, I simply can’t generate the paradox, though I can see that, for someone given to more robust absolutist tendencies, there is a danger of falling into contradiction. That just means s/he should give up on absolutes.
Sorry Ophelia, there seems to be a glitch in the submit comment process. Yesterday I submitted one, and it never appeared. I got to a page which said something to the effect that the search produced nothing, and my comment was not posted. Today I got the same message, so I pinged again, and verily, there were two!
Ah that’s okay Eric – I get that occasionally too, but the comment always (so far anyway) has in fact been posted. Are you sure yours of yesterday never appeared?
Anyway it’s no biggy, it’s dead easy to delete duplicates at this new place.