Justification, Inconsistencies, Contradictions, and Contradictories

Here are three principles of varying plausibility:
1. There can’t be any justified inconsistencies: propositions which are justified for a person and which logically imply a contradiction.
2. There can’t be any justified contradictories: no instances of p being justified for a person while ~p is also justified for a person.
3. There can’t be any justified contradictions: no instance of p&~p can be justified for a person.

The question I want to ask here is whether these principles stand or fall together as a group.

The third principle looks unassailable to me, except for the possibility of different modes of presentation for each conjunct (I assume here that propositions are bearers of truth value, not theoretical devices generated to solve the problems of cognitive significance). So here I’ll just assume that we fix the other features related to cognitive significance in order to focus on the epistemological point, and if we do, I think principle 3 is about as good a principle as we can get (except perhaps for epistemological instances of non-contradiction such as ~(Jp&~Jp), but such a claim is not strictly part of the theory of justification). Principle 3 is hard to argue for, especially the more wedded we are to closure principles about justification, but let us suppose that we can’t abandon 3, whatever else we do.

But the more wedded we are to such closure principles, the harder it is to reject any of the three principles above. We should, however, be suspicious of 1, since it appears to be a datum in Lottery and Preface that the claims justified by the evidence in those cases are inconsistent. There may be some notion of justification for which 1 should be accepted, but it is hard to deny the idea from which the paradoxes begin that the statements in question are justified in some important sense. Especially, the fallibility version of the preface paradox is difficult. If we assume that we are perfectly rational and also aware of our own fallibility, it is hard to deny that it is possible to be justified in believing all of our first-order beliefs and also justified in believing that some of our first-order beliefs are false. If we accept this reasoning, then whatever closure principle we endorse for justification can’t be strong enough to take us from a denial of 1 to a denial of 3, on the assumption that 3 is unassailable.

That leaves 2, which epistemologists often accept (if anyone knows of someone who explicitly denies it, please note it in the comments–it turns out to be an essential premise, for example, in arguments for Restrictivism, the view that any attitude taken toward a proposition is either epistemically required or forbidden.) I’m not sure why they do however. Denying 1 gives some reason to expect that 2 might have to go as well, since one can’t argue for 2 on the basis of 3 without also generating an argument for 1 (as far as I can tell). But if 1 is false, that leaves me suspecting that 2 is false as well.

Here’s an argument to that effect. For 1 to be false, we need a body of evidence that can be partitioned into one part that supports one claim and another part that supports other claims that in fact are inconsistent with the first claim. (For a particular example, let the first partition support your fallibility claim that some of your first-order beliefs are false and the second partition support all of your first-order beliefs.) Moreover, these parts cannot interact in such a way that each partition defeats the support provided by the other partition (otherwise we will lose the argument against 1). But if such partitioning can occur, why can’t the partitioning still occur when the first partition supports p and the second supports ~p?

One might hope for the following kind of answer: the conflict between p and ~p is too obvious to ignore rationally. Maybe so, but the conflict between one’s first-order beliefs and one’s fallibility belief is obvious as well, but to use this conflict to undermine 1 above, we have to be able rationally to ignore the conflict.

So the question is whether it is possible to retain 2 & 3 while rejecting 1. If this can’t be done, then so much the better for coherentism (since the Foley-type attack on coherentism is just that it must reject 1). If any reason for rejecting 1 is also a reason for rejecting 2, then, I think, so much the worse for Restrictivism. And if all three claims above have to be rejected, I have no idea how to start anew in thinking about the theory of justification.


Comments

Justification, Inconsistencies, Contradictions, and Contradictories — 50 Comments

  1. Hi Jon,

    One quick point:

    If ‘x is justified for y’ implies (P) ‘x makes y probably true’, as I think it does, then I believe the fate of 1, 2 and 3 will hang on the reading of ‘probable’ we favor. If we favor an objectivist reading, then, since contradictions are necessarily false, 1 and 3 are true. 2 is also true, according to the objectivist reading of (P), for either p or ~p has an objective probability of .0 and this proposition can’t, therefore, be made probable by the subject’s evidence.

    If, on the other hand, we read (P) in a subjectivist perspective and x has to make y probable to a subject z, then I think 1, 2 and 3 can be falsified. To see why 1 can be falsified in a subjectivist interpretation of (P) consider Frege’s epistemic position in relation to the axioms of his system of logic before he read Russell’s message telling him about the paradox they imply. To see why 3 can be falsified in a subjectivist interpretation of (P) consider Kripke’s example where Pierre seems to be (subjectively) justified in believing an instance of p&~p. If the example proposed by Kripke shows that 3 can be falsified by a subjectivist interpretation of (P), then I think it also shows that 2 is also falsifiable, according to this view.

    I hope some of this makes sense.

  2. Suppose we agree to take a subjectivist interpretation. The Kripke case won’t count here, given my stipulation that we fix all the elements of cognitive significance other than propositional content. The Frege case counts against 1 for sure, but not against either 2 or 3. So I think at most you will lose 1, unless some closure principle forces a denial of 1 to turn into a denial of 2 and 3.

    In any case, though, there are decisive reasons for thinking that justification doesn’t entail any claim about probability that satisfies the standard axioms of probability theory.

  3. Hi Jon,

    In a lottery case you can partition the evidence into the part that supports the claim some ticket will win and the other part which supports all the individual claims that ticket 1 will lose, ticket 2 will lose, etc. I don’t see, though, that the latter partition supports the claim that every ticket will lose. The reason that each particular ticket will lose is probabilistic, but those reasons don’t support the claim that every ticket will lose. It seems a similar point holds for the preface paradox as well. Maybe, though, I’m missing something.

    By the way, how does 1 & 2 relate to multi-premise and single-premise closure? My guess is that 1 is the analog for multi-premise closure, 2 for single premise closure.

  4. Jon,

    Thanks for your reply to my comment.

    I can’t think of a version of closure for justification that BOTH commit someone who distinguishes between objective and subjective justification with the denial of 2 and 3 AND doesn’t confuse the two readings. Can you?

    I believe one could say that Frege had justification to believe in contradictories: the axioms of his system ‘L’ of logic gave him good evidence for him to infer ‘L is consistent’, but, from our point of view, the same axioms gave him good evidence for him to infer ‘L is inconsistent’. Nonetheless, I think this confuses objective with subjective justification.

    As for justification and probability theory, you are right to point out that the axioms of the standard probability calculus don’t suit well with epistemic notions of probability. On the other hand, if you think about objective justification as non-defeasible justification it seems that you are committed with the claim that S can’t be objectively justified in believing p, if p has an objective probability of .0, because if S were objectively justified in believing p there would not be any defeaters of his belief that p, and there is one – ~p.

  5. Jon,
    Here is a simple-minded objection to your argument for 2. Say you partition your evidence into one part that supports p and another part that supports ~p. The problem is that a responsible epistemic agent needs to try to consider all her evidence when forming beliefs. So, when she thinks about whether p is true, she must not only consider the evidence in the partition that supports p, but the evidence in the other partition too. But doing this will mean that she won’t be able to form a justified belief that p or that ~p. After all, the evidence in the ~p-partition would justify a belief that ~p in the absence of the evidence in the p-partition, so how can she form a justified belief in p given that the evidence in the ~p-partition is part of her body of evidence (and vice-versa)? So I don’t see why the fact that you can partition your evidence in the way you describe means that 2 is true.

  6. Good comments here. I’ll respond quickly to each.

    Rodrigo, I don’t understand the first paragraph, can you try again on the closure point? On your last paragraph, though, what you say commits you to the view that there can’t be objectively justified false beliefs. But there are such beliefs.

    Ted, if I’ve got adequate evidence for the claims that ticket 1 will lose and that ticket 2 will lose and . . . ticket n will lose, an extra premise is needed. The extra premise is that there are n tickets in the lottery. From these claims I can competently deduce that no ticket will win. If the information in this partition interacts with the information one has that supports the view that some ticket will win, then all is fine. But the idea is that the partitions don’t interact.

    Suppose, though, that one doesn’t actually deduce that no ticket will win. We don’t want a closure principle that tells us that if we have justification for each of 1. . .n and 1. . .n entail q, then we have justification for q. But the entailment is so simple and obvious in this case that I think we shouldn’t hold out much hope of avoiding the problem here by denying that we’ve got adequate evidence that no ticket will win.

    What I’m rejecting here is your idea that the probabilistic evidence for each claim somehow infects the quality of evidence for the conclusion. My response is this: either the probabilistic evidence is of the sort needed to warrant detaching the claim from the high probability operator or it isn’t. If it isn’t, then we don’t have justification for the claim that a given ticket will lose. But if it is sufficient, then we get justification for the undetached proposition. Once we have such justification, why wouldn’t we be allowed to use the claim in further inferences? In particular, you have to answer that question without bringing in the fact that the evidence for the claim is probabilistic.

    Dylan, the notion of justification in question is propositional justification, so we aren’t talking here about processes of belief formation but rather about quality of evidence. And if we translate your worry into the language of propositional justification, you’ll have to deny what looks pretty obvious in Preface: that the author can have adequate justification for each claim in the book as well as adequate justification for the preface claim that mistakes remain.

  7. There can’t be any justified contradictions: no instance of p&~p can be justified for a person.

    Do you really mean “no instance of p&~p”? In that case (3) seems trivial. Every instance of that schema will be a contradiction on its face. Or do you mean for (3) to preclude justification for propositions that are less obviously contradictions? Do you mean further for (3) to preclude justification for propositions that are necessarily false though not formulable as a first-order contradictions? What Plantinga might call the ‘broadly logically impossible’? Things get more interesting in these latter cases. You might recall van Inwagen expressing some uncertainty over whether (I’m paraphrasing) it is possible that there is 5″ thick transparent steel. Supposing that’s impossible, it certainly seems like I might be justified in believing that such steel is possible. It might also be impossible (now, Rowe) that I’m in less than perfect company: where I am in less than perfect company just in case every existing being has some flaw or other. I could be justified in believing that, I think.

  8. Jon,

    I won’t have to deny that the individual propositions are justified, only that the conjunction of all of them is justified, which seems plausible anyway. Given what the author says in the preface, he isn’t justified in believing that the conjunction of all the claims in the book he makes are true, even if he is justified in believing of each individual claim that it is true. The evidence he has that he’s made a mistake somewhere because he’s fallible doesn’t defeat his justification for the individual beliefs he has, but it would defeat his justification for believing that they’re all true. To get an argument for 2 from the preface case it seems to me you’d have to say that he’s justified both in believing that there’s a mistake somewhere, and for believing that all the claims in the book are true. But isn’t that implausible?

    Finally, it seems like a principle analogous to the one I mentioned in my previous comment is correct. For instance, a proposition’s (epistemic/evidential) probability is typically taken to be its probability given all of a subject’s evidence. Analoguosly, assuming that p is justified by S’s evidence, it seems it would have to be justified given the whole body of S’s evidence. Now you just run my argument… The point is that p can be justified on the p-partition alone and likewise ~p on the ~p-paritition, but neither p nor ~p can be justified on a body of evidence that includes both partitions. And this doesn’t prevent us from saying anything we want to say about the preface or the lottery for the reason given above.

  9. Jon,

    I think the evidence does warrant detaching the probability operator, where this means something like the content of the belief is the proposition minus the probability operator. That proposition is justified but I don’t think it should be treated as certain. If something like this is right then it’ll block your move. I think what we need is a way to keep track of the probabilistic evidence for a claim without the nature of that evidence somehow entering into the content of the belief.

  10. Mike, just because ‘p&~p’ is a contradiction doesn’t guarantee that it can’t be justified. So, I think (3) is true, and so does everybody else, as far as I know, but I doubt anybody thinks it is a trivial truth.

    Dylan, no conjunction principle needs to be used to infer a contradiction from the premises, for the same reason that you don’t need to conjoin the premises in modus ponens to infer the consequent of the conditional. And you’re missing the point about the paradox. It’s not as if the conflict between the individual claims in the book and the preface remark are not noticed or are not obvious. If you insist that combining the evidence will always prevent both p being justified and ~p being justified, there’s no reason on the face of it to think that the same combining won’t prevent the author from being justified in each of the claims in the book as well as in the preface remark.

    Ted, if you get to detach the probability claim, then you are entitled to use the undetached claim in further reasoning. It doesn’t have to be certain to be so used, on pain of not allowing ordinary perceptual claims to be used in further reasoning (since, for most of us fallibilists, hardly anything is certain).

    Maybe you are worried about multi-premise closure and the “leaking” of epistemic status from premises to conclusion. I doubt any such worries will solve the paradoxes in question. If I know that each of tickets 1-100 will lose and know that there are no more tickets, then I can easily know that no ticket will win. There won’t be enough leakage there to undermine the principle. And similarly for justification–if the evidence justifies each of the losing ticket claims and one knows that these are all the tickets there are, there’s no reason to think that the “leaking” problem will keep one from having justification for the claim that no ticket will win. This is not to deny that there may be a leaking problem for multi-premise closure, but that doesn’t mean the problem infects every instance of multi-premise entailment.

  11. I think I’m lost

    Mike, just because ‘p&~p’ is a contradiction doesn’t guarantee that it can’t be justified.

    That would make (3) false, wouldn’t it? Here’s (3).

    . There can’t be any justified contradictions: no instance of p&~p can be justified for a person.

    But you say,

    So, I think (3) is true, and so does everybody else, as far as I know, but I doubt anybody thinks it is a trivial truth

    I didn’t say it was a trivial truth. I said it was trivial in the sense that any sentence that is an instance of the transparently contradictory schema ‘p & ~p’ is obviously a contradiction. It is difficult to find anyone who would fail to recognize that and equally difficult to find anyone who might believe he is justified in believing anything of that is an instance of such a schema.
    But logical impossibilities need not have that form, and some of them (I was suggesting) we might be justified in believing. And so the question of whether (3) should be read narrowly (as applying to all and only instances of that contradictory schema) or broadly.

  12. Jon, I am worried about the “leaking” problem. If it is a problem then I don’t think there’s a general argument from the falsity of 1 to the falsity of 2. In fact, whether an inconsistent body of evidence is affected by the leaking problem seems to determine whether it can be rational to believe its supported claims.

  13. Mike, no, (3) is a denial that contradictions can be justified. It means just what I wrote, it is not some code for impossibilities of some other sort. It isn’t a trivial claim, though, anymore than affirming the truth of any axiom. And if you look at your comment, what you said is that (3) is trivial in the case in which it means what it says. (3) a denial that a contradiction can be true: it denies the possibility of a contradiction correctly falling within the scope of a justification operator.

    Ted, no general argument is needed. It is not as if we need to find that (2) is false in every case that (1) is. It is enough if we take the cases where (1) is false and find one of them that will extend to (2) (and not even that is necessary, but I’m not claiming that anyway). That’s why I wrote what I did about the paradox. There are instances where it is implausible to think that the failure of (1) doesn’t also extend to a failure of (2): namely, some of the paradox cases.

  14. Jon,
    You say: “you’re missing the point about the paradox. It’s not as if the conflict between the individual claims in the book and the preface remark are not noticed or are not obvious.” There may be in some loose sense a “conflict” between the author’s belief which he states in the preface, and his individual beliefs which he states in the individual claims he makes throughout the rest of the book. But there’s no contradiction. Let C1-Cn be the claims he makes in the books. In the preface he says he made a mistake somewhere, perhaps implying that ~(C1 & … & Cn). Now there’s no contradiction between this claim and any of C1-Cn, the only contradiction is between the conjunction of these claims and the preface claim. You’ve got a counterexample to 1, because you’ve got a bunch of propositions here which logically imply a contradiction, and which we can suppose are each justified. But you don’t yet have a counterexample to 2, unless you suppose that the person not only has a justified belief that C1, and a justified belief that C2, … , and a justified belief that Cn, but also has a justified belief that C1 & … & Cn. But it seems to me pre-theoretically implausible to think he’s justified in believing that C1 & … & Cn, given the tremendous evidence he has (ex hypothesi) that at least one of the conjuncts is false.

  15. Dylan, I’ll try one more time. Let c1…cn be the claims of the book, and assume each one is justified. Let P be the preface belief that one of c1…cn is false. There are other ways to set it up, but this will do. If the preface claim is justified, we have a counterexample to 1. You simply don’t need the conjunction to be justified to get justification for the contradiction, though that is sufficient. For example, suppose the preface belief is translated into a disjunction of the falsity of each of the claims. The author can easily deduce the equivalence to the original preface claim, so there is no reason to doubt that justification for the new claim is possible. Then by n-1 applications of disjunctive syllogism, the author can deduce a claim that contradicts one of the premises. No conjunction of the individual claims of the book is needed to get the contradiction.

    To avoid the argument, one will have to defend a strong rejection of closure principles, not just a rejection of the conjunction principle. One approach is easy to deny, but the other is harder. The two approaches we might call performative versions versus static versions. A static principle is: if Jp and J(p entails q) then Jq (call it ‘static’ to honor the state of being justified in the entailment claim). A performative version is: if Jp and you competently deduce q from p, then Jq (call it ‘performative’ because you actually have to do something). To deny the static versions is common, but it is much harder to deny the performative versions, for roughly the same reasons that Williamson and Hawthorne endorse some such performative closure principle for knowledge. Of course, we might reject such a performative closure principle for multi-premise arguments and only allow them for single-premise arguments, but it isn’t clear that there isn’t any principled distinction to be drawn here (see Keith’s “just barely” problem for single-premise closure, for example).

    So, there are ways to preserve (2) while denying (1), by rejecting closure. But if we reject closure, what’s the motivation for rejecting (2)? Without closure, we can’t get from a denial of (2) to a denial of (3), so why reject (2)?

  16. Jon,

    Apparently I was misunderstanding much in your previous comments, because I don’t disagree with what you say in the first 2 paragraphs of your comment above. I think we see the preface paradox similarly.

    On the other hand, I still maintain that we don’t need to think that 2 leads to 3 to find 2 implausible. In the preface case, given the evidential justification there is for ~(C1 & … & Cn), and given that propositions are justified by one’s whole body of evidence, it doesn’t seem to me to be plausible that the subject’s evidence justifies C1 & … & Cn. OK, now I’m just repeating my earlier comment.

    Anyway, sorry for the confusion.

  17. Hi Jon,

    This is a reply to your comment in #6.

    I’m sorry for the cryptic passage on closure for subjective justification. After you called my attention to that obscure passage I have read it again and had a hard time trying to understand it. I will try to clarify it below.

    In #1 I pointed out that justification is normally understood as having an objective and a subjective dimension. In #2 you said that if we have a subjectivist interpretation in mind (something like: S’s belief that p is justified only if, given S’s perspective, p is probably true)

    ‘TheFrege case counts against 1 […], but not against either 2 or 3. So I think you will lose 1, unless some closure principle forces a denial of 1 to turn into a denial of 2 and 3.’

    Now, what I tried to say in #4 is the following. I don’t see how we can have a workable distinction between objective and subjective justification and, at the same time, have a closure principle for subjective justification which allows the denial of 2 and 3. Consider one plausible version of closer principle for SUBJECTIVE justification (where ‘Jxy’ stands for ‘x is subjectively justified in believing that y’; ‘Bxy’ stands for ‘x believes that y’ and ‘Kxy’ stands for ‘x knows that y’):

    (CSJ) [If Jsp & Ks(p –> q) & Bsq on the base of (Jsp & Ks(p –> q)), then Jsq]

    How could (CSJ) be responsible for the denial of 2? Even if coupled with the denial of 1? For one thing, if S knows that p implies q, then he can’t also know that p implies ~q for the latter must be false. 3 is also protected by (CSJ) for obvious reasons.

    Thus, I think we might discuss about whether (CSJ) is the most adequate closer principle for subjective justification, but, if we accept (CSJ), then 1 is false and 2 and 3 are true. Did I miss anything?

    As for your remark that there are objectively justified false beliefs, I need an argument to see this. It is, at least, not an obvious claim that there are such beliefs. If Peter Klein’s defeasibility theory is right (and I don’t know why it wouldn’t be), there is no such thing as objectively (propositionally, undefeated) justified false belief.

  18. Mike, no, (3) is a denial that contradictions can be justified.

    Right, I never denied that. On the contrary. But you write in (10) above–what I’m now certain must have been a typo–that,

    just because ‘p&~p’ is a contradiction doesn’t guarantee that it can’t be justified.

    Setting that aside, I said any sentence that is an instance of the transparently contradictory schema p & ~p is obviously a contradiction. With suitably restricted quantifier, no one would fail to recognize that and no one would believe he is justified in believing an instance of such a schema. No surprise then that (3) commands universal assent. It would be a surprise were (3) making the broader (in my view, more interesting) claim.

  19. Let me take part of (18) back. It seems like I could be have good reason to believe (a), since I could reasonably believe I’ve counted the tildes correctly (when in fact I haven’t). Add a thousand more, if that will make the empirical question more realistic.

    a.~~~~~~~~~~~~~~~~~~~~~~(Vx)(Fx v ~Fx) &~~~~~~~~~~~~~~~~~~~~~~~(Vx)(Fx v ~Fx)

    And (a) is an instance of p & ~p.

  20. Mike, on 19, the key is to distinguish between sentences and propositions. The number of tildes in the sentence won’t affect the plausibility of (3), since the variables there are for propositions. And it is plausible to think that if you miscount the tildes, you don’t believe the proposition expressed by the sentence.

  21. Rodrigo, Klein’s defeasibility account is irrelevant to the theory of justification. The kinds of defeaters relevant to the theory of justification are internal defeaters, not the external defeaters needed to solve the gettier problem.

  22. Jon,

    Re comment 13 this is what I don’t get. I think (1) is false; there can be justified inconsistencies. You wonder whether that implies that there can be justified contradictories. I don’t think so because every instance of justified inconsistencies that might be thought to generate justified contradictories is affected by the leaking problem. About the paradox I don’t think the example you give re knowledge motivates a similar point re justification. After all you don’t know that each ticket will lose, since one of those beliefs is false. Abandoning multi-premise closure is a step in the right direction to solving the paradoxes.

    By the way, I take it that if the argument from the falsity of 1 to the falsity to 2 goes through then you can recover an argument from the denial of multi-premise closure to the denial of single premise closure. That’s interesting!

  23. Jon,

    I am told in (3) that I am not justified in believing any instance of p & ~p. (3) does not say that I am not justified in believing anything that I know is an instance of p & ~p. And there is no question that I have an instantiation of p & ~p in (19) that I might not know is an instance of p & ~p. It is because not every instance of p & ~p is a known instance of that schema that I can be justified in believing the instance in (19).
    For the very same reasons I can be justified in believing any complex theorem that, as it happens, turns out to be necessarily false. Your response, that if I fully understood the proposition expressed by the “theorem” I would not be justified in believing it, though I think true, does not preclude my being justified in believing it. I might have a proof that its true, for instance, and I might have that proof confirmed. Similarly, I might be sure that the instance of p & ~p in (19) is true, since I might have studied the formula and provided a proof. In both cases I’m justified in my belief, though as it happens mistaken.

  24. Ted, you are committed to more than failure of closure to block rejections of (1) from bleeding into rejections of (2). You are committed to the claim that no case in which (1) is falsified is also a case in which (2) is falsified. Denials of closure get you something like “not all”, whereas you are committed to something like “all not”.

  25. Jon,

    Both those commitments seem right to me. The leaking problem seems to explain why rejections of (1) don’t bleed into rejections of (2). Where leaking isn’t a problem the incoherence seems too obvious to ignore. Maybe this will advance the dialectic, though. I think a double premise closure principle is just about as plausible as a single premise closure principle. If one accepts that justified inconsistencies can bleed into justified contradictories then it seems that will bleed into justified contradictions. The key idea is that if one is justified in believing p and justified in believing ~p then one is justified in believing entailments of those propositions. Since p&~p is a consequence of those premises, one is justified in believing a contradiction.

  26. Ted, the leaking problem and the obviousness criterion conflict here. In preface, the conflict is obvious, so if that is your criterion, then a rejection of 1 will lead to a rejection of 2.

    I think that the leaking problem is a red herring here anyway. Suppose you grant that I’m entitled to assert that Andrew will be at the APA. And then you grant that I’m entitled to assert that Robert will be at the APA. And Peter and Joe and Bill and the other Peter and Bina and Jack and Paul and Alex and Claire and Brian. And you grant that I’m entitled to assert that this is an exhaustive list of the department. And then you say I’m not entitled to assert that the entire department will be at the APA. That’s bizarre. And citing the leaking problem doesn’t make it less so. What would be really bizarre is to hear one assert all the things in question and then express uncertainty about the entailed claim. “Here’s a list of who will be at the APA, and that’s the entire department; but I’m hesitant to claim that the entire department will be at the APA.” The obvious response is to say that you better retract something you just asserted.

    Now, you might wish to quibble with the connection between justification and assertion, but that’s not very plausible. A good evidence requirement on assertion is much weaker than a knowledge requirement, and it’s no small task to avoid the stronger requirement.

  27. Ted, one other thought. You really can’t endorse anything beyond single premise closure or all bets are off. If you give me double premise closure, I can sink your boat. First round: combine each individual ticket claim with the next in the sequence. Second round: do it again. Do this as many times as needed to get a conjunction of all the ticket claims.

    Don’t say this is cheating. Either you disallow two-premise closure, or you have to let this pass. Iterations of allowed rules are always allowed.

  28. One way to view the clash between (1), (2), and (3) is to think about how rational belief change works. Some of us some of the time change view based upon evidence, and we might wonder how this is pulled off. We might further wonder about principles for pulling this off.

    Example: A year ago, most people thought there were 9 planets in our solar system. I assume that most of you had good reason for this belief. Yet, now, most of you think that there are but 8 planets. Doubtless it is unreasonable, if even possible, to believe that there are exactly 8 planets and that there are exactly 9 planets, since it is short work to infer that you believe there are and are not 9 planets, and that there are and are not 8 planets.

    Still, at some moment, you had reasons to believe that there are 9 planets, and you had reasons to believe that there are 8 planets, and you had to decide which view to adopt. I take it that this is an argument against (2), in so far as reasonable belief fixation (whether to believe there are 9 planets, whether to believe there are 8) is driven by evidence, what you have grounds to believe, what you are justified to believe.

    A second case against (2) is when you have conflicting evidence for a proposition, p, but no immediate means to resolve the conflict. You would suspend judgment about p; it is reasonable to suspend judgment on p because you have justification both for p and for not-p and no means to resolve the conflict. Also, it is important to be able to distinguish between the case of suspending judgment about p because you have no information about p, and the case of suspending judgment because you have conflicting evidence for p.

  29. Jon,

    So on the basis of our discussion if one allows justified inconsistencies then to block this bleeding into justified contradictions one has to deny either two-premise closure or that iterations of allowed rules are always allowed. I’m very confident that there can’t be justified contradictions (especially where ‘~’ is classical negation) and more confident that two-premise closure is right than that iterations of allowed rules are always allowed. The situation with iterations of allowed rules seems similar to how a degree-theoretic approach handles a forced marched sorites. Each instance of modus-ponens has slightly less truth than the previous. With two-premise closure the justification in the consequent can be slightly less than the justification had by the premises mentioned in the antecedent. Initially it doesn’t make that much difference but as you iterate the difference between the initial premises and the last claim can be great.

    About the assertion business you’d allow, I assume, that the justification for the claim the entire department will be at the APA can be less than the justification for each individual claim. If that’s the case, though, I don’t see why the justification can’t drop below the level required for warranted assertion. The specific claim you mention is bizarre, but that because a list of who will be at the APA functions as a conjunction which if it includes all the members of the department shows that every member of the department will be present.

    Suppose I receive in the mail each day a letter that gives the name of a person that owns a lottery ticket. Each day I am warranted in asserting ‘So and so will not win’. After a long time of this I get a letter that says there is only one more ticket and the owner of the ticket is Julius. Intuitively it’s not right to assert ‘Julius will win the lottery’. I don’t see, though, how you can block this while allowing the assertions ‘Julius will lose the lottery’ and ‘No one will win’.

  30. Ted, no I don’t grant that the level of justification for the universal claim is less than that for the individual claims. One reason for not agreeing on this is that a scientific theory can be more reasonable to believe that the conjunction of its empirical consequences. The universal claim here doesn’t have the explanatory power of a unifying theory, but the theory example keeps one from applying the idea that more information equals lower probability.

    In your lottery example, if you cringe from the claim that Julius will win, you better withdraw some of the earlier assertions!

    Greg, interesting ideas here, but I want to insist that we distinguish between rational belief and quality of evidence. At a given time, your evidence justifies certain claims. When we conceive of this in terms of belief change and the rationality associated with that, we can easily confuse propositional justification with doxastic justification. So we should ask what the evidence shows, independently of what we should say about belief changes and which of them would be justified.

    One reason to avoid doxastic considerations is that it may be arguable that contradictory beliefs are impossible (if we hold fixed the mode of presentation, as I noted earlier). Foley argues for this claim. I’m not completely convinced, but supposed it is true. Then the doxastic version of (2) follows directly: justified contradictory beliefs are impossible. But the propositional version of (2) remains unsupported by such an argument.

  31. I think Jon’s second principle is quite strong. I’m not sure whether Mike’s proposed counterexamples are genuine ones, but the strongest purported counterexample I can think of presupposes much more than most people would accept. It is this: Can I be justified in believing both (a) that I don’t know that the animal is not a cleverly disguised mule and (b) that I know that (the animal is not a mule or the animal is not cleverly disguised)? If I remember rightly, I think on some (not very implausible) theory about justification I can be justified in believing both (a) and (b). Now (a) is in effect ~Kp and (b) is Kq, where p and q are logically equivalent. If you further assume some (I think very implausible) theory about identity condition of propositions on which (a) and (b) are contradictories, then you have a counterexample to Jon’s second principle. I’m sure somewhere or other someone has proposed a theory like that, but of course it is very implausible.

  32. I’m not sure I understand the distinction between propositional justification and doxastic justification.

    Is Foley’s claim that Bel(p) and Bel(not-p) is impossible? Bel(p & not-p) is suspect, but I don’t think that Bel(p) & Bel(not-p) entails Bel(p & not-p). Likewise for substituting ‘Jus’ for ‘Bel’.

  33. Greg,

    Your example is interesting; I’ll have to think about it more. I just have one concern. If you really had justification for p (8 planets) and for ~p (~[8 planets]) at the same time, then why was it the epistemically right thing to do to change your mind about the truth of p (going from believing ~p to believing p)? Plausibly, because your evidence now favored p over ~p. But that suggests that your example wasn’t really a counterexample to 2 after all, doesn’t it?

    And if there’s a time when the evidence favors agnosticism about p, that seems to me to be a case where your evidence doesn’t justify either p or ~p. But to get a counterexample to 2, you need a case where the evidence favors both p and ~p.

  34. Hi Dylan,

    I’d like to distinguish cases where evidence doesn’t justify either p or not-p, and cases where evidence justifies both p and not-p.

    I’m not too committed here to a particular notion of justification; we’d have to specify this before I could assess whether the planets example is a counter-example to (2).

    Rather, I do think there is reason to accommodate justification…and I would include belief, too…failing to distribute, i.e., allow that X(p) and X(p’) does not entail X(p and p’), where X is some species of epistemic modal. Letting p’ be the negation of p rattles our intuitions, perhaps, but I think the main issue behind (2) is whether this distribution property is shared by justification, or even justified belief. I don’t think it does for justification; I’m inclined to think it doesn’t hold for justified belief either, although I am not confident that I grasp this distinction between propositional justification and doxastic justification.

    I imagine that there are ways to do this that rescue a reading of (2), and ways to do this that falsify another reading of (2).

  35. Yu, yes, on Stalnaker’s theory of propositions, you’d get that result, since a proposition is, for him, just a modal profile.

    Greg, I wondered about the smiley face too! As to the Foley point, I think he views Bp and B~p as impossible, except when the mode of presentation is distinct. I’m inclined to agree about B(p&~p), and also inclined to agree with Foley, though I don’t think much hangs on this, because there’s no reason to suppose you can’t have good evidence for something you can’t believe.

  36. Yu,

    I proposed a counterexample to (3), not (2). I said that I might be justified in believing an instance of p & ~p, and (3) denies that. I do not say that I might be justified in believing what I know is an instance of p & ~p. But (3) is silent on that anyway. Here is an instance of p & ~p that I might not know is an instance of p & ~p and that I might be justified in believing:

    a.~~~~~~~~~~(Vx)(Fx v ~Fx)& ~~~~~~~~~~~(Vx)(Fx v ~Fx)

    In this case of course p = ~~~~~~~~~~(Vx)(Fx v ~Fx).
    All of the following are possibly true:

    (i) I am justified in believing that (a) is true.
    (ii) I am not justified in believing (a) is an instance of p & ~p.
    (iii) (a) is an instance of p & ~p.

    Given (i) and (iii), we have a counterexample to (3).

  37. Mike,

    Can you explain to me why (i) is true? That is, why you are justified in believing that (a) is true? I suppose (though I’m not sure) that I can be justified in believing that the sentence “~~~~~~~~~~(Vx)(Fx v ~Fx)& ~~~~~~~~~~~(Vx)(Fx v ~Fx)” expresses a truth (because I’ve miscounted). (I’m not sure of this, because I’m not sure that, when I’ve miscounted, I actually have a belief about the sentence in question.) But, even in this case, I am not justified in believing what the sentence actually expresses.

    I think this is just Jon’s response in 20, though. But I wasn’t sure what your reply to it was.

  38. Hi Jeremy,

    In the situation I envisage, I am justified in believing that (a) is a tautology. Since I am justified in believing that (a) is a tautology, I am justified in believing the proposition in (a) is true. I’m wrong, (a) is not a tautology. (a) is rather an instance of p & ~p.
    I had in mind an analogy like the following. I am justified in believing that the object in (a) is a cat so I am justified in beleving that the object in (a) is a feline. I’m wrong, (a) is not a cat at all.
    Was I justified in believing that the object in (a) was a cat? I think yes, though it was not a cat. Am I justified in believing that it is a feline? Yes. In the initial case, was I justified in believing that (a) was a tautology? Yes, though it was not a tautology. Am I justified in believing that (a) is true? I think, yes. So I am justified in believing that a proposition that I (mistakenly) believe is a tautology–but which in fact is a contradiction–is true, namely (a).

    Here’s a simpler case. Suppose I have good reason to believe what you tell me. You say, “I’ve proven that the proposition in (a) is true”. And suppose you really do have a proof, though it is of course mistaken. I conclude on the basis of your proof that I am justified in believing that the proposition in (a) is true. And indeed I am so justified. But (3) says impossible: (a) is an instance of p & ~p.

  39. Hi Mike,

    Thanks, I think I see. My belief is that the proposition in (a) is true and it is based on the belief that the proposition in (a) is a tautology. But here’s what I’m confused about. My basing belief is either that:

    b) the proposition expressed by the sentence in (a) is a tautology.

    or that

    c) ~~~~~~~~~~(Vx)(Fx v ~Fx)& ~~~~~~~~~~~(Vx)(Fx v ~Fx) is a tautology.

    The former is in no way a tautology, even if you hadn’t miscounted. That sentence could have expressed any proposition at all. It’s not even a necessary truth. So, even if it’s rational or justified for you, it’s not a counterexample.

    But the latter is not anything you believe; you don’t have any beliefs at all about the proposition that ~~~~~~~~~~(Vx)(Fx v ~Fx)& ~~~~~~~~~~~(Vx)(Fx v ~Fx). Nor is (c) justified for you. What’s justified for you is that ~~~~~~~~~~(Vx)(Fx v ~Fx)& ~~~~~~~~~~(Vx)(Fx v ~Fx). (I’ve removed a tilde from the second conjunct.) At least, that’s how it seems to me. But I’m guessing you disagree with this last point.

    -Jeremy

  40. Jeremy,

    I’m not following what you say about (b). The definite description in (b) refers to a proposition P that is an instance of p & ~p, and I am justified in believing P. (3) tells me that’s impossible.
    How is this not exactly like you being justified in believing that Smith robbed the bank and having me tell you “that’s impossible, you could not be so justified. Smith is in fact identical to Batman, and Batman would not rob a bank.” Maybe when you learned that Smith was Batman, your justification would change, but you are now justified in believing Smith robbed the bank. Same for me. Maybe when I learn that P is an instance of p & ~p my justification would change (certainly it would), but I am now justifed in believing P.

  41. Hi Mike,

    When I believe that Smith robbed the bank, I precisely do not believe that Batman robbed the bank. That’s why belief is an opaque context. And, it seems to me, ‘it is justified for me that…’ is even more opaque. It might be very well justified for me that Smith robbed the bank, but not at all justified for me that Batman robbed the bank, because it is not at all justified for me that Smith is Batman.

    Here’s another example, more like the one you mention in 40. I think that “gato” means dog (and suppose it is justified for me that it does mean dog). I look at my dog and, feeling like cleverly expressing myself in Spanish, say, “Esta es un gato.” (Please don’t take me to task on the Spanish. I haven’t had it since high school.)

    Here, it is justified for me that there is a dog. But even though I mistakenly, but justifiedly, believe that “Esta es un gato” means there is a dog, it is surely not justified for me that there is a cat. So, it is justified for me that the proposition expressed by “Esta es un gato” is true. But the proposition expressed by “Esta es un gato” is not justified for me. Unless you think that it is justified for me that there is a cat.

    -Jeremy

  42. Hi Jon,

    I see now. Also, about the epistemic modal ‘X’: I think it needs to be gradable for the point about the failure of distribution to follow.

  43. When I believe that Smith robbed the bank, I precisely do not believe that Batman robbed the bank. That’s why belief is an opaque context. And, it seems to me, ‘it is justified for me that…’ is even more opaque. It might be very well justified for me that Smith robbed the bank, but not at all justified for me that Batman robbed the bank, because it is not at all justified for me that Smith is Batman.

    Jeremy,

    Yes, of course you do not believe that Batman robbed the bank. I’m counting on that! That’s part of why your belief is justified. But the very point is that the person whom you believe robbed the bank IS BATMAN. I know you don’t believe he is Batman. But he certainly is Batman, right?

    Now to my case. The proposition P that I am justified in believing IS AN INSTANCE OF P & ~P. Certainly, I do not know that, and I am counting on the opacity of the context to ensure that I do not know it. But what does (3) say? It says this:

    3. . . .no instance of p&~p can be justified for a person.

    (3) says nothing about propositions that are known to be instances of p & ~p. It says propositions that are instances of p & ~p are never justified for a person. But, contrary to (3), I am justifed in believing a proposition that is and instance of p & ~p. That proposition I am justified in believing is not known to be an instance of p & ~p. It is not that I’m missing the fact that belief contexts and justification contexts are opaque. Rather argument depends on those contexts being opaque.

  44. Mike,

    Here’s how I take you as arguing:

    P1) It is justified for you that the proposition expressed by sentence A is true.
    P2) The proposition expressed by sentence A is that ~~~~~~~~~~(Vx)(Fx v ~Fx)& ~~~~~~~~~~~(Vx)(Fx v ~Fx)
    Therefore, C) It is justified for you that ~~~~~~~~~~(Vx)(Fx v ~Fx)& ~~~~~~~~~~~(Vx)(Fx v ~Fx).

    And C is a counterexample to 3, because the proposition in question is aninstance of p & not-p.

    If this is not your argument, then you’ll let me know. But if this is your argument, then I fail to see how it “depends on those contexts being opaque.” Rather, it requires the context “It is justified for you that…” to allow for substitution. For, the argument proceeds by substituting “~~~~~~~~~~(Vx)(Fx v ~Fx)& ~~~~~~~~~~~(Vx)(Fx v ~Fx)” for “the proposition expressed by sentence A.”

    If this were allowed, then the following arguments should work, as well:

    P1) It is justified for you that the proposition expressed by “Esta es un gato” is true (because it is justified for you that there is a dog and it is justified for you, though false, that “gato” means dog).
    P2) The proposition expressed by “Esta es un gato” is that there is a cat.
    Therefore, C) It is justified for you that there is a cat.

    But C is clearly false (because you have no evidence that there is a cat, there is no reliable process disposing you to that belief, an intellectually virtuous agent wouldn’t believe that there is a cat, etc.).

    Or, using your example (to get away from sentences):

    P1) It is justified for you that Smith robbed the bank.
    P2) Smith is Batman.
    Therefore, C) It is justified for you that Batman robbed the bank.

    Again, C is clearly false.

    Or,

    P1) It is justified for you that you have ticket #399574.
    P2) Ticket #399574 is the winner.
    Therefore, C) It is justified for you that you have the winner.

    So, I do not yet see how to get to your conclusion, that “the proposition P that I am justified in believing IS AN INSTANCE OF P & ~P.” I’m guessing my interpretation of your argument gets it wrong.

  45. Jeremy,

    That’s not my argument. I see why you’re objecting. My argument goes this way. Let (3*) name Jon’s (3) above, so I don’t equivocate.

    1. I am justified in believing the proposition in (a)

    2. The proposition in (a) is (unbeknownst to me) an instance of p & ~p.

    3. So I am justified in believing a proposition that is (unbeknownst to me) an instance of p & ~p.

    4. According to (3*) I cannot be justified in believing a proposition that is (unbeknownst to me or not) an instance of p & ~p.

    5. So either I am not justified in believing the proposition in (a) or (3*) is false.

    6. I am justified in believing in (a).

    7. :. (3*) is false.
    ——————————————————–
    Now the analogue.

    1′. I am justified in believing that Bob robbed the bank.

    2′. Bob is (unbeknownst to me) identical to Batman.

    3′. So I am justified in believing that someone that is (unbeknownst to me) identical to Batman robbed the bank.

    4′. According to (3*’) I cannot be justified in believing someone that is (unbeknownst to me or not) identical to Batman robbed the bank.

    5′. So either I am not justified in believing that Bob robbed the bank or (3*’) is false.

    6′. I am justified in believing that Bob robbd the bank.

    7′. :. (3*’) is false.

    ——————————————
    So what I want to conclude is that (3) is too strong. I can be justified in believing a proposition that is an instance of p & ~p, so long as I don’t know that it’s an instance of p & ~p. (3) would be more plausible were it to claim that I cannot be justified in believing a proposition that I know is an instance of p & ~p. But on this latter question there is an interesting Bryan Frances post over at Knowability
    http://knowability.blogspot.com/.

  46. Hi Mike,

    Perhaps now I see and I grant that, given those premises, the conclusion might follow (provided that 3 is suitably specified as something like, there is a proposition, q, such that q is justified for me and q is an instance of p & not-p; or, 3′: there is an S such that S is Batman and it is justified for me that S robbed the bank).

    But now I disagree with the first premise. It is not justified for you that the proposition in (a) is true. What is justified for you is that ~~~~~~~~~~(Vx)(Fx v ~Fx)& ~~~~~~~~~~(Vx)(Fx v ~Fx). (This is (a) with a tilde removed from the second conjunct.) Your counterexample is not like a case in which some proposition, unbeknownst to you identical with an instance of p & not-p, is justified for you. Rather, your counterexample is a case in which you have mistakenly taken the name (the sentence) of an instance of p & not-p as the name of an instance of a tautology. But the proposition you have mistakenly taken the sentence to express is not identical to the proposition that would serve as part of a successful counterexample.

    The analogous case is therefore not the Batman case described. It is more like a case in which you mistakenly, but justifiedly, take the name of the person who did rob the bank to refer to a person who did not rob the bank. Herb robbed the bank. It is justified for you that Herb’s twin (Frank) is Herb. And, suppose, it is justified for you that Frank robbed the bank (because Frank, lying to protect his brother, told you he did). So, you believe the sentence “Herb robbed the bank.” And, the proposition you express by that sentence is justified for you. But it is not justified for you that Herb robbed the bank, because it is justified for you only that Frank robbed the bank, and Frank is not Herb.

    Maybe that example isn’t too clear (I’m thinking). So, let me just leave it at saying that I need something more in defense of premise 1.

    -Jeremy

  47. But now I disagree with the first premise. It is not justified for you that the proposition in (a) is true. What is justified for you is that ~~~~~~~~~~(Vx)(Fx v ~Fx)& ~~~~~~~~~~(Vx)(Fx v ~Fx). (This is (a) with a tilde removed from the second conjunct.) Your counterexample is not like a case in which some proposition, unbeknownst to you identical with an instance of p & not-p, is justified for you. Rather, your counterexample is a case in which you have mistakenly taken the name (the sentence) of an instance of p & not-p as the name of an instance of a tautology.

    That’s a fair objection I think. Suppose I drop my initial justification for believing the proposition in (a). You’re right, part of my justification required a mistake in counting tildes. Suppose instead Smith says to me sincerely, “Almeida, I proved the proposition in (a)”. And suppose I have good reason to believe that Smith has been working on that proof and good reason to trust in Smith’s logical acumen. At the conclusion of Smith’s proof is exactly the proposition in (a), no tildes missing. Of course, someone might come along and say “Smith, you had to have made a mistake. Your conclusion is a contradiction!” At that point Smith might say “can’t be a mistake, I did the proof three times and arrived at that precise conclusion three times!” That sort of thing is perfectly possible. On review, of course, he will revise his views about the proof. But I think that Smith’s proof does give me justification for believing the proposition in (a).

  48. Pingback: Show-Me the Argument » Philosophers’ Carnival #42

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