Permission to believe?

In a recent paper, Seyed Ali Kalantari and Michael Luntley propose the following prohibitive norm of belief, as superior to other extant formulations of truth norms governing belief.

(1) For any S, p: it is not the case that S ought not to believe that p only if p is true. [Their (11).]

As they note, the formula looks cumbersome, but a more intuitive re-formulation is readily available:

(2) For any S, p: it is permitted for S to believe that p only if p is true. [Their (12).] (Kalantari and Luntley, 2013: 422)

If one leaves aside considerations about the temporal profile of believing and about beliefs apparently made true by being believed—and, of course, if one assumes that beliefs are subject to permissive and prohibitive norms—then the proposal has plausibility. However, puzzles arise when we bring to bear considerations of time and constitution.

Consider the following case. At t1, exactly one person, A, believes that (p and at least two people believe that p), for true p not about persons or beliefs. A has a false conjunctive belief, since it is false that at least two people believe that p. Since it is false, at t1, that (p and at least two people believe that p), according to (2), and plausibly enough, A is not permitted to hold the belief, since they would be so permitted only if it were true that (p and at least two people believe that p). So far, so good. Trouble arises when we consider a second person, B, distinct from A, and ask about what they are permitted to believe.

Is B permitted to believe that (p and at least two people believe that p)?

Suppose the question were raised at t1. In that case, it appears that B is not permitted so to believe, since the belief would then be false and so not true. However, suppose that, at t2, B forms the belief anyway, and comes to believe that (p and at least two people believe that p). Since, on natural assumptions, A and B are distinct both now believe p, it is true, at t­2, that (p and at least two people believe that p). So, as far as (2) advises, it is at t2 permissible for B (and indeed A) to believe that (p and at least two people believe that p).

What should we say about this situation? Is it a situation in which B should be permitted to form the target belief? Or is it right to say, instead that, even though B is in a position to see that were they to form the belief, it would then be true, they are not permitted to form the required belief and must run a dog-leg through, e.g., first forming the belief that (p and exactly one person believes that p)?

For present purposes, I leave the question open. It may be, however, that further reflection on the role of temporal considerations might figure in refining the alleged prohibition.


Kalantari, S. A. and Luntley, M. (2013). ‘On the logic of aiming at truth.’ Analysis 73(3): 419–422.

  1. Clayton said:

    In their paper they wrote, “This formulation of the normativity thesis has not been considered in the literature.”

    That annoyed me greatly. The prohibitive formulation of the norm has been discussed by Jonathan Sutton, Mark Nelson, Daniel Whiting, and one of the central theses of my book was that this was the fundamental epistemic norm.

    Anyway, now that that’s off my chest…

    Really interesting question that you’ve raised. Here’s a stab at an answer. There’s a view that says that epistemic permissions should be understood independently from what’s permissibly believed. It’s similar to the view that says that propositional justification is prior to doxastic justification (doxastic justification is just propositional justification plus a basing requirement). I’ve now started to think that this view might be mistaken, that there’s no helpful notion of propositional justification that is independent from doxastic justification. Is there anything wrong with saying that there are the permissibly held beliefs and permission to hold those beliefs while insisting that there’s just no helpful characterisation of what’s permissible to believe apart from what you’d permissibly believe if you believed? We can identify the permissibly held belief with knowledge, keep the prohibitive norm, and the answer to your question would be that you shouldn’t believe unless your belief constitutes knowledge?

  2. Thanks for that very interesting comment.

    1. Can you say more about the epistemic permissions view. Is it something like: one is epistemically permitted to believe in conditions C (rather than permitted more generally)? I can see how the propositional justification view might go, I think, but can’t see what an analogue for permission would be. Or is it that permission to believe (&c.) should be understood by appeal to what’s true, or the facts, rather than what one believes, so a form of anti-psychologism about reasons on the basis of which one is permitted, or something? Anyway, that’s just a classificatory question.

    2. At first, I was inclined (pretty strongly) to agree that doxastic justification is more basic than any notion of propositional justification. (For one thing, applying a notion of justification to propositions looks odd given that it seems irrelevant to many possible attitudes towards propositions, and seems mainly to tell one about belief and perhaps knowledge.) But then I worried that the thought might be connected with the idea that beliefs, rather than e.g. facts (perhaps including true propositions) can be reasons. Since I think many reasons aren’t beliefs, or believed, I’d be inclined resist a thought of that form. I guess this is connected with the question about what’s at issue: whether beliefs are the things that are justified, or not, or permitted, or not, versus whether the things making beliefs justified, permitted, &c., are themselves beliefs.

    3. You suggest that perhaps “there’s just no helpful characterisation of what’s permissible to believe apart from what you’d permissibly believe if you believed.” Was the idea to be primitivist about permissibility? Or was the idea instead that there’s no helpful characterisation of what’s permissible to believe apart from what you’d permissibly believe if you believed knowledgeably (as seems to be suggested by your final sentence)?

    4. I’m sympathetic with the proposal that one shouldn’t believe unless one’s belief constitutes knowing. (Indeed, it may be that a knowledge-based account could take bi-conditional form, if we ignore issues about things one knows, but shouldn’t.) (I might not put that in terms of belief constituting knowledge, for instance because the characterisation would better fit disjunctivism about belief than it would non-conjunctivism about knowledge. But I think that’s a side issue, and I think you probably meant the constitution proposal to direct us towards (2) below).) There are then two ways of understanding the proposal, roughly:

    (1) One shouldn’t form the belief that p unless one knows that p.

    (2) One shouldn’t form the belief that p unless so doing would bring about that one then knew that p.

    I’m sympathetic with (2), I think. However, I wonder whether (2*) would also do the trick, with respect to my puzzle:

    (2*) One shouldn’t form form the belief that p unless so doing would bring it about that one then believed truly.

    Anyway, plenty more to think about here, especially about the standing of (2), and the strengths and weaknesses (at least as a pro tem solution to the puzzle) of (2*).

  3. Clayton said:

    Hi Guy,

    On 1, my worry might be put like this. You might try to specify the conditions C such that C’s obtaining permits you to believe p but then there’s the worry about the basing requirement. If you believe p for the wrong sorts of reasons or don’t competently reason from your evidence, you might have justification to believe but don’t justifiably believe. Alright, so suppose C obtains _and_ you reason incompetently from your reasons so that we might be inclined to say (i) you have a justification to believe p but (ii) your belief isn’t justified.

    In light of (ii), I’d say that you don’t believe permissibly. If, as I’m tempted to say, you don’t have the permission to believe impermissibly, it looks like C couldn’t have been sufficient conditions for a permission, not unless C included all the stuff that goes into basing. But, the stuff that goes into basing includes not just the reasons that support a belief but the belief itself.

    On 2, I might not have been thinking of propositional justification in the way that you have. I was thinking of it as, roughly, a matter of having a justification, right, permission to believe a proposition and doxastic justification as having to do with the beliefs justifiably held.

    On 3, the idea was really what I tried to flesh out in 1. If we toe the line and say that proper basing is a necessary condition for doxastic justification you might be very sceptical of standard story about the relation between propositional and doxastic justification.

    I think (2) and (2*) are probably in the right direction. This is all very hard to do now as I’m trying to finish off a book review on a completely unrelated issue. Structured procrastination.

  4. Dear Guy, thanks for an interesting thought. Due to my missing background I must say I didn’t really understand the problem.

    Statements like “I believe” and “I’m permitted to believe” are quite restricted to the biological (sociological/psychological/political) domain, while “p is true” as well as using a logical formalism are mathematical. In the case of beliefs and truth I have some difficulties seeing staments made in one domain to be valid in the other and as a result I don’t understand the statement (2) connecting both.

    On the one hand I can try to interpret logical formalism and the statement “p is true” in a biological context. Believing in something is a description of a state of mind and “permitting somebody to believe” describes social communication, independent on whether the given reasons are epistemological (e.g. you should believe the roof is red, because it’s the truth), political (you must not believe in the Armenian Genocide) or other whatever (no, we didn’t kiss). Here I find it hard to draw a clear distinction between “knowing” and “believing”. How can I know the roof is red for instance? If I see it with my eyes, how can I be sure another person will see the roof red too? Next thing we look at is how colour perception works and how the brain constructs qualia, and we might arrive at the insight that truth is a per-person thing and not universal. If I see the roof red, and the person next to me doesn’t, can I say the roor *is* red? In that context (2) which connects beliefs and universal truth doesn’t make sense, at least to me, since “p is true” is either meaningless or has the same meaning as “p is being believed”. There are several ways out of this, but I don’t know which route had been chosen by the authors prior to making the statement, and I don’t know any using classical logic.

    On the other hand I can try to intepret beliefs and permissions in the mathematical domain, i.e. as mathematical relations. In that case a clear definition is needed, something like “believing p = assuming p, without having run an existing test of p”, and, “knowing p = assuming p true after having tested p and found the test to have passed”. The distinction then is only possible if such a test exists. Or, alternatively, “believing p = assuming p, without having tested p, and independent on whether such a test exists”. I don’t know whether such assumptions were made in the cited paper. The truth and the implications of (2) and of your blog entry would depend heavily on these definitions. The problem then becomes a purely mathematical one and loses much of its attractiveness since those definitions would appear quite random.

    That said, I do wonder what you (and Seyed Ali Kalantari et al) had in mind when they made the statement. My guess is to suggest how to handle psychological statements like beliefs and permissions by a mathematical formalism? You imply that (p and at least to people believe that p) becomes true as soon as two people believe that (p and at least to people believe that p). How does this work? Would it also become true if two people believe just p? What is the connection here? And how do you avoid either recursion or triviality? And, most important, does it really make sense to try using a simplistic formalism like classical logic on social and political problems? What are the benefits?

    Hope you can help,
    puzzled regards, Jacob.

    • Thanks for your comment.

      I can’t reply to all of it now. Some initial thoughts. You write: “Statements like “I believe” and “I’m permitted to believe” are quite restricted to the biological (sociological/psychological/political) domain, while “p is true” as well as using a logical formalism are mathematical.” That looks like a claim. A natural question to ask about such a claim would be, is it true? If it is true, then of course it might reasonably be taken to figure in assessments of other claims. If not, it’s not clear to me why it should. For example, suppose it expresses a belief of yours. Why should that matter to assessment of other claims? It might matter to whether or not you will believe those other claims. But unless the expressed belief is true—or, at least, supported by evidence indicating that it might be true—why should it matter to whether others should, or will, believe it? I wouldn’t expect the mere fact that I believe something to have any probative force with respect to others’ beliefs. For that, again, I’d try to provide reasons to think my belief was true, so something others might reasonably be expected to believe, at least insofar as they aim to get things right. But it seems that you want to restrict evaluation as true or not to the domain of logic or mathematics. So, it’s not clear to me how you intend your opening claim to be taken and—given that you seem not to think it’s true—how it might figure in assessment of what I wrote.

  5. Dear Guy,

    my opening is indeed a claim, saying as much as, I, Jacob, have difficulties in understanding a statement about permissions and beliefs in a purely logical context. This claim is perfectly true, I really don’t understand. In everyday life and social communication, which is where I talk about beliefs and permissions, my notion of truth is a per-person one, much as I see reality as a personal experience. A universal, observer independent truth does not make any sense to me, neither does a clear split of beliefs and truths.

    On the other hand, when I use mathematical formalism like classical logic, I do use truth as if it were a universal thing. I feel comfortable doing so because there is an agreement between all mathematicians what truth means, or at least how it can be achieved (by proof, using an accepted formalism). But here I cannot talk about beliefs, permissions, perceptions, feelings and the like, at least not without providing mathematical representations of them.

    So, I personally have difficulties combining the two domains because without knowing such a general agreement what truth could mean in a social context, or without mathematical representations of believing and permitting, I don’t understand the claim made in the paper. There are other kinds of logic with more than two truth values or with location dependent truths, but as far as I can see they were not used here. This doesn’t mean such agreements or representations haven’t been made, it is just that I don’t know them. The original paper is not free unfortunately.

    All in all I must say I didn’t want to assess the truth of what you wrote (or Kalantari et al, for that matter), neither the universal truth in a general sense, nor the mathematical/logical one. I’m sorry if I made that impression. I would just like to understand what you wanted to say, and why.

    So, pure curiosity on my side.

  6. Thanks for the comments.

    My initial reaction was intended to indicate a way in which thinking about truth figures in our ordinary dealings with belief. Crudely, if we believe something, say that it’s Wednesday today, and someone provides us with good reason to think that what we believe is false–because it’s Thursday today and not Wednesday–then we’d change what we believed. So, I think we ordinarily think that what we believe can be true or false, and moreover that this can figure in whether we continue to believe it, change our beliefs, &c. However, that’s not yet to claim that truth is the only thing we care about when it comes to believing–although some people would make that further claim. Rather, it’s just a minimal starting point.

    So, one way of hearing your comments is as challenging that starting point. The problem there is that play with truth appears to be involved essentially in thinking about such challenges and the appropriate response to them. For example, merely characterising a disagreement, without assessing it, seems to depend on holding that the parties to the purported disagreement can’t all be right. A natural idea here is this: if one is right, the other is wrong; and in order for one to be right, what they say must be true; and in order for the other to be wrong, what they say must be false. That all seems fairly ordinary, and has little to do with logic, mathematics, &c. Alternatively, if belief doesn’t involve such play with correctness or incorrectness–as naturally characterised through truth or falsehood–then a natural view would be that beliefs, so construed, can’t conflict. And since they’re not the sorts of things that can be affected by evidence of truth or falsehood, its hard to know how to engage with them, what one might try to do in order to get them to change, &c.

    All that was really to indicate ways in which you probably are committed, despite yourself, to treating beliefs as the sorts of things that can be correct or incorrect, typically at least through what one believes being true or false. And that in turn was a way of indicating a potential avenue of interest for the post. It’s perfectly ordinary to say, for example, that Jill believes that it’s Tuesday today. It’s perfectly ordinary to say, moreover, that what Jill believes–namely, that it’s Tuesday today–is false. And on that basis, one might suggest that Jill shouldn’t believe it, that she has made a mistake, &c. That’s all that’s really involved in the post. And I don’t think any of it is very controversial, or should be. Alternatively, if you’re really committed to thinking we can’t know what Jill believes, or that we can’t say whether what she believes is true or false, or it makes no sense, and so forth, then again I’m at a loss. If we can’t agree that it’s not Tuesday, that it’s false that it’s Tuesday, that Jill believes that it’s Tuesday, so believes something false, then our disagreement, or difference in viewpoint, is too deep to be resolved here.

    So, briefly: I think that talk about beliefs, and assessment of what is believed as true or false, is quotidian, and doesn’t depend on assimilating psychology, or social interaction, to logic or mathematics. (Replacing “that it’s Thursday” or whatever with “p” is just a shorthand, an abbreviation. One can easily fix worries there by replacing “p” throughout by a true declarative sentence. Otherwise, the claims at issue are supposed to be perfectly ordinary.) It may be possible reasonably not to accept those views, despite its ordinariness. But difference at such a fundamental level is very hard to get past. That’s because–unlike ordinary disagreement–it looks as though it’s liable not to be subject to considerations like these: if you show me what I’ve said is false, then I should withdraw (and vice versa); if I say that p and you say that it’s not the case that p, then we disagree, and can’t both be right, &c.

  7. Thankyou for your answer. I still have some questions, although the picture gets a bit clearer now.

    In Christianity there is the idea of “believing the unthinkable” (credo quia absurdum est). Quick googling results in Paulus, Augustinus and some other christian historical sources, apparently it is also in the bible. Here people’s beliefs contradict their own reasoning. Interestingly it is not said that a claim is untrue and should be believed all the same. No, according to the argument a certain claim is true because it contradicts reasoning. The idea was put forward as a (religiously justified) demand. For the speaker belief and truth are tightly connected, logical reasoning and truth are not.

    In your post I’m uncertain about the meaning of “permission”. What is meant by “someone is permitted to believe something”? Is this something issued by an authority, such as a state, or a religious body? See above, or my example of the Armenian Genocide, which according to the Turkish government must not be believed (i.e. is not true). Or do you rather mean something ethical, a rule you suggest everyone should use to adjust her/his own beliefs?

    In your example, Jill thinks it’s Wednesday but it is actually Thursday. Here, the fact that “it is actually” Thursday is a social agreement. The reason it is Thursday is that people have agreed on a calendar and weeks and how today fits within this calendar and so on. So I would say it is Thursday because most people believe it is Thursday. If all people believed it was Friday it wouldn’t be Thursday but Friday. In this example “p is true” and “many people believe that p” are the same thing. Would you agree?

    The interpretation of beliefs influencing truths would also fit with the example in your previous post about believing all the mathematical theorems in books of the University of Warwick library. A “truth” would be something thats agreed by any number of people (this includes the agreement that one truth must not locically contradict other thruths), a “belief” would be my own personal subset of those “truths”. To believe something I must either take it from the general set of agreed truths and pull it into my own subset, or generate it myself from my own subset using a socially agreed method (in my case reasoning). Would you agree here?

    In your original post, you imply that (p and at least to people believe that p) becomes true as soon as two people believe that (p and at least to people believe that p). Why is this? Is the truth of p is affected by people believing that p? I would definetely say yes, but I’m was unsure whether this was what you had in mind.

    What do you think?
    Lots of regards, Jacob.

    • Thanks for further comments.

      1. Sorry, I’d meant to say something more about belief where it’s a form of (something like faith). The issues here are very complex, but here are two initial thoughts. First, belief via faith (rather than normal forms of evidence) would on the face of it be consistent with a truth constraint on permissibility, for faith (or, indeed, revelation) might be perfectly consistent with, indeed indicative of, truth. (Not all would agree about that, and the sort of proposal considered in the discussion with Clayton–on which permissible belief is controlled by a knowledge requirement–might make faith per se problematic. That’s an issue for further discussion. As for the contradiction proposal, it might take any of three forms. (1) It might be the proposal that one might be permitted to believe p even though it conflicts with one’s standing belief that (say) not-p. That might be consistent with the truth requirement, since one might not have been permitted to believe not-p in the first place. (2) It might be the proposal that one might be permitted to believe p even though one believes it to convict with other amongst one’s standing belief. That again might be okay, since one’s belief that there is conflict might be a mistake, even one beyond one’s powers to avoid. (Perhaps what we see as conflict can be seen as conflict free, but only from God’s perspective.) Finally, (3) the proposal might be that one is permitted to believe contradictions. There are thinkers who agree–most prominently, there are dialethist logicians who seem to hold that some contradictions are true. Their view would be no immediate threat to the truth requirement. But the view that one might be permitted, or required, to believe genuine contradictions, where those contradictions are false, would be an issue. That would again be the subject for further discussion.

      2. The proper understanding of “permission” here is delicate, and the subject of ongoing controversy. It’s far from clear to me that this is the right way to think about belief, or indeed judgment. However, roughly, the idea is that, in at least some cases when one does something or other, or adopts one or another stance, the nature of the stance, or our concepts of such stances, imposes conditions on correctness or incorrectness. Thus, if I play chess, I’m permitted to make certain moves, and not others. That’s just what it is to play chess. Similarly, here with belief: one isn’t believing properly, or perhaps at all, if what one does isn’t governed by appropriate standards of correctness, &c. That anyway is the sort of view with which my post is engaging. On the face of it, none of that has much to do with social permissions, thought might lead to complaints by others, &c.

      3. In a sense, that’s right about days, but it’s more complicated. We agree on the rules for classifying days. But having done so, the rules determine whether the world meets the rules, so which day it is. Suppose we decided to change the name we give to Tuesdays to “Wednesday”. That would make the sentence “It’s Wednesday” true as used on Tuesdays. But it wouldn’t make false what I judge now, in judging, on Tuesday, that it’s Tuesday.

      4. The library example looks like a case where truth has little or nothing to do with agreement: the latter would seem to require convincing more than one person to do the relevant counting, or whatever. Why should that be a requirement on truth?

      5. In the original post, I was explicit that “p” is true, independently of the rest of the case. Its truth has nothing to do with being believed (or about belief, as I also made explicit, I think).

  8. Thanks for further clarifications.

    1. I agree on your notes of belief and faith. Coming from a German background I sometimes forget the difference between concepts in one language and in another. We have “belief” and “faith” in English, and “Überzeugung”, “Glaube” and “Zuversicht” in German, which all circle around the same thing and have slightly different meanings. The point is that a statement in one language maybe difficult to translate to the other. German “ich habe Glauben, aber keine Zuversicht” would translate to “I have faith, but I have no faith”, while English “believing needn’t be based on faith” could translate to “Glauben muß nicht auf Glauben basieren”. Interesting.

    2. Thans for making this clear, I think I understand.

    3. Yes, indeed.

    4. The library example has to do with agreement because all those truths must have gotten into those books before they could be read. Question here is, when does a claim become a truth, and is agreement involved here, may it even be agreement only on the way of obtaining the truth from a previously agreed starting point?

    5. You *were* explicit about p being true and not being about persons and beliefs. Just re-read it. I had completely missed this. I must have read “true p” in the sense of “genuine p” or similar. Very embarassing, I’m sorry.

    But I’m still unsure whether I’ve grasped the concept of distinguishing belief from truth. A single person could not tell her beliefs from truths, couldn’t she? Or, more precisely, are believing and knowing independent? Can I believe something without knowing it? Can I know something without believing it?

    Lots of regards, Jacob.

    • Thanks for further comments. I think we’re converging somewhat. Let me say something in reply to a couple of your points.

      4. The truths might not have made it into books had there been no agreement, but that isn’t obvious. Suppose someone discovered some fact–say, in mathematics or chemistry. What they discover is true, whether or not anyone agrees with it, and whether or not he publishes the discovery. Suppose it were something trivial: they count the books in their office and come to know that there are NN books there. Then there’s a fire and they, and all the books, perish, in such a way that no one else will ever know how many books there were. Still, it was true that there were NN books there. Now, suppose that they published the number in an especially dull book, say a diary. No one ever reads the book. Nonetheless, the book reports a truth. Or so it seems to me.

      Your final suggestion includes that a single person can’t tell what they believe apart from truths. I don’t think that’s true. Earlier, I believed that there were seven books strewn across my desk. I know now that I believed that. But I’ve now checked more carefully and realised that there are eight books, so that my earlier belief was false. A further question: can I tell now that my current beliefs are false? Well, not straightforwardly and rationally, since that would involve my believing that p and that it’s false that p, which would seem, at best, irrational. But I can of course change my beliefs in light of evidence, so it’s not as though I’m simply trapped by what I currently believe.

      Your final questions are: (i) can one believe without knowing? and (ii) can one know without believing? The former seems straightforward: I believed that there were seven books on my desk. But I didn’t know there were, since knowing that p requires that p is true. Since p = “there were seven books on my desk” and so false, it wasn’t and isn’t something I could know. As for (ii), the issues are more delicate. Some people think that one can know in cases wherein one’s confidence is too low to count as belief, and other similar cases. Some people think–less plausibly, perhaps–that knowing precludes believing, because for example, one is apt to say, “I don’t believe that p, I know it.” But for present purposes, I don’t need to take a stand on (ii), I think.

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