Rationality is permissibility

Many philosophers seem to think that – even if the notions of a belief’s being “justified” or “rational” are indeed normative notions, as is widely held to be the case – to say that a belief is “justified” is “rational” is to say something stronger than merely that the belief is permissible.

This is a mistake. It is easy to prove that if the notions of a belief’s being “justified” or “rational” are normative at all, then the permissibility of a belief is sufficient for the belief’s being justified or rational.


Here is the simplest version of the proof.

1. If it is not rational for you to believe p, you ought not to believe p.

2. If you ought not to believe p, it is not permissible for you to believe p.

Therefore (by the transitivity of these conditionals 1 and 2):

3. If it is not rational for you to believe p, it is not permissible for you to believe p.

Therefore (by contraposition and double-negation elimination from 3):

4. If it is permissible for you to believe p, it is rational for you to believe p.

That is, the permissibility of a belief is sufficient for the belief’s rationality.

Are the premises of this proof true? (2) seems obvious, given the intended interpretation of ‘ought’ and ‘permissible’; and it seems that (1) would surely be accepted by anyone who thinks that ‘rational’ is a normative concept.

Just in case anyone is tempted to doubt this, here is a supplementary argument for (1).

5. If it is not rational for you to believe p, it is irrational for you to believe p.

6. If it is irrational for you to believe p, you are rationally required not to believe p.

7. If you are rationally required not to believe p, you ought not to believe p.

By the transitivity of these conditionals (5), (6), and (7) entail (1).

(5) seems obviously true given the intended interpretations of ‘rational’ and ‘irrational’; (6) seems obviously true given the intended interpretation of ‘rationally required’; and it is hard to see how anyone who thinks that ‘rational’ is a normative concept could possibly deny (7).

Mutatis mutandis, the same argument seems to work for ‘justified’ as for ‘rational’. The permissibility of your believing p is sufficient for it to be rational or justified for you believe p.


Comments

Rationality is permissibility — 10 Comments

  1. Thanks for the interesting post, Ralph. I think the argument either begs the question or equivocates, from the perspective of someone (like me) who wishes to make the distinction you’re rejecting here.

    That is, take someone who thinks (as I do) that “it is rational for you to believe p” is ambiguous, since it might mean either:

    (A) Rationality permits your believing p.

    or

    (B) Rationality requires your believing p.

    Such a person will see your argument for (1) as equivocating on (A)/(B). In other words, they will see the (implicit) premise in your argument for (1):

    (*) If it is not rational for you to believe p, you are rationally required not to believe p.

    as true on an (A) reading, but false on a (B) reading. So, I just don’t see how your argument for (1) is meant to convince such a person that the (A)/(B) distinction is broken-backed.

  2. Example: I think rationality permits believing anything which is sufficiently highly probable, but rationality does not require (all) such beliefs. For instance, I think rationality permits the belief that one’s lottery ticket is a loser, but rationality does not require this belief. So, when I say “it is rational to believe one’s lottery ticket is a loser”, I have in mind the (A) reading and not the (B) reading (which I reject).

    • Thanks, Branden!

      I don’t see any evidence for your view that ‘It is rational for x to F’ is ambiguous in the way that you describe. Why should we think that sentences of this form can ever mean ‘Rationality requires x to F’?

      On the face of it, this sentence has the same structure as ‘It is just for us to punish the offender severely’, which doesn’t imply that ‘Justice requires us to punish the offender severely’, so far as I can see.

      In general, where ‘G’ is some virtue-predicate, I don’t think that ‘It is G for x to F’ implies that x’s F-ing is necessary for the relevant item to be G. It implies only that x’s F-ing is part of some salient state of affairs in which the relevant item is G.

  3. Thanks Ralph. I think your argument nicely lays out a case for your position. And that position is attractive, maybe even philosophically permissible. But even if it should be, I don’t think it is rational to accept it (!).

    I share Branden’s hesitation about the premise consisting of the antecedent of (5) and the consequent of (6). But neither your (2) nor your (7) seem to me obviously right, either.

    I can feel some sympathy for a line (deflating the ought-not a bit) on which something’s failing to be *optimal* is sufficient for its being something you ought not do (after all, says this line, you really ought to do the optimal thing instead) but not sufficient for its being impermissible (what you did was good enough). That would oppose (2), I guess. Perhaps there are some things that you *ought not* to do that are not such that you *must not* do them.

    And, in a different sort of mood (now inflating the ought-not, though this brings in different considerations too), one might think that while rationality is normative, its dictates are not exhaustive of the normative realm, so that while something might be prohibited by reason, other normative considerations might favor it sufficiently for it not to be something you ought not to do. (7) seems connected not to the claim that rationality is normative but rather to the claim that rationality exhausts the normative.

    I don’t myself reject (2) and (7); but I’m not ready to accept them, either.

    • Thanks, David!

      1. You are right that we can use ‘permissible’ so that it is not the dual of ‘ought’ — i.e., in a way in which ‘not permissible’ is strictly stronger than ‘ought not’. But the formal semanticists seem right to me that ‘ought’ is a kind of necessity modal (even if in any context in which ‘ought’ is contrasted with ‘must’, ‘ought’ is a weaker necessity modal than ‘must’); and it is clear that for every necessity modal there is a corresponding possibility modal. In this context, I intend to understand ‘permissible’ in such a way that it is just the possibility modal corresponding to ‘ought’ in this way.

      2. The way in which I’d address your “different sort of mood” is by emphasizing that terms like ‘ought’ (and ‘must’ and ‘may’ and ‘permissible’ etc.) are either polysemous or context-sensitive — expressing different concepts in different contexts. I believe that ‘ought’ can function as a kind of “rational ‘ought'”, in which it is just equivalent to ‘is rationally required’.

      In short, you are quite right that rationality’s dictates are not exhaustive of the normative realm. But few (if any) of the concepts that can be expressed by ‘ought’ are exhaustive of the normative realm. So this point gives us no reason to doubt that ‘rationally required’ implies ‘ought’.

  4. Thanks, Ralph — that’s helpful. But, I’m still not totally clear on the implications/presuppositions of this. Does your view imply/presuppose permissivism (i.e., the idea that one’s epistemic/evidential state can fail to mandate a single epistemically rational response)? If (instead) one accepts “uniqueness”, then won’t one be inclined to reject the idea that one can be justified in believing that p (e.g., since one’s total evidence fits believing that p), but not (epistemically) required to believe that p (i.e., permitted to not believe that p)?

  5. PS. Personally, I’m OK with permissivism (as my lottery example illustrates), but I can’t see how your argument (alone) could suffice to establish permissivism. Aren’t those who reject permissivism just going to view your argument for (1) are question-begging/equivocating?

    • Thanks again, Branden! My view is compatible with permissivism (of the kind that you and I both find acceptable), but it doesn’t entail permissivism.

      Even if (as my view implies) ‘rational’ just means “rationally permissible”, it could still be that for every thinker x and time t, and for every proposition p on the relevant agenda, there is a unique attitude towards p that it is rationally permissible for x to have at t.

      Permissivism is obviously true of rational choice: if alternative acts A and B have equal expected value (or in a case of incommensurability, neither has greater expected value than the other), then choosing A and choosing B are equally rational. Even if permissivism is false for rational belief, ‘rational’ should have the same kind of semantics in both contexts.

  6. I have views about ‘ought’ that get in the way of my accepting the arguments you give. (Not to be mysterious – I think ‘ought’ means approximately ‘the best’). But kindred arguments seem to me to work. The kindred arguments replace the ‘ought’s’ with ‘obligatory’s’, e.g.:

    1* If it is not rational for you to believe that p, then it is obligatory for you not to believe that p.

    Those arguments seem good to me.

    As you say, the conclusion, 4, is compatible with Uniqueness. That is an asset, as I see it.

    In fact, the conclusion allows that there is always an attitude that is the uniquely permissible one, for any given body of evidence. If that is true, then for a attitude to be rational might be equivalent to its being permissible. For an attitude to be rational then also implies implies that it is obligatory – not permissible not to take. This implication conflicts with the beginning of your posting, where it says that it is a mistake to think that something stronger than permissible is implied by being rational. But arguing for that mistake is another matter.

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