Abstract
Given any proposition, is it possible to have rationally acceptable attitudes towards it? Absent reasons to the contrary, one would probably think that this should be possible. In this paper I provide a reason to the contrary. There is a proposition such that, if one has any opinions about it at all, one will have a rationally unacceptable set of propositional attitudes—or if one doesn’t, one will end up being cognitively imperfect in some other manner. The proposition I am concerned with is a self-referential propositional attitude ascription involving the propositional attitude of rejection. Given a basic assumption about what constitutes irrationality, and a few assumptions about the nature of cognitively ideal agents, a paradox results. This paradox is superficially like the Liar, but it is importantly different in that no alethic notions are involved at all. As such, it stands independent of the Liar and is not a ‘revenge’ version of it. After setting out the paradox I discuss possible responses. After considering several I argue that one is best off simply accepting that the paradox shows us something surprising and interesting about rationality: that some cognitive shortfall is unavoidable even for ideal agents. I argue that nothing disastrous follows from accepting this conclusion.
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Notes
Throughout this paper, the notion of rationality I discuss is a synchronic one, that is, a notion of rationality that governs a subject’s propositional attitudes as they are at some given moment. This is to be contrasted with a diachronic notion of rationality, which governs transitions from one set of propositional attitudes to another. So, to illustrate, it is a requirement of synchronic rationality that one’s beliefs be consistent (let’s say) but it is a requirement of diachronic rationality that when one’s beliefs are inconsistent, one give up those inconsistency-generating beliefs that are least justified (let’s say). There is a debate to be had about whether one of these notions of rationality is to be cashed out in terms of the other, but that debate doesn’t matter for anything I’ll say in this paper.
Though I would like to be able to provide an argument for the principle, I would not know where to look for premises—it seems too basic for such. If one took the notion of rejection to be analysable in terms of assertion and negation, as per the Fregean view (above), one could argue for it from claims about negation, unless one were a dialetheist. But the dialetheist, as we have seen, already has reason to reject the Fregean view. If one takes the notion of rejection as primitive, one has a good reason for accepting the principle, for without it, it becomes hard to say what the opposition between acceptance and rejection consists in.
This is a view Graham Priest defended at one point, as evinced by his (2006), pp. 98–99. He has since backed off from it, though not in print, as far as I know.
Exceptions might be cases in which one is under- or misinformed about the contents of a proposition which one endorses or denies. Maybe in such cases one can accept that one accepts something while failing to actually accept it. But the case is not clear. One might hold, for instance, that if a lack of comprehension of P stops one from having attitudes of acceptance or rejection to it, that same lack of comprehension would stop one from having second-order propositional attitudes involving P.
The form of self-reference that goes on here is a bit less straight-forward than in the case of the Liar sentence, though I do not think it in any way problematic. While the Liar says of itself that it is false, the Rejecter says of the speaker that the speaker rejects it. Self-reference is still achieved, but it runs by way of the speaker’s attitudes. Although less popular now, in the past various recipes for combating paradoxes have involved banning self-reference from the language, most famously the recipe given in Tarski (1933). Whether the type of anti-paradox legislation that rules out Liar-like self-reference will also automatically rule out R is not obvious: it would depend on the fine print.
There are other responses to R that are also reminiscent of gappy solutions. I discuss these in the next section.
Terence Parsons discusses a similar sophism in his (1984), formulated using denial rather than rejection: ‘I deny this very sentence’. He notes one cannot coherently deny it, but doesn’t take the matter much further than that. Caie (2012) discusses a close relative of the Rejecter (formulated in terms of disbelief) and proposes a response to it. I’ll discuss that response in Sect. 4.
The Rejecter is also worth comparing to a paradox discussed by Graham Priest in his (2005), chapter 6. It involves a proposition p: “it is irrational to believe that p” (he regards it as a variant of the ‘irrationalist’s paradox’ due to Greg Littman). To believe it would be to believe something which one considers irrational, and since that is irrational, one ought not believe it. But if it’s indeed irrational to believe it, then that shows that p is true, and that one ought to believe it. One ends up in a situation where one ought and ought not believe p.
If we reformulate p as ‘one ought to reject p’, a resemblance between Priest’s paradox and the Rejecter emerges. The two involve some of the same issues. For instance, its (reformulated) derivation arguably involves something like a normative analogue of our assumption A: one ought to reject what one accepts one ought to reject. As such, we can see Priest’s discussion as an anticipation of the Rejecter.
However, Priest’s discussion is brief, effectively restricted to a discussion of option (ii), above. It’s not clear how Priest’s paradox would fare on the other options: at least prima facie, it seems possible to reject p (i.e. take option iii) without landing in irrationality; one could reject something without believing that one ought to. Option (iv) also seems prima facie safe. Furthermore, Priest’s bullet-biting solution to his paradox is to accept that there are dialetheias concerning what’s rational; while my proposed response (below) will also be of a bullet-biting nature, it does not involve buying a contradiction, and so is far less logically committal.
This makes our paradox an interesting challenge for dialetheists. While arguably no-one has it easier than them when it comes to alethic paradoxes, the very ideology they need in order to account for disagreement generates a paradox that they cannot respond to in their patented manner.
There may be some mileage in classical solutions, but they don’t quite seem to get the job done. Suppose one were an epistemicist about indeterminacy. Then one might suggest that though there is a fact of the matter about which stance one takes to R, we are in principle ignorant of which one it is. In that case, the assumptions (b) and (c) seem to fail; possibly also (a). So in that case, if the stance one is in fact taking is one of (i) through (iii), irrationality does not ensue. But since one may in fact be taking stance (iv), it is not determinately the case (by epistemicist lights) that one is not in an irrational state. The best result the epistemicist can secure here is that one also isn’t determinately in an irrational state. Supervaluationism about indeterminacy hits the same snag. Of course, one could claim that though it is indeterminate whether one is taking stance (i), (ii) or (iii), it is determinate that one isn’t taking stance (iv). One way of guaranteeing this is to say that taking stance (iv) is simply (psychologically or metaphysically) impossible, as Priest does. But as noted above, it is unclear what the motivation would be for saying this. Saying that (iv) would be irrational would be to beg the question: we want to know whether or not we are in fact rational when it comes to R, and we don’t take it as given that we are.
However, the diagnosis of confusion in terms of neither accepting nor rejecting may have something going for it. When we first come to consider proposition R, we presumably don’t yet have any attitudes towards it. In other words, we start out with stance (iii). It’s hard to see how, in the process of considering R, we would naturally end up in a state of indeterminate attitudes towards it, instead just remaining in the unopinionated state that we started out with. Since all options look equally bad, there doesn’t seem to be anything that would motivate us to change our set of attitudes, irrationality-inducing as that set may be.
The assumptions are of broadly conditional form, which means that one would strengthen them by either weakening the antecedent or strengthening the consequent, and that one would weaken them by either strengthening the antecedent or weakening the consequent. Here both the antecedent and consequent are strengthened in each case, but in the case of A the antecedent is strengthened in two ways and the consequent in one, while in the case of B and C the antecedent is strengthened in one way and the consequent in two ways.
Someone might object at this point that it might conceivably be indeterminate whether one’s attitudes to a proposition are indeterminate, i.e. one’s attitudes might be higher-order-indeterminate. Perhaps, but one would not want to endorse that option in the case of R or R*. For if it is indeterminate whether one’s attitudes are determinate, and having determinate attitudes gets one into trouble (as we have already seen) then the best result one can hope for with respect to R or R* is that it is indeterminate whether they get us into trouble. Now perhaps one might decide to go for that result if one were convinced that nothing better could be had, but it clearly falls short of the result that the indeterminism about R was supposed to secure for us.
See Makinson (1965).
Perhaps what I describe as sacrificing rationality for something else could, in the case of the preface paradox, be described as one kind of rationality (practical rationality) trumping another (theoretical rationality). If so, take me to be speaking specifically about theoretical rationality, everywhere above. It does not really matter for the case at hand, because with R no such trumping is going on, and no other kind of rationality is involved.
As this is a disjunctive claim, there in in principle three ways in which it could be true. One might think there could be fully transparent agents, but not ones that are simultaneously fully rational; or one might think there could be fully rational agents, but not ones that are fully transparent; or that agents are never fully transparent nor ever fully rational. I’ve argued for the disjunction by assuming for the sake of argument that we have a fully transparent agent, and arguing that they would end up having irrational attitudes to R. But that argument does not commit me to any one of the three options listed. One might believe, as Priest at one time did (see footnote 4) that it’s metaphysically impossible to accept and reject the same proposition. If so, then the argument would commit one to believing that there are no fully transparent agents (with views on the Rejecter). But I want to merely defend the weaker, disjunctive claim.
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Acknowledgments
I would like to thank Michael Bench-Capon, Jason Turner, Robbie Williams and Francesco Berto and audiences at Leeds, Manchester, Amsterdam and Aberdeen for comments on drafts of this material, as well as several anonymous referees. This paper was prepared within the 2013–15 AHRC project The Metaphysical basis of Logic: the Law of Non-Contradiction as Basic Knowledge (grant ref. AH/K001698/1).
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Brouwer, T.N.P.A. A paradox of rejection. Synthese 191, 4451–4464 (2014). https://doi.org/10.1007/s11229-014-0541-z
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DOI: https://doi.org/10.1007/s11229-014-0541-z