teorema Vol. XXVI/1, 2007, pp.131-137 131 DISCUSIÓN «In-Between Believing» and Degrees of Belief Darrell Patrick Rowbottom RESUMEN Schwitzgebel (2001) -de ahora en adelante «S»–– ofrece tres ejemplos para convencernos de que hay situaciones en que los individuos no se pueden describir adecuadamente como creyendo que p o no creyéndolo, sino que están más bien en «estados de creencia intermedios».1 Argumenta a continuación que no hay estrategias «bayesianas» para explicar tales estados y propone una explicación disposicional. No tengo ninguna objeción fundamental a la idea de que podría haber «estados de creencia intermedios». Lo que argumentaré más bien es que: (I) S no presenta argumentos convincentes que apoyen el que haya realmente tales estados; (II) S no muestra, contrariamente a lo que afirma, que no se pueda dar cuenta de los «estados de creencia intermedios» en términos de grados de creencia; (III) la explicación disposicional que hace S de los «estados de creencia intermedios» es más problemática que la alternativa de los «grados de creencia». ABSTRACT Schwitzgebel (2001) -henceforth «S»- offers three examples in order to convince us that there are situations in which individuals are neither accurately describable as believing that p or failing to so believe, but are rather in «in-between states of belief».1 He then argues that there are no «Bayesian» or representational strategies for explicating these, and proposes a dispositional account. I do not have any fundamental objection to the idea that there might be «inbetween states of belief». What I shall argue, rather, is that: (I) S does not provide a convincing argument that there really are such states; (II) S does not show, as he claims, that «in-between states of belief» could not be accounted for in terms of degrees of belief; (III) S's dispositional account of «in-between states of belief» is more problematic than the «degree of belief» alternative. I. THREE DISPARATE EXAMPLES S's first example concerns an individual named Konstantin, who lived across the hall from S during his freshman year. At the time, S «fully and Darrell Patrick Rowbottom 2132 completely believed» that his surname was whatever it was. At eighty, S will have no memory of Konstantin at all. But at points in the middle, S will remember correctly or not depending on context. Against the view that the belief will remain, but simply become less easy to access, he suggests «at some point, the belief must pass from fully present, if difficult to access, to absent; and it seems odd to say that this happens at some individual moment» [Schwitzgebel (2001), p. 77]. Here, however, there seem to be two distinct problems. First, S does not consider the possibility that the memory -not belief- might remain fully present, yet that this might become impossible (for S) to access in a moment; that a belief can become absent precisely in virtue of a memory becoming inaccessible.2 Second, and more trenchantly, even when S was living across the hall from Konstantin, there must have been possible contexts in which he would not have been able to remember the name, or even Konstantin; if he'd become blind drunk, or taken a large dose of LSD, for instance. So this seems to imply that all belief states are «inbetween states», although the example relies on positing a point at which S «fully and completely» believed. It therefore seems that remembering correctly or not depending on context cannot be correlated with «in-between believing», after all. The second example is of Rohsini. When teaching her 4th grade class, she sometimes lists the low prime numbers, and always does so correctly. But on other occasions, she provides a definition of the primes which does not exclude «1», even though she «knows that 1 is not a prime» [Schwitzgebel (2001), p. 77]. If we press her, S says, then she will modify her definition in order to exclude «1», although «For the most part, she would happily assent to her erroneous definition» [Schwitzgebel (2001), p. 77]. However, this seems to be a case where the beliefs in question are simply inconsistent from a narrow logical point of view. If Roshini is confronted with (and grasps) the fact that her list of primes should include «1», according to her definition, then she only has two rational choices. She can cling to the definition and add «1» to the list, or alter the definition such that it precludes it from the list.3 No appeal to «in-between believing» is required; even brilliant (and reasonable) people have inconsistent beliefs, as the case of Russell's paradox shows. The final example is of Antonio, who feels very strongly that God exists in some contexts, but equally as strongly that He does not in others. But note that it is «feelings», and not beliefs or thoughts, which S appeals to. This is problematic since it is plausible that there is no determinate relationship -if there is any link, howsoever tenuous- between the extent to which one believes a proposition and the strength of one's feelings about it. This point is familiar to advocates of the subjective interpretation of probability, and was first made by Ramsey [(1926), p. 169]: 'In-Between Believing' and Degrees of Belief 133 We can, in the first place, suppose that the degree of a belief is something perceptible by its owner; for instance that beliefs differ in the intensity of a feeling by which they are accompanied, which might be called a belief-feeling or feeling of conviction, and that by the degree of belief we mean the intensity of this feeling. This view would be very inconvenient, for it is not easy to ascribe numbers to the intensities of feelings; but apart from this it seems to me observably false, for the beliefs which we hold most strongly are often accompanied by practically no feeling at all; no one feels strongly about things he takes for granted. So although Antonio might experience a sort of mild euphoria while in the middle of a church service, and thereby «feel sure that there must be a divine force guiding the world» [Schwitzgebel (2001), p. p. 78], it is unclear that this directly reflects his (synchronic) degree of belief in the same proposition. Likewise if he «feels certain God is involved» when a child is born, or when a friend dies. This is exactly why Ramsey suggested betting procedures in order to measure degrees of belief.4 Nevertheless, it is possible that Antonio's «feelings» might have some influence on the extent to which he believes the proposition; that they might motivate a change. So perhaps S could revise his example by suggesting that Antonio's betting behaviour on the existence of God will change by scenario, in line with his emotional state? I come to this in the next section. We have seen that S's examples are disparate. The first could concern memory loss, and have little or nothing to do with belief; what's more, it is internally inconsistent. The second appears to concern inconsistent beliefs. And the third, which is arguably the best, seems to rely on a dubious link between strength of feeling about p and degree of belief in p. II. ARGUMENTS CONCERNING THE «BAYESIAN» VIEW After presenting his three examples, S suggests that each involves «inbetween states of belief». He then endeavours to argue that neither a «Bayesian» nor a representational approach could be successful in explicating these. I will concentrate on what he says concerning the former.5 Although S calls the view he discusses a «Bayesian» one, this is liable to cause serious confusion. For in fact he seems to be concerned with degrees of confidence -a.k.a. degrees of belief- rather than the process by which these are to be updated. As Gillies [(1998), §1] explains: Bayesianism involves two assumptions. The first is that C(h, e & b) satisfies the standard axioms of the mathematical theory of probability [...] The second assumption is that the degree of confirmation is changed the light of new evidence e by a process known as Bayesian conditionalisation. Darrell Patrick Rowbottom 4134 So S appears to attack only the view that synchronic degrees of belief are sufficient to explain «in-between believing».6 His initial argument is as follows: It is not a matter of degree of belief fluctuating over time; rather Roshini and Antonio are, at a single time, disposed quite confidently to assert one thing in one sort of situation and to assert its opposite in another. This argument is flimsy, however, because the changes can easily be accounted for by degrees of belief provided that the background information of the individuals differs in those situations. In short, one might consistently have the following degrees of belief: D(p, B)=0; D(p, B1) = 1. Change the context, and the (relevant conditional) degree of belief in p will change. This is precisely what leads De Finetti [(1937), pp. 146-147] to suggest: Whatever be the influence of observation on predictions of the future, it never implies and never signifies that we correct the primitive evaluation of the probability P(En+1) after it has been disproved by experience and substitute for it another P*( En+1) which conforms to that experience and is therefore probably closer to the real probability; on the contrary, it manifests itself solely in the sense that when experience teaches us the result A on the first n trials, our judgment will be expressed by the probability P(En+1) no longer, but by the probability P(En+1|A), i.e. that which our initial opinion would already attribute to the event En+1 considered as conditioned on the outcome A. S continues by suggesting that degrees of belief cannot be used to account for differences in feeling, say in the example of Antonio. But as we have already seen in the previous section, it is unclear whether differences in feeling are indicators of, although they may sometimes be motivators for, belief; Ramsey's point that «no one feels strongly about things he takes for granted» needs to be countered. Nevertheless, perhaps S means to suggest that there can be changes of degree of belief without changes in information -or at least relevant information (i.e. evidence)-. Take the case of Antonio and revise it as suggested previously, such that his betting behaviour on «God exists» changes purely on the basis of his mood. To be specific, we can stipulate that changes in information in the specified scenarios do not affect his (degree of) belief, or even that he'll believe differently if he's happy than if he's sad, say, in an otherwise identical situation. This is an interesting idea. But it does not show that «in-between believing» cannot be explained in terms of synchronic degrees of belief. Rather, it seems to suggest that degrees of belief can be highly unstable, and subject to change on the basis of factors that Bayesians don't consider. In fact, it seems that a state of «in-between believing» p might be described exactly as 'In-Between Believing' and Degrees of Belief 135 a state in which synchronic degree of belief in p is highly sensitive to changes in context.7 I can now explain why the earlier complaint about S's use of «Bayesian» is more than a cavil. S does have the seed of argument against a Bayesian account of rational belief change, in so far as this fails to consider changes in mood and what counts as a rational change in degree of belief in response to a change in mood. Yet in so far as Antonio's changes in belief seem to be thoroughly irrational, it is only a seed. For it to grow, it would need to be shown that sometimes it is perfectly rational to adjust one's degree of belief in a proposition on the basis of mood alone, trivial cases -such as believing «I am happy» as a result of feeling happy- aside. III. PROBLEMS FOR THE DISPOSITIONAL ACCOUNT So far, I have shown that S does not argue convincingly for an «inbetween state of belief» which cannot be accounted for by degrees of belief. I shall close by suggesting that the dispositional account which he proposes is less appealing than the «Bayesian» alternative.8 S invokes the following example, from Ryle [(1949), pp. 134-135], of what it is to believe that some ice is dangerously thin: [A] to be unhesitant in telling oneself and [B] others that it is thin, [C] in acquiescing in other people's assertions to that effect, [D] in objecting to statements to the contrary, [E] in drawing consequences from the original proposition, and so forth. But it is also [F] to be prone to skate warily, [G] to shudder, [H] to dwell in imagination on possible disasters and [I] to warn other skaters. S then suggests that «Roughly speaking, the greater the proportion of stereotypical dispositions a person possesses, and the more central these are to the stereotype, the more appropriate it is to describe him as having the belief in question» [Schwitzgebel (2001), p. 81]. But now take the individual who has dispositions A, E, F, G, & H, yet not B, C, D, & I. A credible explanation is that he is a nasty prankster who is sure that the ice is dangerously thin, but would delight in seeing someone else fall through it! Here, then, there seems to be «a further truth about the subject's real state of belief underlying his mixed dispositional profile» [Schwitzgebel (2001), p. 82]. Is this not just a synchronic degree of belief, plus some appropriate mechanism (and/or implicit policy) for updating it? It might be added that talk of «the proportion of stereotypical dispositions» implies that there is a finite number of these, in the aforementioned Darrell Patrick Rowbottom 6136 case, even though this is far from clear. If there is a finite number, can S state them? If not, how exactly is a proportion to be measured, or even made sense of? The first of these problems, at least, is addressed by the (rather complicated) discussion of «excusing conditions» in Schwitzgebel (2002). But what is still lacking is an argument that the dispositional account is preferable to all possible (or at least currently conceivable) accounts using degrees of belief; that it enjoys more explanatory power, and/or is preferable in terms of theoretical virtues (such as simplicity). I have argued that this is unclear at best, since S's criticisms of degrees of belief -as potential means of explicating «in-between believing»- fall wide of the mark. School of Physics Department of Philosophy University of Edinburgh University of Bristol James Clerk Maxwell Building 9 Woodland Road Mayfield Road Bristol BS8 1TB, UK Edinburgh EH9 3JZ, UK E-mail: Darrell.Rowbottom@bristol.ac.uk NOTES 1 Price (1969) and Dennett (1987) provide precedents. 2 Saying that the ability to recall something can vanish in a moment is not the same as saying that the thing itself vanishes. One could say that there are no available mnemonic triggers in principle, and not just in practice, at such a point. See also Bernecker (2007), who argues that remembering that p does not imply believing that p. 3 She might be content to tell the occasional white lie to her students, to help them to understand more easily, of course. But in that event, it's also clear that no appeal to «in-between believing» is required. 4 For more on this, see Gillies [(2000), pp. 55-65]. On a novel problem with this account, see Rowbottom (2007a). 5 I also think that S's arguments against the representational view are rather weak. He writes: «to speak of the subject as "sort of" or "halfway" representing something is unnatural» [p. 80], but does not consider that to speak of a better or worse representation is perfectly natural, especially in pictorial cases. Intuitively speaking, an impressionist painting of the Houses of Parliament is a less accurate representation than a wooden model, made to scale. 6 Bayesianism does not require a subjective interpretation of probability, either. Keynes (1921), for example, advocates a logical view where probabilities are relations between propositions. His claims concerning rational degrees of belief are derivative from this view. 7 See also the further examples, along with another discussion of degrees of belief, in Schwitzgebel [(2002) pp. 260-262]. My criticism applies equally to these. 8 Once again, note that I am not advocating Bayesianism - in fact I reject it, as I explain in Rowbottom (2007b) - but only the idea that «in-between believing» can 'In-Between Believing' and Degrees of Belief 137 be explained by degrees of belief. As argued above, pace Schwitzgebel (2001), there is nothing especially Bayesian about this view. REFERENCES BERNECKER, S. (2007), «Remembering without Knowing», in Australasian Journal of Philosophy, 85 (Forthcoming). DE FINETTI, B. (1937), «Foresight: Its Logical Laws, Its Subjective Sources», in Kyburg, H.E. and Smokler, H.E. (eds.), Studies in Subjective Probability, New York, Wiley, (1964), pp. 93-158. - (1974), Theory of Probability: A Critical Introductory Treatment, Vol. I, London, John Wiley & Sons. DENNETT, D.C. (1987), The Intentional Stance, Cambridge, MA, M.I.T. Press. GILLIES, D.A. (1998), «Confirmation Theory», in Gabbay, D.M. and Smets, P. (eds.), Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. I, Dordrecht, Kluwer, (1998), pp. 135-167. - (2000), Philosophical Theories of Probability, London, Routledge. KEYNES, J.M. (1921), A Treatise on Probability, London, Macmillan. PRICE, H.H. (1969), Belief, London, Allen & Unwin. RAMSEY, F.P. (1926), «Truth and Probability», in Kyburg, H.E. and Smokler, H.E. (eds.), Studies in Subjective Probability, New York, Wiley, (1964), pp. 61-92. ROWBOTTOM, D.P. (2007a), «The Insufficiency of the Dutch Book Argument», in Studia Logica (Forthcoming). - (2007b): «Intersubjective Corroboration», in Studies in History and Philosophy of Science (Forthcoming). RYLE, G. (1949), The Concept of Mind, New York, Barnes & Noble. SCHWITZGEBEL, E. (2001), «In-Between Believing», in Philosophical Quarterly, 51, pp. 76-82. - (2002), «A Phenomenal, Dispositional Account of Belief», in Noûs 36(2), pp. 24975.