tum does not play a large role in most of the critical discussions that follow. The
major exception is Jeffrey’s (1990) theorem where the Bel-Ves pair is only unique
up to a fractional linear transformation. I discuss what a characterisational repre-
sentationist might do with this weaker uniqueness condition in §6.2.2.
32 Those who accept that agents can at one time have multiple, fragmented systems of belief might deny this point (cf. Lewis 1982). However, the kind of non-uniqueness that these theorists claim to exist is conceptually quite distinct from the kind of non-uniqueness we are discussing here: these theorists are usually motivated to appeal to fragmented belief states when a single coherent belief state cannot explain an agent’s apparently irrational behaviour and preferences, whereas we are now looking at a situation where multiple belief states can each individually be used to explain the agent’s behaviour/preferences equally well.
3.4.4 The interpretation o f the theorem's primitives
The point o f characterisational representationism is to define what it is to have such- and-such credences and utilities largely in terms o f preferences, by appeal to a rep resentation theorem. If any such project is to be successful, then the basic notions involved in the interpretation o f those theorems cannot themselves be understood in terms o f credences or utilities. Generally speaking, if the goal is to define
X
in terms o fY,
then it had better not be the case thatY
is to be understood, in turn, in terms o fX.
Thus, from the Non-Circularity condition, we see that if characterisa tional representationism is to be founded upon some theorem or other, it’s a mini mal requirement upon that theorem that it can be interpreted without reference to agents’ credences and utilities.’3There are at least two basic formal elements to any representation theorem: a preference relation >, and a set BOP o f objects o f preference. Often, BOP is itself constructed from a number o f further sets. If a given representation theorem is to satisfy the present Non-Circularity condition, then neither >, nor B O P, nor any other primitive elements involved in the statement o f the theorem should be given an interpretation which requires reference to credence or utility states. For instance, it would obviously not do for characterisational representationism to define > as follows:
x > y (relative to an agent
S)
iffS
has a higher utility for x than fo ryLikewise, suppose that BOP is supposed to represent a collection o f gambles con ditional on a proposition
P
, where it’s required that the agent has a particular cre dence valuen
forP
(e.g.,n
= 0.5). Unless we already know what it is to have cre dencen
inP,
preferences over such bets will not be very useful in the characterisation o f what it is to be in such-and-such a credence state more generally.33 To be clear, some philosophers are happy to countenance non-reductive definitions of im portant concepts, wherein the definiendum forms part of the definiens. I am assuming, however, that the goal of characterisational representationism (and preference functionalism more generally) is reductive. Recall that much of the appeal that characterisational representationism holds is due to its promise to solve the old philosophical problem that arises from the interdefinability of credence and utility (or belief and desire).
Furthermore, from the Naturalisability condition we know that if we are to pro vide a naturalistic characterisation o f what it is to be in certain credence and utility states, and if a representation theorem is to play a central role in that characterisa tion, then the basic notions o f the theorem should be naturalistic— or at least readily naturalisable.
3.4.5 Summary
Let us summarise. The following desiderata are important for characterisational representationists generally (whether naturalistic or non-naturalistic); subsidiary desiderata are also listed:
(1) The theorem’s preference conditions should be satisfied (or approximately satis fied) by the majority of ordinary human agents (at least under appropriately speci fied circumstances).
(la) The theorem’s preference conditions must be satisfiable.
(2) Assuming that S is an ordinary agent and satisfies T s preference conditions, T
should provide a plausible (if slightly idealised) homomorphic model of S’s cre dences, utilities, and preference-forming procedure.
(2a) “Bel and Ves ought to be capable of assigning values to (more or less) the same propositions, rather than having distinct, non-overlapping domains.
(2b) Bel and T)es ought to be capable of modelling hyperintensional credences and utilities—they ought to be capable of distinguishing and assigning distinct val ues to metaphysically—and perhaps even logically and mathematically— equivalent objects of thought.
(2c) Bel and Des ought to assign values to all and only the objects of thought to wards which the relevant agent has credences and utilities, respectively.
(2d) Bel ought to be capable of modelling the total credence states of non-ideal reasoners with potentially indeterminate or imprecise credences; it should not be restricted to models of agents who are probabilistically coherent, logically omniscient, deductively infallible, and so on.
(2e) The manner by which Bel and Des combine to determine preferences should be plausible, under the relevant circumstances.
(4) It should be possible to understand and specify the basic notions involved in the interpretation of the theorem independently of any prior knowledge regarding the relevant agents’ credences and/or utilities.
Furthermore, if a naturalistic variety o f characterisational representationism is the goal, then a further desideratum is:
(5) The basic notions of the theorem should be naturalistic/readily naturalisable.
In Chapters 5 through to 7, I will evaluate a range o f theorems in light o f these desiderata. I will argue that none o f them satisfy each o f (T) to (4); furthermore, I will argue that none satisfy (5).
(la ), (3), and (4) seem non-negotiable. However, readers might note the em phasis on ordinary agents in (1) and (2), and may want to weaken the relevant cri teria if their only goal is to characterise credences and utilities for ideally rational agents. One might take this as part o f a two-step strategy for characterising cre dences and utilities in general: first give an account for the ideal case, and then ‘de- idealise’ so that it applies to ordinary agents. Taking this line may suggest replacing (1) and (2) with:
( l f) The theorem’s preference conditions should be satisfied (or approximately satis fied) by ideally rational agents in idealised conditions.
(2f) Assuming that S is ideally rational and satisfies T s preference conditions, Tshould provide a plausible homomorphic model of S’s credences, utilities, and preference forming procedure.
We can plausibly assume that ideally rational agents are probabilistically coherent, hence adopting (2') might suggest relaxing (2b) and (2d) in particular. Furthermore, it is plausible that ideally rational agents apply a different decision rule than ordi nary agents (or the same rule, but better and more consistently), so (2e) would need to be interpreted accordingly.
Something like this two-step strategy for understanding empirical phenomena is applied throughout the sciences, and I strongly suspect that it will be required for
present project as well. We should, for instance, certainly focus our attention on properly functioning, species-typical human beings in normal circumstances with slightly idealised cognitive processes free from various, well-known confounding factors (e.g., injury, intoxication, etc.). In that sense o f ‘idealisation’, we should indeed attempt to characterise credences and utilities for the ideal case and then see what can be done about de-idealisation. The two-step strategy works best, however, when (i) the relevant idealisations don’t leave us vastly removed from the actual, target phenomenon, and (ii) it is reasonably clear how to ‘de-idealise’.
What we are after is a characterisation o f credences and utilities in general. It’s hardly likely, however, that the metaphysics o f credences and utilities is disjunctive, in the sense o f being one way for ideally rational agents and a wholly different way for ordinary agents. So, we should expect any plausible approach to credences and utilities for ideally rational agents to be a special case o f a more general account for agents o f all kinds. Thus, if we are going to develop an account o f credences and utilities for ideally rational agents, it should be readily generalisable— that is, it should be reasonably clear how to extend (or ‘de-idealise’) the account so as to apply also to ordinary agents.
What is unclear is whether this ‘de-idealisability’ condition will be met if all we have is a theorem which merely satisfies (1') and (2'). Moreover, showing that it can be met will essentially involve showing that there is a theorem in the vicinity which satisfies (1) and (2). Characterisational representationism w on’t be fully vin dicated unless progress can be made towards a theorem which satisfies the original desiderata, relevant to the ordinary person on the street. A theorem that applies only to angels is not enough.
In Chapter 6 , 1 will suggest that Jeffrey’s representation theorem may satisfy (1') and (2'), though it does this at the cost o f strong uniqueness results. However, the idealisations needed are extreme: Jeffrey’s theorem only applies to highly idealised subjects, his representation result is only plausible for the ideally rational agent, and it is not clear whether and how his conditions can be weakened to account for the ordinary subject. In Chapter 8, however, I will suggest an improvement— a theorem which is many respects similar to Jeffrey’s but comes much closer to satisfying (1) and (2) (as well as (3) and (4)), and which has the Standard Uniqueness Condition.
Ch a p t e r f o u r