Representation Theorems and the Grounds of Intentionality

Abstract

This work evaluates and defends the idea that decision-theoretic representation theorems can play an important role in showing how credences and utilities can be characterised, at least in large part, in terms of their connection with preferences. Roughly, a decision-theoretic representation theorem tells us that if an agent’s preferences satisfy constraints C, then that agent can be represented as maximising her expected utility under a unique set of credences (modelled by a credence function 3el) and utilities (modelled by a utility function Des). Such theorems have been thought by many to not only show how credences and utilities can be understood via their relation to preferences, but also to show how credences and utilities can be naturalised—that is, characterised in wholly non-mental, non-intentional, and nonnormative terms. There are two broad questions that are addressed. The first (and more specific) question is whether any version of characterisational representationism, based on one of the representation theorems that are currently available to us, will be of much use in directly advancing the long-standing project of showing how representational mental states can exist within the natural world. I answer this first question in the negative: no current representation theorem lends itself to a plausible and naturalistic interpretation suitable for the goal of reducing facts about credences and utilities to a naturalistic base. A naturalistic variety of characterisational representationism will have to await a new kind of representation theorem, quite distinct from any which have yet been developed. The second question is whether characterisational representationism in any form (naturalistic or otherwise) is a viable position—whether, in particular, there is any value to developing representation theorems with the goal of characterising what it is to have credences and utilities in mind. This I answer in the affirmative. In particular, I defend a weak version of characterisational representationism against a number of philosophical critiques. With that in mind, I also argue that there are serious drawbacks with the particular theorems that decision theorists have developed thus far; particularly those which have been developed within the four basic formal frameworks developed by Savage, Anscombe and Aumann, Jeffrey, and Ramsey. In the final part of the work, however, I develop a new representation theorem, which I argue goes some of the way towards resolving the most troubling issues associated with earlier theorems. I first show how to construct a theorem which is ontologically similar to Jeffrey’s, but formally more similar to Ramsey’s—but which does not suffer from the infamous problems associated with Ramsey’s notion of ethical neutrality, and which has stronger uniqueness results than Jeffrey’s theorem. Furthermore, it is argued that the new theorem’s preference conditions are descriptively reasonable, even for ordinary agents, and that the credence and utility functions associated with this theorem are capable of representing a wide range of non-ideal agents—including those who: (i) might have credences and utilities only towards non-specific propositions, (ii) are probabilistically incoherent, (iii) are deductively fallible, and (iv) have distinct credences and utilities towards logically equivalent propositions. Show more