be found in Frank Ramsey’s ‘Truth and Probability’ (1931), which we will discuss
in Chapter 7. This involved a CEU theorem in particular, which was developed for
the purposes of constructing a system for the measurement of credences and utili
ties. Since the 1950s, Ramsey’s ideas about measurement have been taken up and
developed substantially by philosophers, psychologists, and economists looking to
create similar measurement procedures (see especially Davidson, Suppes et al.
1957, Krantz, Luce et al. 1971, Chs. 4-5, Suppes 1974, Davidson 1990, Weirich
2015, 46). In all such cases, representation theorems are employed to show how
sufficiently rich evidence regarding behavioural preference patterns can be used to
empirically constrain the range of credence and utility states that an agent might be
in. We might call this a measurement application of a representation theorem.
Ramsey’s general strategy was to assume that CEU is descriptively accurate with respect to an agent S's decision-making procedure. Given then that we can empiri cally ascertain S's preferences, Ramsey proposed to determine her credences and utilities using the CEU representation theorem that he developed. That is, if S is preference-rational with respect to his theorem’s conditions C, then according to the Decision-theoretic Interpretation o f that theorem and in light o f its Standard Uniqueness Condition, S would be a probabilistically coherent expected utility maximiser only i f she has credences Del and utilities Des— there is only one prob ability function Del which can give rise to her preferences according to CEU, and the only possible Des functions compatible with her preferences are positive linear transformations o f one another. Since we began with the assumption that S does conform to CEU, it follows immediately that we can be confident that S has cre dences Del and utilities Des. To the extent that his initial assumption was justified, Ramsey’s theorem appears to give us a way to work backwards from knowledge of preferences to knowledge o f credences and utilities.
Ramsey’s measurement system is a prime example o f how representation theo rems— especially those with the Standard Uniqueness Condition— can help supply us with a solution to the classic problem o f separability, wherein two distinct quan tities usually only have observable consequences when in interaction with one an other— thus posing the problem o f how to disentangle their respective influences in order to supply a measure for each quantity. In the present situation, this problem is particularly pronounced: according to folk psychology, the main effects o f cre dences— i.e., preferences and intentional action— are only manifest when they in teract with utilities, and vice versa. As Davidson puts the problem,
If a person’s [utilities] for outcomes were known, then his choices among courses of action would reveal his credence; and if his credence [sic] were known, his choices would disclose the comparative value he puts on the outcomes. But how can both unknowns be determined from simple choices or preferences alone? (1990, 316-7)
For instance, consider the following experiment. An ordinary playing card is placed face-down on a table in front o f a subject S. No information is given about which card it is. The experimenter gives the subject two choices:
(a) A banana if the card is numbered; an apple otherwise (b) An apple if the card is numbered; a banana otherwise
Suppose that S chooses (a). The problem for the experimenter is to determine why
S made this choice. Two hypotheses are immediately apparent, each o f which pre suppose that S is maximising her expected utility: either she prefers bananas to ap ples and is more confident that the card is numbered than that it’s not; or, she prefers apples to bananas and is more confident that the card is not numbered. The choice o f (a) over (b) does not provide any clear evidence for one hypothesis over the other, and yet the two hypotheses offer contradictory claims about S's credences and util ities. Much o f the appeal o f many representation theorems with the Standard Uniqueness Condition originates with their apparent capacity to solve this prob lem— with enough information surrounding the agent’s preferences, these theorems suggest that we can narrow down the range o f competing hypotheses to what is in effect a unique model o f the agent’s credences and utilities.
So much for the measurement application. Note that while it involves a commit ment to the epistemological thesis that preferences provide information about cre dences and utilities, the use o f representation theorems in this capacity does not carry any commitment to the metaphysical thesis that credences and utilities are characterisable largely in terms o f preferences. Historically, however, characterisa- tional representationism has been only a small step on from a Ramseyan measure ment application (though perhaps a giant leap for philosophers).
Many historical proponents o f characterisational representationism have been sympathetic to some form o f operationalism and/or behaviourism with regards the psychological attributes. Ramsey him self seems to have wanted his preference con ditions to underlie both a measurement system and a characterisation o f credences, asserting that the notion o f graded belief “has no precise meaning unless we specify more exactly how it is to be measured” (1931, 167). The main difference between characterisational representationism and the measurement application is that, ac cording to the former, preferences don’t just supply good evidence about credences and utilities— rather, having (or being disposed to have) appropriate preference pat terns is in some important sense a part o f what it is to have credences and utilities.