A ttitude A scription’s A f nity to Measu rement

The relation between two systems of attitude ascription that capture all the empirically signiŽ cant aspects of an agent’s thought and speech may be analogous to that between two systems of magnitude ascription that are equ ivalent relative to a transformation of scale. If so, ju st as an object’s weighing eight pounds doesn’t relate that object to the number 8 (for a different bu t equally good scale wou ld use a different nu mber), similarly an agent’s believing that P needn’t relate her to P (for a different bu t equally adequ ate interpretive scheme cou ld use a different proposition). In either case the only reality picked ou t by any system of ascription is what is common to all equ ivalent rivals. By emphasizing some contrasts between decision theory and belief-desire psychology, it is argued here that if attitude ascription is appropriately analogous to measu rement, then not only is being related to a proposition an artifact of the system of representation chosen, bu t so are belief and desire. 1 Measurement and its artifacts Non-eliminativism about propositional attitudes does not, it has been said, requ ire their construal as relations to propositions. Without attempting to resuscitate adverbial or sententialist accounts of such ascriptions, some recent authors have contended that an agent’s believing that P no more requ ires her to stand in a relation to P than does an object’s weighing Ž ve pounds requ ire it to stand in a relation to the number 5. So long as the chosen measurement scale keeps track of the relevant empirical relations among objects (such as balancing on an equal arm balance), it does not matter which particu lar numbers are used as indices of those relations. Similarly, so long as a system of attitude ascription keeps track of such phenomena as an agent’s preferences among ou tcomes or dispositions to assent, it does not matter which propositions are used to index International Journal of Philosophical Studies Vol. 7 (3), 323–348 ISSN 0967–2559 print 1466–4542 online © 1999 Taylor & Francis Ltd them. Because the choice of a number to index a magnitude (proposition to index thoughts or behaviour) is within certain limits arbitrary, the urgency of the idea that in having a magnitude an object bears a relation to a number (in thinking or behaving thus and so the agent bears a relation to a proposition) is lessened. In spite of their relational su rface grammar, sentences reporting attitudes need not, according to this line of thought, be given relational tru th conditions. By challenging the question’s presupposition, this conclusion may exonerate us from answering the question how standing in a relation to a proposition can be causally efŽ cacious.1 Some deŽ nitions will ease formulation of the mooted analogy. Say that U is a relational system iff U is a Ž nite sequence , where A is a (non-empty) set of elements (called the domain of U) and R 1 , . . ., R n are relations on A. Where U = and U ¢ = < B, S 1 , . . ., S n > are relational systems, U ¢ represents U iff U ¢ is a homomorphic image of U, that is, iff there is a function ¦ from A into B such that for all x 1 , . . ., x k in A , R i (x 1 , . . ., x k ) implies S i (¦ x 1 , . . ., ¦ x k ). U is a num erical relational system iff the domain of U is a set of real numbers, and U is a form al relational system iff its domain consists of abstract objects such as numbers, points, sets, etc. (E ssential to measurement is the use of numerical relational systems to represent relational systems the elements of whose domain are given empirically.) Once a relational system has been given a formal representation, the question arises to what degree that representation is unique. Where a formal relational system U ¢ = represents relational system U = by means of the mapping ¦ , a transformation T from B onto itself is admissible with respect to ¦ just in case T[¦ (x)] also bears witness to the representation of U by U ¢ . The set of all admissible transformations determines the scale type or the degree of uniqueness of the system of measurement chosen. (A mong the better-known scale types deŽ nable on numerical relational systems are nom inal scales, on which all one–one transformations are admissible, ordinal scales, on which all monotone transformations are admissible, interval scales, on which all positive linear transformations are admissible, ratio scales, which are uniquely determined except for an arbitrary unit of measurement, and absolu te scales, on which no transformations are admissible (an example is counting).)2 It is natural to hold that where T is an admissible transformation of ¦ , then if ¦ (x) 1 T[(¦ (x)] the particu lar entity onto which ¦ maps x is to some extent an artifact of the system of representation chosen. This is perhaps why assigning the number 5 to an object as its weight need not be understood as placing it in a relation – for instance, the weight-in-pounds relation – to that number. If it were to be so understood, then by virtue of weighingin-pounds what it does the object would stand in a relation to a great many other numbers as well. Such a view of measurement would also raise the question how an object’s having the weight-in-pounds that it I N T E R N A T I O N A L J O U R N A L O F P H I L O SO P H I CA L ST U D I E S