G . H . M E R R I L L

A N O T E O N P R O X I E S

A feature of the proxy relation which is crucial to the position of semantic

instrumentalism developed in [2] is that the sentence '~- is a proxy for ~' may be true even though '71 exists' is false. Typically, for example, the semantic instrumentalist would be inclined to make such assertions as

(1) The empty set is a proxy for the possible world w.

while denying the existence of possible worlds.

However, there arise two related problems which are not settled by my treatment of proxies in [2]. First, many feel that a 'positive' assertion such as (1) cannot be true if any of its terms (e.g., 'the possible world w') fail to

denote. 1 Second, if we may truly speak of a proxy relation, then there must be relata. But again, in the interesting cases the term V in ' r is a proxy for ~' will be denotationless, and hence one of the relata will be missing. 2 In

order for semantic instrumentalism to appear as a cogent position these

difficulties must somehow be resolved. As pointed out in w of [2], we do have somepresystematic views of what

possible worlds are like. These views (which may vary from philosopher to philosopher) will be expressed in certain sentences. Call a set of such

sentences a tale in the sense of [I]. A possible worlds tale will include sentences containing such predicates as 'is a possible world', ' . . . i s in possible world ', etc. as well, perhaps, as terms such as 'the actual world'. Now we may construe the proxy relation as a relation between objects (denoted by names in the metalanguage) and expressions (names of the object language) in such a manner that (1) gets expanded to

(2) In ~ , the empty set is a proxy for 'the possible world w' in ~:

where ~ is a model of the tale ~:. And (2) will be true just in case ~ is a model of ~: and the empty set is the object in the universe of ~ which 7a assigns to the expression 'the possible world w' (which occurs in ~:). It is easy to see how (2) is to be generalized for any object x (in the universe of ~ ) and any term r/(occurring in the tale ~:). Note that this amounts to

Erkenntnis 14 (1979) 371-372. 0165-0106/79/0143-0371 $00.20 Copyright �9 1979 by D. Reidel Publishing Co., Dordrecht, Holland, and Boston, U.S.A.

372 G. H. MERRILL

reading 'is a proxy for ' as 'is a possible des ignatum o f ' if this latter relation

is conceived as relative to a model for the tale in question. An alternative

would be to treat the proxy relation as a relation among linguistic entities

and rephrase (1) as

(3) The metalinguistic name ' the empty set' is a proxy for the object

language name ' the possible world w'.

A nominalist , certainly, would prefer this last approach.

When (1) is now regarded as an abbreviated version o f (2) (or (3)), any

confusion over the nature of the proxy relation is seen to disappear and we

should no longer hesitate to speak of proxies of non-existing objects.

Loyola University of Chicago

NOTES

x Quine, Eberle, and Schock, among others, hold such a view. 2 I am indebted to Arnold Vander Nat for th!s criticism.

BIBLIOGRAPHY

[1] Eberle, Rolf: 'A Logic of Believing, Knowing, and Inferring', Synthese 26, 1974. [2] Merrill, G. H. : 'Formalization, Possible Worlds, and the Foundations of Modal

Logic', Erkenntnis 12 (1978), 305-327.

Manuscript submitted 7 May 1977 Final version received 2 August 1978