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The principle-based conception of modality: Sullivan's question addressed.

Peter Sullivan asks a question about the Modal Extension Principle which is at the centre of the approach to metaphysical modality which I proposed in "Metaphysical Necessity: Understanding, Truth and Epistemology".(1) The relevant part of the Modal Extension Principle states that in the case of a concept C which is not de jure rigid, an assignment s is admissible only if the semantic value of C with respect to s is the result of applying the same rule as is applied in the determination of the actual semantic value of C. Sullivan's question is this: how are we to understand the Modal Extension Principle without encountering insuperable obstacles?

Sullivan mentions two obstacles, which correspond to the two ways of understanding the Principle which Sullivan considers. On the first construal, the Principle states that s is admissible only if it assigns to C its actual extension. Given the role of admissibility in the principle-based conception, this first construal has the "unintended result" (as he delicately puts it) that no concept could have an extension which differs from its actual extension. On the second construal, admissible assignments are simply restricted to assigning to any given concept a semantic value which it could have. This, says Sullivan, is circular in any explication of metaphysical modality; and I agree.

There is, however, a third way, and it is what I intended. As always, we distinguish between a rule and what it applies to--what it bites on, as Sullivan puts it. Take first, for illustration, the special case of a defined concept such as bachelor. Its actual semantic value is determined by applying a certain rule, R let us call it, to the actual extensions of the concepts man and unmarried. In this example, R is simply the operation of taking the intersection. Under the third, and intended, way of understanding the Modal Extension Principle, an assignment s is admissible only if the semantic value it assigns to bachelor is that which is obtained by applying R to the extension which s assigns to the concept man and to the extension which s assigns to the concept unmarried.

Sullivan's first construal would instead in this example take the Modal Extension Principle as applying R to the actual extensions of man and of unmarried.(2) On the intended reading, by contrast, while the rule R is held constant from the actual world, what it is applied to can vary with the assignment. The output of the fixed rule R is then not constant. The output can vary with the assignment which determines the extensions to which it is applied. Hence it is not true that on the intended reading, an assignment is admissible only if it assigns to bachelor its actual extension. An admissible assignment can assign a semantic value other than the actual semantic value of bachelor provided that it assigns a different semantic value either to man or to unmarried.

This may seem all very well for the structured concepts, and for the defined concepts; but what of atomic concepts? The same overarching principle still applies. Even for an atomic concept, there will be some account of how its actual semantic value is determined. No doubt there are almost as many theories of the nature of this determination as there are theorists of it. The principle-based conception of modality is neutral on which of those theories is correct. The principle-based conception insists only that whatever is the correct account of the determination in the actual case, that same account is respected by an admissible assignment to any concept which is not de jure rigid.

Suppose, again just for the sake of illustration, that the actual extension of an observational shape concept diamond-shaped consists of all objects which have the same shape as those which, as they actually are, would produce a certain kind of experience in a properly-perceiving subject. That its actual extension is so fixed does not require the concept to be taken as defined. Such a fixing of its semantic value would on some theories be regarded as a consequence of the concept's possession condition, together with a theory of how the semantic value is fixed from that possession condition. Now assignments, under the conception I outlined in the original paper, also assign truth-values to propositions, conceived of along Russellian lines, as built up from objects, properties and relations. For each object, it will be fixed, by a given assignment s of the sort I am considering, whether according to s that object has the same shape as those which, as they actually are, would produce the relevant kind of experience in a properly-perceiving subject. An assignment s is then admissible only if it assigns to diamond-shaped an extension which includes precisely those objects which, according to s, are of the same shape as those which, as they actually are, would produce a certain kind of experience in a properly-perceiving subject. (Here I am presuming not merely, as I said in the original paper, that assignments are total, but also that they are sufficiently comprehensive to determine the extensions of all properties and relations on which the actual semantic value of a given atomic concept depends.) There is, then, no obstacle to an atomic concept being assigned, by some admissible assignment s, an extension other than its actual extension. That can be so, provided that at least one of the various properties and relations on which its actual extension depends also has, again according to s, different objects falling under it than actually fall under it.

It may now seem that this is much too thin, and that the problems which motivated Sullivan's second interpretation will reappear. Will we now be counting assignments as admissible that correspond to no genuine possibility? The Modal Extension Principle is, however, just one of a battery of constraints upon admissibility of an assignment. Conformity to the Modal Extension Principle is merely a necessary condition of admissibility, and not a sufficient condition. The substantive claim of the principle-based conception of modality is that when an assignment also meets the other constraints on admissibility--the constitutive principles dealing with the nature of objects, properties and relations--then every admissible assignment corresponds to a genuine possibility.

CHRISTOPHER PEACOCKE Magdalen College Oxford OX1 4A U UK

(1) The two papers in question are detailed in the References at the end of this paper. Though I aim here to answer Sullivan's questions head-on, I do want to acknowledge that the formulations in the original paper were overly streamlined, and I am grateful for Sullivan's clarificatory question and for the opportunity to address it. I also thank the Leverhulme Trust for continuing support.

(2) If that were correct, there would have been no point in my distinguishing the first and second parts of the Modal Extension Principle. Under Sullivan's first reading the treatments in the second part, for de jure rigid concepts, would apply equally to all other concepts.


Peacocke, Christopher 1997: "Metaphysical Necessity: Understanding, Truth and Epistemology". Mind, 106, pp. 521-74.

Sullivan, Peter 1998: "The `Modal Extension Principle': A Question About Peacocke's Approach to Modality". Mind, 107, pp. 653-60.
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Title Annotation:Peter Sullivan, Mind, vol. 107, p. 653, 1998
Author:Peacocke, Christopher
Date:Oct 1, 1998
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