Elucidations and Resources

Philosophy and Phenomenological Research Vol. LXIV, No. 3, May 2002

The Principle-Based Account of Modality: Elucidations and Resources CHRISTOPHER PEACOCKE

New York University

In their searching contributions to this Symposium, Gideon Rosen, Timothy Williamson and Crispin Wright identify a set of issues crucial for assessing the principle-based treatment of modality I presented in Chapter Four of Being Known. I thank them for such focused and thoughtful discussions. This response is organized as a series of questions and proposed answers that aim to address the issues they raise. I hope their contributions will be as helpful to the reader as they have been to me in understanding what is, and what is not, involved in the principle-based conception. My response will not consist only in defense and elaboration. On some issues, I will argue that the position formulated in Being Known needs supplementation. On others, especially those concerned with actualism and possibilia, it needs revision and a new positive theory.’

( I ) Does the principle-based account rely illegitimately on modal information? Consider the rule which determines the actual semantic value of a given concept. Crispin considers the rule The extension of bachelor is actually determined as the intersection of the extensions of unmarried and man. He argues that such a rule “will have as good a title as any to be regarded as metaphysically necessary”, and says that “a thinker who is to base conclusions about necessity upon them had better know that they have this status if her conclusions are to be soundly drawn”. Crispin describes knowledge of the rules determining semantic value as “implicitly modal”; and so, he concludes,

’

I have had the benefit of personal discussion of some of these issues with Kit Fine, Gideon Rosen and Timothy Williamson, and with the members of David Charles’ discussion group in Oxford. BOOK SYMPOSIUM

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the principle-based account represents the epistemology of the modal as “running in a circle” (all quotations from p. 661). I start by distinguishing the following two questions: (a) If a rule R determines the actual extension of a concept C , is it necessary that R determines the actual extension of C? (b) Is the very notion of a rule R’s determining the actual extension of the concept C explicitly or implicitly a modal notion?

We can call question (a) the question of the necessitation of the relation, and question (b) the question of the character of the relation, where the relation in question is of course that of determining the actual extension of a concept. These two questions can have different answers. I agree that the answer to the question of the necessitation of the relation-uestion (a)-is positive. (On the principle-based account, we would indeed need to use this fact in giving the truth-conditions for propositions containing iterated Occurrences of necessarily and possibly.) But the fact that it is necessary that a given rule R determines the actual semantic value of a certain concept is not one that is drawn upon by the principle-based account in determining the truth-conditions of propositions containing uniterated modalities. For fixing the right truthconditions for propositions containing only single, uniterated Occurrences of modality, the principle-based account requires only the truth of propositions of the form ‘Rdetermines the actual semantic value of C’. It does not require their necessity. Crispin speaks of a quite general structural problem (p. 658). If such a problem exists, it is one which must arise even at the first level, with single, unembedded Occurrences of modal operators. Now if the very relation of determining the actual semantic value of a concept were fundamentally modal in character, there would still be circularity even at that first level. There is a distinguished tradition, certainly concerning intensions (even if not concepts), that simply constrains and explicates them in modal terms. In Meaning and Necessity, Carnap laid down as a ‘convention’ (to fix his intended use) that ‘Two predicators have the same intension if and only if they are L-equivalent’ (Proposition 4- 13). L-equivalence, if one works through Carnap’s definitions, amounts to the holding of a universally quantified biconditional linking the two predicators “in all state-descriptions”; and for Carnap, “our state descrip tions represent the possible worlds”.* I myself, however, would answer question (b), the question of the character of the relation of determining actual semantic value, in the negative. The character of the relation does have consequences for the metaphysical truths involving the concepts in question. They

*

Meaning and Necessity, Second Edition (Chicago: University of Chicago Press, 1967,

Fifth Impression) pp. lOand 14. Proposition 4-13 is on p. 19.

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are, consequences of something not itself explained in terms of metaphysical modality. The rule that determines the actual extension of a concept is reflected in facts that concern the level of Fregean sense. The facts in which it is reflected are facts about which thoughts involving the concept are informative in various circumstances, and which are not. Recognition of these facts is not something that needs to draw on the thinker’s use of modal concepts. More generally, on my own views, the identity of the extension-determining rule for a given concept is fixed by the possession condition for the concept, together with what in A Study of Concepts I called a ‘Determination Theory’.3 In such a simple case as bachelor, the possession condition will state that the thinker finds transitions between t is a bachelor and t is a man and t is unmarried compelling, and does so regardless of what auxiliary information he may or may not have. In this case, the Determination Theory will imply that the actual extension of the concept is the one which makes instances of these transitions always truth-preserving. None of this draws on the thinker’s grasp of the concepts of metaphysical necessity. Things are the other way around. These facts about the rule that determines the extension of bachelor are available to be drawn upon in explaining the truth-conditions and understanding of metaphysical necessities involving the concept bachelor. This example is as simple as can be, but I hold that the model it instantiates is generalizable. In all the more complex, and philosophically interesting, cases, the rule that determines the actual extension of a concept is fned from the concept’s possession condition and a Determination Theory which operates on the materials in that possession condition. Modal truths involving the concept are consequential upon the rule thus fixed. Does grasp of modality still lurk in the background? Is not the identity of Fregean Sinne constrained by the fact that thoughts A(C) and A(D) are distinct if and only if it is possible for a thinker rationally to judge A(C) and whilst withholding judgement on A(D)? Isn’t the possibility in question here metaphysical possibility, and must it not then be at least tacitly or implicitly grasped by anyone employing the Fregean notion of Sinn, and hence of a rule for that Sinn, in the first place? I reply that although the modal condition about the conditions of distinctness of senses is correct, that condition too is consequential on something more fundamental, which is not modal. In every case in which it is possible for a thinker rationally to judge A(C) but not to judge A(D), that possibility A Srudy ofconcepfs (Cambridge, Mass.: MIT Press. 1992). ‘Possession condition’ I here

use in a relaxed way for a statement of what it is to possess a given concept, without the reductive implications of the theory of that book. The relaxed use would cover the cases of understanding given by implicit conceptions, as discussed in my paper ‘Implicit Conceptions, Understanding and Rationality’, Philosophical Issues 9 (1998) 45-88. BOOK SYMPOSIUM

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is consequential on facts about the conditions for possessing C and for possessing D.For example, the complex thought A and B is distinct from the complex thought, to which it is a priori equivalent, not-(not-Aor not-B). It is indeed possible to judge the former (for particular A and B ) without judging the latter. But the ground of this possibility is the difference between the possession condition for the concept of conjunction and the possession condition for the complex concept not-(not-cor not-e). The former possession condition, for instance, requires the thinker to find the transition to the conjunction from the two premises A and B to be compelling; the latter does not. This answer may still not satisfy. How is someone to assess, even tacitly, whether something is the correct formulation of a possession condition for a given concept without being sensitive to what it is possible for someone possessing that concept to judge rationally? The answer to this question is one of the points at which the philosophical theory of concepts is best integrated with some of the insights of simulation theory. If you possess a concept F, you can assess by simulation what contents containing F it is rational for someone with certain background attitudes, and in certain informational states, to judge. You imagine yourself with those attitudes, and imagine being in those informational states. You then consider what it would be rational to judge in the imagined circumstances. Proposed possession conditions for concepts can be assessed according as what they count as rational judgements in various circumstances accord with the deliverances of such simulations. If something is a correct formulation of a possession condition, that will have various modal consequences: but it is not apparent that anything in this way of assessing proposed possession conditions for concepts involves the use of modal thought. ( I I ) Can the principle-based account handle atomic concepts satisfactorily?

What does the Modal Extension Principle require for an assignment to an atomic concept to be an admissible assignment? What exactly does it mean to say that an admissible assignment to a concept must respect the rule which determines the actual extension of that concept? Timothy Williamson is right that this needs more clarification.“ For the intention is of course not that admissible assignments to a concept preserve its actual extension. I have come to think that to treat this properly, we need to bring an ontology of properties (or something equivalent to it) into the account of assignments at an earlier stage, and more explicitly, than was done in Being Known. A similar question was raised by Peter Sullivan, in his note ‘The ‘Modal Extension Principle’: A Question about Peacocke’s Approach to Modality’, Mind 107 (1998) 65360. The seeds of the present approach are in my reply ‘The Principle-Based Conception of Modality: Sullivan’s Question Addressed’, Mind 107 (1998) 847-49.

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On an extended notion of an assignment, mentioned at several points in Being Known, assignments assign n-place properties to n-place concepts (‘property-values’), and also assign extensions to properties.’ To illustrate how the extended notion of an assignment can help in the required clarification, take the atomic concept square, considered as an observational concept. We distinguish, in a way now familiar from the literature, between concepts and properties.6 Two different concepts may pick out the same property; concepts are at the level of sense, properties are at the level of reference. There is a shape property of which the following holds a priori: when the subject is perceiving properly, a judgement a is square, made in accordance with the possession condition for square, will be true if and only if the object referred to by a has that property. One such property is of course that of being square. One clause of the possession condition for square will state that when the thinker is taking experience at face value, and the experience has a nonconceptual content that represents a perceptually given object as being square, the thinker is willing to judge that it is square. It is a priori that the property of being square is one that the perceived object will have if such an experience is veridical. A corresponding point applies to the other clause of the possession condition for square. This is the clause which states that for an object not currently given in the thinker’s perceptual experience, to judge that it is square is to be committed to its having the same shape as objects presented in such genuinely perceptual experiences. Again, it is a priori that objects that have that same shape will be square. We can summarize all this by saying that the possession-condition for the concept square a priori fixes the property of being square. Now let us return to extended assignments. A natural way to formulate the view that admissible assignments to concepts must respect the rule determining actual semantic value of the concept square is as follows: An extended assignment of a property-value P to the concept square is admissible only if the property P is one which is a priori fixed by the possession-condition for the concept square. As we noted, the property which is a priori fixed by the possession-condition for the concept square has, as an a priori matter determined by the nature of the concept, the same actual extension as the concept square. So the displayed requirement can be said to cany over the same rule for determining

See for instance pp. 127-28, and the obvious constraint linking assignments of extensions and properties on p. 128. For an early, clear statement, see H. Putnam, ‘On properties’, in his Matliematirs, Matter and Method: Pliilosophiral Papers Volume 1 (Cambridge: Cambridge University Press, 1975). BOOK SYMPOSIUM

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the semantic value of the concept square under admissible assignments as determines the concept’s actual semantic value. Extended assignments that are admissible determine restricted Lewisian ‘ersatz’ possible worlds. It makes sense to speak of one object, but not another, having a given property under an extended assignment, as well as making sense to say that one object, and not another, falls under a given concept according to that assignment. There is no threat of modal collapse here. We do not carry over to an admissible extended assignment the actual semantic value of a concept. Rather we carry over as the concept’s propertyvalue, under that assignment, the property which is a priori fixed by the concept’s possession-condition. For this response to be developed more fully, we would of course have to carry through the task of explicating the notion of a concept’s a priori fixing a property for arbitrary possession-conditions. The hope is that, in carrying through this task, the account for square instantiates an abstract form that is generalizableacross cases. ( I l l ) Can the principle-based account accommodate the full range of necessities?

Many philosophically interesting necessities are neither matters of definition, nor do they immediately follow from primitive principles acceptance of which is required for possession of the concepts involved. Crispin mentions principles of colour incompatibility, the Peano axioms, and Euclid’s axioms for geometry. He doubts that the status of such necessities is clarified by the principle-based account. I wholly agree with Crispin that these cases are central and important. In fact, in other writings, I discussed both the general phenomenon, and (as it happens) two of those cases-colour incompatibilities and the Peano axioms-in more detaiL7 I do not agree that they indicate any limitation of the principle-based account. The principle-based account says what we would have to do to explain why they are necessary. We would, according to that account, have to explain their necessity from the rules that determine the actual extensions of their constituent concepts, together with the Modal Extension Principle. The principle-based account seems to me to locate the challenge presented by these cases in exactly the right place. Suppose the rules are what we grasp in possessing those concepts, and suppose we can explain the necessity of these cases from those rules, by means of the Modal Extension Principle. This is precisely to explain how recognition of their necessity can flow from appreciation of what is involved in grasping the concepts. The challenge is ~

~~

See ‘Implicit Conceptions’, op. cir. and ‘Explaining the A Riori: The Programme of Moderate Rationalism’, in New Essays on rhe A Priori, ed. P. Boghossian and C. Peacocke (Oxford: Oxford University Press, 2000).

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then twofold: to formulate the rules for the relevant concepts involved in these principles, that is, to give those concepts’ possession conditions; and then to show how they determine the necessity of the principles in question. As an illustration, let us consider how we could derive the necessity of ‘If something is red (at a given point), then it is not green (at that same point)’ within the principle-based conception, and with plausible possession-conditions for the concepts red and green.’ In discussing these matters, we need to distinguish the following four kinds of item: the shades, which we can take as finely-grained;the colours themselves, such as red and green, of which the shades are shades; the colour-concepts, such as red and green, which are true or false of physical objects; and the colour-propertiesof objects. Here are a few principles about shades and colours. Each shade is either definitely a shade of a given colour, or is definitely not a shade of that same colour, or is not definitely one or the other. Distinct shades are necessarily distinct. If a shade is a shade of a given colour, it is necessarily so; if it is not, it is necessarily not. All these necessities are at the level of reference, rather than the level of sense and concepts, and they result from what individuates the shades and the colours themselves. A first approximation to a possession-conditionfor the concept red, sufficient for our purposes here, is this:

red is that concept C to possess which a thinker must be willing to judge of a perceived object that it is C when he is taking perception at face value, and his perceptual state represents the object as having a shade which is in fact a shade of the colour red; for objects unperceived by the thinker at the time of the judgement, he must be willing to judge that it is C if it has the ground of the disposition to be perceived in the way mentioned in the preceding clause when it is so perceived; and these are all the cases which have to be mentioned in the possession condition. We could formulate a similar first approximation to a possession condition for the concept green, pari passu. According to the principle-based account of modality, the rule given in the displayed possession-condition must be respected by any admissible assignment. This rule allows variation in semantic value across admissible assignments. It permits an object to be in the actual extension of the concept red, consistently with that same object not being in the extension of red in other admissible assignments. The rule is also evidently one in which possession of the concept is anchored to the way which objects are perceived to be. These Amongst the various simplifications forced by limited space, I will be operating under the assumption that an object has only one shade at any given point. The derivation below is really a derivation of a conditionalized conclusion, with this assumption as antecedent. BOOK SYMPOSIUM

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points will still hold if we inboduce a level of properties in the way envisaged in the answer given to question (11). Now consider the following propositions (1) - (3): (1) Anything which is red (at a given point) is some shade of red (at that point).

(2) If something is a shade of red (at a given point), it is not a shade of the colour green (at that point). (3) Anything which is green (at a given point) is some shade of the colour green (at that point). (1) and (3) are true because of the possession-conditions for the concepts red and green respectively. If the semantic values of red and green are fixed from the above possession-conditions in such a way as to make its rule always lead to true judgements when the thinker is perceiving properly, any case in which something falls under the concept red must be one in which it has some shade of the colour red; and similarly for the concept green. (2), as noted above, follows from facts about the individuation of shades and colours. (1) (3) jointly entail (4): (4) Anything which is red (at a given point) is not green (at that point).

So far, this is a non-modal conclusion. But under the principle-based conception of necessity, and with these possession-conditions, we also have the necessitation of each of the premises (1) through (3). (1) and (3) hold under any admissible assignment, since they are consequences of the rule which determines the actual semantic value of the colour concepts red and green respectively. (2) holds under any admissible assignment because it is a consequence of what is constitutive of shades and colours. The principle that N ( p q ) 3 ( N p z N q ) is easily seen to be verified by the principle-based conception. So since (1) through (3) are necessary, what is entailed by them is also necessary. Hence we have the necessitation of (4):

(5) Necessarily, anything which is red (at a given point) is not green (at that point). This is, then, in outline, an explanation of the necessity ( 5 ) within the principle-based conception, using a perceptually-sensitive possession condition for the colour-concepts in question, and without writing acceptance of either (4) or (5) primitively into those possession conditions. On this account, the necessity (5) really does flow from what is involved in one’s grasp of the

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colour concepts, but in a way which does not involve derivations from premises or transitions mentioned in those possession conditions. Colour-incompatibilities are just one kind of case, and I have given only a simplified treatment. The range of apparently necessary propositions is vast and diverse; other kinds of case must be treated very differently. My general point here is just that the existence of this range of cases does not in itself at all tell against the principle-based conception. Our task is rather to provide, for the other cases, possession-conditions and determination theories for the concepts involved, and from which we can derive the relevant necessities. I conjecture that there is much illumination to be gained about the varieties of concept-possession and their relation to reality by carrying through that enterprise. (IV) Is the principle-based account necessarily incomplete?

The principle-based account contains a ‘Characterization of Necessity’, stating that necessity is truth under all admissible assignments. Crispin says, and I agree, that this Characterization is itself necessary. Crispin, however, objects that “the necessity.. .of the Characterization cannot in principle be delivered by Peacocke’s account unless we presuppose it” (p. 657). I disagree. We, as philosophical theorists, have reason to accept the various Principles of Possibility and the Characterization. The Principles and the Characterization provide the best explanation of the truth conditions of modal contents. If we suppose that the Principles of Possibility are correct, and that the Characterization states the rule determining the correct actual application of necessarily to contents, then, combining these suppositions with nonmodal information, we can explain why the boundary between the true and the false modal propositions lies where it does. This reason for accepting the Principles and the Characterization as stating the rule for necessarily is defeasible, potentially open to overturning by better explanations, like any other broadly abductive inference. But provided the conditions for a good abduction are met, and if abduction can ever yield knowledge, this can be a route to our explicit knowledge, as theorists, of the Principles of Possibility and the Characterization as stating the extension-determining rule for necessarily. (Crispin is not objecting to abduction as a way of coming to apprehend truths.) The Principles of Possibility, together with the Characterization as stating the rule determining the correct application of necessarily, themselves jointly imply that the Characterization is necessary. The argument runs as follows. The Principles of Possibility include the Modal Extension Principle, according to which admissible assignments respect the rules determining the actual extensions of concepts. The Characterization of Necessity states the rule determining the correct actual application of necessarily to contents. So,

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by the Modal Extension Principle, any assignment not respecting that Characterization is not admissible. It follows that the Characterization of Necessity holds under all admissible assignments. Hence by the Characterization of Necessity itself, it follows that the Characterization is necessary. It is crucial that-contrary to the earlier quotation from Crispin-this argument once again does not presuppose the necessity of the Characterization. It presupposes only the truth of that Characterization-that it gives the rule which determines the correct application of necessarily in the actual world. That it does so is something we have abductive reasons for believing. There is no epistemic or constitutive circularity in this argument. That the Characterization states the rule determining the correct application of necessarily to contents in cases other than that of the Characterization itself is well-confirmed. The argument then just applies the same rule to necessarily itself. Of course we can also assess, using our pre-philosophical intuitive understanding of necessity, whether the Characterization is itself necessary. Someone may be tempted to argue: “Since that intuitive assessing of the modal status of the Characterization is obviously a substantive, nontrivial task, necessity cannot consist in truth under all admissible assignments!”. To argue thus would be a mistake. When our understanding of some notion consists in merely tacit knowledge of a definition, an explicit statement of that definition can be informative to someone who already possesses intuitive grasp of that notion. It is notoriously the case that a correct definition of chair can be informative to someone who has used the notion for decades. To have merely tacit knowledge of a definition of a given concept is for some conception with the content of that definition to be influential in various ways in the thinker’s application of the concept. This does not entail that the thinker explicitly knows that definition. So the fact that the task of intuitively assessing the modal status of Characterization is a substantive one is entirely consistent with the thesis that understanding modality involves tacit knowledge that necessity is truth under all admissible assignments. The task of assessing what is in fact the correct definition of chair is equally a substantive one, consistently with the definition having the same content as the implicit knowledge that underlies the thinker’s understanding of chair.’ I should add that I do not accuse Crispin of endorsing the argument just criticized. But when the error in that argument is acknowledged, I do not see what other grounds a thinker might have for saying there is any incompatibility between the substantivecharacter of the task of assessing, using our pretheoretical understanding, the modal status of the Characterization and the thesis that understanding necessity involves tacit knowledge of the Characterization. See ‘Implicit Conceptions’, op. cit.

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In sum, I do not think that any of the three limitations described by Crispin really exists. I do, however, agree with Crispin that the task of explaining why the Characterization is itself necessary has a quite distinctive structural character. The task is an instance of a more general structural type: that type in which one has some principle which is said to define some philosophically interesting notion F, and in which, if the principle is to have any plausibility at all, it must itself be shown to have the property F. Other concepts, besides necessity, which generate such distinctive structural tasks are the concept of the a priori, and of course the concept of truth. It is a plausible condition of adequacy on any account put forward as constitutive of the a priori, or of truth, that it has the resources to explain how the account is itself, by its own lights, a priori, or true, respectively. The condition of adequacy is not in principle unmeetable. I have argued that in the case of necessity, it is met by recursive application of the Modal Extension Principle, and by taking the Characterization of Necessity as one input to that Principle. An interesting question, worth further reflection, is whether the abstract form of this answer in the modal case is generalizable to other cases with the same structural feature. ( V ) Does the principle-based conception validate even the weak modal system T? A substantive theory of modality is unlikely to be acceptable, or is at the very least incomplete, if it does not validate even the weak modal system T. The distinctively modal part of T contains the two axiom schemata N A I A and N ( A ~ B ) ~ N A I N B together ), with the rule of proof that if A is a theorem, then so is N A . In the course of attempting to establish that the principle-based conception validates NAIA, I argued that all instances of this schema hold because the assignment s@ which assigns to each concept its actual semantic value is an admissible assignment. Hence, I argued, if we have NA, under the principle-based conception, A holds under all admissible assignments, so it holds under s @ , and hence is true. Tim Williamson correctly remarks that an assignment that assigns to every concept its actual semantic value might still be inadmissible, in case it assigns (for example) an object an incorrect fundamental kind. The lacuna is real, but I think it can be filled straightforwardly and intuitively. We need to consider that assignment s@ which not only assigns to each concept its actual semantic value, but also, in assigning properties and relations (from some background range thereof) to objects and n-tuples of objects, assigns to them the properties and relations they actually have. This assignment s@cannot violate anything which is constitutive of those objects, since what it assigns are the properties and relations they actually have. It will also respect the Unified Modal Extension Principle. In passing, Tim

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suggests that there may be a difficulty in showing that any particular assignment is admissible, because one would have to show that one’s selected list of Principles of Possibility is complete (p. 652). Here I disagree. One can know that assignment S @ is admissible without yet knowing that one has captured all the constitutive principles relevant to the individuation of objects, properties and relations: for one can know that those principles all have a certain form, whatever they may be. Those principles will all require-in the case of objects-things of a given kind to have, in any admissible assignment, certain of the properties and relations they actually have. But by choice of the assignment s @ , it will certainly respect any constraints of that form. This response is of the sort at which Tim hints when he notes that a reconstructed proof “might appeal to some kind of general constraint on Principles of Possibility” (p. 652). (VI) Can the principle-based theory give an acceptable account of merely possible objects?

Being Known contained some brief remarks on possibilia, favouring an actualist treatment, without doing the decent thing of going on to supply one. The objections of Gideon Rosen and Tim Williamson to those brief remarks are well-taken. I agree too with Gideon’s remarks against those varieties of actualism which seek to construct possibilia as ordered pairs (or the like) of actual objects. I do continue to want to give an account under which, for instance, on the natural reading, ‘There could be something which doesn’t actually exist’ comes out true. After I completed Being Known, it occurred to me that there is a different treatment of possibilia, one which is squarely within the spirit of the principle-based account. The treatment is one under which possibility is regarded as more fundamental than the existence of possibilia. I outline the treatment here. Consider a relatively uncontroversial case. There is a unique possible human c who would result from normal (non-meiotic) development from the actual sperm a and egg cell 6 . We label as ‘R’ the relation which holds between x, y and z when x develops normally from sperm y and egg cell z . The existence of the possible human c consists in the truth of the proposition that it is possible that there is something that bears R to a and b (that is, M3xRxab). It consists in this truth because R is the same relation which contributes to the individuation of actual humans. The same relation which contributes to the individuation of actual humans contributes to the individuation of possible humans. In this respect, not only the Modal Extension Principle, but also the constitutive principles for possibilia, extend the same principles from the actual to the genuinely possible. Possible objects of other kinds that are actually instantiated are individuated in the same way, by apply-

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ing to possible objects the same principles as apply to actual objects of that kind. What I call ‘the principle-based account of possibilia’ does not hold merely that the existence of possibile c requires the truth of the proposition M3xRxab. That would be agreed also by the person who believes in bare possibilia. It would also be accepted by a Lewisian modal realist, provided he also believes in essence of biological origin. The further claim of the principle-based account of possibilia is that for the proposition M3xRxab to be true is for it to be consistent with the principles of possibility (and other non-modal truths) that there exist an admissible assignment under which Rxab is true. It is this further claim which makes the treatment one according to which the possibility of a proposition is more fundamental than the existence of a possibile. For a believer in bare possibilia, or for a Lewisian modal realist, the possibility of the proposition 3xRxab is to be explained in terms of the existence of a certain sort of possibile. For the principle-based account, it is to be explained in terms of its relations to the principles of possibility. This account of what it is for M3xRxab to be true is a natural extension of the Prinicple of Plenitude (Being Known p. 149), which stated in effect that a proposition is possible if it is not ruled impossible by the other principles of possibility. Here the same conception of plenitude is applied to possible objects, with the additional requirement that it is not only consistency with the principles of possibility, but also with the non-modal truths, that is needed. This last is demanded if we are not to have the consequence that there is a possible object that is identical with Hesperus but not with Phosphorus.” That there is no admissible assignment which makes true x is identical with Hesperus and distinct from Phosphorus is not entailed by the Principles of Possibility alone. But it is when combined with the nonmodal information that Hesperus is Phosphorus. What is meant by ‘consistent’ in the condition ‘the existence of an admissible assignment verifying Rxab is consistent with the Principles of Possibility and other nonmodal truths’? It had better not mean simply that the following is possible: all the Principles of Possibility hold, all nonmodal truths hold, and there is such an admissible assignment. That is simply too tight a circle. It is to explain possibilia in terms of the possibility of an existential quantification-and it was precisely such applications of possibility that were to be explained. I suggest that the notion of consistency needed at this point is model-theoretic in character. The consistency in question requires that there be a model which verifies the Principles of Possibility, the non-

lo

My thanks to Justin Broackes for drawing to my attention the need for some restrictions to rule out such a possible object. BOOK SYMPOSIUM

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modal truths, and the existence of an admissible assignment of the kind in question.” The treatment suggested here for possible humans can be generalized to possible objects of other actual kinds. In a fuller development, it must also be generalized to kinds not instantiated in the actual world. A merely possible object may be a possible K for some kind K not instantiated in the actual world. So the account must also elaborate a notion of possible kinds as well. Any principle-based account of possibilia along these lines will treat the merely possible objects as having derivative existence. According to such an account, the existence of a mere possibile is derivative from the consistency of the existence of a certain kind of admissible assignment with the Principles of Possibility and other nonmodal truths. But while a merely possible human being has only derivative existence, an actual human being does not have merely derivative existence. Your existence does not consist in the model-theoretic consistency of a certain set of propositions. So under a principle-based account of possibilia, merely possible humans are not things of the same sort as actual humans. This is not, then, a modal-realist account, even if the ontology of derivative objects is genuine and within the range of our most wide-ranging quantifiers. When the quantifiers are construed as having their widest legitimate range, I am in agreement with Tim that the Barcan formula and its converse are a species of logical truth. This is something to which one can agree without believing in bare possibilia, and without being a modal realist. A principle-based account of possibilia needs more detailed elaboration. I have attempted some in a paper ‘Principles for Possibilia’.’’ A principlebased account of possibilia also vindicates Gideon’s point that for M3xFx to be true is for it to be possible that there is an admissible assignment that verifies Fx. It vindicates the point not merely in the sense that such an equivalence is a consequence of the theory. It vindicates the point also in the sense that the theory treats the notion of possibility, as constrained by the Principles of Possibility, as explanatorily prior to that of the existence of possibilia. Could we not have these last attractions by simply treating the notion of possibility as primitive? We could: but the need for a theory of understanding for modal notions would remain. Tacit knowledge of the Principles of Possibility provides the account of understanding. The Principles also allow us to explain how the account of the truth of M 3 x F x in terms of the possibility of I’

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When the proposition whose possibility is in question contains operators such as ‘actually’, the notion of model-theoretic consistency and consequence in use here may need to employ variable domains. But that is not yet to employ a substantive notion of a possibile. Christopher Peacocke, ‘F’rinciples for Possibilia’, forthcoming in Noh 36 (September 2002). CHRISTOPHER PEACOCKE

a certain kind of assignment does not simply take us in a circle, taking us back to an ontology of merely possible, but non-actual assignment^.'^ ( V l l ) 1s the principle-based account of modality subject to just the same dificulties of access and epistemology as allegedly attend Lewisian modal realism?

Gideon formulates the issue precisely. Any objections I may have to Lewisian modal realism from difficulty of access can hardly be based on the causal inertness of the modal realist’s possible worlds. Abstract objects are equally causally inert; yet they are used extensively throughout the principlebased account of modality. As Gideon says, abstract objects have also been used extensively in my other writings on concepts. So what might my problem with modal realism be? My own position may seem either inconsistent, or at best to contain an unmotivated asymmetry as between its unfavourable treatment of the modal realist’s possible worlds on the one hand, and its hospitability towards the abstract objects (assignments, sets, and the rest) used in the principle-based theory on the other. In response, I distinguish. Abstract objects are not things of the same kind as material objects. The modal realist’s possible skyscrapers are, however, meant to be things of the same kind as the actual skyscrapers in the actual world. Does this difference matter? David Lewis famously argued that it does not.14 I think the difference makes a crucial difference, not for the reasons Lewis criticized, but for another reason. Abstract objects conform to a suitably qualified version of the thesis that they are, in Quine’s words, “known only by their laws”.” The qualifications are important. Significant laws for a category of abstract object may be discovered only decades, even centuries, after thinkers first grasp concepts of that category of object. (This is a favourite phenomenon cited by those sympathetic to rationalism.) So the laws, even primitive ones, not denved from others, may not be immediately obvious. The laws must also include principles of application to non-abstract objects if they are really to capture what is distinctive of those objects. No full account can be given of what it is for something to be an expression-type if we omit what it is for a token to be of that abstract type. It is widely accepted that an account of natural numbers must explain what it is for them to be the numbers of given concepts or properties. I would hold a corresponding thesis about real numbers and magnitudes or quantities. Finally on this list of qualifications, I think the general thesis about abstract objects is better formulated as one l3

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On such circularities in some explications of 03xFx, see ‘Principles for Possibilia’, op. cit. On fhe Pluraliry of Worlds (Oxford: Blackwell, 1986). especially pp. 110-15. Onrological Relativity and Other Essays (New York: Columbia University Press, 1969). p. 44-45.

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about individuation-about what it is to be a given abstract object, its nature-than as one about epistemology. So if we are to have a slogan here, it would be better formulated as ‘Abstract objects are individuated only by their fundamental principles’. The merely possible objects of the principle-based approach, and the possible worlds it acknowledges, conform to this characteristic of abstract objects. The possibilia, under the above treatment, are individuated only by their fundamental principles, by the condition from which their existence is derivative. Under this treatment, a merely possible skyscraper is not something of the same kind as an actual skyscraper. Similarly, each possible world is conceived as a set such that there is some admissible assignment which counts as true each proposition or thought in that set. (The propositions will contain non-abstract objects, so such possible worlds are not pure abstract objects; but the impure abstract objects are abstract objects nonetheless.) Such a possible world is not something of the same kind as the entity which is the Goodmanian sum of all the objects, events, space and time that actually exist. If a category of abstract object is individuated by its fundamental principles, those principles give the nature of those objects. Not only do we not need to say that objects of that category are of the same kind as any material things. It would also be incorrect to say so, because it would mean that there are aspects of their nature not captured by those fundamental principles. In the particular case of modality, if the principle-based account gives the correct truth-conditionsof modal contents, to add also that the possible worlds are of the same kind as the total actual universe, and that non-actual Fs are things of the same kind as actual Fs, would not be doing any explanatory work. David Lewis argued that our contingent knowledge requires causal contact with its subject-matter, while our necessary knowledge does not: ‘‘Modaland mathematical knowledge fall together on the right side of the line”.16 I would revise this slightly: it seems to me a posteriori knowledge that requires the relevant kind of causal contact, and the a priori knowledge that does not. Knowledge that water is H,O,or that I came from particular named sperm and egg cells, is knowledge which requires causal contact with the subject-matter. The contents here are necessary, but a posteriori. When it is the a posteriorda priori distinction which coincides with that for which causal contact is or is not necessary, we seem to have some further support for the principle-based conception. For, I would argue, a priori knowledge is explicable in terms of what is involved in grasping the concepts involved in the content of the a priori knowledge.” The principles of possi-

16

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On the Pluraliry of Workis,p. 11 2. See ‘Explaining the A Prior?, op. cit.

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bility, conceived as involved in understanding modal notions, provide just such a resource for a priori knowledge of the relevant range of modal truths. This response to question VII is conditional upon some variety of the principle-based approach succeeding in giving the correct truth-conditions for modal contents. I would be the first to agree that more work is needed to establish whether it can. We have to consider whether it is accommodating the full range of possibilia, the full range of possibilities, and whether there are other hidden problems. But if some form of principle-based account can give the correct truth-conditions, the difference. between the ways it regards abstract objects on the one hand and the modal realist’s worlds and possibilia on the other is a difference that has, in the context of a general theory of abstract objects, a motivation.

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