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Possible worlds and a theoryof meaning for modallanguageBarbara Davidson a b & Robert Pargetter a ba University of Wollongongb La Trobe UniversityPublished online: 15 Sep 2006.
To cite this article: Barbara Davidson & Robert Pargetter (1980) Possible worldsand a theory of meaning for modal language, Australasian Journal of Philosophy,58:4, 388-394, DOI: 10.1080/00048408012341381
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Australasian Journal o f Philosophy Vol. 58, No. 4; December 1980
POSSIBLE WORLDS AND A THEORY OF MEANING FOR MODAL L A N G U A G E
Barbara Davidson and Robert Pargetter
§ 1. Possible world semantics, proposed formally by S. Kripke ~ and interpreted by, for example, D. Lewis 2 and A. Plantinga, 3 has been seen by some as providing a plausible account of the meaning of the modal expressions in language. The account is a referential theory of meaning for the modalities in that the terms of the theory do refer, namely to existents called possible worlds. Its popularity comes largely from its ability to provide an account of what it is for modal propositions to be true, an account which assigns to modal propositions truth values which coincide with our intuitions in most instances; that is, the theory makes true modal propositions we think to be true.
However many philosophers remain critical of the theory. The major objection to a possible worlds account of the nature of modality concerns the fundamental notion of a possible world that such an account employs. Many philosophers have rejected the possible world semantics as an account of meaning for modality because of ontological worries about possible worlds. These worries tend to be expressed in one of two ways. For some concern is that there are no possible worlds other than the actual world. But there are also those who claim that the concept of a possible world is incomprehensible.
The aim of this paper is to defend the possible world semantics against objections based on such ontological concerns. We will argue first that the concept of a possible world employed in the semantics is comprehensible. Furthermore, it will be argued that there is evidence which supports the claim that there are possible worlds other than that which we inhabit. Thus any rejection of the possible world semantics as an account of meaning for the modalities in modal language must be based on considerations other than those relating to the ontological commitments of the theory.
§2. For a theory to be an adequate account of anything it is a necessary requirement that the fundamental concepts involved in the theory are comprehensible. That is, such concepts must be able to be consistently applied and not be nonsensical or impossible to understand.
Is the concept of a possible world comprehensible? Some philosophers merely assert that it is not. For example, Lawrence Powers states 'that the
S. Kripke, 'Semantical Considerations on Modal Logic', Acta Philosophica Fennica (1963). 2 D. Lewis, Counterfactuals, Basil Blackwell, 1973.
A. Plantinga, The Nature of Necessitv, Oxford Universily Press, 1974.
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Barbara Davidson and Robert Pargetter 389
whole idea of possible wor lds . . , seems ludicrous'. 4 However, others attempt to argue for the incomprehensibility of this concept. Tom Richards, for example, argues that the concept of a possible world cannot be intelligibly interpreted, s Richards' main arguments centre around difficulties in articulating exactly what possible worlds are, how they can be distinguished from one another and, in particular, how the actual world can be distinguished from the merely possible ones. Intuitively, possible worlds are taken to be 'ways things could have been' or 'possible states of affairs'. But Richards claims that these expressions cannot be given an intelligible interpretation on which criteria for the individuation and identity of possible worlds can be stated.
Robert Stalnaker attempts to answer these objections by claiming that those who reject the notion of a possible world as incomprehensible are really expressing 'general scepticism about whether the theory of possible worlds has any fruitful application', 6 and so the fruitfulness of the theory overcomes this objection. However, the 'sceptic' can respond to such a reply, as Powers does, that the theory of possible worlds may well be fruitful, but this alone is not sufficient to demonstrate the comprehensibility of the concept of a possible world. Such fruitfulness might come from the theory providing a formal modal theory for modal language, and nothing more.
Of course, an explanation is required as to why this model theory is fruitful if its fundamental concept is incomprehensible; and surely we would need a viable alternative theory to justify the view that this is mere model theory. However, there is a more direct reply to this objection. The comments here will be directed towards Richards' arguments for the incomprehensibility of possible worlds. They also show that the notion of a possible world is not 'ludicrous'.
Richards' arguments to the incomprehensibility of the possible world semantics hinges on the claim that in the absence of definite criteria for individuation and identity the concept of possible worlds has no intelligible interpretation. His main argument is developed against Lewis' view of possible worlds as 'totalities of existents though not of existents that exist in our world'. 7 This interpretation, he claims, cannot sustain the intended distinctions between ways things could have been and the way things are. For if the way things are and ways things could have been are to be the totalities of existents then ways things could have been must be included in the way things are. Furthermore, the claim is that on this interpretation of possible worlds 'our ' world cannot be individuated or identified. He argues that once "our catalogue headed 'What there is' or (!) 'The way things a re ' " is extended to include existents that do not exist in this world then the boundaries of each possible world cannot be distinguished. Nor can 'our ' world be distinguished from all the others since the only way this could be done would be via the pre-Lewis notion of existence.
4 L. Powers, COMMENTS on R. Stalnaker, 'Propositions' in Issues in the Philosophy of Lanugage ed. A. F. MacKay and D. D. Merrill, Yale University Press, 1976, p. 95.
s Tom Richard,s, 'The Worlds of David Lewis', Australasian Journal of Philosophy, 53 (1975). 6 R. Stalnaker, 'Propositions' in Issues in the Philosophy of Language ed. A. F. MacKay and D. D.
Merrill, p. 85. 7 Richards, ibid., p. 107.
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390 Possible Worlds and a Theory of Meaning for Modal Language
That is, 'our' world is what is said to exist using the pre-Lewis concept of existence. Thus other possible worlds would be individuated according to what their inhabitants would say exists - - using the pre-Lewis concept of existence. This criteria, as Richards remarks, is inadequate for the individuation or identification of possible worlds. Hence, he concludes that the concept of possible worlds is not a concept of objects which can be individuated and identified and so is not a concept of objects at all. Therefore, the theory of possible worlds is incomprehensible.
It would seem to be a rather stringent requirement that it is necessary that precise individuation and identity criteria be able to be stated for the terms of a theory to be comprehensible. Consider, for example, wars, nations and persons. Precise individuation and identity criteria are lacking for these, yet we do not find the concepts of wars, nations and persons incomprehensible and, therefore, reject the theories involving them as likewise incomprehensible. The inability to articulate what wars, nations and persons are, and the imprecision in the criteria for their individuation and identity does not render those concepts unintelligible. Nor should it in the case of possible worlds; we should not be surprised if such criteria are not forthcoming for possible worlds, nor should we claim that concept incomprehensible if indeed they cannot be given. In general, explicit criteria for identity have not been shown to be essential for a theory or concept to be comprehensible. Thus Richards' argument does not establish that the concept of a possible world is incomprehensible.
Nevertheless, since on Lewis' approach to possible worlds no object is in more than one world, individuation and identity criteria for possible worlds are available. Possible worlds can be individuated in terms of the pimitive, dyadic relation 'is in the same world as'. We do understand what it is for two objects to both be in this world and this relationship which holds between the objects of this world is exactly the same as the relationship which holds between the objects in some other possible world. Thus wedo understand what it is for two objects to be in the same world, and using this relation, Lewis can individuate worlds. Each world is the totality of all objects x and y such that x is in the same world as y. Of course, the way we determine that this relation holds between objects in the world in which we exist may well vary from the way we determine this for objects in other possible worlds, but the relation itself does not vary. This is sufficient for us to understand that relation. Thus possible worlds are bound by the objects existing in them. Possible worlds are equivalence classes of objects since objects can exist in at most one world, so the relation 'is in the same world as' is an equivalence relation. Hence, possible worlds are disjoint and so two worlds are identical if and only if they contain exactly the same objects.
Abstract objects require a special mention. Lewis says, in Counterfactuals, that abstract objects 'inhabit no particular world but exist alike from the standpoint of all worlds' (p. 39) and they 'are their own unique counterparts at all worlds'. (p. 40) Taken together, these comments indicate that abstract objects have counterparts in all possible worlds and that the properties of these counterparts do not vary from world to world (with one exception, namely the
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Barbara Davidson and Robert Pargetter 391
property of existing in a particular world). That is, whereas the properties of a counterpart of a non-abstract object may differ from the object itself, this is not so for abstract objects. So, on the criteria given, there is exactly one possible world which contains all and only abstract objects and for any worlds that contain non-abstract objects, no two different worlds will contain exactly the same objects.
It is interesting to note that if we allow transworld identity of objects (as does Plantinga, for example) individuating possible worlds in this way does not yield a satisfactory identity criterion. On this view it might be that two different worlds contain exactly the same objects. That is, the worlds might differ just in respect of the relative positions, or properties, of the objects existing in them. 8 But both individuation and identity criteria can be given by a counterpart theorist. The following discussion is directed towards such a counterpart theory.
It might be argued that the relation 'is in the same world as' is not primitive and, without any analysis of this relation the concept of a possible world derived from it is unacceptable. But consider the criteria used to individuate and identify time slices. 9 Two objects (or events) are said to be in the same time slice if and only if they exist simultaneously. Time slices are individuated by the universal generalisation, 'all objects (or events) x and y such that x and y exist simultaneously'. Two time slices are identical if and only if they contain exactly the same objects (or events). Analogously with possible worlds, time slices will be equivalence classes of objects (or events) only if we maintain that an object (event) exists in at most one time slice. The important point here is that, regardless of whether 'is simultaneous with' is a primitive relation, it does not
seem to require further analysis to be acceptable for use in individuating and identifying time slices. Neither would it seem that 'being in the same world as' must be further analysed to be acceptable as a concept used to individuate and identify possible worlds. Similar analogous comparisons can be made with other relations, for instance 'is the same colour as'.
This is not to accept, however, that no further analysis is possible. An analysis of 'is the same world as' could perhaps be given in terms of the more familiar relation 'is temporally related to' on non-abstract objects.~° Intuitively, any two non-abstract objects are in the same possible world if and only if they are temporally related. A possible world can then be individuated as the union of the set of abstract objects (or a set of their counterparts) with a set of non- abstract objects such that each object in this latter set is temporally related to every other object in that set. Any two possible worlds containing exactly the same objects are identical.
It has been suggested to us that such an analysis could be problematic depending on the view one takes regarding the nature of time. One such suggestion is that if our view of time is one which allows branching within a
8 This point is made by R. Montague in Formal Philosophy, Yale University Press, 1974, p. 153. 9 See J. J. C. Smart, Philosophy and Scientific Realism, ch. 7. ~0 This was suggested to us by Frank Jackson and Chris Murphy and is in line with the analogy
Stalnaker draws between possible worlds and alternative courses of events.
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392 Possible Worlds and a Theory of Meaning for Modal Language
possible worm then there might be objects in that world which are not temporally related.
The view that time branches has some plausibility. As Stalnaker claims, we do implicitly accept the notion of 'alternative possible futures' or 'alternative courses of events'. ~ This lends some plausibility to a view of time which allows at least forward branching. But only one 'branch' represents the actual course of events. So the best way of interpreting such a situation is to say that one branch represents the actual world and other branches represent other possible worlds. Any shared segment of a branch is thus more strictly seen as a set of actual temporally related objects and one or more sets of their counterparts in other possible worlds. On this view, time then does not branch within a possible world, and such an interpretation is quite consistent with our temporal analysis of'is in the same world as', and independently seems to be the best view of such a branching theory of time. However, if one wishes to allow branching time within the same possible world, the individuation criterion could be modified to have all pairs of objects either emporally related directly, or indirectly through some other object which is temporally related to both objects of the pair.
Whether or not one accepts this temporal analysis of 'is in the same world as', we have a clear answer to Richards' objection that 'the concept of a possible w o r l d . . , is not a concept of objects at all, let alone a concept containing the needed identity and individuation conditions'. (p. 109) Such criteria can be given (at least for Lewis, if not for the transworld identity theorist). Possible worlds are just sets of objects than can be individuated and identified in terms of the relation 'is in the same world as'. However, Richards has a supplementary objection. He challenges the possible world theorist, such as Lewis, to distinguish this world from the other possible worlds'. Lewis' theory involves an indexical theory of actuality on which the actual world is the possible world of which I am a member. Richards claims that "this will not do at all, for no criterion is provided for recognising this totality as distinct from the other totalities'. (p. 107) However, this criterion is provided by the identity and individuation criteria we have already given; and so this further objection of Richards' can be dismissed.
Thus we conclude that no case has been adequately made that the theory of possible worlds is incomprehensible and prima facie the theory and all the terms involved are comprehensible.
§3. Having established the comprehensibility of the concept of a possible world, what basis is there for the claim that possible worlds do not exist?
Richards argues that 'the way things are' is not a referring expression- but indicates that one is speaking assertively, and similarly, 'ways things could have been' does not refer to any entity but serves to 'indicate that one is speaking consistingly but not assertively'. ~2 However, 'the way things are' does involve an implicit reference to an entity, namely 'our' world. 'That is how the world is'
~ Stalnaker, ibid., p. 81. t2 Richards, ibid., p. 106.
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Barbara Davidson and Robert Pargetter 393
is an acceptable paraphrase of ~that is the way things are'. So, using Richards example, to say 'Things are this way: Ford is unpopular with Congress', that is, 'The world is such that Ford is unpopular with Congress' is to refer to Ford, Congress and 'our' world. Similarly 'way things could have been' implicitly refers to entities which we call possible worlds.
Stalnaker denies that possible worlds, as we have individuated them, exist. According to Stalnaker, possible worlds exist but they are not entities o f the same sort as the actual world. He argues that the claim that the actual world alone is real has content only if " ' the actual world' means something other than the totality of everything there is"? 3 So, since this is what we do mean by 'the actual world', our ontology cannot admit other things of the same sort as the actual world. Yet, on the criteria we have given, possible worlds have the same ontological status as the actual world.
However, there is primafacie evidence to suggest that we often do not mean by 'the actual world' the totality of everything there is. Sometimes we make statements like 'Some things which don't actually exist might have' which we take to be true. How should such a statement be interpreted? It would seem that either we must accept that the actual world is not the totality of everything there is or we must deny that what we have said is an existential statement. To take the latter course is fraught with difficulty. It was to attempt to explain the truth conditions of such statements that the theory of possible worlds was developed, since no alternative, adequate theory was available.
Thus the non-existence of possible worlds has not been demonstrated. If such a proof was available then this would show the falsity of any theory committed to their existence. It is in the context of this lack of independent evidence against the existence of possible worlds that Stalnaker claims, rightly in our view, that to undermine the theory of possible worlds it must be shown that (i) there are problems for the possible worlds theorist and (ii) a theory which is preferable to that involving possible worlds is available.
An alternative theory could be preferable in various respects. For example, the concepts involved in the theory might be intuitively clearer than that of possible worlds; its evaluations might coincide to a greater degree with our intuitions, that is, it might better explain why the propositions we think to be true; or the ontology the theory requires might be more acceptable.
Therefore, in the absence of a preferable alternative, the possible world semantics should not be rejected as an account of meaning for modality.
Lawrence Powers objects to this sort of response on the grounds that none of the above considerations bear on the truth of the theory of possible worlds and it is only the truth or falsity of the theory that is our proper concern. This amounts to the claim that no proof of the existence of possible worlds has been given. Now it is not clear what sort of proof could be given since we do not have direct access to other possible worlds, but we do have some supporting evidence. The possible world semantics has been highly successful in providing an account of meaning for modality. Suppose we are willing to add to this, as the
~3 R. Stalnaker, "Possible Worlds', Nous, 10 (1976), p. 70.
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394 Possible Worlds and a Theory of Meaning for Modal Language
possible world theorist believes, that no other theory is available which is as fruitful and which is a preferable alternative to the theory of possl!-le worlds on the criteria we have indicated. Then we do have evidence that the possible world semantics is the correct account and so is evidence for the existence of possible worlds. The methodology is the same as that so commonly used to justify the existence of the theoretical entites involved in the fruitful theories of modern physics.
§ 4 . We have argued that the concept of a possible world is comprehensible and that in the absence of a preferable alternative theory, the success of the possible worlds theory as an account of meaning for modality constitutes evidence for its truth. Hence ontological worries regarding possible worlds do not provide sufficient grounds for rejecting possible world semantics as an account of meaning of modality.
In presenting the argument to this conclusion we have assumed that the theory of possible worlds is successful in providing such an account. Richards, however, argues that this assumption is not justified. Richards suggests that it is a necessary condition for success that 'a theory of meaning [for modality] . . , must show how our understanding of the language in question is possible'?4 For a theory to satisfy this requirement, for every proposition of the language in question, it must at least be able to be determined whether or not the truth conditions which the theory yields for that proposition are satisfied. Since there are modal propositions for which this cannot be achieved (as we cannot directly inspect other possible worlds) the possible world semantics is not the success we have assumed.
Is it true that the condition Richards has specified is necessary for a theory to be a successful account of meaning for modality? Consider statements about the past. Truth conditions for such statements can be given but we cannot always determine whether or not these are fulfilled since, in many cases, inspection cannot be carried out. Yet this does not render the theory which yields truth conditions for statements about the past useless. Nor then would it seem that the theory of possible worlds is useless because we cannot directly inspect other possible worlds and thereby cannot always determine whether the truth conditions yielded by the possible world semantics are satisfied.
Hence, it is not at all obvious that this requirement is a necessary condition that a theory must satisfy to provide insight into the meanings of the terms of a language. It may, at best, serve as a criterion for choosing between alternative theories along with other considerations such as those concerning alternative ontologies. ~ 5
University of Wollongong La Trobe University Received July 1979
~4 Richards, ibid., p. 105. ,5 We are indebted to Frank Jackson, Robert Farrell, and a referee's comments on an earlier
version of this paper.
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