by Edward R. Moad
In this paper, I will briefly explain actualism about possible worlds, showing that an essential pillar of the theory is the claim that truth is distinct from, and ontologically prior to, truth in a world. The rest of the paper is premised on the idea that an interesting philosophical defense of this claim calls for an analysis of truth itself, and is not intended as an objection to actualism, but rather to underscore the interest actualists should have in the question of what truth is. First, I will consider the idea, drawn from Adams and Alan McMichael, that truth differs from truth in a world in its being a matter of correspondence between a proposition and an independent object; that object being, in McMichael's words, the `concrete universe'. Then, I will show that, given such an analysis of truth, the truth conditions for propositions about non-actual possibilities violate the central tenet of actualism, as articulated by Adams, above.
Adams defines a `world' (or `world-story') as a maximal consistent set of propositions, and the `actual world' as the `true story'; that set including all and only true propositions. Plantinga's possible worlds, on the other hand, are maximal states of affairs, i.e. a state of affairs that, «for every state of affairs S, either includes or precludes S.» Here, «S includes S* if it is not possible that S obtain and S* fail to obtain,» and «S precludes S* if it is not possible that S and S* obtain.»Foot note 2 Of these possible worlds, the actual world is a maximal state of affairs such that every state of affairs it includes is actual. States of affairs are abstract objects, all possible worlds are states of affairs, and the actual world is a possible world. Therefore, the actual world is an abstract object, but it is not a proposition. Plantinga's reason for postulating a distinction between the two is that, «propositions have a property -- truth or falsehood -- not had by states of affairs.»Foot note 3
Maximal consistent sets of propositions, on the other hand, are books. On this theory, «the set of propositions true in a given world W is the book on W,» and, «a proposition p is true in a state of affairs S if it is not possible that S be actual and p be false,» and is true in a world «if it is impossible that W obtain and p be false.» These latter are not definitions of truth, but truth in a world. Like Adams, Plantinga makes it clear that, «truth is not be explained in terms of truth in the actual world, or truth in α; the explanation goes the other way around.»Foot note 4
Thus, actuality is to be analyzed in terms of truth. «`In the actual world, p',» writes Adams, «is to be analyzed as, `The proposition that (p) is true.'»Foot note 5 Analysis of actuality in terms of truth is a central feature of actualism, with important implications. «In the true story theory of actuality, the notion of truth is presupposed, if not as primitive, at least as prior to the notion of actuality, since the latter is analyzed in terms of the former.»Foot note 6 Since «truth in w» is, for Plantinga, a relation a proposition bears to a state of affairs in w, truth in the actual world is explained as a relation a proposition bears to an actual state of affairs. On pain of circularity, then, actuality cannot be analyzed as a relation to a proposition true in the actual world. Likewise, truth cannot be analyzed as a relation a proposition bears to an actual state of affairs. So, neither truth nor actuality can be analyzed in terms of relations between states of affairs and propositions.
Adams, on the difference between actualist and possibilist views of truth, writes that the actualist «sees the truth of a proposition in a possible world as basically a matter of relations of consistency between propositions, rather than of correspondence with an independent object.»Foot note 7 The key here is that the possibilist does see the truth of a proposition in a possible world as correspondence with an independent object, and consequently, a possible world is an independent object. Thus, for the possibilist, there is no difference between truth and truth in a world; truth is just truth in this world. Actualism, however, is an analysis of actuality in terms of truth that attempts to answer, in no world-relative terms, the question, as Adams puts it: «In what does the actuality of the actual world consist?»Foot note 8
Then some analysis of truth is necessary to complete the actualist analysis, for its central feature is that actuality is analyzed in terms of truth and not the converse. If such an analysis is to clarify the distinction between the actual and possible worlds, there must be a clear distinction between truth and truth in a world. Conditions for truth in a world, alone, are not sufficient to clarify this distinction. A positive analysis of truth distinct from truth in a world is called for, particularly in light of the fact that the issue over whether there really is such a distinction is the central point of difference between actualism and possibilism. Despite Adams' suggestion, above, that the notion of truth might be taken as a primitive, it is hard to see how anything at all can be said in defense of the proposition that truth is distinct from, and ontologically prior to, truth in a world, if there is nothing to be said about what truth is. In «Theories of Actuality» and «Actualism and Possible Worlds», where Adams and Plantinga, respectively, construct their actualist theories, such an analysis is absent. Only «truth in a world» is treated: by Plantinga, notably, as part of his explanation of essences and truth conditions of modal propositions, and by Adams, as we saw, in denying that truth in a world is a correspondence relation with an independent object.
This denial may be a clue to putting such an analysis together. It seems natural to presume that Adams sees truth as what truth in a world is not -- correspondence with an independent object. `Independent', here, likely means `independent of the proposition'. If so, then actualism precludes the actual world from being the independent object correspondence to which makes true propositions true. Of course, the actual world consists of just such propositions. So what is this independent object?
Another actualist, Alan McMichael, helps here. «The actuality -- non-actuality distinction is based on the true -- false duality of propositions: one of the worlds is actual because it contains all the true propositions.»Foot note 9 Two pages before, we find, «the actual world is not actual merely in the sense that it exists -- all possible worlds exist -- but rather in the sense that this concrete universe corresponds to it.»Foot note 10 So the actual world is the maximal consistent set of all the true propositions, and its actuality consists in its corresponding to the concrete universe. It looks like a proposition is true iff it corresponds to the concrete universe. If this is true and a world consists of propositions, then actuality just is truth.
For, Plantinga, however, a world consists, not of propositions, but of states of affairs. But he distinguishes them, as we saw, on the basis of the fact that propositions bear the properties of truth or falsehood, while states of affairs bear the properties of actuality or non-actuality. Truth, then, cannot be distinct from actuality simply on the basis of the fact that propositions bear the former, while states of affairs bear the latter. Neither distinction -- either that between worlds and books, or that between truth and actuality -- can be maintained unless at least one of them can be analyzed independently of the other. So the distinction between worlds and books collapses, along with any distinction between truth and actuality that one may have hoped to base on a distinction between worlds and books, and actuality turns out to be truth after all.
A problem arises for actualism, now, with the question of the truth conditions of modal propositions. A proposition is true iff it corresponds to the concrete universe. A maximally consistent set of propositions are all true (the set is the actual world) iff they all correspond to the concrete universe. For any true proposition, then, some feature of the concrete universe must be the «truth-maker» -- that to which it bears the relationship in virtue of which it is true. So propositions about non-actual possibilities, if true, are true in virtue of features of the concrete universe. What features of the concrete universe can be the «truth-makers» for propositions about possible worlds?
McMichael gives the following truth conditions for modal propositions:
These conditions, modified in light of our analysis of truth, then, are as follows:
`It is possible that A' is true iff a possible world w, such that w includes the state of affairs expressed by A, is a feature of the concrete universe.
`It is necessary that A' is true iff the inclusion, in every possible world, of the state of affairs expressed by A, is a feature of the concrete universe.
Given the actualist theory as understood here, if propositions about non-actual possibilities can be true, then maximally consistent sets of propositions -- some of which are false -- are features of the concrete universe. Furthermore, propositions like `it is possible that A', if true, are members of the actual world in virtue of corresponding to a proposition `A' that is not a member of the actual world, but is a member of a maximally consistent set of propositions which itself is a feature of the concrete universe. Propositions like `it is necessary that A', if true, are members of the actual world in virtue of corresponding to a proposition `A' that is a member of every maximally consistent set of propositions (including the actual world) that is a feature of the concrete universe.
The issue at hand is whether or not the situation into which we have been led is acceptable under the original actualist mission. That mission was to show that «true statements in which there are said to be nonactual possible worlds» are «reducible to statements in which the only things there are said to be are things which are in the actual world and which are not identical with nonactual possibles.» But we have seen that, given the preceding analysis of truth, true propositions about nonactual possible worlds entail that those possible worlds are features of the concrete universe. True propositions about non-actual possible worlds, then, entail that those worlds exist. But while true propositions about possible worlds are members of the actual world (the maximal consistent set of all true propositions), the possible worlds themselves are not. Indeed, no consistent set could contain them all.
An analysis of truth as correspondence between a proposition and the concrete universe, then, renders actualism false, as it entails that true statements about non-actual possible worlds are not reducible to statements in which the only things said to be are things which there are in the actual world. Here, possible worlds (maximally consistent sets of propositions) are said to be, but they cannot be part of the actual world (the set of true propositions).
There seem to be two ways for an actualist to respond. The first is to deny that being a feature of the concrete universe is equivalent to existence, in which case the proposed analysis of truth, as correspondence to the concrete universe, does not render the problematic entailment between true propositions about non-actual possible worlds and the existence of those worlds. But to do so begs the question of the meaning of `concrete universe'. If being a part of it does not entail existence, then it becomes merely an empty term meant to serve as a point of reference for `correspondence' in what turns out to be an ad-hoc analysis of truth.
A second possible response is to deny that correspondence to the `concrete universe' is the correct analysis of truth. In this case, the actualist could either offer a different analysis of truth, or else no analysis at all. As I had previously pointed out, the most natural option -- given actualist intuitions -- would seem to be some analysis in line with the correspondence theory. But we have already seen that an understanding of truth as a correspondence to the `concrete universe' violates the essential actualist commitment. To what, then, are we to understand truth as a correspondence? The problem with the `concrete universe' was that it was understood as that of which being a part entails existence. Then, whatever the actualist takes to be that with which correspondence constitutes truth, it must be something of which being a part does not entail existence. But then, truth could be correspondence with the non-existent, and this eliminates all that might have appealed to an actualist's intuitions about a correspondence theory of truth.
In the latter case, perhaps the argument could be made that, as Adams suggests, truth is a primitive notion, and that, therefore, no analysis is possible. However, as previously pointed out, this puts the actualist in a vulnerable position in relation to possibilism, if we are to understand the central controversy between the two views in terms of the question as to whether or not there is a metaphysical distinction between truth and truth in a world. Consider a possibilist charge that, given the actualist contention that there is such a distinction between truth and truth in a world, the actualist is obligated to explain the basis of the distinction between the two, along with that of the ontological priority that the former allegedly bears in relation to the latter. But such an explanation cannot be given unless the salient differences between the two can be identified, and this requires a clear idea of what constitutes truth. Without this, it might be said, the case for actualism seems to amount to the claim that `something we know not what' is distinct from truth in w, and is in fact that in terms of which truth in á is to be understood, and that therefore, actualism is true.
Of course, this is not a knock-down argument for possibilism (nor do I intend to defend possibilism). It remains quite possible that truth is an un-analyzable primitive that is distinct from and ontologically prior to truth in w. But any actualist whose philosophical interest is anything over and above simply defending actualism ought to wonder if, indeed, nothing more can be said as to what makes truth itself distinct from truth in w. This should motivate interest, on the part of actualists, in whether or not any other analysis of truth might be given that explains this distinction, and it introduces the question as to whether, and how, any of the various theories of truth currently on offer might prove compatible with actualist intuitions and commitments.
Edward R. Moad
Department of Philosophy
National University of Singapore
3 Arts Link
phimer [at] nus.edu.sg
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