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There might be nothing THOMAS BALDWIN 1. In recent papers Peter van Inwagen (1996) and Jonathan Lowe (1996) have discussed the ‘fundamental’l question of metaphysics ‘Why is there anything at all?’. In different ways they argue that the nihilist hypothesis that there might be just nothing can be set aside, either because it is impos- sible for there to be nothing (Lowe 1996: 118) or because this hypothesis is ‘as improbable as anything can be’ (van Inwagen 1996: 99). By contrast I shall here defend the nihilist hypothesis. The point at issue does not simply concern the metaphysics of existence. It also connects with debates concerning modal concepts. David Lewis explicitly declares ‘there isn’t any world where there’s nothing at all. That makes it necessary that there is something’ (1986: 73). The reason for this, as Lewis explains, is that because he conceives a world as a maximal mereological sum of spatiotemporally interrelated things, there cannot be an empty world, since mereology does not permit ‘empty sums’. A little surprisingly, David Armstrong, whose combinatorial theory of possibility is in many respects opposed to that of Lewis, also embraces this conclusion, because ‘the empty world is not a construction from our given elements (actual individuals, properties and relations)’ (1 989: 93). Armstrong takes this view despite the fact that his theory permits the construction of repre- sentations of ‘contracted worlds’ which lack actual individuals, properties and relations because he conceives of worlds as maximal states of affairs and holds that where there is nothing at all, there is no state of affairs. Thus for both Armstrong and Lewis the nihilist hypothesis is to be rejected because the conception of a possibility (or world) has sufficient substance, as a mereological sum or a state of affairs, to demand the existence of something as a part or constituent. Despite the agreement of the two Davids on this issue, Peter van Inwagen himself shows how a contrary position can be developed: he writes ‘By a possible world, we mean simply a complete specification of a way the World might have been.’ (1993: 82) At first this sounds all too reminiscent of Lewis, and when he adds that by the phrase ‘the World’ he means ‘the totality of everything there is’ it is not so clear that this allows for the possi- bility of there being nothing at all. But he then proceeds to write of the World as ‘a mere collection’ so that ‘any use of the phrase “the World” is This is how Heidegger describes the question in Heidegger 1959. It is characteristi- cally unclear what, if any, answer to it Heidegger offers. ANALYSIS 56.4, October 1996, pp. 231-238. 0 Thomas Baldwin

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There might be nothing THOMAS BALDWIN

1. In recent papers Peter van Inwagen (1996) and Jonathan Lowe (1996) have discussed the ‘fundamental’l question of metaphysics ‘Why is there anything at all?’. In different ways they argue that the nihilist hypothesis that there might be just nothing can be set aside, either because it is impos- sible for there to be nothing (Lowe 1996: 118) or because this hypothesis is ‘as improbable as anything can be’ (van Inwagen 1996: 99). By contrast I shall here defend the nihilist hypothesis.

The point at issue does not simply concern the metaphysics of existence. It also connects with debates concerning modal concepts. David Lewis explicitly declares ‘there isn’t any world where there’s nothing at all. That makes it necessary that there is something’ (1986: 73). The reason for this, as Lewis explains, is that because he conceives a world as a maximal mereological sum of spatiotemporally interrelated things, there cannot be an empty world, since mereology does not permit ‘empty sums’. A little surprisingly, David Armstrong, whose combinatorial theory of possibility is in many respects opposed to that of Lewis, also embraces this conclusion, because ‘the empty world is not a construction from our given elements (actual individuals, properties and relations)’ (1 989: 93). Armstrong takes this view despite the fact that his theory permits the construction of repre- sentations of ‘contracted worlds’ which lack actual individuals, properties and relations because he conceives of worlds as maximal states of affairs and holds that where there is nothing at all, there is no state of affairs. Thus for both Armstrong and Lewis the nihilist hypothesis is to be rejected because the conception of a possibility (or world) has sufficient substance, as a mereological sum or a state of affairs, to demand the existence of something as a part or constituent.

Despite the agreement of the two Davids on this issue, Peter van Inwagen himself shows how a contrary position can be developed: he writes ‘By a possible world, we mean simply a complete specification of a way the World might have been.’ (1993: 82) At first this sounds all too reminiscent of Lewis, and when he adds that by the phrase ‘the World’ he means ‘the totality of everything there is’ it is not so clear that this allows for the possi- bility of there being nothing at all. But he then proceeds to write of the World as ‘a mere collection’ so that ‘any use of the phrase “the World” is

This is how Heidegger describes the question in Heidegger 1959. It is characteristi- cally unclear what, if any, answer to it Heidegger offers.

ANALYSIS 56.4, October 1996, pp. 231-238. 0 Thomas Baldwin

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a mere manner of speaking; use of this phrase is no more than a device for speaking collectively about all individuals’ (1993: 112),2 and these remarks are precisely intended to head off the implication that because the World has some substance it couldn’t be that there is nothing at all. With- out entering into the metaphysics of modality in any detail, therefore, I shall assume that a position of the kind adopted by van Inwagen is prima facie defensible, and thus that the debate on the nihilist hypothesis should not be regarded as one to be settled outright by the immediate implications of the concept of possibility.

2. Armstrong describes the nihilist hypothesis as ‘a superficial idea’ that is attractive only ‘at a relatively shallow level of reflection’ (1989: 25). Let us nonetheless paddle about in these shallows by constructing an argument for this hypothesis. I shall call this argument the ‘subtraction argument’. It has three premises:

( A l ) There might be a world with a finite domain of ‘concrete’ objects. (A2) These concrete objects are, each of them, things which might not

(A3) The non-existence of any one of these things does not necessitate

Let these premises be granted; then I argue as follows: By ( A l ) , starting from the actual world W, there is an accessible possible world w, whose domain of concrete objects is finite. Pick any member x1 of this domain: by (A2) there is a world accessible from wl , w2, which is just like w1 except that it lacks x , and any other things whose non-existence is implied by the non-existence of xl. Since, by (A3), the domain of w2 does not contain things which do not exist in wl , it follows that the domain of w2 is smaller than that of w l . This procedure of subtraction can then be iterated, until we get to a world wmin whose domain consists of one or more concrete objects, such that the non-existence of one implies the non-existence of all. By (A2) the non-existence of one of these objects is possible, so there is a world wnil just like wmin whose domain lacks all these objects; and since, by (A3), the non-existence of these things does not require the existence of anything else, wnil is a world in which there is no concrete object at all.

If one now allows that accessibility between worlds is transitive (the characteristic S4 assumption), it follows that wniI is accessible from, or possible relative to, the actual world. I take this conclusion to be the nihil- ist hypothesis that was to be established by the subtraction argument. It may be objected that, at least as far as the subtraction argument goes, the

In 1996 (102) he writes, in a slightly different idiom, of ‘Reality’ as a ‘fictitious object’.

exist.

the existence of any other such thing.

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domain of wnil still includes plenty of abstract objects, such as the natural numbers, so that its existence cannot properly be regarded as the possibil- ity of there being nothing at all. This must indeed be conceded; but whatever view one takes about the existence or not of such objects as the natural numbers, the focus of most interest (and certainly that of van Inwagen and Lowe) is on the possibility of there being no ‘concrete’ objects, in a sense still to be specified. So it is, I think, legitimate to concen- trate primarily on this case while remaining, so far as possible, detached from presumptions concerning the existence or not of abstract objects.

3. The premisses of the subtraction argument clearly require further comment. The first premiss asserts the possibility of there being just a finite domain of concrete objects, which immediately raises the question of what significance is to be attached to this talk of ‘concreteness’. The intuitive thought is that concrete objects are individuals such as cabbages, kings, and pieces of sealing wax. As Lewis has shown (1986: 81-6), however, intuitions in this area are vague and conflicting. I shall take it that the primary mark of concreteness is failure to satisfy the identity of indiscern- ibles. This connects with the familiar criterion of spatio-temporal locatedness via the assumption that space-time provides a way of distin- guishing exactly similar objects. The status of unit sets may be thought to be problematic on this view, since it may be thought that they should count as concrete if their member is a concrete ~ b j e c t ; ~ and yet to include them would immediately generate an infinity of such objects by indefinite itera- tion, contrary to ( A l ) . But I think they can be legitimately excluded on the grounds that they do satisfy the identity of indiscernibles since the identity of the member of a unit set is an intrinsic property o f the set which also determines its identity. Even though there can be two exactly similar phys- ical objects, xI and x2, the unit sets ( x I ] and (xz) are not in the same way exactly similar since they have different intrinsic properties.

With concreteness understood in this way, the claim that there might be only a finite number of concrete objects looks reasonable. To reject it, one has to hold, not only that there is in fact an infinite number of individuals (Russell’s Axiom of Infinity), but that there has to be. One might try to substantiate this thought by invoking the infinite divisibility of space-time; but regions of space-time do not count as concrete objects by the identity of indiscernibles test, since although otherwise indistinguishable objects can be distinguished by their space-time location, space-time regions them- selves cannot be thus distinguished. So the first premiss of the subtraction argument appears a reasonable presumption in this context: if the only way to deny the nihilist hypothesis that there might be nothing was by

Lewis takes this view (1986: 84).

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maintaining that there has to be an infinite number of things, then the denial of the nihilist hypothesis would be clearly unreasonable.

4. The second premiss of the subtraction argument is likewise plausible if one thinks of standard cases of cabbages, kings and pieces of sealing wax. But it conflicts with the thesis that there is a ‘necessary being’, where the being in question is taken to be a concrete object. Van Inwagen has shown that as long as one grants the characteristic S.5 assumption that accessibil- ity is symmetric as well as transitive, the premiss required here is, in fact, only that there might be a necessary concrete being - this is the premiss of his ‘Minimum Modal Ontological Argument’ (1993: 82-94). Despite his demonstration that there is a valid version of the Ontological Argument which requires only this modal premiss, however, van Inwagen also takes the view that we have no reason to accept this premiss, since he holds that the only reason one might have for it depends on the Cosmological Argu- ment, and that turns out to have a wholly unbelievable premiss which implies that all truths are necessary.( 1993: 100-107) I do not dispute the last part of this reasoning, but the general strategy here is risky, since it is hard to see that van Inwagen has established that the only reason one might have for accepting the premiss of his Ontological Argument depends on the Cosmological Argument. For this reason, therefore, it is worth trying to construct a separate argument against the conclusion of the Onto- logical Argument.

The argument I want to propose has, again, three premisses: ( B l ) It is a mark of concrete objects that they do not satisfy the Identity

of Indiscernibles. So the identity of a concrete object is not deter- mined by the intrinsic properties which determine what kind of thing it is.

(B2) In the case of any being whose existence is necessary, the fact that its existence is necessary is determined by the kind of thing it is, and thus by its intrinsic properties.

(B3) For any being whose existence is necessary, the intrinsic proper- ties which determine its existence also determine its identity.

These three propositions imply that there cannot be a concrete object whose existence is necessary. I have already discussed (B l ) , and (B2) is, I think, uncontentious. But (B3) is not so easy to vindicate. In its favour, however, lies the consideration that the only familiar instance of a putative argument for a necessary being of this kind, namely the Ontological Argu- ment for the existence of God, invokes a property, perfection, which, if it implies existence, equally implies uniqueness. For just as it can be argued that a God whose essence does not ensure her existence is less perfect than a God whose essence does ensure this, it can be similarly argued that a God

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whose essence does not determine who in particular she is is less perfect than a God whose essence does determine this. After all, in the former case, the God has to be conceived as distinguished by further extrinsic properties which do not belong to her essence; and a God of this kind is surely less perfect than a God whose essence ensures her uniqueness and thus rules out the need for these extra extrinsic properties - at least by the standard of reasoning which is invoked to argue for the greater perfection of an existent over a non-existent God. I confess that I do not at present see how to generalise from this case to a general defence of (B3), mainly because other plausible grounds for necessary existence are not easy to find. None- theless, given the familiar deep connections between existence and identity (as instanced by the Fregean slogan ‘no entity without identity’), it does appear to me that (B3) is a reasonable hypothesis. Hence my Counter- Ontological Argument has some substance in defence of the claim that there cannot be a concrete object whose existence is necessary, and thus in support of the second premiss of the subtraction argument (A2) that concrete objects are things whose existence is only contingent.

5. The third premiss of the subtraction argument (A3) can be regarded as expressing an implication of the conception of concrete objects as traditional ‘substances’ - things whose existence is independent of the existence of other things. It is not, however, easy to think of a direct argument for this premiss, and I think the best way into the issues it raises is to consider the kind of predicate which illustrates the fallaciousness of the inference schema:

(C) (VX)O(FX) I- O(Vx)(Fx)

For although the subtraction argument is not just an instance of this schema, if non-existence were the kind of predicate which provides coun- terexamples to this schema, this fact would strongly suggest that (A3) is incorrect. Thus, for example, one familiar type of counterexample to (C) is provided by predicates which involve an ordering of a domain of more than one object, such as ‘is at least as heavy as anyone else’; and in this case the thesis comparable to (A3) is incorrect - for if we consider a world in which the person who is, in actual fact, the heaviest person is not as heavy as someone else, then, in that world there must be someone else who is at least as heavy as anyone else. But this kind of case does not pose any seri- ous threat to (A3): for non-existence is clearly not a predicate of this kind since it does not involve any such ordering of the domain.

Another kind of counterexample to (C) arises from the need for a back- ground, as in the familiar thesis that although each of our beliefs might be mistaken: it cannot be that all of them are mistaken since the truth of a good number of our background beliefs is a necessary condition of any of them having the content they do have. Thus the objection to a subtraction

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argument for scepticism with premises concerning the possibility of mistaken belief analogous to (A1)-(A3) will be that the premiss analogous to (A3) is incorrect: for as more and more of a thinker’s beliefs are supposed to be mistaken, it is necessary to assume that the thinker has ever further true beliefs which provide a background that stabilises the content of his beliefs, including those which are assumed to be mistaken. Again, however, there seems little prospect of using this kind of case to argue against (A3) itself: for the truth of a denial of existence does not similarly presuppose a background of true existential claims that are not called into question. Perhaps the justificatioa of a denial of existence requires some such background: but that is a different matter.

The Lewis-Armstrong conception of possibilities can also be regarded as invoking the existence of something as a background condition of there being a possibility at all. For on their conception, the step from wmin to wnil conflicts with the condition that wnil be a possibility at all, despite the fact that it is acknowledged that the existence of the concrete object(s) remain- ing in the domain of wmin is contingent. It is, therefore, (A3) that is again called into question, and again in a way comparable to a way in which (C) is falsifiable. For one can regard this line of thought as comparable to that which applies to another kind of situation which provides a counterexam- ple to (C): the situation in which, although each of us can get away without doing the washing-up, someone has to do it, In this situation, after all but one person have slipped away, there is a requirement that the last person left in the kitchen may not leave the washing-up undone unless he brings in someone else to do it; so again the assumption comparable to (A3) is to be rejected. Yet the analogy does not help the critics of (A3); for although it cannot be that the washing-up is done unless someone does it (there is no ‘empty case’ in this situation), the abstract conception of a possibility does appear to permit a possibility which is not a possibility of, or for, anything - namely the possibility that there be nothing at all.

The final line of thought to be considered here is Jonathan Lowe’s argu- ment that there must be some concrete objects because otherwise the truths of arithmetic would not have the necessity that we take them to have (1996: 115-8). For again, with (A2) in place (which Lowe accepts), it is (A3) that will have to be rejected. Lowe’s argument rests on a treatment of natural numbers as ‘Aristotelian’ properties of sets and a denial of the existence of the empty set; for although he allows indefinite iteration of the abstraction operation whereby sets are constructed from members, he demands the existence of at least one concrete object to get the whole show moving. Hence, even though it is conceded that the existence of such an object is contingent, Lowe argues that some such object must exist, since this condition is a prerequisite of the necessary truth of arithmetic.

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It seems to me, however, that if one holds that the truth of arithmetic depends on the existence of concrete truth-makers whose existence one takes to be contingent, one cannot just invoke standard intuitions concern- ing the necessity of arithmetic in order to dismiss the nihilist hypothesis. On the contrary it looks more reasonable to reject either the necessity of number theory or the ‘Aristotelian’ conception of numbers or the denial of the empty set. Indeed this last point appears especially pressing: on the Aristotelian theory of number, the existence of the number 0 demands that there be at least one 0-membered set, i.e. the null set. But, for Lowe, there is no such set: so his arithmetic is not that familiar theory to whose intui- tive necessity he appeals, but a radical revision of it which makes no reference to the number 0. If Lowe wants to invoke the intuitive necessity of arithmetic, then the arithmetic should be the standard theory; but, given his Aristotelian theory of number, he then requires the null set after all and his argument against the nihilist hypothesis will have collapsed: for given the standard iterative hierarchy of pure sets, there will be no need for any concrete objects.

6. So far as I can judge, therefore, there are good enough reasons to accept the three premisses of the subtraction argument, and, therefore, its nihilist conclusion. Although van Inwagen also (though not for the same reasons) accepts that there might be nothing, he attempts to deflate this conclusion by showing that the possibility that there is nothing has a probability of zero, because this possible world is merely one among an infinite number of such worlds all of which are equally probable or, rather, improbable.

It is, perhaps, of some small comfort to the nihilist to note (as Lowe observes, 1996: 113-4) that, on van Inwagen’s reasoning, the actual world is just as (im)probable as the null world. But, although I have no strong views about the probability of the null world, which appears to me a ques- tion for physicists, if anyone, van Inwagen’s argument for his conclusion that this probability is zero is defective. As he acknowledges, it rests on the thesis that all worlds have the same probability of being actual; and this thesis is one which we can find good reason not to accept once we consider the existence of properties which affect the probability of outcomes. There is, for example, a familiar relationship between age and the chance of death, arising from the limited durability of such essential organs as the human respiratory and circulatory systems. Hence, if we compare the actual world, in which G. E. Moore died in 1958 at the respectable age of 85 with a possible world which is just like the actual world except that Moore is still alive (in 1996) at the extraordinary age of 123, then we surely have good reason to think that it is much less probable that this possible world should have been actual than the world which is, in fact,

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actual. Of course, within this possible world Moore’s physiology will differ in some respects from that of the actual G. E. Moore; but these differences will themselves involve improbable properties for a human constitution, so introducing essential detail of this kind will not diminish the improbability of the outcome. It may also be said that there is not just one world which is like the actual world except that it contains a 123-year old G. E. Moore: there are infinitely many such worlds differentiated by different specifica- tions of the details of Moore’s life in the period 1958-1996, and since these are all equiprobable, they can have only zero probability, just like the actual world. But this equiprobability thesis is just a version of that which is here in question and, intuitively, one can easily think up more or less probable ways of filling out the details of Moore’s life in this period (e.g. residing in Cambridge versus travelling to Mars and back).

Van Inwagen’s basic thought is, I think, that once one grasps that worlds are maximally determinate states of affairs, so that there is an infinite number of alternatives to any given world, one should then acknowledge that all worlds have the same probability, namely zero. It is not clear to me what kind of non-theological basis there is for any judgment that one might make concerning the absolute probability of a particular world’s being actual. But even if one were to acknowledge that the actuality of any one world in particular is, for van Inwagen’s kind of reason, improbable, it still does not follow that one should hold that the probability is the same for all worlds. For some worlds will involve combinations of properties and outcomes, such as a 123 year-old Moore, which we know to be much less probable than other combinations, such as an 84 year-old Moore.4

University of York, York, YO2 SDD, UK

[email protected]

References Armstrong, D. 1989. A Combinatorial Theory of Possibility. Cambridge: Cambridge

Heidegger, M. 1959. Introduction to Metaphysics. Trans. Manheim, New Haven: Yale

Lewis, D. 1986. On the Plurality of Worlds. Oxford: Blackwell. Lowe, E. J. 1996. Why is there anything at all? Aristotelian Society Supplementary

van Inwagen, P. 1993. Metuaphysics. Oxford: Oxford University Press. van Inwagen, P. 1996. Why is there anything at all? Aristotelian Society Supplementary

University Press.

University Press.

Volume 70: 11 1-120.

Volume 70: 95-1 10.

4 This is a revised version of my Chairman’s comments at the 1996 Joint Session; many thanks to Timothy Williamson for advice on how to improve them.