Original ArticlesResponse to Kathrin KoslickiKit Fine
dialectica Vol. 61, N° 1 (2007), pp. 161–166 DOI: 10.1111/j.1746-8361.2007.01097.x
Response to Kathrin Koslicki Kit Fine†
Koslicki’s paper is an extraordinarily perceptive and comprehensive discussion of my published work on the nature of material things. Although she is sympathetic to my criticisms of the standard mereological approaches to this topic, she is not so happy with my positive views. She has three main objections in all, which she summarizes as follows: Fine’s theory gives rise, first, to a proliferation of primitive sui generis relations of parthood and composition, whose characteristics must be imposed on them stipulatively by means of distinct systems of postulates, tailored to the different domains of objects. Secondly, we noted that, given its ‘superabundance’ of objects, Fine’s theory is committed to its very own population of ‘monsters’. Thirdly, once rigid embodiments are abandoned, the explicitly mereological aspect of Fine’s hylomorphic theory is preserved only at the cost of abandoning the Weak Supplementation Principle. This, in turn, along with the other formal properties of Fine’s system, makes us wonder why one should consider the primitive sui generis operations introduced by Fine’s theory to be genuinely mereological at all (pp. 157–158).
Let me briefly consider the first and third of these objections but devote most of my attention to the second. Proliferation It was not my intention in the papers I have so far published to provide a general theory of part-whole but merely to present those aspects of it that were especially relevant to the constitution of material things. I believe that a general theory, once developed, would reveal these particular aspects of it to be less fragmentary and stipulative in character than might appear from the published papers. But whether this is so or whether there is a more satisfactory way of developing such a theory is perhaps best discussed once the details of the theory and its rivals are at hand. Weak supplementation According to the Weak Supplementation Principle (WPS), if a whole w has a proper part p then it must have a part that is disjoint from p and so, in particular, it must have a proper part that is not itself a part of p. Koslicki follows Peter † Philosophy Department, New York University, 5 Washington Place, New York NY 10003 USA; Email:
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Simons in taking this principle to be partly constitutive of the notion of part and criticizes my theory of variable embodiment on the grounds that if is not to be a mystery what a variable embodiment /F/ is then its underlying principle F must be a proper part of it, in violation of WPS (p. 155). I am not sure that it would be a mystery what a variable embodiment is if F were not a part of /F/. But since I believe that F is a part of /F/, we may let the point stand. As Koslicki mentions in her paper (p. 156), I have objected to WPS on the grounds that Socrates is a part of singleton Socrates even though there is no proper part of singleton Socrates that is not a part of Socrates. A defender of the faith might criticize my example on the grounds that Socrates is not a part of singleton Socrates (except perhaps in a metaphorical sense). But Koslicki seems to be willing to accept that Socrates is in fact a part of singleton Socrates. What she criticizes instead is my claim that singleton Socrates has no part disjoint from Socrates for, she wants to say, ‘it has additional parts (though not additional members) besides Socrates, viz. its formal components, whose nature is presumably spelled out in some fashion by reference to the axioms of set-theory’ (fn. 29). I can see that one might take the method of forming a set from its members to be a formal component, though otherwise it is not clear to me what the formal components (in the plural) might be. But no matter, since I do not see how the view can be made to work. For suppose the formal components are f, g, h, . . . , which I assume are the same for every set or, at least, for every singleton. Consider now singleton {f, g, h, . . .} (i.e. the set {{f, g, h, . . .}}). It has {f, g, h, . . .} as a proper part but the other proper parts, viz. f, g, h, . . . , are all parts of {f, g, h, . . .}! Koslicki might argue that the formal components are not the kind of thing that can be members of a set. I do not see why but even this point might be allowed to stand. For if the formal components of {Socrates} are capable of saving WSP from counter-example, then the formal components of /F/, conceived in an analogous manner, should also be capable of saving the principle from counter-example. Super-abundance My theory gives rise to ‘monsters’, objects whose existence we are ordinarily inclined to reject. It will, for example, predict the existence of a ‘car-bouquet’, which starts off being like a car and ends up being like a bouquet of flowers. This is indeed a difficulty for the theory and it is one that I have struggled with for many years. However, it is worth pointing out that there is a difficulty here for any view. For there appears to be no precise and principled line of division between those objects – such as cars and bouquets of flowers – whose existence we are ordinarily inclined to accept and those objects – such as ‘car-bouquets’ –
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whose existence we are ordinarily inclined to reject. It therefore appears that there can be no theory that is internally satisfactory in providing a precise and principled basis for determining what exists and yet also externally satisfactory in being consonant with what we ordinarily take to exist.1 In my previous writings on the topic I was inclined to abide by the internal criterion of satisfactoriness, since it seemed to me intolerable that what exists should be a vague or arbitrary matter. And when it came to the conflict with our ordinary views, I was inclined to tell some story about how our ordinary language quantifiers were implicitly restricted to those objects that were important or salient to us or about how we might be led to change our views as to what exists on the basis of philosophical theory (just as we have been led to change them on the basis of scientific theory). I was never really convinced by either of these stories and I have now what I regard as a more satisfactory resolution of the conflict. It turns on the account of postulation in ‘Our Knowledge of Mathematical Objects’ and ‘Relatively Unrestricted Quantification’ (as Koslicki surmises in her perceptive remarks on p. 129 and in footnote 27). The key insight is that, within certain domains of objects, what exists is inevitably an arbitrary matter. Take the case of mathematics, which would normally be regarded as a paradigm of precise and principled existence, and consider, in particular, the case of numbers. What numbers are there? Certainly the natural numbers. But also the negative integers, the rationals, the reals, and the complex numbers. But why stop there? Why not follow Conway (1976) in admitting the ‘surreal’ numbers? Have we now come to an end? No, and it is evident that there is no end to be reached. For whatever we take to be the numbers, we can always add a ‘point at infinity’ or fill in some ‘gaps’. The situation is just the same for the cumulative hierarchy of sets. For whatever sets we take there to be, we can always suppose that there are various new sets – be it the universal set (analogous to a point at infinity) or large subsets of the universe (analogous to the gap-fillers). Ironically, the situation is also the same for mereology. It might appear that, in contrast to the case of sets, we might reach a natural stopping-point in the case of mereological sums. For we can consistently suppose that any objects whatever will form a sum. But the appearance of naturalness simply arises from considering the existence of sums in isolation from other kinds of object. Suppose we also admit singletons into our ontology. Then under innocuous assumptions, it follows that we cannot admit the unrestricted existence of both singletons and sums.2 Thus once we allow the unrestricted existence of singletons, some arbitrary restriction must be placed on the existence of sums. 1 This topic has been discussed by Lewis (1986) and Sider (2001), and also by Koslicki (2003) herself. 2 The matter is discussed in Lewis (1991), Rosen (1995), Uzquiano (2007) and in my ‘Relatively Unrestricted Quantification’.
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Given the inevitability of an arbitrary line of division, it is no objection to a theory that it imposes such a division. However, it may well be wondered whether material things constitute a domain for which these analogies with the domains of sets or sums or numbers are appropriate. Certainly, the standard proponent of the mereological view will find them appropriate since, for him, a material thing just is a special kind of mereological sum. But someone like myself will have no reason to believe that material things are mereological sums or even to believe that there are mereological sums. Moreover, it may well be thought that there is a critical disanalogy between the two kinds of domain for there is a sense in which the objects of the mathematical domains are introduced rather than given. The complex numbers, for example, are not simply given to us but are introduced as the solutions of certain equations. It may now be supposed that arbitrariness in existence is characteristic of objects that are introduced since it is the possibility of introducing new objects that accounts for the arbitrariness of any particular stopping point. But surely material things – elementary particles or people or the like – are given, not introduced; and so there is no reason to think that they will suffer from the same kind of arbitrariness in their existence. It may be conceded that the arbitrariness will only arise for objects that are introduced but this is still compatible with taking some material things to be given even if others are introduced. An analogy with the mathematical or the mereological cases may again be helpful. For we might suppose with Kronecker that ‘God made the integers; all the rest is the work of man’. Thus taking the integers to be given, the other numbers (or objects of mathematics) may be introduced as the solutions to equations or the like. Or again, we might suppose with Aristotle that the elements consist of indefinitely divisible stuff (earth, air, fire and water). Some mereological sums – the sum of two quantities of water, for example – will then be given to us, while other mereological sums – the sum of some water and some earth, for example – will be introduced. The sentiment that inspired Kronecker’s remark about the integers might be seen to inspire a similar sentiment about the material world. For it is not altogether unnatural to suppose that some material objects – perhaps elementary particles and the like – are God-given while the others are the ‘work of man’.3 There would then be no special difficulty in supposing that the boundaries to the domain of material things were arbitrary as long as they were arbitrary in the right way, i.e. with respect to the objects that were introduced. What goes for material objects in general will go for the rigid and variable embodiments of my theory in particular. Thus it might be supposed that some (perhaps all) of them are introduced 3 We might think of the given material things as Aristotelian in character and the introduced material things as Platonic in character. In this way, we achieve some sort of rapprochement between the restrictive Aristotelian stance and the more permissive Platonic stance.
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while the others (perhaps none) are given. There will then be no special difficulty in making the theory consonant with our ordinary views as to what exists as long as the putative monsters of the theory are not among the embodiments that are taken to be given. According to the present position, what there is will be relative to what has been introduced. There is no absolute sense in which there is what there is since what there is is always capable of being extended through the introduction of new objects. Koslicki (fn. 27) finds the relativity of my position unattractive; and it must be admitted that one does not normally suppose that what there is might be relative to what one ‘takes’ there to be. But the position is in a way quite faithful to the facts if not to our philosophical predilections. Prior to the admission of complex numbers, mathematicians would have agreed that there is no solution to the equation x2 = −1 while, after the admission of complex numbers, they would have agreed that there is a solution. Surely the earlier and later mathematicians were both correct in what they said and nor is it plausible that the later mathematicians had relaxed a restriction that was previously in place since, in denying that there is a solution to the equation, the earlier mathematicians would not have recognized that there was any restriction on what the solution might be. This suggests that the quantifier was unrestricted all along and that what made the later statement acceptable was the introduction of complex numbers into the ontology. A similar kind of relativity seems to be at work in our discourse about material things. We may imagine that some future religious sect holds the view that cars are endowed with souls who migrate to a neighboring bouquet of flowers after a gestation period of nine months (stranger religious views have been held). The putative bodies of these souls are called ‘car-bouquets’ and, although everyone is willing to recognize the existence of car-bouquets, there is considerable disagreement over whether they have souls. Again, we may explain why it is correct for us to deny the existence of car-bouquets and yet also correct for the future generations to affirm their existence by appeal to a difference in what each of us has introduced into the ontology. Although this is a hypothetical example, it is plausible that there are many actual cases of this sort. We recognize the existence of certain groupings of stars (the constellations) but not others while other cultures recognize the existence of different groupings. But how can this be? Surely each culture is correct in recognizing the constellations that it does; and it is hard to believe that they mean something different by ‘constellation’ or by ‘there is’. And so this again suggests that the difference consists in which groupings of stars each culture is willing to countenance in its ontology. Thus the present position is not only able to provide a theoretically satisfying vindication of our ordinary views on what there is; it also appears to be especially well-suited to explaining how our views on what there is might change or differ.
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Kit Fine References
Conway, J. H. 1976, On Numbers and Games, New York/London: Academic Press. Koslicki, K. 2003, ‘The Crooked Path from Vagueness to Four-Dimensionalism’, Philosophical Studies 114, pp. 107–134. Lewis, D. 1986, On The Plurality of Worlds, Oxford: Blackwell. Lewis, D. 1991, Parts of Classes, Oxford: Clarendon Press. Rosen, G. 1995, ‘Armstrong on Classes as States of Affairs’, Australasian Journal of Philosophy 73, pp. 613–625. Sider, T. 2001, Four Dimensionalism: An Ontology of Persistence and Time, Oxford: Oxford University Press. Uzquiano, G. 2007, ‘Unrestricted Unrestricted Quantification: The Cardinality Problem of Absolute Generality’, in: A. Rayo and G. Uzquiano, eds, Absolute Generality, Oxford: Oxford University Press, pp. 305–332.
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