Abstract
Our knowledge of the most basic alternative possibilities can be thought of as generated recursively from what we know about the actual world. But what are the generating principles? According to one view, they are recombinational: roughly, alternative possibilities are generated by “patching together” parts of distinct worlds or “blotting out” parts of worlds to yield new worlds. I argue that this view is inadequate. It is difficult to state in a way that is true and non-trivial, and anyway fails to account for our knowledge that there might have been other things, properties, relations, and combinations of these than there actually are. I sketch and defend an alternative view based on the distinction between determinable and determinate properties: roughly, alternative possibilities are generated by “intra-determinable” variation, variation from one determinate to another of the same determinable.
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Notes
So my use of ‘fact’ will not be factive; I will call something a fact even if it does not actually obtain.
For ease of exposition, I have suppressed a minor complication. If Descartes’ demon is fooling us all, actual experience mostly yields merely possible basic facts rather than actual basic facts. So strictly speaking, the initial input should be characterized as consisting of “basic facts provided by actual experience” rather than “actual basic facts”. But the key idea is unaffected: our basic modal knowledge is anchored in actual experience, even if this experience is delusional.
Actually, I will talk indiscriminately of what worlds represent, what they contain, what exists at them, what goes on that them, etc.
Throughout ‘distinct’ means ‘wholly distinct’, that is, having no parts in common.
For ease of exposition, I have suppressed another minor complication. If y is a duplicate of any part of x, then no duplicate of x can exist without a duplicate of y also existing. So (a*) should read: If there is a world at which x and y both exist and are distinct and y is not a duplicate of x or any of x’s parts, then there is also a world at which a duplicate of x but no duplicate of y exists. (b*) needs a similar amendment.
Throughout my world talk is a little informal. Here I talk of “applying” a principle to a world or of the world being “input” for the principle when that world makes true the antecedent of the principle. Elsewhere I talk of “inferring” and “generating” worlds, etc. This refers of course to the capacity of certain principles to tell us what worlds exist. I don’t mean to imply any ontological dependence of the worlds themselves on our principles.
A minor terminological point. Perhaps there are properties (and relations) that, though not themselves actually instantiated, can be defined in terms of those that are. I would still count any such properties as alien; I use ‘alien’ for any property (or relation) that is not actually instantiated. But others would not (see, e.g. Lewis 1986, p. 91).
Lewis of course was well aware that aliens generate problems: “We can’t get the alien possibilities just by rearranging non-alien ones. Thus our principle of recombination falls short of capturing all the plenitude of possibilities.” (1986, p. 92).
More generally, if C and C* are any wholly distinct collections—none of their members overlap, even in part—D is any possible distribution of F over C, and D* is any possible distribution of F* over C*, then there is a single world at which D is the distribution of F over C, and D* is the distribution of F* over C*. See Denby (2006).
The complete intrinsic nature of something can be thought of as the conjunction of all its intrinsic properties. And a property is a complete intrinsic nature if it’s the complete intrinsic nature of some possible thing.
For reasons to posit naturalness see Lewis 1983.
Ignoring the possibility of analyzing things into their parts before recombining. After all, the intuition seems just as compelling restricted to the metaphysical atoms of the actual world: surely there could have been more or fewer of them, however many there are.
I will often just use ‘determinable’ for ‘property family’ and I will talk of determinates “belonging to” a determinable or being “from” a determinable, etc.
Moreover, I argue below that determinablism should apply only at the level of natural properties and the haecceities, compounds and intermediates probably don’t qualify. So investigating them further would not be worthwhile anyway. I discuss determinables and determinates further in Denby (2001).
For ease of exposition, when I’m discussing determinablism, I concentrate on properties, ignoring relations. But the generalization to relations seems straightforward, at least if they too are categorizable into determinables and determinates governed by analogues of (1), (2) and (3) and they can be thought of as properties of pairs, triples, etc. For then we need only let the individual variables in [D1] range over pairs, triples, etc., for [D1] (and its subsequent modifications) to cover possibilities involving relations too.
Notice that (1), (2) and (3) are negative; they tell us only about what is not possible, not about what is possible. So they do not allow us to infer any worlds at all, even in combination with all the actual basic facts and all the information about which properties are determinates of which determinables. That’s why they do not imply [D1]. And that’s why, even if (1), (2) and (3) are constitutive of the notions a determinable and its determinates, [D1] is not trivial. By contrast, [I] is positive; it tells us which worlds there are. And [I] plus the actual basic facts plus information about which properties are intrinsic does generate all the worlds generated by [R2]. That’s why [R2] is trivial.
While extending the range of the property-quantifiers to cover plural properties, including non-distributive ones, and extending the determinable-determinate distinction to cover them. I assume that this raises no new difficulties.
Notice that by exploiting the cardinality determinable, we can conclude that there might have been zero particles—in effect, that there might have been nothing at all. Many would object. Lewis, e.g., denies that this is a possibility (1983, pp. 73–74), as does Armstrong (1989, pp. 24–25 and pp. 63–64). On the other hand, many would not. And it perhaps has pre-theoretic intuitions on its side (as Lewis and Armstrong both concede). I tend to agree with Lewis and Armstrong that whether there could have been nothing is a case of “spoils to the victor”. Moreover, since it is clearly a special case, it would not really be ad hoc to modify [D2] in such a way as to exclude it (and there are several straightforward ways to do this).
Talk of “collections of properties” makes the exposition smoother, but note that it is intended as an idiom of plural quantification, not as set talk.
Perhaps naturalness is a matter of degree—properties are more or less natural. If so, just read ‘perfectly natural’ for ‘natural’ throughout.
And this is a more appropriate role for naturalness than precluding extrinsic properties from the scope of the generating principles (see above p. 7). For it corresponds to one of the original motivations for positing naturalness in the first place, viz. accounting for fundamental similarities in nature.
Again this is not to deny the possibility of fixes to recombinationism to enable it to specify the manner of coexistence. For instance, part (b*) of [R2] could be modified to allow the duplicates to exist in any spatiotemporal arrangement, perhaps as follows: If there is a world at which x exists but y does not and a world at which y exists but x does not, then for any possible spatiotemporal arrangement A, there is a world containing distinct duplicates of x and y coexisting in arrangement A. Thus modified, [R2] would generate the first sort of unicorn-world, those containing unicorns-qua-horses-with-horns. But this amendment brings its own difficulties—for one thing, it introduces an extra modal element, the notion of a possible arrangement, into [R2]—and it wouldn’t capture unicorn worlds in the other senses anyway.
Parallel remarks apply to information about which properties are natural and which are mathematically or mereologically linked. It is not objectionable that such information is presupposed in applications of [D5] rather than explained by them because this information does not consist of basic facts.
This is one reason why it won’t do to think of determinables as mere disjunctions of determinates: their internal structures typically exceed what can be encoded by Boolean operations on their determinates.
What about shapes in higher dimensions or curved spaces? Aren’t these specific alien determinables? I don’t think so. They are still shapes, after all, and the shape determinable is not alien. What these examples show is that the shape determinable has a complicated internal structure—perhaps it is multidimensional or tree-structured (see the following remarks).
References
Armstrong, David M. (1989). A combinatorial theory of possibility. Cambridge, UK: Cambridge University Press.
Denby, David A. (2001). Determinable nominalism. Philosophical Studies, 102(3), 297–327.
Denby, David A. (2006). The distinction between intrinsic and extrinsic properties. Mind, 115(457), 1–17.
Lewis, David K. (1983). New work for a theory of universals. Australasian Journal of Philosophy, 61, 343–377.
Lewis, David K. (1986). On the plurality of worlds. Oxford, New York: Basil Blackwell.
Sider, Ted (2001). Maximality and intrinsic properties. Philosophy and Phenomenological Research, 63, 357–364.
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I would like to express my thanks to an anonymous referee for this journal whose valuable comments resulted in several improvements.
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Denby, D. Generating possibilities. Philos Stud 141, 191–207 (2008). https://doi.org/10.1007/s11098-007-9159-z
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DOI: https://doi.org/10.1007/s11098-007-9159-z