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About the article
Published Online: 2014-03-13
Published in Print: 2014-04-01
Two views in the vicinity of Sider’s are those defended by Kit Fine (2009) and Jonathan Schaffer (2009). Their views differ from Sider’s in various respects, so it will be simpler to focus on Sider’s view alone, although I think similar criticisms can be extended to their positions as well.
The theory of natural properties that Lewis and Sider accept has broad motivations and wide-ranging applications, as is clear from the discussion in Lewis (1983). I am focusing on its uses in their theories of intentionality, but that shouldn’t be thought of as the whole story. Similarly, the idea of structure needn’t be assimilated to the natural property model, though it does provide a convenient framework for making sense of the idea.
It’s possible to have a similar view where naturalness does not come in degrees. On that view, something is either natural or not. This more absolute conception of naturalness may be more amenable to Sider’s views, since it better captures the idea of the world’s fundamental structure. It’s also hard to make sense of degrees of naturalness when extending the notion of naturalness to cover logical vocabulary, as below.
Compare Sider (2011, sec. 11.3).
There may be another natural interpretation of what it is for a dispute to be structural: it is for a dispute to be about structure or to concern what is structural. That is not what I have in mind in what follows.
Throughout this paper, I am using “significant” and “insignificant” as technical terms, signifying the properties of disputes that make them worthwhile and not worthwhile respectively (which are, in my view, the property of being connected to the rest of our inquiry in the right way and the property of being insular). “Significant” can also carry connotations of being meaningful or genuine, but that is not my intention; the intended reading is that significant disputes matter.
For instance, in computer science, modal logics have been used to help understand distributed systems (a simple model might treat each computer as a possible world and relations of accessibility as network connections between them, allowing theorists to model how information is shared in the system), alongside other, more general applications in modeling computer operations, the evolution of databases over time, error-handling, and so on. In mathematics more generally, modal logic has been useful in clarifying the concept of provability (as in George Boolos (1993)).
Sider also discusses these examples (2011, 73). See also Mark Johnston (1992), where Johnston argues that even if personal identity cannot be reduced to, and doesn’t supervene on, the fundamental physical properties and relations of the sort Derek Parfit (1984) takes to be the only plausible candidates, it doesn’t follow that we shouldn’t care about personal identity or that it isn’t the relation that really matters to us.
I do not mean to suggest that the mere fact that some dispute targets a conceptually deep notion is enough to guarantee its significance (see Sections “Sufficiency” and “An alternative picture” for why I think it is not enough). Some disputes about necessity, for instance, might well be insignificant. In the cases I’ve been discussing, however, we have good reason to think that the disputes do have important connections.
It can be difficult to make sense of this suggestion, but we could imagine that there is some primitive fact about what the correct selection of connectives is, or we might tell a story which privileges one group over the other (perhaps in creating reality, God created conjunction and negation, leaving disjunction to emerge from those as an after-thought).
Of course it’s not inconceivable that how many things there are might matter for some question in mathematics, say, or physics or metaphysics, but on the face of it, without filling in the story, it’s hard to see what that question would be. Nonetheless, some philosophers have held that it does matter, especially finitists in the philosophy of mathematics (of which F. P. Ramsey and the later Wittgenstein may have been examples). The important point for me is that, as I will argue in a moment, the mere fact that how many things there are can be stated in structural terms isn’t enough to show that anything hangs on the issue.