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³ Zangwill, ‘Negative Properties’, 528–556.

⁴ Armstrong, A Theory of Universals, 25–27. Armstrong argues that although we say things like ‘lack of water caused him to die’, which seems to impute to the negative property not being hydrated certain causal powers, we should not take such remarks seriously. This is because we do not generally treat claims like ‘lack of poison caused him to remain alive’ with the same seriousness as ‘lack of water caused him to die’ and yet prima facie they make the same kind of causal claim. Moreover, Armstrong argues that science has already provided us with a rough guide to the kinds of positive properties and relations that exist and the properties and relations identified by science are sufficient to explain the causal outcome of any situation. So there is no need to suppose that there are negative properties with causal powers. Following Braun, David, ‘Causally Relevant Properties’, Philosophical Perspectives 9 (2005)Google Scholar, AI, Connectionism and Philosophical Psychology, 447–475, we disagree with Armstrong on this point: negative properties (if there are any) do have causal powers (see §3 for a full account of the causal powers of negative properties).

⁵ Zangwill, ‘Negative Properties’, 531.

⁶ What is a property? This is a thorny issue. For present purposes we conceive of properties as the entities that ground causal powers and similarity relations. Our discussion is therefore framed in terms of a metaphysically substantive conception of properties, rather than say a conception according to which properties are mere shadows of language and where their ontic status can be determined by examination of our predicative practices given our actual languages (or our predicate practices given any possible language). Although we adopt this position, we do not defend it here and nor do we have to: assuming a metaphysically substantive view of properties is needed to make sense of the present debate surrounding negative properties.

⁷ That said, Zangwill, ‘Negative Properties’, 532–533, proceeds in the other direction, defining certain negative facts in terms of negative properties.

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¹⁶ Lewis, ‘Void and Object’, 282–283.

¹⁷ Helen Beebee, ‘Causation and Nothingness’ in Causation and Counterfactuals, 293, suggests but does not endorse (A) and (C).

¹⁸ Though for an attempt to restrict such cases see McGrath, Sarah, ‘Causation by Omission: A Dilemma’, Philosophical Studies 123 (2005), 125–148CrossRefGoogle Scholar.

¹⁹ Lewis, David, ‘Events’ in Philosophical Papers, Volume 2 (New York: Oxford University Press, 1986), 241–269Google Scholar.

²⁰ One might draw the even stronger conclusion that, therefore, negative properties don't exist, because absences don't exist. Although some of us are sympathetic to this further claim, we cannot defend it here; arguing the point against the existence of absences would take us too far afield.