Abstract
This paper defends the case against (sparse) disjunctive properties by means of four Armstrongian arguments. The first of these is a logical atomist argument from truthmaking, which is, broadly speaking, ‘Armstrongian’ (Armstrong 1997). This argument is strong – although it stands or falls with the relevant notion of truthmaking, as it were. However, three arguments, which are prima facie independent of truthmaking, can be found explicitly early in Armstrong’s middle period. Two of these early arguments face a serious objection put forward forcefully by Louise Antony (2003) and Alan Penczek (1997), respectively. I consider these objections and argue that they fail. Thus, even if the argument from truthmaking is indecisive, disjunctive properties should be rejected.
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Notes
For simplicity, here and throughout the paper, I shall state only the binary instance of the plural case and assume that what I say holds, mutatis mutandis, for all plural cases.
Lewis's claim is not quite that natural and sparse are co-extensional terms (1986, pp. 60–61, n. 44), but this can be ignored here.
It deserves mentioning that the low status assigned to abundant properties in metaphysics does not mean that they are philosophically uninteresting. For instance, on Lewis’s own view, they are required ‘to provide the semantic values for a systematic, compositional semantics for our language and to characterize the contents of our intentional attitudes’ (1983, p. 219). This non-metaphysical importance may be overlooked by the illuminating use of the pejorative terms ‘second-class’ and ‘third-class’.
One prominent attempt at defining truthmaking involves substituting the right-hand side of (T) with ‘E is an entity in virtue of which 〈p〉 is true’ (cf. Rodriguez-Pereyra 2002). However, I cannot see that the ‘in virtue of’ notion should be clear enough for this to be helpful.
This thesis is highly ‘a prioristic’. Ironically, although the argument can properly be called ‘Armstrongian’, Armstrong (the empiricist) would be very critical of it. For further discussion of this line of criticism, see Walter (2002).
This argument obviously relies on Armstrong’s universal realism, but in an earlier work he formulates a more general – and hence better – version of the argument which prima facie does not:
[D]isjunctive properties offend against the principle that a genuine property is identical in its different particulars. Suppose a has property P but lacks Q, while b has Q but lacks P. It seems laughable to conclude from these premises that a and b are identical in some respect. Yet they both have the ‘property’, P or Q. (1978, II, p. 20)
But then, it might be pointed out, his formulation just seems to assume the same ‘powerful truism’ for a ‘genuine property’ rather than a ‘universal’, and it is also more overtly rhetorical.
The name, the Eleatic Principle, is due to Graham Oddie (1982).
An earlier case of adducing this type of example in defence of disjunctive properties is Meixner (1992). His example is being male-or-female (being sexed).
Note that, if need be, it is also straightforward to use this response against any disjunctive properties that might reveal themselves as being included in apparently non-disjunctive properties, such as being a domesticated bovine.
On some views, determinables are disjunctive properties, such that e.g. being red is held to be equivalent or identical to being-carmine-or-scarlet-or-crimson-or…, etc. If correct, determinables would immediately be a counterexample, as a determinate of a determinable cannot be construed as a conjunction of the determinable with something else. Fortunately, determinables are not disjunctive, see Meinertsen (forthcoming).
For helpful comments on earlier drafts of this paper, I am grateful to audiences at Complutense University of Madrid and Fudan University, including Donnchadh O’Conaill, Nikk Effingham, Malcolm Forster, Boris Hennig, Adam Marushak, Andrea Strollo, and Erwin Tegtmeier, and, in particular, the anonymous reviewers for Philosophia.
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Meinertsen, B.R. Against Disjunctive Properties: Four Armstrongian Arguments. Philosophia 49, 95–106 (2021). https://doi.org/10.1007/s11406-020-00245-y
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DOI: https://doi.org/10.1007/s11406-020-00245-y