 The tradition of theorising about “simple” and “complex” properties is a particularly important antecedent for the contemporary use of ‘natural’, for two reasons. First, one can ask both whether a property is more or less simple than some other property, and whether it is perfectly simple. Second, whereas it is supposed to be relatively easy to tell in many cases that a property is complex, identifying perfectly simple properties is generally not supposed to be easy: such claims need to be argued for as part of some ambitious metaphysical theory. The central difference between this traditional use of ‘simple’ and the contemporary use of ‘natural’ is that the former use is bound up with a battery of assumed analogies between properties and other kinds of entities—concrete objects, or linguistic expressions—which the latter use does not require. The claim that a property is complex is understood to entail that in some sense it has other properties as “parts”, from which it is “put together”; the perfectly simple properties are exactly those that lack parts—the analogues of letters or words in the realm of linguistic expressions. The paradigm for “parthood” is the relation between the conjunction of two properties and each of those two properties: for example, being red and being square would be taken to be parts of being red and square. Indeed, for most of the history of this tradition this seems to be the only clearly recognised form of complexity; insofar as properties like not being red and square are recognised at all, they seem to be excluded from the domain to which distinctions of simplicity are to be applied. Only relatively late, in the works of authors like Moore and Russell, do we find a picture where conjunction is merely one of several different operations for building complex properties, others including disjunction, existential quantification, etc. The contemporary use of ‘natural’ is plausibly seen as a cleaned-up version of this older tradition, purged of the additional assumptions that might be read into the mereological terminology. It is compatible with the thesis of “intensionalism”, according to which necessarily coextensive properties are identical; Lewis was in fact an influential defender of this thesis. Given intensionalism, the fact that a property can be derived from other properties by logical operations like conjunction cannot rule out its being perfectly natural, since even a perfectly natural property \(F\) will be identical to the conjunction of \(F\)-or-\(G\) with \(F\)-or-not-\(G\), for any other property \(G\). However the contemporary use is also compatible with finer-grained views about the identity of properties, and it would be natural for proponents of such views to hold that no perfectly natural property is a conjunction, disjunction, existential quantification, etc. Such generalizations will be considered further in  §4.10  below.