Abstract
The paradox Lowe is referring to is the following. If P is the predicate ‘non-predicable’, then if for any predicate there is a property, there is a property of non-predicability, but if P has this property, we can use P as a predicate and there is no property. We have a paradox, because P is such that in order to be a property it is not a property, which is self-contradictory. This version of Russell’s paradox can therefore be used against the reduction of properties to predicates. But if properties are not identical to predicates, there is an ‘intimate connection’ (Lowe) between them and a part of the difficulties caused by the formal treatment of properties is located in the subtlety of the relations between predicates and properties. We usually establish a correspondence between the two by means of formal transformations.
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- 1.
As properties are either general or particular, some philosophers introduce an ontological distinction between two different modi essendi. Moore in the Principia Ethica attributed ‘being’ to the universals and ‘existence’ to the particulars (and therefore to the quality instances); Meinong declared the universals subsist (bestehen) and the particular properties exist. Russell in the problems of Philosophy, used this meinongian distinction (see Hochberg 2002, p. 108 ff. for a summary of the development of these notions).
- 2.
For a presentation of Lewis’s theory of natural properties, see Oliver (1996, pp. 38–44). D. Lewis introduced a distinction between sparse and abundant theories of properties. If properties are sets of particulars, we obtain an abundant theory of properties. In order to obtain a sparse theory of properties, D. Lewis proposed to select a minority elite of properties, the natural ones. What remains a bit mysterious is the selection method for natural properties.
- 3.
According to H. Hochberg, Moore introduced in 1903 the distinction between natural and non-natural properties in the context of his fight against naturalism in ethics. Hochberg assumed that this distinction has in fact a Brentanian origin:
The key to understanding Moore’s early view was his acceptance of a familiar theme in the Brentanist school at the turn of century — the analysis of objects as bundles of quality instances (tropes, Husserl’s ‘moments’ (…) For Moore, at that time, a natural property like yellow was a universal which had quality instances or tropes that were constituents of ordinary objects (or sense data) — yellow objects (Hochberg 2002, p. 107)
- 4.
There is a strong overlap between formal theories of properties and philosophy of mathematics. The main topics discussed at the intersection of the two are: typed or untyped properties (in case of higher order properties), compound properties, reduction of mathematics to logic and therefore the possibility of a general and formal theory of properties. For a recent survey of property theory (cf. Jubien 1989; U. Mönnich)
- 5.
Ersatzism according to D. Lewis is a form of anti-modal realism. Whereas modal realists assume the existence of possible worlds, on the same footing as our brave actual world, ersatzists reduce possible worlds e.g. to linguistic ersatz (sets of sentences) or to other ersatz. We may call properties ersatzist philosophers who reduce properties to predicates, concepts etc (cf. Marcus 1993).
- 6.
But we have to notice that in some definition of emergence it is specified that there is an influence of the emergent property on the behavior of the parts of the basis of the emergence. For example: a property P is an emergent property from on object O mereologically complex iff P supervenes upon properties of the parts of O, iff P is a property not possessed by any of the parts of O, iff P is distinct from any structural property of O, and P has a determining influence on the parties of O (I underline). As a matter of fact, the term ‘influence’ is vague, and we should have to analyze this concept.
- 7.
- 8.
Swoyer (2000, 2.1.) contrasts very sharply different types of arguments concerning the existence of properties: transcendental and demonstrative arguments, on one hand, and inference to the best explanation, on the other hand. He urges that ‘most of the arguments advanced on behalf of properties appear anemic when jugged by the demonstrative ideal, but that they look much better when viewed as inferences to the best explanations’.
- 9.
Lowe (2002, p. 140) accepts both particular and universal ways of being. He calls the universal ways of being « properties » and the particular way of being « modes », a tribute to Locke’s metaphysics.
- 10.
See A. Oliver’s development on methodology for metaphysicians, especially what concerns a difference between ideological economy and ontological economy (Oliver 1996, pp. 2–5).
- 11.
The relation of compresence is a Russellian one (Russel 1948). A and B are compresent iff a and b are located at the same moment. This relation is used by tropists in order to provide unification of thick particulars constituted of tropes. Some writers (e.g. P. Simons, A. Denkel) disbelieved the possibility of accounting for unification in terms of compresence and turn themselves to ‘internal foundation relation’ (cf. Mertz 2002, p. 169). Russelian compresence is very close to Whitehead’s ‘togetherness’. (cf. Process and Reality, p. 20)
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Nef, F. (2010). Properties. In: Poli, R., Seibt, J. (eds) Theory and Applications of Ontology: Philosophical Perspectives. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8845-1_7
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