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 | |  Natural Kinds | |
Though not all view natural kinds as properties, for many philosophers they are important properties that carve nature at its joints (Campbell et al. 2011). Paradigms include the property of being a specific sort of elementary particle (e.g., the property of being a neutron), chemical elements (e.g., the property of being gold), and biological species (e.g., the property of being a jackal). Natural kinds are often contrasted with artificial kinds (e.g., being a central processing unit). The chief issue here is whether there are any natural kinds or whether our classifications are primarily a matter of cultural and linguistic conventions that represent just one of many ways of classifying things (so that joints are a result of the way that we happen to carve things up).In recent years a good deal of work has been done on the ontology of natural kinds and the semantics of natural kind terms (involving such issues as whether they are rigid designators), as can be seen from the entry on natural kinds. 7.12 Purely Qualitative PropertiesSome properties involve or incorporate particulars. The properties of being identical with Harryand being in love with Harry involve Harry. Even those who think that lots of properties exist necessarily often believe that non-qualitative properties like these are contingent; they depend upon Harry, and they only exist in circumstances in which he exists. By contrast, purely qualitative properties (like being a unit negative charge or being in love) do not involve individuals in this way. The distinction between properties that are purely qualitative and those that are not is usually easy to draw in practice, but a precise characterization of it is elusive. 7.13 Essential Properties and Internal RelationsEssential properties are contrasted with accidental properties, properties that things just happen, quite contingently, to have (see the entry on essential vs. accidental properties). My car is red, but it could have been blue (had I painted it), so its color is an accidental property. In contrast, it is sometimes suggested, natural kinds provide examples of essential properties; for instance, being human is an essential property of Saul Kripke (although some acknowledge natural kinds without taking them to be essential properties). According to some philosophers, there are alsoindividual essences, essential properties that characterize individuals univocally (Plantinga 1974). According to tradition, an essential property of an individual is so defined: it is such that, necessarily, if that individual exists, then it has the property in question. Fine (1994) criticizes this conception by noting that, for example, Socrates cannot exist without the property of being a member of the singleton of Socrates, and yet this property seems to have nothing to do with his essence. He then takes the notion of being an essential property as primitive.Internal relations are usually understood as the relational analogues of essential (monadic) properties. For example, if a bears the relation R to b, then R internally relates a to b just in case, necessarily, if they both exist, then a bears this relation to b. Relations that are not internal, that contingently link their relata, are external. See the entry on relations for details. 7.14 Intrinsic vs. Extrinsic PropertiesSome properties are instantiated by individuals because of the relations they bear to other things. For example, the property being married is instantiated by Bill Clinton because he is married toHillary Clinton. Such properties are sometimes called extrinsic or relational properties. Objects have them because of their relations to other things. By contrast, intrinsic or non-relational properties are properties that a thing has quite independently of its relationships to other things. See the entry on intrinsic vs. extrinsic properties for details. 7.15 Primary vs. Secondary PropertiesThe distinction between primary and secondary properties goes back to the Greek atomists. It lay dormant for centuries, but was revived by Galileo, Descartes, Boyle, Locke, and others during the seventeenth century. Locke’s influence is so pervasive that such properties still often go under the names he gave them, primary and secondary qualities. The intuitive idea is that primary properties are objective features of the world; on many accounts they are also fundamental properties that explain why things have the other properties that they do. Early lists of kinds of primary properties included shape, size, and (once Newton’s influence was absorbed) mass. Today we might add charge, spin or the four-vectors of special relativity. By contrast, secondary properties somehow depend on the mind; standard lists of secondary properties include colors,tastes, sounds, and smells. 7.16 Supervenient and Emergent PropertiesSupervenience is sometimes taken to be a relationship between two fragments of language (e.g., between psychological vocabulary and physical vocabulary), but it is increasingly viewed as a relationship between pairs of families of properties. To say that psychological properties supervene on physical properties, for example, is to say that, necessarily, everything that has any psychological properties also has physical properties and any two things that have exactly the same physical properties will have exactly the same psychological properties. There are no differences in psychological properties without some difference in physical properties. Supervenient properties are sometimes distinguished from emergent properties. 7.17 Linguistic TypesIt is commonplace to contrast linguistic types and tokens. For example, the word ‘dog,’ quaabstract repeatable entity, is a type, but any concrete written or oral realization of it is a token. Admittedly, it is typical to attribute properties to a linguistic type, e.g. being short to the word ‘dog’, but not to attribute the type to one of its tokens; we do not normally say, e.g., that ‘dog’ is possessed by a concrete ink-made mark that we see on a piece of paper. Hence, some may resist the idea that linguistic types are properties whose instances are linguistic tokens. Yet, it is a quite natural view, and if one follows it, such properties should seemingly be conceived of as possibly structured, since words and sentences have parts (Wetzel 2009; Davis 2014). 7.18 Categorical Properties vs. Causal PowersIn naturalistic ontology, one can see two conceptions of properties at play: properties as powers or dispositions to act or being acted upon, and properties as categorical or manifest qualities, mere ways in which objects happen to be. It seems clear that having a property often amounts to having a certain causal power and in some cases the only informative things we can say about a property are what powers (capacities) it confers on its instances. For example, the things we know about determinate charges have to do with the active and passive powers they confer on particles that instantiate them, their effects on the electromagnetic fields surrounding them, and the like. In the light of examples such as this, some philosophers have urged that all properties are causal powers (e.g., Achinstein 1974; Armstrong 1978, ch. 16; Shoemaker 1984, chs. 10 and 11; Hawthorne 2001; Bird 2005, 2007; see Tugby 2013 for an attempt to argue from this sort of view to a Platonist conception of properties). In such an extreme view the very distinction between having a power (which might not be exercised) and manifesting it is lost and thus Martin (1993) and Armstrong (2005), while maintaining that all properties bestow causal powers, thereby having a ‘dispositional side,’ acknowledge that they also have a ‘qualitative side.’ Martin (1997) and Heil (2003) have proposed to understand the relation between these two sides as identity, but Armstrong demurs (2005, 315) and prefers an account in terms of his own N-relation theory of natural laws. Supporters of the idea that properties and powers must go hand in hand keep flourishing: Yates (2013) relies on Kit Fine’s (1994) essentialism to explain how bestowing powers is essential to properties and Ingthorsson (2013) assays how properties can be both qualitative and dispositional.Some philosophers, however, insist that there must be categorical properties irreducible to powers (Ellis 2001, 2010; Molnar 2003). Bird (2005) has disparagingly called such categorical properties ‘quiddities,’ and argued that they would be unknowable and indistiguishable from one another, but Ellis (2010) has responded that properties that we would intuitively regard as categorical, such as ‘shape, size, orientation, speed, handedness, direction, angular separation,’ can be recognized via ‘common patterns of spatio-temporal relations’ and thus after all ‘there is nothing wrong with quiddities.’8. Formal Theories of PropertiesFormal property theories are formal systems that aim at formulating ‘general noncontingent laws that deal with properties’ (Bealer & Mönnich 1989, 133). They thus allow for terms corresponding to properties, in particular variables that are meant to range over properties and that can be quantified over. This can be achieved in two ways. Either (option 1; Cocchiarella 1986) the terms standing for properties are predicates or (option 2; cf. Bealer 1982) such terms are subject terms that can be linked to other subject terms by a special predicate that is meant to express a predication relation (let us use ‘pred’) pretty much as in standard set theory a special predicate, ‘∈’, is used to express the membership relation. To illustrate, given the former option, an assertion such as ‘there is a property that both John and Mary have’ can be rendered as ‘∃P(P(j) & P(m))’. Given the second option, it can be rendered as ‘∃x(pred(x,j) & pred(x,m))’. (The two options can somehow be combined as in Menzel 1986; see Menzel 1993 for further discussion).Whatever option one follows, in spelling out such theories one typically postulates a rich realm of properties. Traditionally, this is done by a so-called comprehension principle which, intuitively, asserts that, for any well-formed formula (‘wff’) A, with n free variables, x1, …, xn, there is a corresponding n-adic property. Following option 1, it goes as follows:(CP) ∃Rn∀x1…∀xn(Rn(x1,…,xn)↔A).Alternatively, one can use a variable-binding operator, λ, that, given an open wff, generates a term (called a ‘lambda abstract’) that is meant to stand for a property. This way to proceed is more flexible and is followed in the most recent versions of property theory. We will thus stick to it in the following. To illustrate, we can apply ‘λ’ to the open formula, ‘R(x) & S(x)’ to form the one-place complex predicate ‘[λx(R(x) & S(x))]’; if ‘R’ denotes being red and ‘S’ denotes being square, then this complex predicate denotes the compound, conjunctive property being red and square. Similarly, we can apply the operator to the open formula ‘∃y(L(x,y))’ to form the one-place predicate ‘[λx∃y(L(x,y))]’; if ‘L’ stands for loves, this complex predicate denotes the compound property loving someone (whereas ‘[λy∃x(L(x,y))]’ would denote being loved by someone). To ensure that lambda abstracts designate the intended property, one should assume a ‘principle of lambda conversion.’ Given option 1, it can be stated thus:(λ-conv) [λx1…xnA](t1, …, tn) ↔ A(x1/t1, …, xn/tn).A(x1/t1, …, xn/tn) is the wff resulting from simultaneously replacing each xi in A with ti (for 1 ≤ i≤ n), provided ti is free for xi in A.) For example, given this principle, [λx(R(x) & S(x))](j) is the case if and only if R(j) & S(j) is also the case, as it should be.Standard second-order logic allows for predicate variables bound by quantifiers. Hence, to the extent that these variables are taken to range over properties, this system could be seen as a formal theory of properties. Its expressive power is however limited, since it does not allow for subject terms that stand for properties. Thus, for example, one cannot even say of a property Fthat F = F. This is a serious limitation if one want a formal tool for a realm of properties whose laws one is trying to explore. Standard higher order logics beyond the second order obviate this limitation by allowing for predicates in subject position, provided that the predicates that are predicated of them belong to a higher type. This presupposes a grammar in which predicates are assigned types of increasing levels, which can be taken to mean that the properties themselves, for which the predicates stand for, are arranged in a hierarchy of types. Thus, such logics appropriate one version or another of the type theory concocted by Russell to tame his own paradox and related conundrums. If a predicate can be predicated of another predicate only if the former is of a type higher than the latter, then self-predication is banished and Russell’s paradox cannot even be formulated. Following this line, we can construct a type-theoretical formal property theory. The simple theory of types, as presented, e.g., in Copi 1971, can be seen as a prototypical version of such a property theory (if we neglect the principle of extensionality assumed by Copi). A type-theoretical approach is also followed in the property theory embedded in Zalta’s (1983) theory of abstract objects.However, for reasons sketched in §7.3, type theory is hardly satisfactory. Accordingly, many type-free versions of property theory have been developed over the years. Of course, without type-theoretical constraints, given (λ-conv) and classical logic (CL), paradoxes such as Russell’s immediately follow (to see this, consider this instance of (λ-conv): [λx ~x(x)]([λx ~x(x)]) ↔ ~[λx~x(x)]([λx ~x(x)])). In formal systems where abstract singular terms or predicates may (but need not) denote properties (cf. Swoyer 1998), formal counterparts of (complex) predicates like ‘being a property that does not exemplify itself’ (formally, ‘[λx ~x(x)]’) could exist in the object language without denoting properties; from this perspective, Russell’s paradox would merely show that such predicates do not stand for properties. But we would like to have general criteria to decide when a predicate stands for a property and when it does not. Moreover, one may wonder what gives these predicates any significance at all if they do not stand for properties. There are then motivations for building type-free property theories in which all predicates stand for properties. We can distinguish two main strands of them: those that weaken CL and those that circumscribe (λ-conv) (some of the proposals to be mentioned below are formulated in relation to set theory, but can be easily translated into proposals for property theory).An early example of the former approach was offered in a 1937 paper by the Russian logician D. A. Bochvar (Bochvar 1981), where the principle of excluded middle is sacrificed as a consequence of the adoption of what is now known as Kleene’s weak three-valued scheme. An interesting recent attempt based on giving up excluded middle is Field 2004. A rather radical alternative proposal is to embrace a paraconsistent logic and give up the principle of non-contradiction (Priest 2006). A different way of giving up classical logic is followed by Fitch, Prawitz and Tennant, who in practice give up the transitivity of logical consequence (see Rogerson 2007, for a recent analysis of these attempts). The problem with all these approaches is whether their underlying logic is strong enough for all the intended applications of property theory, in particular to natural language semantics and the foundations of mathematics.As for the second strand (based on circumcribing (λ-conv)), it has been proposed to read the axioms of a standard set theory such as ZFC, minus extensionality, as if they were about properties rather than sets (Schock 1969; Bealer 1982; Jubien 1989). The problem with this is that these axioms, understood as talking about sets, can be motivated by the iterative conception of sets, but they seem rather ad hoc when understood as talking about properties (Cocchiarella 1985). An alternative can be found in Cocchiarella 1986, where (λ-conv) is circumscribed by adapting to properties the notion of stratification used by Quine for sets. This approach is however subject to a version of Russell’s paradox derivable from contingent but intuitively possible facts (Orilia 1996) and to a paradox of hyperintensionality (Bozon 2004) (see Landini 2009 and Cocchiarella 2009 for a discussion of both). Orilia 2000 has proposed another strategy for circumscribing (λ-conv), based on applying to exemplification Gupta’s and Belnap’s theory of circular definitions.Independently of the paradoxes (Bealer & Mönnich 1989, 198 ff.), there is the issue of providing identity conditions for properties, specifying when it is the case that two properties are identical. If one thinks of properties as meanings of natural language predicates and tries to account for intensional contexts, one will be inclined to assume rather fine-grained identity conditions, possibly even allowing that [λx(R(x) & S(x))] and [λx(S(x) & R(x))] are distinct. Presumably it will be at least maintained that two notational variants such as ‘[λx(R(x) & S(x))]’ and ‘[λy(R(y) &S(y))]’ stand for the same property. On the other hand, if one thinks of properties as causally operative entities in the physical world, one will want to provide rather coarse-grained identity conditions. For instance, one might at least require that [λx A] and [λx B] are the same property if it is contingent that it is physically necessary that ∀x(A ↔ B) (although one will have to digest the idea that the identity [λx A] = [λx B] is only contingently true, if it is physically necessary that ∀x(A ↔ B)). Bealer 1982 tries to combine the two approaches (see also Bealer & Mönnich 1989).Formal systems of property theory are often provided with an algebraic semantics that associates primitive predicative terms of the language with ‘basic’ properties and the lambda abstracts with complex properties obtained from the basic ones by means of operations that generate new properties from given ones (Bealer 1973, 1982; McMichael & Zalta 1981; Leeds 1978; Menzel 1986; Swoyer 1998; Zalta 1983). Thus, for example, one assumes that there is an operation, &, that maps each pair of properties, P and Q, to the conjunctive property P & Q. If ‘P’ and ‘Q’ stand for P and Q, respectively, then ‘[λx(P(x) & Q(x))]’ will stand for P & Q. For another example, it is typically assumed that there is an operation, PLUG1, that, given a two-place relation R and an object d, generates the monadic property PLUG1(R,d). If ‘R’ and ‘d’ denote R and d, respectively, then the property PLUG1(R,d) will be denoted by the lambda term ‘[λx R(d,x)].’ The property in question is the one that something has when d bears the relation R to it.This way of talking certainly suggests that there are complex, structured properties that really have ‘parts’ or constituents pretty much like the linguistic expressions that we use to speak about them. However, although some philosophers are willing to take this road (Armstrong (1978, 36–39, 67f), Bigelow and Pargetter 1989; Orilia 1998), many others (Bealer 1982; Cocchiarella 1986) believe that the appearance that some properties are literally structured is an artifact of our use of structured terms to denote them. But our use of structured terms and structural metaphors doesn’t mean that the properties themselves are genuinely structured or that they literally have parts (Swoyer 1998, §1.2). | |
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