Tropes and Ontic Predication Markku Keinänen Postdoctoral researcher Department of Philosophy University of Turku "Substance & Attribute" conference in Tampere

What are tropes? Trope theorists (i.e., bundle of tropes theorists) introduce tropes to determine objective exact similarities between objects. Thus, objects are exactly similar in respect of mass, charge, or length, etc., and tropes are introduced to determine such shared features of objects.

What are tropes Tropes (introduced by trope theorists) are particular properties.Thus, tropes are: 1) Particulars and exists as single units. Spatio-temporal tropes exist only in a single, unscattered location. 2) Categorially simple: tropes are either simple or all of their parts are further tropes.

What are tropes 3) Tropes can exist as compresent (or spatio-temporally co-located) with each other. 4) A trope has a thin nature: a trope is eiher identified with a single particularised feature possessed by an object, or alternatively, it is the nature of each trope to determine a single feature of an object.

What are tropes Trope theorists analyse the property bearing objects as aggregates of tropes that fulfil certain conditions. Thus, tropes are particulars of their own and do not earn their particularity (or identity) from other entities, e.g., from the property bearing substrata.

What are tropes Tropes are often considered to have a location of their own independent of the location of the things they constitute.

Ontic predication Ontic predication is the relationship between an object and the properties possessed by the object. All trope theorists advocate the Constituent Analysis of Ontic Predication: the property tropes possessed by object a are certain kinds of parts of a.

Ontic Predication Two important benefits are obtained from the adoption of the constituent analysis: 1) There is no threat of redundancy, which would result from considering tropes as entities mereologically disjoint from objects ( as substance attribute theorists do)

Ontic predication 2) Trope theorists seem to gain qualitative economy by avoidance of the primitive category of property bearers (substances or substrata) Trope theorists usually maintain that all fundamental entities belong to the categories of property and relation tropes.

Objections to the constituent analysis 1) General Objection: it is a fundamental mistake (a category mistake, perhaps) to consider properties as any kind of parts of objects 2) Specific objection: trope theorists have failed to construct any reasonable analysis of ontic predication

Objections to the constituent analysis I will defend trope theories against the above claims.

The constituent and the attribute analysis The advocates of properties make the following three assumptions: 1)Bearers of properties are objects 2)Objects share various features (they are exactly similar in these respects) and properties are introduced determine these features of objects

The constituent and the attribute analysis 3) There is a single uniform primary way to analyse the relation between objects and their monadic properties (monadic ontic predication)

The constituent and the attribute analysis The alternative category systems these metaphysicians advocate conform with either of the following two schematic primary ways to analyse ontic predication:

The constituent and the attribute analysis [CA]: Constituent Analysis of Ontic Predication: thing a has property P, if and only if, there is property P and P is a certain kind of constituent (or part) of a. [AA]: Attribute Analysis of Ontic Predication: thing a has property P, if and only if, there is property P and P is a non- constituent attribute of a.

The constituent and the attribute analysis Contradictory intuitions supporting either of these schematic ways to analyse ontic predication: 1) (Attribute analysis) Properties are attributes of objects determing the ways objects are, not any kind of parts of objects

The constituent and the attribute analysis 2) (Constituent analysis): Monadic properties determine the intrinsic features of objects. Thus, they seem to be included into their bearers, they are nothing external to their bearers. Further, it is natural to assume that properties of objects have exactly the same location as objects by being parts of objects.

Advantages of the constituent analysis The the connection between object and its properties is analysed by means of part whole relation. Thus, trope theorists may need less formal relations to analyse this connection. A trope theorist can give a straightforward explanation of the co-location between object and its properties.

Argument from Category Mistake It is a straightforward category mistake to consider properties as any kinds of parts of objects. All parts objects are further objects. By contrast, properties are non-substantial entities determining the ways objects are. Properties cannot exist without presence of objects, while all parts of objects are capable of independent existence.

Argument from Category Mistake (trope theorist answer) 1)The terms of part-whole relations need not belong to the same ontological category. Rather, there can be different kind of part whole relations between different kinds of entities. 2) In its turn, the claim that it is a category mistake to consider properties as parts of objects is either trivial or begs the question against c.a.

Argument from Category Mistake (trope theorist answer) The claim is trivial if made inside some categorial scheme assuming the attribute analysis. The claim begs the question if meant as argument against the categorial schemes that assume the constituent analysis:

Argument from Category Mistake (trope theorist answer) In comparison of the different categorial schemes, we do not have neutral standards against which category mistakes could be made. Still, it might be advisable to try to distinguish between the trope parts of objects and more object-like parts of objects.

Compresence theories and ontic predication Compresence theories are advocated by Williams (1953) and Campbell (1981,1990) Compresence theories claim that theories are ”junior substances”: any individual trope t can exist independent of any other trope that is not a proper of t.

Compresence theories and ontic predication Objects are replaced with the aggregates of compresent (i.e., mutually co-located) tropes Thus, ”ordinary objects” are rejected as a fundamental or derived category, they are just logical constructions out of property tropes

Compresence theories and ontic predication An object has several distinct properties if it is constituted by several distinct property tropes Single individual tropes are metaphysically possible. Thus, in limiting case, there is single property trope in some definite location. Such a trope forms a limiting case of ontic predication – an object having just one property.

Compresence theories and ontic predication The greatest advantage of the compresence theorist analysis of ontic predication is its simplicity: Ontic predication is analysed solely by means of mereological part whole relation and compresence. No necessary connections between wholly distinct existents are introduced.

Compresence theories and ontic predication Moreover, compresence theorist can form a straightforward account of complex tropes in terms of conjunctive compresences: Campbell (1990) idea is as follows: a quantity trope t (e.g., a mass trope) is conjunctive compresence of simpler tropes of the same determinable quantity, if

Compresence theories and ontic predication 1) t is an aggregate of compresent simpler mass tropes in a location having the value of the sum of these tropes or 2) t is an aggregate of mass tropes in different locations having the value of the sum of these tropes

Compresence theories and ontic predication By means of the idea conjunctive compresence, we can build a complete theory of complex quantity tropes that is independent of their functioning as properties of objects. One can analyse away the necessary connection between distinct mass tropes.

Further advantages of compresence theories A transparent conception of tropes as particular natures: An individual trope can be identified with its nature. For instance, a 1 kg trope is an instance of being 1 kg that self-instantiates. Given that the spatio-temporal location of tropes can be grounded, we have straightforward conception of compresence.

A difficulty for compresence theories To ground the location of tropes, one has to introduce relational tropes: the available accounts of relational tropes seem to introduce existential dependencies

Reasons to reject compresence theories 1) It appears impossible to individuate the tropes that determine the feature F of a given object a. Basic reason: instead of a single trope t, there can always be a conjunctive compresence of simpler property tropes.

Reasons to reject compresence theories 2) Compresence theorists cannot explain the behaviour of tropes. Why do tropes form stable bundles? Why do the tropes of certain basic physical quantity always exist as parts of compresent bundles? Because the empirical inquiry does not operate by individual tropes, no scientific explanation is available to this fact.

Reasons to reject compresence theories 3) Compresence theories cannot explain why tropes form stable bundles, i.e., natural objects belonging to certain natural kinds. The behaviour of each individual continuant trope is independent of the behaviour of each other trope. There is no explanation why a given stable bundle is constituted by these rather than some other tropes. Again, no empirical explanation can be given either.

Reasons to reject compresence theories Compresence theories give a clear account of ontic predication. However, the they fail to give an adequate theory of natural individual objects.

Dependence theories Dependence theories (e.g., Simons 1994; Denkel 1996, 1997) claim that individual tropes cannot occur alone but only as constituents of complete objects (substances) Substances are constituted by means of existential dependence relations (strong rigid and strong generic dependence) in which tropes are to each other.

Rigid and generic dependence Entity e is strongly rigidly dependent on entity f, iff SRD(e, f) ≡ ¬( □ E!f) ∧ □ ((E!e → E!f) ∧ ¬( f ≤ e )) Entity x of kind P is strongly generically dependent on entity y of kind R, iff SGD (P(x), R(y)) ≡ □ ∀ x □ (Px → □ (E!x → ∃ y (Ry ∧ ¬(y ≤ x )))) ∧ ◊ ∃ x Px ∧ ¬ □ ∃ x Rx

Dependence theories Substances are aggregates of mutually dependent tropes in which all of the ”existential needs” of the individual tropes are fulfilled. Therefore, substances are independent existents.

Strong nuclear theory In what follows, I concentrate on a single dependence theory, Strong Nuclear Theory (SNT), which is a further development of Simons’s (1994) Nuclear theory. As does Simons, this position uses rigid and generic dependencies in substance construction.

Strong Nuclear Theory In comparison with a theory based solely on generic dependencies (Denkel’s Saturation theory), SNT has two advantages: 1) One can identify substances through change by means of necessary tropes. 2) Since tropes are not bound to substances by means of compresence, co-located substances are allowed for.

Strong Nuclear Theory In SNT, rigid dependencies help in singling out the necessary tropes of substances and bind individual tropes to a particular substance In their turn, generic dependencies guarantee that each substance has distinct tropes falling under distinct determinables as its constituents

Strong Nuclear Theory SNT is a theory of simple substances – only fundamental substances are considered as trope bundles. Thus, an advocate of SNT does not introduce complex tropes (e.g., structural tropes) to construct complex substances.

Strong nuclear theory Roughly the construction is as follows: 1) There are certain distinct tropes t 1, … t n rigidly dependent on each other. Each of these tropes belongs to a distinct determinable kind. Moreover, tropes t 1, …, t n form the necessary tropes (i.e., the nucleus) of a substance i. As tropes of a determinate kind t 1, …, t n also determine the kind K to which substance i belongs.

Strong nuclear theory 2) As the tropes of a substance of kind K tropes t 1, …, t n are generically dependent on tropes that belong to certain determinable kinds D 1, …, D m (n  m), the determinable kinds to which t 1, …, t n belong included. Moreover, there are tropes belonging each of the determinable kinds D 1, …, D m that are rigidly dependent on the nuclear tropes of substance i. Each such trope is a constituent of substance i at some moment in time. In addition to nuclear tropes (which are constituents of i at each moment), such tropes can include some tropes contingent to i.

Strong Nuclear Theory 3) The basic entities occurring in spatio- temporal relations are trope bundles that constitute some substance i. Each such trope bundle contains the nuclear tropes of i and (possibly) some tropes contingent to i. Each such trope bundle contains exactly one trope from each of the determinable kinds D 1, …, D m.

Strong Nuclear Theory 4) Each trope must be a constituent of some substantial trope bundle constituting a substance. Consequently, the free floating tropes are ruled out. Moreover, the location of each trope t is determined by the location of the trope bundle in which t occurs.

Strong Nuclear Theory As in Simons’s theory: 1)The belonging of fundamental objects to natural kinds is explained by means of necessary tropes. 2)Co-located substances are allowed for. Compresence is not sufficient for ontic predication.

Strong Nuclear Theory Unlike in Simons’s theory: 1) Complete substances are the basic entities occurring in spatio-temporal relations. The location of tropes is upwardly grounded by the locations of the entire substances.

Strong Nuclear Theory 2) Thus, the trope constituents of substances are rendered necessarily compresent with each other. Compresence is thus necessary (though not sufficient) for ontic predication. Tropes functioning as properties of an object cannot be widely dispersed.

Strong Nuclear Theory 3) Multiple tropes of a single determinable kind functioning as properties of a single object are ruled out. For instance, object a cannot instantiate several distinct mass tropes.

Strong Nuclear Theory One can give the following straightforward analysis of ontic predication in SNT: tropes functioning as properties of object i are those rigidly dependent parts of i that are also necessarily compresent with i.

Some disadvantages of SNT 1)Substance atomism is presupposed: all substances are constituted by simple substances that are trope bundles. Tropes are the genuine atoms of the world. 2)No clear conception of the substantial change of simple substances is available.

Some disadvantages of SNT 3) It is difficult to understand the relation between substances and processes. Are they mereologically disjoint? 4) No plausible ontology of space-time is developed in this connection. Might be a difficulty of many rival categorial schemes.