Reductionist theories of particulars

Realists admit a two-type ontology including universals and particulars, while nominalists insist that there is only one category of objects, namely particulars. Realists have sufficient resources to attempt to reduce the category of particulars to that of universals. One way of reducing particulars to universals is known as the bundle theory, according to which particulars are constituted by all of their properties. This approach is reminiscent of Berkeley’s conception of things as clusters of ideas (‘sensations’), except that properties are assumed to be independent of the perceiving subject. Another possibility is to reduce particulars to properties plus an extra object, called the bare substratum, whose role is to be the literal bearer of the properties without actually possessing them. This conception is not surprisingly called the substratum theory.

Let us consider the bundle theory in some detail. The first problem we have to face is that not every set of properties constitutes a particular object. For instance, the set consisting of the property of being a horse and the property of being winged does not identify any particular, because no object is a winged horse. In order to deal with this problem, the relation of co-instantiation (compresence, collocation) is introduced. The above-mentioned properties are not co-instantiated, hence they cannot constitute an individual. A particular is constituted by properties which are mutually co-instantiated. However, there is a small technical problem here. If we treat co-instantiation as a two-place relation, then the condition that every property in a set is co-instantiated with every other property from this set is not sufficient to ensure that all the properties are co-instantiated together. It is possible to find an example of three properties P, Q, and R such that P is co-instantiated with Q, Q is co-instantiated with R, and P is co-instantiated with R, and yet P, Q and R fail to occur together (for example we can choose R as the property of not being P or not being Q, and assume that P co-occurs with Q, P co-occurs with not-Q, and Q co-occurs with not-P). One solution can be to assume the hierarchy of higher-level relations of compresence binding the relations of compresence between properties, but this leads to the proliferation of numerically distinct relations of compresence. Another way out is to accept that the relation of co-instantiation can admit a varying number of arguments, but it is doubtful if this solution is formally correct. The substratum theory avoids this difficulty, because the substratum acts as the “glue” clumping together all the properties.


Another issue is completeness. Not every set of co-instantiated properties can be identified with one individual object. The set {redness, smoothness} is exemplified by many objects (for example some red apples). We can reduce particulars to complete sets of properties only. A complete set of properties can be broadly characterised as a set such that if we added a new property to it, we would get an inconsistent set. But it is unclear what type of inconsistency is involved in this definition: logical, nomological, or perhaps metaphysical. Also, it may be questioned whether sets of all properties possessed by particular objects are in this sense complete. Why does it create an inconsistency to add to all the properties possessed by this horse the property of having wings? The existence of inconsistency can be perhaps defended if we assumed that the set of all properties of a given object contains also negative properties (in the case of the horse the property in question would be the property of not being winged).


Several objections can be raised to the bundle theory, according to which complete sets of co-instantiated properties constitute particular objects. One such objection is that subject-predicate sentences about particulars become necessarily true. In the true sentence “This table is wooden” the noun phrase “this table” refers to a particular set of properties T, and the sentence can be translated as stating that the property of being wooden belongs to this set T. But each set possesses its elements necessarily, so the sentence cannot be false. If this table, understood as a set, didn’t have the property of being wooden, it would be a numerically different object. Another way of expressing this objection is that all properties of particulars become essential. We could try to circumvent the problem by modifying the interpretation of the above sentence so that its subject is identified with the set T minus the property of being wooden, and the thought expressed in the sentence is that the property of being wooden is co-instantiated with the rest of the properties in T. But a downside of this solution is that an attribution of a different property to the same table, for instance “This table is white”, will have to be interpreted as a sentence about a different object, i.e. the set T minus the property of being white. It is debatable whether the substratum theory is affected by a similar problem. If the subject of the sentence “This table is wooden” is identified as the set of all properties plus the bare substratum of the table, then the same argument in favour of the necessity of the property ascription goes through. However, the sentence can be interpreted as having the bare substratum as its subject, and in this case it will be contingent (the bare substratum exemplifies its properties contingently).


Another difficulty for the bundle theory is related to the problem of change. It is commonly accepted that objects can change in time by acquiring new properties or losing old ones, without losing their numerical identity. But sets of different properties are numerically distinct. The same problem seems to affect the substratum theory, unless we decide to explicate the relation of identity between various temporal stages of an object in terms of the preservation of its bare substratum (but in that case it seems that the identification of a particular object with the set of all its properties plus the substratum turns out to be vacuous – instead, we simply take the substratum as identical with the object). One possible solution may be to treat an object as the bundle of all its past, present and future properties indexed by moments of time. This suggestion corresponds well to the conception of the existence in time known as perdurantism, of which we will talk more later in the course.


Finally, the bundle theory is criticised for implying the necessary truth of the Principle of the Identity of Indiscernibles (PII). This follows immediately from the extensionality of sets: two sets containing the same elements are numerically identical. Hence there can be no numerically different bundles of the same properties. This consequence is unwelcome because of the strong arguments in favour of the possibility of the PII being false (and even in favour of its actual falsity) which we discussed earlier in the course. Again, the substratum theory has the upper hand because it is possible to have two individuals with exactly the same properties, if only their substrata are numerically distinct (the possibility of making the PII false seems to be the main advantage of the substratum theory). The bundle theory may be rescued if we agreed to replace properties with tropes. It is possible to have two individuals made up of perfectly similar tropes, hence the spirit of the PII is preserved.


The substratum theory assumes that when we “subtract” all properties from a given object what is left is a property-less pure object, called a bare substratum. The substratum cannot posses any properties, because metaphysically it has to be ready to accept any properties as their bearer. If the substratum possessed any properties, this would lead to a regress, since it would need its own bare substratum presumably with its properties and so on. The only attribution that can be made directly about the substratum regards its numerical distinctness from other substrata. Hence it can be maintained that bare substrata ground the numerical identity and distinctness of objects, known as their “thisness” or haecceity.


The main criticism of the substratum theory comes from the empiricists, who point out that because bare substrata lack any properties they cannot be perceived or in any way identified or known. It is also claimed that the notion of a bare substratum is inconsistent. On the one hand it is assumed that bare substrata don’t posses any properties, but on the other hand we characterize them in some ways: we say that they are ‘bare’, that they act as literal possessors of properties, that they ground numerical identity and difference. But aren’t these things properties of bare substrata?


A solution which tries to combine the strengths of the bundle theory and the substratum theory without their weaknesses is called the nuclear theory (proposed by Peter Simons). According to it, properties of every object can be divided into two parts: the inner nucleus and the outer fringe. The inner nucleus contains properties that are essential, and therefore such that an object cannot lose them without losing its identity (we will characterize precisely the notion of an essential property in the next lecture). Thus the nucleus plays the role of a bare substratum. The outer fringe, on the other hand, contains properties that can be lost and gained without a change in the numerical identity. But this solution has to be worked out in details in order to make sure that it copes with the problems we talked about earlier. In particular, if we elect to identify particular objects with their inner nuclei (this seems to be necessary in order to deal with the problem of necessary attributions and the problem of change), we have to make sure that no two distinct objects possess all the properties from the nucleus.

Reading:

M.J. Loux, Chapter 3 "Concrete particulars I", pp. 84-107, Metaphysics: A Contemporary Introduction

Also recommended:

J. Van Cleve, "Three Versions of the Bundle Theory".
P. Simons, "Particulars in Particular Clothing: Three Trope Theories of Substance".