Abstract
This paper is the first trope-theoretical reply to E. J. Lowe’s serious dilemma against trope nominalism in print. The first horn of this dilemma is that if tropes are identity dependent on substances, a vicious circularity threatens trope theories because they must admit that substances are identity dependent on their constituent tropes. According to the second horn, if the trope theorist claims that tropes are identity independent, she faces two insurmountable difficulties. (1) It is hard to understand the ontological dependence of tropes on substances. (2) The identity-conditions of tropes cannot be determinate, which threatens the determination of the identity-conditions of substances. Our reply to the first horn of Lowe’s dilemma is to deny the identity dependence of tropes. Yet we can avoid the second horn because our theory can explain the ontological dependence of tropes on substances and the fully-determined identity-conditions of both tropes and substances.
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Notes
Lowe (1998, 58) uses the term “individual object” for all entities that have determinate identity-conditions and form countable unities (are countable). Substances are individual objects that are not ontologically dependent on further entities (Lowe 1998, ch. 6). They also have the traditional function to act as the bearers of property tropes (modes).
Lowe allows of tropes or modes that do not have determinate identity. As such, they are not identity dependent on their bearers. This does not mean, however, that tropes or modes are ontologically independent because they are adjectival of their bearers (ways those bearers are) (Lowe 1998, 79–83).
According to K. Campbell and D. Ehring, too, the individuation of tropes is “basic and unanalysable”, or “primitive” as Ehring puts it (Campbell 1990, 69; Ehring 2011, 76–91). However, our position differs from them essentially because in their theories tropes are not strongly rigidly dependent (cf. note 6 for definition) on any entity (Campbell 1990, 21; Ehring 2011, 77), whereas in the SNT tropes are mutually rigidly existentially dependent entities. So the nature of tropes is different in this respect in these different accounts. For Campbell and Ehring, they are “junior-substances” (strongly independent particulars); for us they are not. Our theory is a dependence theory, whereas Campbell's and Ehring’s accounts are independence theories. So we defend a distinct trope theory for Lowe's criticism. In this respect, the SNT is of the same type as Peter Simons’ Nuclear Theory (Simons 1994), from which the SNT is, indeed, developed. Our defence is also different from the way Campbell and Ehring could reply to Lowe, since part of it is the analysis of inherence and our analysis must differ from their analyses as for them tropes are junior substances while we maintain them to be rigidly dependent.
The problem of the persistence of tropes overlaps both questions. We have discussed it in Keinänen and Hakkarainen (2010).
As such, being an individual differs from being a particular, which are distinct category-features of entities. They should not be conflated, for, in principle, universals may be individuals, too: countable entities with identity-conditions (cf., e.g., Lowe’s Neo-Aristotelian ontology where kind universals are individual objects). So there are actually three category distinctions involved here: (1) countable versus not countable, (2) having identity-conditions versus not having identity-conditions, (3) particular versus universal. For example, masses such as water may be particulars that are not countable but have identity-conditions (Lowe 2006, 75–78). The exact formulation of the third of these distinctions is the most controversial issue. We do not discuss it in this context as the particularity of tropes is not a topic of this paper. We simply assume that particulars can be exactly similar and still numerically distinct (Maurin 2002, 17, 20–22; cf. Ehring 2011, 30–45). It is a formal category-feature of tropes that they are particulars as well as the feature of universals that they are universals.
Lowe does not use these terms to put the distinction between individuation and identification. His terminological choice is to speak about individuation in a metaphysical and an epistemic sense (Lowe 2003, 75). It corresponds to our distinction between individuation and identification.
Let “≤”be a relation of improper parthood (cf. Simons (1987, 112) for the definition) and “E!” the predicate of (singular) existence. As does Simons (1987, 303), we can define strong rigid dependence as follows: entity e is strongly rigidly dependent on f iff ⇁(□ E!f) ∧ □ ((E!e → E!f) ∧ ⇁(f ≤ e)). Weak rigid dependence is defined by replacing ⇁(f ≤ e) with ⇁(f = e). Unlike Lowe’s (1998, 137) definition (D1) of rigid dependence, Simons’ definition of weak rigid depencence rules out the rigid dependence of entities on themselves and on necessary existents. If such cases are not taken into consideration, identity dependence entails weak rigid dependence (cf. Lowe 1998, 149–150).
Lowe (1998, 206) makes a stronger claim that a substance as a trope bundle would be identity dependent upon (all of its) constituent tropes but the trope theorist need not accept it.
Tropes are countable in principle, which does not entail that we are actually able to count them in every case.
Since our account of trope identification relies on the claim that tropes are mutually rigidly dependent entities, it is not available to trope theorists (such as Campbell 1990) who assume that tropes are not strongly rigidly dependent on any entity, cf. section 4 for more discussion.
In addition to tropes as monadic properties, there are relational tropes. It suffices here that we limit ourselves to tropes as monadic properties.
However, in the SNT, we can introduce relational tropes instantiated by the proper parts of a complex substance to determine its features not determined by features of its proper parts (Keinänen 2011, 447).
As we do not introduce quality tropes, we avoid the specific problems pertaining to their identification: e.g., do spatially extended shape tropes have further shape tropes as their proper parts? Do two distinct macro-objects having the same proper parts possess distinct shape tropes?
Lowe, too, admits that an entity can be rigidly dependent on another entity without being identity dependent on it (cf. the example of Socrates and Socrates’ life in section 2). According to the SNT, identity dependence can be analyzed in terms of strong rigid dependence. Therefore, the former cannot be used in explaining the latter but the converse holds. SRD but not identity dependence is a primitive formal relation, which contributes to the over-all economy of our position (cf. below).
Although not giving a general analysis of identity dependence, Lowe (2006, section 3.1) considers the relation of characterization between a mode and the substance having the mode a primitive formal relation, which explains the identity dependence of the mode upon the substance.
Trope x of kind P is strongly generically dependent on trope y of kind R, if SGD (P(x), R(y)) ≡ □ ∀x □ (Px → □ (E!x → ∃y (Ry ∧ ⇁(y ≤ x)))) ∧ ◊∃x Px ∧⇁□ ∀x Rx holds. Cf. Simons (Simons 1987, 294 ff.) for further discussion.
Hence, in the context of the SNT, the obtaining of these formal relations spells out when simple substances are identity dependent on their trope parts. Nevertheless, a full analysis of identity dependence, e.g., of complex substances on their necessary parts, is a more complicated matter.
Here, we rely on that the best a posteriori examples of the highest determinables of the determinate features of simple substances are physical quantities (such as mass, charge and spin). A possible a posteriori objection to the SNT might be that the photon is a simple substance that has only one property. However, it is far from clear that this is indeed the correct ontological account of the photon. Physically, in addition to spin, it has the direction of the spin and energy/relativistic mass. Ontologically, there are more than one option to account for this as the direction of the spin and energy/relativistic mass may be explained metaphysically in more than one way (cf. Morganti 2009, 195 ff.; Simons 1994, 570). Instead, it is much clearer that all the other fundamental particles in the Standard Model bear two properties at least (see Morganti 2009, 197).
Ehring’s term is “trope swapping across objects” (2011, 79).
Hence, we adopt what Schaffer (2001, 248) calls “the standard quantitative individuation principle” (QI): x and y are distinct tropes iff they are primitively quantitatively distinct.
Schaffer (2001, 249) has also the more metaphysical objection to the primitive identity of tropes that it is not clear whether its advocate can exclude repeatable entities, i.e., universals. If tropes have a primitive identity, nothing seems to rule it out that, instead of two or several tropes in distinct locations (e.g., two or several redness tropes), there is a single trope having a scattered location. Hence, it would be difficult to distinguish between tropes and universals if it is assumed that particulars, in contrast to universals, cannot have scattered location. It seems to us that here Schaffer conflates individuality and particularity. We also consider Ehring’s reply to Schaffer sufficient (Ehring 2011, 91). Still we do not agree with Ehring that a trope can have a scattered location. As we have argued elsewhere, they have a specific location (Keinänen and Hakkarainen 2010, section 2).
Other piling problems, which concern one object, such as identifying its several exactly similar tropes (“perfect piling”) or tropes of the same determinable kind (“imperfect piling”), do not rise in the SNT (cf. Ehring 2011, 86–91). According to it, as was seen just above, an object has only one trope of each determinable kind. This is a good feature of the SNT.
Cf. Simons (1994, 573–574) and Schaffer (2001, 254–256) for discussion of the possible implications of the superposed micro-particles to the trope theory. According to Lowe (1998, 62 ff.), the superposed electrons are quasi-individuals, entities having determinate countability but no determinate identity-conditions.
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Acknowledgments
For comments of the earlier drafts, we would like to thank the four referees of Erkenntnis as well as Fabrice Correia, Antti Keskinen, Philipp Keller, E.J. Lowe, Arto Repo, and the audiences at the University of Geneva, University of Tampere and University of Turku. This work has been financially supported by the Academy of Finland research projects “Tropes, Change and Dispositional Essentialism” and “British Empiricism and Trope Nominalism”.
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Keinänen, M., Hakkarainen, J. The Problem of Trope Individuation: A Reply to Lowe. Erkenn 79, 65–79 (2014). https://doi.org/10.1007/s10670-013-9459-y
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DOI: https://doi.org/10.1007/s10670-013-9459-y