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Whatever Binds the World’s Innermost Core Together Outline of a General Theory of Ontic Predication

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Abstract

Nexuses such as exemplification are the fundamental ties that structure reality as a whole. They are “formal” in the sense of constituting the form, not the matter of reality and they are “transcendental” inasmuch as they transcend the categorial distinctions between the denizens of reality, including that between existents and non-existents. I shall advocate a moderately particularist view about (external) nexuses and argue that it provides not only the best solution to Bradley’s regress, but also an elegant account of symmetrical relations (both formal and material), as well as of temporal and modal change. These advantages are illustrated by the reconstruction of an Aristotelian ontology of exemplification involving substances, kinds and material attributes.

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Notes

  1. When I write that nexuses are “subsistents”, I do not mean that they exist in some diminished manner (e.g. as unactualised possibles), but that they quite simply are neither existent nor non-existent. Following Routley’s (1982), I assume that non-existents (including subsistents) can be referred to or quantified over and possess identity conditions.

  2. The fact that transcendental ties and relational existents (as well as transcendental properties and qualitative existents) are indifferently expressed by predicates has encouraged the unfortunate habit of referring to them indistinctly as “attributes”, safe for occasionally qualifying transcententals as formal attributes and relational or qualitative existents as material attributes. Trying to step outside of this tradition necessitates arkward paraphrases, such that it is difficult to avoid this unfelicitous terminology altogether.

  3. Contrary to Mertz (1996), I use the expression “ontic predication” exclusively to refer to the application of transcendentals to their terms. Thus “ontic predication” is not synomymous with “exemplification” which designates the application of material attributes to their bearers.

  4. Though a transcendental attribute neither exists nor does not exist, it may be said to be at a given world, since subsistence is a mode of being. The subsistence of an attribute will be referred to as its occurrence, for in this paper transcendental attributes will be assayed as occurrents.

  5. Multiple dependence does not, pace Simons (2003), account for the “why” of ontic predication, since the fact that a nexus cannot occur in a world unless its relata exist at the same world is not a sufficient ground for the nexus being ontically predicated of its relata. Indeed, multiple dependence of the nexus on its relata allows for the relata to exist without the nexus occurring, assuming that at least some of the transcendental relational claims are contingent.

  6. There is another approach to assay all nexuses as internal, namely the stance that times and worlds are additional relata on which nexuses supervene. While this view avoids wholescale necessitarianism, it implies relationalism which I will discuss and reject in Sect. 4.1.

  7. One could object that the commitment to actually infinite hierarchies of merely subsisting nexuses comes at no cost. However, the ontological cost is not at issue here, but the explanatory complexity of the proposed account.

  8. Or equal to 2, if the signature of its type is a singleton, as in the case of symmetrical unit connections (see below).

  9. The graphs in this paper are based on the Conceptual Graphs formalism developed by John Sowa (2000). They are bipartite directed graphs composed of class nodes represented by boxes and relational nodes represented by ellipses or diamonds. Ellipses represent many-to-many ties, while diamonds stand for functional relationships; all relationships are supposed to be internal. The direction of the relations is indicated by arrows. A box with the label “A” designates an arbitrary item of class A; it can be read as an A-sorted existential quantifier or unbound A-sorted variable. A box with the label “A:b” designates a definite item b of class A. A box with label “A:{*}” denotes an arbitrary plurality of items of class A, or a single item of class A. We say that an item of class A is among a plurality of items of class A; if the latter is a plurality of one, then being-among is tantamount to being-identical-to.

  10. It may be speculated whether this two-fold account of ontic predication could not be simplified by reducing modes to roles, i.e. by regarding each monadic nexus as an abstraction from a way of participating in a connection. Surely this would be straightforward enough for categories like substance or attribute, which happen to be congruent with roles of exemplification. However, I will not explore this issue any further in the context of this paper.

  11. The same objection holds against the attempt to save the view that all nexuses are internal by assuming time and worlds as additional relata on which nexuses are supposed to supervene. This attempt fails since times and worlds quite simply are not common or garden variety relata of nexuses.

  12. Temporal relations between times and accessibility relations between worlds can be defined in terms of temporal and modal counterpart relations between events (Russell 1936; Chisholm 1996, p. 60; Lewis 1968, 1986a). Special Relativity implies that temporal relations have reference frames as parameters; reference frames could be assimilated to worlds as suggested by Bigelow (1996).

  13. If one is not simply “noneist” (in the sense of Routley 1982) about the latter.

  14. So-called haecceities (Duns Scotus 1950, II.3.1.4, 76), Adams 1979; 1981, Plantinga 1970; 1974, pp. 70–77) are not counter-examples to this discriminatory principle, since the particularity of a particular is a formal property that is nothing over and above the particular itself.

  15. A consequence of the view of particulars as individual essences is that the difference between universals and particulars is only one of degree of generality, particulars as individual essences being the essences of the least degree of generality.

  16. One may think that the characterisation of a kind K by an attribute A could be defined in terms of the occurrent exemplification of A by substances of kind K, especially since I allow for non-present and non-actual unit exemplifications. This definition could run as follows: an attribute A characterises a kind K if and only if every substance of K exemplifies attribute A at at least one time and in at least one world. This definition would appear to give justice to the fact that characterisation indicates a generic tendency rather than a strict generality. However, such an extensional conception seems to be incompatible with the intensionality of laws of essence. Intuitively laws of essence are more than mere regularities. It is laws of essence that ground or explain regularities of occurrent exemplification, not the other way round.

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Acknowledgments

Research leading up to this article has been supported by the National Research Fund, Luxembourg and cofunded under the Marie Curie Actions of the European Commission (FP7-COFUND). The paper is based on talks given by the author at the international workshop “The Ontology of Relations: Material, Formal, Transcendental”, September 17–19, 2011, at the Maison des Sciences de l’Homme in Nancy (France) and at the international conference “Truth-Makers and Proof-Objects”, November 23–25, 2011, at the École Normale Supérieure in Paris (France). Special thanks for discussions and comments go to François Clémentz, Javier Cumpa, Kit Fine, Richard Gaskin, Gerhard Heinzmann, Pierre Livet, Kevin Mulligan, Frédéric Nef, Ulrich Nortmann, Manuel Rébuschi, Peter Simons, Andrew Spear, Niko Strobach, and an anonymous reviewer.

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    Luc Schneider

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Schneider, L. Whatever Binds the World’s Innermost Core Together Outline of a General Theory of Ontic Predication. Axiomathes 23, 419–442 (2013). https://doi.org/10.1007/s10516-012-9194-z

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