Abstract
Primary to both ontology and epistemology is the attributional union that properties and relations have with their subjects. Yet, the tradition’s understanding of attribution has been assessed as shallow, and its contemporary analysis deemed locked in a non-progressing stalemate. Central here is the historically dominant inherence/constituent construal of attribution, what, I argue, has remained obscure and unattended as to its background assumptions and their implications. On the analysis offered herein, I make precise and detail errors of the defining assumptions of inherence theory and the two-tiered nature it requires of attribution. Brought into relief will be the four elements involved in every attributional union, and what are the errors in a sequence of collapsing identities among them that define inherence theory. Along the way, clarification and warrant is provided for the alternative theses and their implications defining an adherence theory of attribution, key features synopsized in the last section.
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Notes
Under the terms “constituent vs. relational” the current debate goes back to Wolterstorff (1991). Galluzzo and Loux (2018) gives papers on both theories. Also for relationalism see van Inwagen (2011), and for additional defenses of “constituent” ontology and references see Moreland (2013) and Yang (2018). “Relationalism” is sometimes defined to include class nominalism where a property F is identified with the set of subjects it characterizes, and thus F as such has as part of its composing being each one of its subjects. In contrast, by attributional adherence as used herein an attribute and its subject(s) share no being in common—the connectedness is completely external. A subject a can be composed of attributes (particularized as “instances”) each having subjects which jointly as networks of facts compose a, but none of these composing attributes (as instances) have a as a subject. Something approaching this understanding of attribution has been argued as a best fit for modern physics, especially in regard to issues of quantum entanglement and space-time, e.g., see Morganti (2019) and Ladyman (2020).
The analysis offered herein falls under what in the literature is the general topic of “Groundedness” (and related topic of “Truthmaking”). For an overview of the topic of groundedness and references, see Bliss & Trogdon (2014).
Distinguishing attribution from mere mereological conjunction, the attributional union within facts, e.g., as in :Is-a-Planet(a), necessitates the existence of some and the absence of other attributional unions and so would-be facts, e.g., the existence of :Is-Extended(a) and :Has-Mass(a), and the absence of :Is-a Meteor(a) and :Is-a-Galaxy(a). Yet, for the attributional union construed as a unity independent of any prerequisite relevance between the attribute and its subject(s)—as the unity by associations and the extensional unities of sets, sums, and Aristotelian “heaps”—then the unity and so existence of any such “fact” would not imply nor preclude any other like “attributional” union and so “fact.” D. M. Armstrong, for example, once held such a view of facts under a Humean inspired “Doctrine of Independence” and the correlative view that all attribution is contingent (1997, pp. 139–147), but latter favored an inherence theory requiring the opposite extreme of all attributions being necessary (2005). On the following adherence analysis, it is possible to account for the having of both contingent and necessary attributions.
See note 11.
Abetting his inherence theory, Aristotle may have confused these two senses of containment, e.g., see Cate. 15b17-26 and Meta. 1023a7-17.
This is a basis for a “power” or “dispositional essentialist” theory of attribution found in the literature, e.g., Martin (1997), Martin & Heil (1999), Molnar (2003), and Mertz (2016). Intensions in being jointly essential to attribution and about (“toward”) would-be other conforming entities would identify them as the primary source of dispositionality.
I note that the herein proposed combinatorial theory of attribution differs profoundly form the “operator” theory advanced by Peter Forrest (2006, 2018). Though Forrest is open to attributes being “causally efficacious,” he holds they need not be treated as such. Moreover, for him attributes proper are universals, contrary to the arguments herein, and the fact that if attributes are causally efficacious in unifying themselves to their subjects, these causal acts would make the attributes particular and not universal. Also, Forrest would have relations reduce to properties which I argue is impossible.
It is the criterial nature of intensions which implies their status as universals. Realism in regard to universals has two forms: (a) an attribute Is-F is construed as identical to its intension F and taken to be numerically the same attribute in attributional unions with numerically different F-conforming subject n-tuples, or (b), as implied by adherence theory (below), an intension F is numerically the same component in each attribute instance Is-Fi, each instance individuated and proprietary to an F-conforming n-tuple. With the former the n-tuples are said to exactly-resemble-F-ly, whereas with the latter and in a primary sense it is the instances, Is-Fi, Is-Fj, Is-Fk, …, that among themselves exactly-resemble-F-ly. In either case and due to its criterial nature, an intension F is numerically identical across its different attributional unions, i.e., is a universal. This follows from the fact that otherwise for two numerically different but both F-conditioned attributional unions, and so derivative exact F-resemblances, if the intensions involved, F and F′, were themselves numerically different, then F and F′ each precisely as an intension—as a criterion for would-be conforming subjects—would have to be different from the other. And, F and F′ would as non-identical criterions have to be the specifications of different subject-conditions, i.e., be non-synonymous and so define completely different attributes (with possibly different extensions), and between which there would be no exact resemblances. The insights here are not possible when under inherence theory intensions are identified with their grounds.
The proposed epistemology of structural isomorphism is one of indirect representational realism. Defining of it, intensions F, though necessary components of attributes Is-F and their facts, both extra-conceptual and conceptual, need not as conceptual be numerically nor specifically the same as those that are extra-conceptual in order to be informative about the extra-conceptual. This is contrary to the Aristotelian-Thomist thesis of “identity” of knower and known. Under epistemic structuralism, real/unreduced intension-conditioned relations—where for each the descriptive conditions had by one relatum are, via the inter-linking relation, connected necessarily to conditions descriptive of the relation’s other relata—as such form extra-conceptual and conceptual organized structures. And equally importantly, relations form trans-structural correspondences that in chains of so linked structures preserve representational isomorphisms across them, e.g., across the extra-conceptual—conceptual boundary. Information is passed via sameness of structure, not sameness of intension or attribute (As locus classicus, Russell 1948, pp. 250–255, 460–475; also Mertz 1996, pp. 33–35). This is possible in an ontology of attribute adherence, but not in one of attribute inherence (e.g., as adopted by Aristotle and Aquinas) that requires the reductive elimination of relations (below).
The inclusive domain of intensions herein differentiates them from G. Frege’s “senses” (Sinne), the latter not generated or sustained in their existences by mental activities (Frege 1952).
Frank Lewis (2011) describes Aristotle’s adoption of the I-Schema’s two-stage attribution. There are texts indicating how Aristotle would have the I-Schema handle other forms of attribution. For example, at Cate. 1b10-15 the attribution of the genus of a species, e.g., white is a color, would be ontologically equivalent to (x)(Is-White(x) & Is-Colored(x)), where x is a primary substance, e.g., Socrates. The I-Schema would then be applied twice here. And for accidental attribution, e.g., Socrates is white, at Physics 190a13-21 and Meta. 1015b16-34, Aristotle would apparently have the accident White be a constituent of the peculiar whole Socrates-as-White (these referred to in the literature as “kooky” entities; see Cohen (2008)). Here Is-White(Socrates) ≡ (Socrates equals-as-contingently-coinciding-with Socrates-as-White), where Is-White(Socrates-as-White) ≡ (Socrates-as-White = (Is-White in an essential union with the essential components of Socrates [the resultant whole being Socrates-as-White])). For Aristotle on the inherence of accidents in their subjects see Lewis (1982).
This attribution of a substantial form Is-F on prime matter is a problematic exception to Aristotle’s inherence theory: prime matter has no attributes and is simple, and so cannot have Is-F as an attribute or part. More obvious as a problem for Aristotle’s inherence theory of attribution is that for attributes from categories other than substance they are held ontically posterior to substance (e.g., Meta. 1088b4), and yet attributes as elements of their subjects would be ontically prior to these subjects (Meta. 1070b3-4). Both problems are eliminated with adherence theory.
Along Aristotelian lines, James Moreland (2013) has proposed a constituent ontology conforming to the I-Schema and utilizing bare particulars. For the attribution Socrates is human, this assays as: Human(Socrates) ≡ (Socrates = (Human “tied-to” (U) a bare particular (Y))). Here, Human is a universal and “tied-to” is a non-attribute, subject-irrelevant connector, i.e., what can be but arbitrary association.
Aristotle’s insight in regard to energeia is, I have argued (Mertz 2016, pp. 188ff.), fundamental to and explanatorily potent for an adherence theory of attribution. In order for an attribute to achieve a unity with—adhere to—a subject (or subjects) with which it shares no being, the attribute must be the sustaining cause (by Bradley’s Regress) of an act of unification whose effected union is external to it. An attributional “tie” or “nexus,” equally had by properties and relations, is not passive containment, but rather an external-achieving intension-conditioned combinatorial-act.
To be seen, under the I-Schema and the erroneous theses implicit in INH, every intension F is identical to an attribute Is-F which exists as a subject of itself—Is-F(Is-F). In this way, the intension Attributeless-Entity would indeed have an extension—itself, the inherence assumptions then giving plausibility to it being a legitimate entity.
I take this to be the unity Aristotle intended as had by “heaps” in contrast to any attribute-unified whole, and I have argued that such unification, idealized and hypostatized, would account for theoretical entities of Set Theory and Mereology (Mertz 2016, pp. 53–66). To assume all possible pluralities of entities have been associated, and then abstracting away the idealized associations and the requisite minds, is to get what is posited by Classical Extensional Mereology as the Axiom of Unrestricted Composition: Whenever there exist some things, there exist a unified composite (a sum or fusion) of those things. (I note that the father of set theory, Georg Cantor, did not eliminate the role of mind in accounting for the unities of all possible sets, attributing these unifications rather to the combinatorial agency of the Divine Intellect. See Hallett (1984).).
For arguments that non-symmetric, including asymmetric, relations cannot be reduced to symmetric relations see MacBride (2018).
Consistent with what was seen under the I-Schema and reiterated below, this option of an attribute having grounds identical to its subject is implied by I-B and subsumed I-A.
See Physics 185a30-32, Meta. 1028a17-25, 1038b27-28, 1069a25, 1089b23-25.
Parmenides, 130c-e.
For more details on how the adherence analysis offered contributes to clarifying this and the related classic distinctions between intrinsic and extrinsic attributes, and analytic and synthetic propositions, see Mertz (2016, pp. 173–187.
For an explanation of “formal” or “continuous unity” in this context see Mertz (2016, pp. 220–228). Aristotle characterized this continuous unity as that among the distinguishable but not distinct. See Physics 227a9-16; Meta. 1014b21-26, 1023b32-33. In contemporary terms this type of unity among the non-identical is characterized as “closer than relation,” but, more accurately, it is “closer than attribution.” (Attribution itself is “closer than association,” with association the “loosest” form of unity, e.g., the unity of a random “heap”.) The formal unity of attribute instances stands in contrast to that of nominalistic tropes construed as homogeneously simple entities with yet two constituent aspects—one qualitative, F (e.g., the intension Squareness), and the other an individuator. It has been suggested that this “plural-simplicity” is possible by a simple trope being numerically the same ground for both a qualitative and an individuating aspect. The apparent assumptions here are that: these two aspects of a trope Fi are both attributes of it; are identical to their respective grounds, fF and fi (inherence thesis I-B); and that the latter grounds are identical, i.e., fF = fi. But what this would mean is that whenever there were grounds fi for an aspect of individuation, which every trope regardless of its specific qualitative aspect F will have, there would be as identically the same grounds fF for the specific qualitative aspect F, and so every trope would have to be of the same qualitative nature F. Thus, every trope would have to have any qualitative aspect that any trope has, and so every trope would be equally square, circular, red, green, etc.
Mertz (2016, pp. 206ff.).
It is worth observing that on the analysis above what gets grounded is an attribute on a subject n-tuple, and the two are always non-identical. Hence, a grounding relation cannot be reflexive, i.e., it is not the case for any attribute Is-F that Is-Grounded-in(Is-F,Is-F). It might be thought that, to the contrary, there are attributes such as Is-Abstract that as a subject grounds itself as an attribute—that we would have the fact :Is-Abstract(Is-Abstract). However, on the adherence theory implication that attributes are individuated as instances unique to their subject n-tuples, we would actually have with this example the facts :Is-Abstracti(intension Abstract) and :Is-Abstractj(attribute Is-Abstracti), both where attributes Is-Abstractj, Is-Abstracti, and the intension Abstract are all pairwise non-identical.
These latter types of unity, respectively, inter-attribute and emergent, plus unity by association (all these unities being among the discrete), plus formal unity (unity among the continuous), are, I propose, in their various relevances to attribution, a synthesized inventory of all forms of composition. See Mertz (2016, pp. 250–266).
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Mertz, D.W. The Classic Inherence Theory of Attributes: Its Theses and Their Errors. Acta Anal 38, 495–516 (2023). https://doi.org/10.1007/s12136-022-00534-z
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DOI: https://doi.org/10.1007/s12136-022-00534-z