Against the Compositional View of Facts

It is commonly assumed that facts would be complex entities made out of particulars and universals. This thesis, which I call Compositionalism, holds that parthood may be construed broadly enough so that the relation that holds between a fact and the entities it ‘ties’ together counts as a kind of parthood. I argue, first, that Compositionalism is incompatible with the possibility of certain kinds of fact and universal, and, second, that such facts and universals are possible. I conclude that Compositionalism is false. What all these kinds of fact and universal have in common is a violation of supplementation principles governing any relation that may be intelligibly regarded as a kind of parthood. Although my arguments apply to Compositionalism generally, I focus on recent work by David Armstrong, who is a prominent and explicit Compositionalist.     

Predication and the Problem of Universals

Abstract

This paper contrasts the scholastic realisms of David Armstrong and Charles Peirce. It is argued that the so-called ‘problem of universals’ is not a problem in pure ontology (concerning whether universals exist) as Armstrong construes it to be. Rather, it extends to issues concerning which predicates should be applied where, issues which Armstrong sets aside under the label of ‘semantics’, and which from a Peircean perspective encompass even the fundamentals of scientific methodology. It is argued that Peirce's scholastic realism not only presents a more nuanced ontology (distinguishing the existent from the real) but also provides more of a sense of why realism should be a position worth fighting for.     

Nomic Universals and Particular Causal Relations: Which are Basic and Which are Derived?

Armstrong holds that a law of nature is a certain sort of structural universal which, in turn, fixes causal relations between particular states of affairs. His claim that these nomic structural universals explain causal relations commits him to saying that such universals are irreducible, not supervenient upon the particular causal relations they fix. However, Armstrong also wants to avoid Plato’s view that a universal can exist without being instantiated, a view which he regards as incompatible with naturalism. This construal of naturalism forces Armstrong to say that universals are abstractions from a certain class of particulars; they are abstractions from first-order states of affairs, to be more precise. It is here argued that these two tendencies in Armstrong cannot be reconciled: To say that universals are abstractions from first-order states of affairs is not compatible with saying that universals fix causal relations between particulars. Causal relations are themselves states of affairs of a sort, and Armstrong’s claim that a law is a kind of structural universal is best understood as the view that any given law logically supervenes on its corresponding causal relations. The result is an inconsistency, Armstrong having to say that laws do not supervene on particular causal relations while also being committed to the view that they do so supervene. The inconsistency is perhaps best resolved by denying that universals are abstractions from states of affairs.

Armstrong on Probabilistic Laws of Nature

D. M. Armstrong famously claims that deterministic laws of nature are contingent relations between universals and that his account can also be straightforwardly extended to irreducibly probabilistic laws of nature. For the most part, philosophers have neglected to scrutinize Armstrong’s account of probabilistic laws. This is surprising precisely because his own claims about probabilistic laws make it unclear just what he takes them to be. We offer three interpretations of what Armstrong-style probabilistic laws are, and argue that all three interpretations are incompatible either with some feature of Armstrong’s broader metaphysics or with essential features of his account of laws (or both).     

Scattered Exemplification and Many-Place Copulas

Can there be relational universals? If so, how can they be exemplified? A monadic universal is by definition capable of having a scattered spatiotemporal localization of its different exemplifications, but the problem of relational universals is that one single exemplification seems to have to be scattered in the many places where the relata are. The paper argues that it is possible to bite this bullet, and to accept a hitherto un-discussed kind of exemplification relation called ‘scattered exemplification’. It has no immediate symbolic counterpart in any Indo-European natural language or in any so far constructed logical language. In order to remedy this, a notion called ‘many-place copula’ is introduced, too.     

Indiscernible universals

Universals have traditionally thought to obey the identity of indiscernibles, that is, it has traditionally been thought that there can be no perfectly similar universals. But at least in the conception of universals as immanent, there is nothing that rules out there being indiscernible universals. In this paper, I shall argue that there is useful work indiscernible universals can do, and so there might be reason to postulate indiscernible universals. In particular, I shall argue that postulating indiscernible universals can allow a theory of universals to identify particulars with bundles of universals, and that postulating indiscernible universals can allow a theory of universals to develop an account of the resemblance of quantitative universals that avoids the objections that Armstrong’s account faces. Finally, I shall respond to some objections and I shall undermine the criterion of distinction between particulars and universals that says that the distinction between particulars and universals lies in that while there can be indiscernible particulars, there cannot be indiscernible universals.     

Recycling Religion: Lance Armstrong’s Postmodern Spirituality of Suffering and Survivorship

For much of his triple career as heroic cancer survivor, sports champion, and, latterly, fallen idol, Lance Armstrong, a professed atheist, has worn a silver necklace with a cross pendant. Why does he wear this Ur-symbol of Christian religious faith? Speculative answers range from ‘residual superstition’ to ‘fashion jewellery’ and ‘tactical deception’. Here, Armstrong’s own declared beliefs as refracted through his autobiographical accounts are analysed within a mono-mythic framework, with particular emphasis on ‘survivorship’, his implicit spirituality of suffering. The Armstrong case of a personalised construction of faith praxis sheds light on the eclectic ‘liquid’ religio-spiritual style of postmodernism. It helps portray the negotiation of the religious-in-the-secular, the sacred-in-the-profane (and vice versa), and illuminates the problematic nature of dualistic accounts of religion and spirituality in contemporary culture. Armstrong’s ‘recycling’ of traditional religious iconography out of context of origin demonstrates the persistence, durability, and elasticity of religio-spiritual symbolic culture.     

Against instantiation as identity

Some people object to realism about universals because they think that instantiation, the connection between something and the universals that characterize it, is too mysterious. Baxter and Armstrong try to make instantiation less mysterious by taking it to be a kind of partial identity. However, I argue that their accounts of instantiation, and any similar ones, fail.     

Structural Universals as Structural Parts: Toward a General Theory of Parthood and Composition

David Lewis famously argued against structural universals since they allegedly required what he called a composition “sui generis” that differed from standard mereological composition. In this paper it is shown that, although traditional Boolean mereology does not describe parthood and composition in its full generality, a better and more comprehensive theory is provided by the foundational theory of categories. In this category-theoretical framework a theory of structural universals can be formulated that overcomes the conceptual difficulties that Lewis and his followers regarded as unsurmountable. As a concrete example of structural universals groups are considered in some detail.     

Towards a theory of communicative competence

In this, the second of two articles outlining a theory of communicative competence, the author questions the ability of Chomsky's account of linguistic competence to fulfil the requirements of such a theory. ‘Linguistic competence’ for Chomsky means the mastery of an abstract system of rules, based on an innate language apparatus. The model by which communication is understood on this account contains three implicit assumptions, here called ‘monologism’, ‘a priorism’, and ‘elementarism’. The author offers an outline of a theory of communicative competence that is based on the negations of these assumptions. In opposing the first two assumptions he introduces distinctions, respectively, between semantic universals which process experiences and those that make such processing possible, and between semantic universals which precede all socialization and those that are linked to the conditions of potential socialization. Against elementarism, he argues that the semantic content of all possible natural languages does not consist of combinations of a finite number of meaning components. Differences in systems of classification preclude this, and such differences can be seen to infect all respects of intercultural comparison. Using the notion of ‘performative utterance’, the author elucidates the role of dialogue‐constitutive universals as part of the formal apparatus required of a”; speaker's capacity to communicate. He then notes what would be required of a general semantics based on a theory of communicative competence; and finally points out how this theory might be used for social analysis.     

Exemplification as molecular function

Since the publication of Universals and Scientific Realism (Armstrong 1978a, b) until Sketch for a Systematic Metaphysics (Armstrong 2010), via Universals: An Opinionated Introduction (Armstrong 1989), a World of States of Affairs (Armstrong 1997), and Truth and Truthmakers (Armstrong 2004), David Armstrong has developed one of the most influential theories of instantiation in contemporary analytic metaphysics (see, for example, Lewis, in Aust J Phil 61(4), 343–377, 1983; Baxter in Aust J Phil, 79, 449–464, 2001; Forrest, in Aust J Phil, 83, 213–228, 2006). Instantiation has been advocated by Armstrong to give a solution to what he has called the “pressing problem” of “the multiple location of property universals” (Armstrong, in Universals: An opinionated introduction. University Press, Cambridge, 1989, pp. 89–90). Here I argue that Armstrong’s theory of instantiation fails to solve the problem because it involves two kinds of instantiation to account for particulars “having” and “sharing” universals. As a viable alternative to Armstrong’s theory, I propose a theory of instantiation capable of accounting for both phenomena in a univocal way.     

The Partial Identity Account of Partial Similarity Revisited

This paper provides a defence of the account of partial resemblances between properties according to which such resemblances are due to partial identities of constituent properties. It is argued, first of all, that the account is not only required by realists about universals à la Armstrong, but also useful (of course, in an appropriately re-formulated form) for those who prefer a nominalistic ontology for material objects. For this reason, the paper only briefly considers the problem of how to conceive of the structural universals first posited by Armstrong in order to explain partial resemblances, and focuses instead on criticisms that have been levelled against the theory (by Pautz, Eddon, Denkel and Gibb) and that apply regardless of one’s preferred ontological framework. The partial identity account is defended from these objections and, in doing so, a hitherto quite neglected connection—between the debate about partial similarity as partial identity and that concerning ontological finitism versus infinitism—is looked at in some detail.     

On the mereological structure of complex states of affairs

The aim of this paper is to elucidate the mereological structure of complex states of affairs without relying on the problematic notion of structural universals. For this task tools from graph theory, lattice theory, and the theory of relational systems are employed. Our starting point is the mereology of similarity structures. Since similarity structures are structured sets, their mereology can be considered as a generalization of the mereology of ordinary sets. In general, the mereological systems arising from similarity structures turn out to be not Boolean but Heyting systems. Employing Armstrong??s notion of thick particulars, similarity structures are shown to capture the mereological structure of complex ??chemical states of affairs?? such as ??being butane?? or ??being isobutane??; structural universals are not needed.     

Tooley’s account of the necessary connection between law and regularity

Fred Dretske, Michael Tooley, and David Armstrong accept a theory of governing laws of nature according to which laws are atomic states of affairs that necessitate corresponding natural regularities. Some philosophers object to the Dretske/Tooley/Armstrong theory on the grounds that there is no illuminating account of the necessary connection between governing law and natural regularity. In response, Michael Tooley has provided a reductive account of this necessary connection in his book Causation (1987). In this essay, I discuss an improved version of his account and argue that it fails. First, the account cannot be extended to explain the necessary connection between certain sorts of laws—namely, probabilistic laws and laws relating structural universals—and their corresponding regularities. Second, Tooley’s account succeeds only by (very subtly) incorporating primitive necessity elsewhere, so the problem of avoiding primitive necessity is merely relocated.     

Platonism and metaphor in the texts of mathematics: Gödel and Frege on mathematical knowledge

In this paper, I challenge those interpretations of Frege that reinforce the view that his talk of grasping thoughts about abstract objects is consistent with Russell's notion of acquaintance with universals and with Gödel's contention that we possess a faculty of mathematical perception capable of perceiving the objects of set theory. Here I argue the case that Frege is not an epistemological Platonist in the sense in which Gödel is one. The contention advanced is that Gödel bases his Platonism on a literal comparison between mathematical intuition and physical perception. He concludes that since we accept sense perception as a source of empirical knowledge, then we similarly should posit a faculty of mathematical intuition to serve as the source of mathematical knowledge. Unlike Gödel, Frege does not posit a faculty of mathematical intuition. Frege talks instead about grasping thoughts about abstract objects. However, despite his hostility to metaphor, he uses the notion of ‘grasping’ as a strategic metaphor to model his notion of thinking, i.e., to underscore that it is only by logically manipulating the cognitive content of mathematical propositions that we can obtain mathematical knowledge. Thus, he construes ‘grasping’ more as theoretical activity than as a kind of inner mental ‘seeing’.

     

No Fact of the Matter

One familiar form of argument for rejecting entities of a certain kind is that, by rejecting them, we avoid certain difficult problems associated with them. Such problem-avoidance arguments backfire if the problems cited survive the elimination of the rejected entities. In particular, we examine one way problems can survive: a question for the realist about which of a set of inconsistent statements is false may give way to an equally difficult question for the eliminativist about which of a set of inconsistent statements fail to be ‘factual’. Much of the first half of the paper is devoted to explaining a notion of factuality that does not imply truth but still consists in ‘getting the world right’. The second half of the paper is a case study. Some ‘compositional nihilists’ have argued that, by rejecting composite objects (and so by denying the composition ever takes place), we avoid the notorious puzzles of coincidence, for example, the statue/lump and the ship of Theseus puzzles. Using the apparatus developed in the first half of the paper, we explore the question of whether these puzzles survive the elimination of composite objects.     

Emergentism and supervenience physicalism

I argue that it is intuitive and useful to think about composition in the light of the familiar functionalist distinction between role and occupant. This involves factoring the standard notion of parthood into two related notions: being a parthood slot and occupying a parthood slot. One thing is part of another just in case it fills one of that thing's parthood slots. This move opens room to rethink mereology in various ways, and, in particular, to see the mereological structure of a composite as potentially outreaching the individual entities that are its parts. I sketch one formal system that allows things to have individual entities as parts multiple times over. This is particularly useful to David Armstrong, given Lewis's charge that his structural universals must do exactly that. I close by reflecting upon the nature and point of formal mereology.     

PRESENTISM,PERSISTENCE AND COMPOSITION

Pace Benovsky's ‘Presentism and Persistence,’ presentism is compatible with perdurantism, tropes and bundle‐of‐universals theories of persisting objects. I demonstrate how the resemblance, causation and precedence relations that tie stages together can be accommodated within an ersatzer presentist framework. The presentist account of these relations is then used to delineate a presentist‐friendly account of the inter‐temporal composition required for making worms out of stages. The defense of presentist trope theory shows how properties with indexes other than t may be said to exist at t. This involves an account of how times other than t exist at t, and how times may be multiply located at any given time. Benovsky's objection to bundles of universals is shown to assume that a bundle of properties must have the properties of its element properties.     

Catachrestic Plural Forms. Gregory of Nyssa and Theodore Abū Qurrah on Naming and Counting Essences

The fourth-century thinker and theologian Gregory of Nyssa was a convinced realist about universals. According to him, there is just one substance man for all the individuals of the species man and this universal substance is completely instantiated by each individual. In two of his treatises – the Ad Ablabium and the Ad Graecos – he draws linguistic consequences from this realist position. This enquiry results in the thesis according to which it is incorrect to use natural kind terms (such as names of species) in the plural form, because that would involve stating a plurality of substances, when in fact there is just one substance for all the individuals of a given kind. In consequence, since the substance of all individual human beings is the same, the word ‘man’ can only be used adequately in the singular form. In this contribution, Gregory's reasoning is reconstructed. In the second part of the paper, the posterity of his theory and its endorsement by Theodore Abū Qurrah at the turn of the eighth and ninth centuries are examined.