Two Crucial Problems: Bradley’s Regress and Self-exemplification

One important motivation, possibly the main one, behind attempts at analysis such as the ones above is the worry to avoid the so-called Bradley’s regress regarding exemplification (Baxter 2001, 449; Munford, 2007, 185). One construal of the regress that has passed into the literature goes like this (although it is not clear to what extent Bradley himself had this version in mind; for references to analogous regresses prior to Bradley’s, see Gaskin 2008, ch. 5, §70). Suppose that the individual a has the property F. For a to instantiate F it must be linked to F by a (dyadic) relation of instantiation, I1. But this requires a further (triadic) relation of instantiation, I2, that connects I1, F and a, and so on without end. At each stage a further connecting relation is required, and thus it seems that nothing ever gets connected to anything else. This regress has traditionally been regarded as vicious (see, e.g., Bergmann 1960), although philosophers such as Russell (1903, §55) and Armstrong (1997, 18–19) have argued that it is not. In doing so, however, they seem to take for granted the fact that a has the property F (pretty much as in thebrute fact approach; see below) and go on to see a’s and F’s instantiating I1 as a further fact that is merely entailed by the former, which in turn entails a’s, F’s and I1’s instantiating I2, and so on. This way of looking at the matter tends to be regarded as a standard response to the regress. But those who see the regress as vicious assume that the various exemplification relations are introduced in an effort to explain the very existence of the fact that a has the property F. Hence, from their explanatory perspective, taking the fact in question as an unquestioned ground for a chain of entailments is beside the point (cf. Loux 2006, 31–36; Vallicella 2002). It should be noted, however, that this perspective suggests a distinction between an ‘internalist’ and an ‘externalist’ version of the regress (in the terminology of Orilia 2006a). In the former, at each stage we postulate a new constituent of the fact, or state of affairs, s, that exists insofar as a has the property F, and there is viciousness because s can never be appropriately characterized. In the latter, at each stage we postulate a new, distinct, state of affairs, whose existence is required by the existence of the state of affairs of the previous stage. This amounts to admitting infinite explanatory and metaphysical dependence chains, but, according to Orilia (2006, §7), since no decisive arguments against such chains exist, the externalist regress should not be viewed as vicious. An extensive defense of a similar approach can be found in Gaskin 2008. See Maurin 2015 for a sustained criticism.

A typical line for those convinced that the regress is vicious has consisted in proposing that instantiation is not a relation, at least not a normal one. Some philosophers hold that it is a sui generis linkage that hooks things up without intermediaries. Strawson (1959), following W. E. Johnson, calls it a non-relational tie and Bergmann (1960) calls it a nexus. Broad likened instantiation to metaphysical glue, noting that when we glue two sheets of paper together we don’t need additional glue, or mortar, or some other adhesive to bind the glue to the paper (Broad 1933, 85). Glue just sticks. And instantiation just relates. It is metaphysically self-adhesive. An alternative line has been to claim that there is no such thing as instantiation at all and that talk of it is just a misleading figure of speech. At this point it is natural to resort to metaphors like Frege’s claim that properties have gaps that can be filled by objects or the early Wittgenstein’s suggestion (if we read him as a realist about properties) that objects and properties can be hooked together like links in a chain. Although most realists about properties nowadays still tend to adopt one or another of these strategies, Vallicella (2002) has offered a penetrating criticism of them. His basic point is that, if a has property F, we need an ontological explanation of why F and a happen to be connected in such a way that a has F as one of its properties (unless F is a property that ahas necessarily). But none of these strategies can provide this explanation. For example, the appeal to gaps is pointless: F has a gap whether or not it is filled by a (for example, it could be filled in by another object), and thus the gap cannot explain the fact that a has F as one of its properties.
Before proposing the above-discussed account of exemplification as partial identity, Armstrong (1997, 118) has claimed that Bradley’s regress can be avoided by taking a state of affairs, say x’s being P, as capable by itself of holding together its constituents, i.e. the object x and the propertyP. Thus, there is no need to invoke a relation of exemplification linking x and P in order to explain how x and P succeed in giving rise to a unitary item, namely the state of affairs in question. There seems to be a circularity here for it appears that we want to explain how an object and a property come to be united in a state of affairs by appealing to the result of this unification, namely the state of affairs itself. But perhaps this view can be interpreted as simply the idea that states of affairs should be taken for granted in a primitivist fashion without seeking an explanation of their unity by appealing to exemplification or otherwise; this brute fact approach, as we may call it, seems to be Van Inwagen’s standpoint (1993, 37).
Lowe (2006) has tried to tackle Bradley’s regress within his multifarious approach to exemplification. In his view, characterization, instantiation and exemplification, qua ‘formal,’ are to be sharply distinguished from garden-variety relations such giving or loving, which guarantees that characterization, instantiation and exemplification do not give rise to Bradley’s regress (Lowe 2006, 30, 80, 90). In explaining this, Lowe vacillates between taking them to be internal and declaring them non-existent, (Lowe 2006, 111, 167). Perhaps, they are considered non-existent precisely because internal, but separating internality from non-existence may be a better choice, since after all formal relations are in Lowe’s ontological inventory. Moreover, it is really their internality, rather than lack of existence, that is appealed to in the attempt to avoid Bradley’s regress, as shall now illustrate by turning back to the above Fido example. What a mode instantiates and what it characterizes belongs to its essence. In other words, a mode cannot exist without instantiating the attribute it instantiates and characterizing the object it characterizes. Hence, mode b, by simply existing, instantiates attribute B and characterizes Fido. Moreover, since exemplification (the occurrent one, in this case) results from “composing” characterization and instantiation, b’s existence also guarantees that Fido exemplifies B. According to Lowe, we thus have a bunch of truths, that b characterizes Fido, that b instantiates B, and that Fido exemplifies B (i.e., is barking), all of which are made true by b. Hence, there is no need to postulate as truthmakers states of affairs with constituents, Fido and b, related by characterization, or b and B, related by characterization, or Fido and B, related by exemplification. This, in Lowe’s opinion, eschews Bradley’s regress, since this arises precisely because we appeal to states of affairs with constituents in need of a glue that contingently keep them together. Nevertheless, there is no loss of contingency in Lowe’s world picture, for an object need not be characterized by the modes that happen to characterize it. Thus, for example, mode b might have failed to exist and there could have been a Fido silence mode in its stead, in which case the proposition that Fido is barking would have been false and the proposition that Fido is silent would have been true. One may wonder however what makes it the case that a certain mode is a mode of just a certain object and not of another one, say another barking dog. Even granting that is essential for b to be a mode of Fido, rather than of another dog, it remains true that it is of Fido, rather than of the other dog, and since b might have failed to exist, one may still think that this being of is also a contingent glue. The suspicion then is that the problem of accounting for the relation between a mode and an object has been traded for the Armstrongian one of what makes it the case that a property-universal P and an object x make up the state of affairs x’s being P. But the former problem, one may urge, is no less thorny than the latter (for a take on Bradley’s regress analogous to Lowe’s and worries along the lines of those voiced here, see Simons 2011 and MacBride 2011, respectively).
As it should be clear from this far from exhaustive survey, Bradley’s regress deeply worries ontologists and the attempts to tame it keep flowing (see, e.g., Peacock 2012, for an approach resorting to Russell’s notion of a relating relation, as opposed to a relation that is not doing its relating work; Tegtmeier 2013, for a view according to which a fact itself grounds its unity; Schneider 2013 for an appeal to ‘unrepeatable nexuses’ in the context of an Aristotelian framework in the spirit of the one defended in Lowe 2006).
We have dealt primarily, more or less explicitly, with the exemplification of properties by items other than properties, e.g., ordinary objects. But presumably properties may also exemplify properties. For example, if properties are abstract objects, as is usually thought, then seemingly every property exemplifies abstractness. But then we should also grant that there is self-exemplification, i.e., a property exemplifying itself. For example, abstractness is itself abstract and thus exemplifies itself. Self-exemplification however has raised severe perplexities since the early days of Plato.
In various passages throughout his dialogues Plato appears to hold that all properties exemplify themselves, when he claims that Forms (which are often taken to be his version of properties) participate in themselves. This claim serves as a premise in what is known as his third man argument which, he seems to think, may show that the very notion of a Form is incoherent (Parmenides, 132ff). But it is not clear why we should hold that all properties exemplify themselves (Armstrong 1978, 71). For instance, why should we think that honesty itself is honest?
A more serious worry related to self-exemplification is Russell’s famous paradox. If every predicative expression corresponds to a property, then the expressions ‘is a property that does not instantiate itself’ should do so. This raises the question: does this property instantiate itself? Suppose that it does. Then it is a property that does not instantiate itself; so if it does instantiate itself, it doesn’t instantiate itself. Now suppose that it does not instantiate itself. Then it is one of those properties that do not instantiate themselves; so it does instantiate itself. Such a property, which instantiates itself if and only if it does not instantiate itself, appears to defy the laws of logic, at least classical logic. This puzzle and related conundrums still occupy logicians and no consensus on how to eschew them is in sight; see on this §§7.2 and 8.

3. Traditional Explanations

Properties are typically introduced to help explain or account for phenomena of philosophical interest, especially in doing ontology. The existence of properties, we are told, would explain qualitative recurrence or help account for our ability to agree about the instances of general terms like ‘red.’ In the terminologies of bygone eras, properties save the phenomena; they afford a fundamentum in re for things like the applicability of general terms. Nowadays philosophers make a similar point when they argue that some phenomenon holds because of or in virtue of this or that property, that a property is its foundation or ground, or that a property is the truthmakerfor a sentence about it. These expressions signal explanations (for a defense of the legitimacy of ontological explanations, cf. Swoyer 1999; for qualms about an explanatory recourse to properties, see Quine 1961, 10; Quinton 1973, 295).
In seeking explanations in ontology (as in other disciplines) we must frequently weigh tradeoffs between various desiderata, e.g., between simplicity and comprehensiveness, and even between different kinds of simplicity. But one tradeoff is so pervasive that it deserves a name, and we will call it the fundamental ontological tradeoff. The fundamental ontological tradeoff reflects the perennial tension between explanatory power and epistemic risk, between a rich, lavish ontology that promises to explain a great deal and a more modest ontology that promises epistemological security. The more machinery we postulate, the more we might hope to explain—but the harder it is to believe in the existence of all the machinery. As we shall see in the following, the inevitability of this tradeoff keeps playing a crucial role in current discussions of properties.

Properties keep being invoked to explain a very wide range of phenomena. Insofar as each of the explanations is plausible, it serves as part of a cumulative case for the existence of properties. In the following subsections we shall survey several of the most common explanations philosophers have asked properties to provide (for a longer list see Swoyer 1999, §3). In the next section we shall discuss more novel attempts to appeal to properties in providing explanatio

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Two Crucial Problems: Bradley’s Regress and Self-exemplification

3. Traditional Explanations

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Two Crucial Problems: Bradley’s Regress and Self-exemplification

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