The previous section revealed that holism is an established concept which dovetails neatly with an in-discrete view of connection, and which enables talk of mutual
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interdependence to proceed without privileging either the individual or the totality. In the work of Donald Davidson holism also has broader implications for an understanding of how the world is. In this section I look at a philosophical discourse which has a lot to say about what we say about how the world is, the discourse of vagueness, and which some would like to extend to the world directly. One implication of in-discreteness, as I have been presenting it, is that belief in the distinctness, completeness and determinateness of objects of all kinds is undermined. To some commentators this emphasis on indeterminacy may seem to bring in-discreteness close to the much better documented concept of vagueness. This section will start by looking at vagueness to distinguish between the epistemic and linguistic type on one hand and ontological forms on the other, followed by a look at how vagueness in the world has been treated, before discussing the implications of Davidson’s model of holism for indeterminacy. The conclusion will be that indeterminacy is not the same as epistemic vagueness as it is primarily ontological. Further, hopeful talk of “ontological vagueness” is misguided, as the vagueness concept does not provide the metaphysical tools to get to grips with an indeterminate reality. The distinction between indeterminacy and vagueness is clear once one realises that indeterminacy does not imply a lack of precision, but only the absence of uniqueness.
Vagueness
It is to be expected that there is no one clear definition of vagueness, if you take the word itself seriously. According to Dorothy Edgington223 the notion of vagueness has much in common with the idea of uncertainty of beliefs. In both cases there is an apparent absence of a fact of the matter, and this can lead to problems when an attempt is made to elucidate the “fact” by progressive clarification. In the vagueness literature “fact” means an objective situation which makes a description uniquely true, and to the extent that a belief in vagueness is associated with a belief that a precise description of that fact is in-principle possible, then the holder of such a belief is a realist. It is not the clarification, but the very existence and nature of the fact which is at stake in the
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(1997), “Vagueness by degrees”. In Vagueness: A reader (Ed. Rosanna Keefe & Peter Smith, pp 294- 316). (Cambridge, MA; MIT Press/Bradford Books).
distinctions between epistemic and ontological vagueness, and between vagueness and indeterminacy, as I will show.
In the case of descriptions, the term “bald” is unproblematic when applied to a man with zero hairs on his head, and clearly wrong when used to describe presidential hopeful John Kerry. Troubles arise when clarification of just what “bald” really means is attempted by progressively refining the definition, and this is easily done, from either end of the hairiness scale, by unproblematically adding (or subtracting) a hair. A bald head plus one hair is still bald, a hairy head minus one hair is still hairy. Each individual increment fails to threaten the bald/hairy description. Unfortunately, after a few million iterations of impeccable logic we discover that the now hairy head is still entitled to the descriptor “bald”, while the now shiny dome is still entitled to the descriptor “hairy”. We have been led astray by the Sorites (or “heap”) Paradox. “Bald” is a vague term. We are led astray by our belief that there exists a determinate point, before which it is nearly certain that “bald” is a true description, and beyond which it is nearly certain that “bald” is a false description. There is a maddeningly ill-defined point at which "bald" should cease to be true. This point, the existence of which is the focus of my interest in vagueness, is the so-called “borderline” case which is said to be so distinctive of vagueness.
The way borderline cases operate can be clearly seen in the baldness example. It is obvious that the possessor of the shiny dome and the possessor of quite a large number of hairs which nevertheless struggle to hide their shiny dome will both fit comfortably into the category “bald”. Conversely, John Kerry, and the possessor of a similar hairstyle minus the aforementioned large number of hairs will both be regarded as hairy. The trouble arises in that intermediate zone when the descriptor “bald” doesn’t quite seem to fit, and it is here that the borderline cases occur. Two different ways of thinking about this intermediate zone exist, with different logical implications, though they are symmetrical. One way says that someone in the zone is neither bald nor not bald - in other words, the zone represents a gap between the way “bald” and its complement can be applied, hence “truth” does not apply to any cases falling in the gap. The other way says that such a person is both bald and not bald - in other words, “bald” and its complement overlap, leading to a so-called glut where being “bald-and-not-bald” results in too many “truths”.
Notice that I have actually introduced two different ways of thinking about vagueness in the course of the baldness example, though they are not usually disentangled. The first was the notion of difference by degrees, which allows a sorites- style argument to progressively lead us by unimpeachable premises to a paradoxical conclusion. The second was the absence of a special tipping-point, resulting in borderline cases, which is a way of problematising just some of those differences. The former approach, in the view of Otavio Bueno and Mark Colyvan224, gives a purer vision of vagueness because it is not beholden to either of the alternatives which an emphasis on borderline cases must confront – a commitment to either gaps or gluts.
I mentioned in the first paragraph that vagueness operates in the realm of linguistic description, and everything that followed apparently reinforced this. Vagueness resulted from trying to say or think about things, and it was an exact characterisation of the thing which proved impossible to clarify satisfactorily. The borderline cases approach tends to group together cases with seductively clear applications: Those surely in (“bald”), those surely not in (“not bald”), and the borderline cases which are disputable. Here, the surety of most descriptions is acknowledged while space is left for commonsense uncertainty. Of course the borders of the borders will then be in dispute, and so on, so what this process reinforces is the epistemic and linguistic nature of the vagueness in question, and the enduring belief that there might exist a particular point which marks the border in question – the vagueness is seemingly part of our knowledge about the world, and how we struggle to capture it in words, not about the world itself.
Is there vagueness in the world?
Rather than thinking about vague descriptions of things, it may seem that there actually are vague objects. Mount Wellington, for example, is uncontestably itself right at the summit pinnacle, but somewhat less clearly so several kilometres from the summit further down the ridge towards Chimney Pot Hill. It is true that we could think of "Mount Wellington" as a vague description, but unlike a head with a determinate number of hairs, or a colour sample with a determinate wavelength, there simply does not seem to be a fact of the matter about where Mount Wellington becomes Chimney
Pot Hill. A progression of difference by degrees can be constructed linking the two features. Is the descriptor "Mount Wellington" an example of epistemic vaguenesswhich is accurately responding to truly ontological vagueness?225
Belief in vagueness in the realm of linguistic description does not commit its believers to any position on the nature of the world. Many subscribers to linguistic vagueness also believe in a crisply-defined world, which it is nevertheless beyond our powers to capture in anything other than a vague way. This perspective, of a certain cognitive fallibility, is quite compatible with the borderline cases approach to vagueness, since it allows regions of relative infallibility around the “True” and “False” ends of the continuum and confines the confusion and error to the borderline cases. These, it is hoped, can be refined and defined-away (or “precisified”) to a minimum. A similar method of reducing cognitive fallibility operates in the case of apparently vague mountains, and other objects whose status depends on the assignment of some value by people. For mountains there is a geographical convention which regards the lowest point between them as a "saddle", which is therefore neither one peak nor the other – a truth- value gap, literally. Since a conventional description is in this case refinable by further conventions, I would regard the vagueness of a mountain as only apparently ontological. This apparent mismatch between language and the “real” world is operating all the time, and is seemingly inevitable. We now know, thanks to chemistry, that apparently solid surfaces are full of holes, while quantum physics tells us that the “holes” and their surrounds are probabilistic manifestations of short-lived subatomic particles. Bertrand Russell argued that precision (as he saw it, the converse of vagueness) was a one-to-one mapping of the phenomenon onto a symbol, and this was achieved by getting closer and closer to the phenomenon, progressively reducing the many-to-one vague mappings, though never actually reaching the perfect mapping. Vagueness considered in this way cannot be eliminated.
A different way of thinking about the determinability of borderline cases results in a more realist view of the probable existence of ontological vagueness, but about which nothing can be said. Michael Tye proposes a three-valued semantics which respects the indeterminism of borderline cases, to the extent that a property is vague if there is no determinate fact of the matter about whether there could be objects that are
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neither instances, borderline cases, or non-instances of it. For Tye, this would be a consequence of the world being "in certain respects, intrinsically, robustly vague..."226 A similar kind of noncommittal realism informs Terence Parsons and Peter Woodruff's defence of the very idea of vague identity, an idea earlier demolished by Gareth Evans' famously short paper "Can there be vague objects?" They conclude that "genuine worldly indeterminacy of identity is perfectly coherent" but "whether there actually is genuine indeterminacy of identity is something that we think is presently not settled."227
However there does seem to be some support for the idea of an ontological vagueness which is properly reflected in, rather than forever hidden behind, linguistic and epistemic vagueness. The approach of focussing on difference by degrees denies the relevance of borderline cases, which have proved to be such a focal point for analyses of linguistic and epistemic vagueness. Rather it “opens the way to an understanding of vagueness as a uniform phenomenon”, as Bueno and Colyvan modestly put it. Taking vagueness as “a uniform phenomenon” means at least seriously entertaining the possibility that the world is vague, in some as yet unknown sense, since it requires the vagueness formerly quarantined into the problematic borderline cases to be spread out along the spectrum of all possible cases. At the very least this means that there comes a point where vagueness is no longer reducible by cognitive means, even though nothing can be said about what that "irreducibility" amounts to. Even Russell, who famously argued that vagueness was essentially a linguistic matter, nevertheless also believed that it was ineliminable, even from the apparently precise realm of logical connectives228. Anything which is so deeply implicated in such explicitly precise (that is, intentionally non-vague) thought must, to anyone but a full anti-realist, be indicative of some relation
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Tye (1997), “Sorites paradoxes and the semantics of vagueness”, p.293. In Keefe & Smith, pp 294- 316).
227 Parsons & Woodruff (1997), “Worldly indeterminacy of identity”, In Keefe & Smith, p.321. These two
papers come from a landmark 1997 collection called Vagueness: A reader, and represent the strongest statements there in support of ontological vagueness. A 2004 vagueness collection, edited by J.C.Beall, makes no reference to it.
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(Russell, “Vagueness”, 1922 lecture) “Words such as "or" and "not" might seem, at first sight, to have a perfectly precise meaning: "p or q" is true when p is true, when q is true, and false when both are false. But the trouble is that this involves the notions of "true" and "false"; and it will be found, I think, that all the concepts of logic involve these notions, directly or indirectly. Now "true" and "false" can only have a precise meaning when the symbols employed --- words, perceptions, images, or what not --- are themselves precise. We have seen that, in practice, this is not the case. It follows that every proposition that can be framed in practice has a certain degree of vagueness; that is to say, there is not one definite fact necessary and sufficient for its truth, but a certain region of possible facts, any one of which would make it true. And this region is itself ill-defined: we cannot assign to it a definite boundary.”
to the world. This view therefore allows that linguistic description works as well as could be expected to capture a world which is in varying degrees vague, though this is a conclusion that Russell himself vehemently denied. Putting it another way, if talk of vagueness is indispensable to understanding the world, then this indispensability is itself an argument in favour of ontological vagueness.
Vagueness as difference by degrees says nothing about the world directly. In avoiding the need to think of descriptions as necessarily falling within a given categorical boundary it opens a door to understanding vagueness as arraigned along a continuum, from the fully distinct at one extreme to the fully indistinct at the other. Bueno and Colyvan offer as a strength of their formulation the ability to construct sorites-type progressions which elucidate many vague things in surprisingly many productive ways. Such progressions, unlike the strictly numerical progression which marked the progress of the bald-to-not bald hair-counting exercise, need not be totally ordered, but can be partially ordered. That is, some progression must be apparent along a given path of ordering, but it need not be the only possible path. The existence of multiple possible paths for ordering is to be expected when the objects connected are not numbers, since numbers themselves have only one identifying (and identifiable) feature. Bueno and Colyvan give an example of compositional vagueness, where the vague term “religion” can be applied to potentially many quite different things. A crude path linking "religion" to "non-religion" can be constructed; eg Christianity, Buddhism, Brazilian soccer, Australian Rules Football, schoolyard kickabouts. Of course each stage is arguable, but the trend is obvious; there are features in common, perhaps more than one, which enable a similarity relation between adjacent elements in the series. While the entire series may be informed by the degree of religiosity to be found in each element, connections between adjacent elements need not be totally subsumed under this head. This solution seems quite compatible with Wittgenstein’s account of the family- resemblance relation between concepts, and for many of the same reasons - it too sought to undermine our intuitions about the clarity of supposedly necessary distinctions between things.
A prototypical example of a vague object is a cloud - it is "fluffy" with indistinct boundaries; another could be a cat - it too is fluffy with indistinct processes of fur-exchange with its surrounds. There is some physical fact-of-the-matter which denies us the possibility of making firm determinations about the fluffiness in question, and
here increasing precision cannot result in a reduction of vagueness. Bueno and Colyvan's partly-ordered sorites speaks to a similar kind of ineliminable vagueness, one where the nature of the boundary is a consequence of the composition of the "object" in question. They note that some writers refer to this as "multidimensional vagueness", with the crucial factor being the impossibility of reducing the orderings to a single dimension. The question now is, in what does this ineliminable vagueness consist, and is it really vagueness anyway? This is where in-discreteness and the concept of indeterminacy may help. My claim is that everything is in-discrete, which is potentially analogous to the
claim that everything is vague, but I would rather say that it is actually analogous to the
claim that everything is indeterminate. This is due to my insistence that no “thing” has the discreteness and determinacy apparently demanded by attempts to sharpen
predicates, which is the usual route to solving puzzles about borderline cases – in-
discreteness will inevitably result in a multiplicity of determinations about the nature of a thing.
Overlapping strands can represent the duration of elements of reality or the concreteness of persons in a sporting team – the key idea is that unities exist as unbounded collectives, marked by the arrival and departure, or birth and death, of individual components, whose coming and leaving does not threaten the collective’s existence. This form of in-discreteness manifests as the inability of any single end-point to sever the entire collection and bound it, hence a kind of continuity persists. The consonance with the compositional or multidimensional vagueness of Bueno and Colyvan’s partially-ordered sorites linking religion with non-religion is very strong, and the connection with Wittgenstein’s family-resemblance even stronger. Nesting is a more subtle manifestation of in-discreteness, possibly closest to a temporal vagueness in character. It concerns transitions between states, such as occurs in the phenomenon of growth or the passage of time. Here a successor state incorporates in its entirety a predecessor state, with some infinitesimal addition; in other words, a progression of difference-by-degrees.
Now although I have given each of the manifestations of in-discreteness a description which links it to characterizations of vagueness, I think that this is