U N EPÍLOGO COMO UN PUNTO DE PARTIDA

In the opening section of this work I considered the nature of the relation between appearance and reality, and I proposed that the dominant way of conceiving of this relation was as no-relation; that in fact connection between the two was deemed to be blocked. A related proposition was that a similar blocking of connection occurs in the usual ways of thinking about the world, where the special nature of subjectivity lends the internality of thought some qualities which by definition cannot be shared with the world. In both situations it is perhaps closer to the mark to think of the relation between the two metaphysical entities (appearance/reality; thought/world) as being dominated by the apparently self-evident nature of their existence as entities – this would result in a barrier to connection being considered rather as a lack of connection, or a gap resulting from the absence of common characteristics. The idea of a gap tallies nicely with the idea that on that dominant view each metaphysical realm is taken to be bounded, and such a bounding is regarded by me as a problem.

Something which is discrete keeps itself to itself. This is equally true of a person (“discreet”) and an inanimate object. It is the “keeping to itself” that matters, and

which makes an object that object rather than an arbitrarily labelled piece of some other object. It is separate from other things, not apparently connected to them. Hence it may be that the question of connection cannot be divorced from the question of thingliness, and that it may seem that the definiteness with which an object is said to exist is inversely proportional to the degree to which it is connected to its surroundings. A strong desire to avoid this trade-off appears to dominate the conception of autopoiesis – a concept that is given more detailed consideration below (see the discussion at the end of this section on discreteness). Two possibilities for the implementation of a trade-off between objecthood and connection suggest themselves here: a Hegelian view of a unity which finds part of its power concentrated into a single entity, draining power away from the remainder of the unity to result in a Thing– No-thing duality122; or a Spinozan view of relational existence, where on the contrary the intensification of power in the Thing is reflective of the increased powers of its surrounds, not their diminution. In neither case can discreteness and connection be divorced, but this “connected” way may not be the best way to get to grips with discreteness. A third option is to consider the characteristics of discreteness by itself; discretely, as it were; and I will begin with this. The remaining two options for considering discreteness will turn out to be heavily dependent on the presupposing of a kind of unity, which means that they are themselves outcomes of a certain discrete-ised thinking.

Simple discreteness

The kind of unity presupposed by the notion of discreteness is the unity of a singular thing; the commonsense or everyday idea of a unity being a one-ness. Aristotle’s logic represents the acme of commonsense by formalising this view of unity into what has become known as the “laws of thought”:

1. The law of identity: “Whatever is, is.”

2. The law of non-contradiction: “Nothing can both be and not be.” 3. The law of excluded middle: “Everything must either be or not be.”123

122

Thanks to Anna Lehrbaum, Notre Dame University, Fremantle, whose paper “Logic and conflict” at the 2004 AAP Conference, South Molle Island, alerted me to the distinction between antagonism and conflict, and the possibilities of a Hegelian analysis of discreteness.

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The cumulative effect of these mutually supportive dictums is a world of discrete entities. A discrete entity need not have an interior which is a simple unity of total sameness. Aristotle’s substances, to which these laws of thought were to be applied, include composites whose parts may also have a principle of structure, such as living bodies and their organs. They are subordinate, however, to a more encompassing unity, particularly one with the power of self-movement. Its interior entities of a unity can be conceived as ranked or ordered according to their degree of fit with the overall entity, though this obviously is more applicable to a composite such as a series of numbers or a set with a variety of members. A bound is a determinate place in the internal ordering of an entity, within which the entity is said TO BE (ie, its components are similar enough), and beyond which it is said NOT TO BE (ie, they are now too different). In this respect an entity such as a category can also be regarded as a discrete object which is subject to the identity-firming power of non-contradiction. Here is an example of the category “five” containing only instances of numbers greater-than-or-equal to five and less-than six.

A set of categories constitutes a series of objects, and since the bound constitutes the “surface” of an entity, two entities in this series can do no more than touch – they are said to be “mutually exclusive”. The next category after “five” has a membership rule that complements “five” – it contains only numbers greater-than-or- equal to six. There is no overlap124. Aristotle spells out the nature of this bound in the Metaphysics when he discusses differences – he conceives of the category as consisting of entities ordered by their possession of the characteristic in question:

But surely that which is greatest in each class is complete. For that is greatest which cannot be exceeded, and that is complete beyond which nothing can be found. For the complete difference marks the end of a series (just as the

124 _{However there is a complication in the case of numbers of a particular kind, the real numbers, which I}

will discuss later in this chapter as an example of continuity. The way the categories are defined in the example would result in the upper and lower bounds having slightly different natures,

other things which are called complete are so-called because they have attained an end), and beyond the end there is nothing; for in everything it is the extreme and includes all else and therefore there is nothing beyond the end, and the complete needs nothing further.125.

Here, the crucial and fundamental aspect of bounding is the completeness of the class – anything other than a bound would allow this completeness to be potentially violated, which would threaten the supposed determinateness and definiteness with which the class can be known.

Simple discreteness has much in common with full-blooded atomism – each demands that an object have a fully inviolate boundary, and that its creation and destruction be marked by complete transmission of causal powers from and to its predecessor and successor objects. Putting it another way, objects should not leak or otherwise promiscuously mingle with their surroundings. Their boundary must be impermeable. This makes discreteness very attractive as a basis for the symbols which some hold to be constitutive of mental representations. Defenders of this view, such as the cognitive scientists Eric Dietrich and Arthur Markman, find a compelling equation between the subjectively-experienced precision of thought and the necessity for the representational content of thought to be similarly precise. This compulsion will be discussed in a larger context later in this chapter, the context being cognitive science in general. Dietrich and Markman locate their view of discreteness against a conception of continuity, of which more later. Hence they insist that mental content must be discrete because continuous representations cannot do the following: Discriminate, combine, sustain internal structure, or be independent of worldly covariation126. Combination with other symbols, and conversely, decomposition of complex symbols, is of prime importance and brings with it further requirements which illustrate discreteness - “It might seem that being a discrete composable entity follows directly from being an enduring representational entity, but not all enduring mediating states make finite, localizable, and precise contributions to larger states.”127

125_{Metaphysics, I. 1055a10-17.} 126

Dietrich & Markman (2003), “Discrete thoughts: Why cognition must use discrete representations.” Mind & Language, 18 (1), 95-119. p.105.

127

Markman and Dietrich (2000), “In defense of representation.” Cognitive Psychology 40, 138–171. p.149. Emphasis added.

It is only a short distance from believing that thought must be discrete because that is how thought works best, to believing that thought must be discrete because that is how the world works. While an adherence to the concept of representation, which though dominant is being contested, does not commit one to a belief in discrete representations, a belief in symbolic representation certainly does. Cognitive science is a very diverse area, but it owes its origins to the relatively unified efforts of a number of disciplines driven by a reductive research programme which sought to explain the generation of high-level functions from low-level processes; these disciplines included cognitive psychologists with input-output engineering models of the mind, computer scientists interested in artificial intelligence, linguists interested in the constructive powers of syntax, neuroscientists who were increasingly discovering highly-specific modules for low-level processes, and philosophers interested in the nature of language. The focus on a reductive-constructive paradigm explains the interest in representations which can combine and decompose algorithmically. Interestingly, most alternatives to the dominant symbol-processing paradigm require a less self- contained brain to engage more fully with its surroundings, where those surroundings are defined variously as body, culture, or environment. That is, the alternatives to symbolism tend to claim a great deal more connection with other significant entities than the dominant paradigm would allow, and this in some quarters is allied with a critique of symbolism. Some of these issues are investigated later in the present chapter, so for now, I want only to reiterate that the deep philosophical buttressing of a belief in the necessity for discreteness, which I addressed generally in Chapter One, is reflected in a number of applied areas of research which do not readily draw on philosophical support for their positions. Next I will look at the two other ways of characterizing discreteness, which place it in relation to other entities.

Relational discreteness – dialectical unity

A unity with an otherwise undifferentiated interior may respond to external force in two broad ways: It may remain undifferentiated, and stolidly persist in being that thing, or it may change, to concentrate its resources so as to bring to prominence a previously minor component which comes to dominate the unity. In both cases we should be wary of accepting at face value the ascription of unvarying sameness to the unity – in these

cases, “undifferentiated” means that whatever differences there are simply do not matter for the current state of the unity. But differences there will be. The Aristotelian idea of identity as self-identity allows for internal differentiation within composite substances, but differences are subordinated to the identity conferred by substance. The alternative, of a unity changing to a new configuration, was considered by Hegel as an example of self-contradiction128.

Self-contradiction is a dynamic process, in stark contrast to the fixity of self- identity (but bearing in mind the dynamism of the really real, which is inherent in Aristotle’s view of substance). Some element of the internal differentiation which previously played no part in defining the unity is called into prominence by the particular circumstances; conceptually, you might call this a path to something having “meaning”, as something of the prior unity now becomes distinctive of that unity. Hegel calls the logical principle that “the negative is just as much positive” a “quite simple insight”. By this he means that there was already a capability in the thing to become something different, but it does so as a process rather than an instantaneous recognition of something already present:

… what is self-contradictory does not resolve itself into a nullity, into abstract nothingness, but essentially only into the negation of its particular content, in other words, that such a negation is not all and every negation but the negation of a specific subject matter which resolves itself, and consequently is a specific negation, and therefore the result essentially contains that from which it results; which strictly speaking is a tautology, for otherwise it would be an immediacy, not a result. Because the result, the negation, is a specific negation, it has content. It is a fresh Notion but higher and richer than its predecessor; for it is richer by the negation or opposite of the latter, [and] therefore contains it, but also something more, and is the unity of itself and its opposite.129

This new “thing” is indeed a discrete thing in that it has a distinct thingliness, but it is not discrete in a separable way, because it is intimately, constitutively, bound to its context. However by the standards of identity the thing clearly has achieved separate

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being – it is, considered in isolation, nothing but itself, and nothing of its essential nature is shared with any other. The space of the prior unity is now divided without remainder into Thing – Non-thing, and the relations which characterise it are now internal to that unity, rather than being the external relations which inevitably must act between atomic, discrete entities. The internality of relations is complemented by what could be called the movement towards self-determination, shared with all living things130, as the thing (in Hegel’s system, a pure concept) brings itself to reality.

The apparent dynamism of this process is perhaps its biggest weakness – there seems to be no reason for the new configuration to persist more than fleetingly, without an accompanying story about how some configurations can attain greater permanence than others. It is consistent with postulating a metaphysic of self- determination that something akin to self-maintenance, a kind of autopoietic independence, is plausible. The most significant aspect of this kind of dialectic discreteness is that it exists in the realm of thought, albeit thought imbued with more metaphysical muscle than most writers of a non-idealist bent would allow, and in this kind of ecology relative impermanence is not a drawback. For thought as conceived in this way, the dialectic provides an indissoluble unity between the form and the content of thought, thus achieving an advance of sorts over Kant131, and an advance over simple atomism. This last is the only thing I want to take from the discussion, as any more would be beyond my scope.

Relational discreteness – modal intensity

As I discussed in Chapter Two, Spinoza’s conception of God’s infinitude results in reality which is a metaphysical One while also being an ontological Many. Such individuals as there are can be apprehended by reason as an intensification or thickening of the finite modes, as their power depends positively upon the strength of their relations with other “individuals”, rather than negatively by taking power from them. It is also clear, however, that the discreteness and clarity with which individuals are perceived owes much to the rational powers of the perceiver, since there is no story to be told

129

G.W.F. Hegel, The Science of Logic [online], § 62. Quoted in Lehrbaum.

130 _{De Boer (2004), “The dissolving force of the concept: Hegel’s ontological logic.” The Review of}

Metaphysics, 57 (4), 787-822. p.807.

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about how individuals can have any kind of existence independent of their constitutive substance, which is God. Hence to the usual ways of dividing up the philosophical pie this looks like an epistemic view of discreteness rather than an ontological one. Nothing is genuinely separate from God in Spinoza’s metaphysics, in spite of the efforts of commentators such as Deleuze to downplay the super-normal attributes of God by stressing the “plane of immanence” on which His works are laid out.

Instead of conferring unity on an entity, essence just is the effort made to maintain unity in the face of pressures towards dissolution, an effort which will be relatively more or less successful rather than absolutely so. As a consequence it serves no purpose to insist on the inviolability of a creature’s boundary in a relational metaphysic, since this will be just as much a contested region of its being as its deep interior, and to a large extent relations which maintain and build will be roughly balanced by relations which ablate and diminish. Regardless, therefore, of the reality of creatures, it seems clear that their status as “creatures” is far from stand-alone discreteness. This was the attraction of a relational metaphysic – it means that some relations will be fully ‘internal’ to the creature, some will be fully ‘external’, and many will reach across what is conventionally taken to be its boundary. The creature struggles to separate itself from its surrounds, and it struggles always in vain, since the only true unity is God. The partial unity which results is of interest, however, because it represents something which is neither discreteness nor its complement, continuity. Although the connection which this partial unity is indicative of is rendered insignificant by the all- encompassing monism, it would be significant in a pluralist metaphysic. This will become more apparent later in this chapter.

Autopoiesis and cognition – a case of a necessary boundary?

How discrete is the kind of boundary which the surface of a self-maintaining organism represents? Autopoiesis was invented by Humberto Maturana as a term to replace “circular organization”, which had itself resulted from an appreciation that feedback and recursive processes in general were the core contributors to biological unity. The central concept both terms were trying to capture was autonomy132, and in making the self-

132

Maturana (1980), “Introduction.” In Humberto Maturana & Francisco Varela (Eds.) Autopoiesis and cognition: The realization of the living. (pp.xi-xxx) (Dordrecht: D.Reidel)..p.xvii.

maintenance of autonomy a central issue for biology and cognition, Maturana and his collaborator Francisco Varela were also addressing the key metaphysical issues of identity and teleology. An autonomous system is to some extent a closed system, and we will see later in this chapter that this is a potentially problematic insight when