The Evolution of Modern Metaphysics: Making Sense of Things (133 page)

To return to the connection with material in the retrospective: of especial interest is the connection with Leibniz’ calculus. I have been talking about intensive difference as though it were exclusively a matter of difference between degrees of intensity. But the calculus, especially as conceived in its early days under Leibniz’ own influence, rather than as conceived later through its rigourization in the nineteenth century,
⁵⁶
reminds us that each degree of intensity is
itself
a sort of intensive difference (cf. p. 237). To see why, consider an extensity with different degrees of some intensity distributed across it. For instance, consider a poker, on which each point has some degree of heat: those at one end, perhaps, are very hot; those at the other end much cooler. Now the sheer fact that any given point on the poker
has
a degree of heat depends on the distribution of heat around it. It would be impossible, for instance, for one particular (indivisible) point to be very hot if it lay within a section of the poker that was otherwise uniformly cold – just as it would be impossible for one particular (indivisible) point to be red if it lay within a section that was otherwise uniformly grey. What are fundamentally given as differing in heat are sections of the poker, not points on it, albeit sections that may themselves have sub-sections of variable heat, in which case their own heat is some kind of mean. A yet clearer case, perhaps, is that of speed. Thus consider an ant running continuously along the poker from left to right, accelerating all the while. What are fundamentally given as differing in speed are portions of its journey, not points on the journey. Thus we talk of its (mean) speed along a given section of the poker, by construing this as the ratio of the length of that section to the time that the ant takes to traverse it, under some suitable measure. (And the ant’s acceleration
means that the different speeds along different sections increase from left to right.) To talk of its speed
at a particular point
on the poker, as it were the reading on its internal speedometer at that point, is derivative. Very well, but how is it derived? How does talk of the ant’s speed along different sections of the poker subserve talk of its speed at different points on the poker? Here at last we see the relevance of the calculus. The calculus answers just this sort of question. That is its genius. It enables us to construe the ant’s speed at a particular point on the poker as the limit of its speeds along ever smaller sections of the poker that include that point.
⁵⁷
And the very fact that such questions are answered in this way, nay the very fact that they are answered at all, is the kind of thing that I have in mind when I say that a degree of intensity is itself a sort of intensive difference: there can be no ‘punctual’ instance of any given intensity save insofar as there are suitable intensive differences between ‘regional’ instances of it.
⁵⁸

4. The Execution of the Project. Sense

Deleuze’s attempt to account for how things make sense in terms of a positive conception of difference begins with intensive difference then: a sort of difference that not only
can
be conceived positively but
must
be conceived positively. Intensive differences ground what he calls ‘the transcendental field’ (
Logic of Sense
, p. 98, and ‘Immanence’, pp. 25–26
⁵⁹
). The project is to show how, within this field, all discrete entities, including the subject, are constituted along with their various features.
⁶⁰
I shall try in this section to give a sketch of how Deleuze executes his project. (But I must issue a warning. Even the word ‘sketch’ is presumptuous. The project is colossal.)

I said in the previous section that intensive difference is as much a feature of the virtual as it is of the actual. In fact it is on the cusp. It is a feature of that actualization of the virtual (or, as we should rather perhaps put it, that actualization-of-the-virtual) of which the virtual and the actual are themselves ultimately abstractions. Consider again some point on the poker with a particular degree of heat. The sheer fact that the point has this degree of heat, I argued, depends on the distribution of heat around it. I had in mind sections of the poker. But the considerations that I invoked apply as much to the temporal as they do to the spatial. Just as it would be impossible
for this point to be very hot if it lay within a section of the poker that was otherwise uniformly cold, so too it would be impossible for some (indivisible) instant in the point’s history to be an instant at which it was very hot if that instant lay within a period during which the point was otherwise uniformly cold. This is part of the reason why the instantiation of heat has both a virtual aspect and an actual aspect. Not that any
particular
history is a precondition of the point’s having the degree of heat it has. The point could have that degree of heat while heating up, or while cooling down, or while enjoying a period of uniform heat – which for current purposes we may as well regard as a limit case of its cooling down. In itself, the degree of heat, construed as an intensive temporal difference, is a change of heat that is neither a heating up nor a cooling down. It is what Deleuze calls a ‘pure event’, a becoming that ‘[pulls] in both directions at once’ (
Logic of Sense
, p. 1). Deleuze deliberately uses this more paradoxical formulation, saying that the becoming pulls in both directions rather than in neither, because he thinks we do well to acknowledge a paradox in reality itself, a paradox that is ‘resolved’ – the reason for the scare quotes should become clear in due course – in the actualization of the virtual, that is to say in a distribution of further degrees of heat in favour of one direction over the other. (Cf.
Logic of Sense
, 12th Series.) But of course, any such actualization of the virtual merely involves further instantiations of heat to which the same considerations apply. The perpetual splitting of the actual from the virtual is the perpetual ‘resolution’ of paradox in the creation of fresh paradox. It is as if paradox itself, the paradox inherent in intensive difference, is the driving force of eternal return (see pp. 119–124 and
Logic of Sense
, pp. 66–67).

Now I have been talking about instantiations of intensities as though these always had to be part of some smooth transition from one degree of intensity to another. In fact, however, a point on some surface may be bright because it lies on the very edge between two smaller adjacent surfaces, each of which is itself uniformly bright though one is brighter than the other. It is in this connection that Deleuze invokes what he calls ‘singularities’, pure events of a special kind. He characterizes these as follows:

Singularities are turning points and points of inflection; bottlenecks, knots, foyers, and centres; points of fusion, condensation, and boiling; points of tears and joy, sickness and health, hope and anxiety, ‘sensitive’ points. (
Logic of Sense
, p. 52)

The actualization of the virtual involves countless singularities. And these critically shape the development of the virtual and its further actualization.

To get a sense of how, consider the fact that intensities are instantiated correlatively and conjointly. For instance some cooling down may be correlated with a transition from red to grey, indeed from bright red to dull grey. Virtual tendencies, if we abstract from their dynamism, may then be thought of as journeys through spaces of possibilities – what are technically known
as ‘state spaces’ – where these are metaphorical spaces of the limited kind which, as I observed parenthetically in the previous section, are apt even for the characterization of intensive difference. Each point in any such space represents some combination of degrees of intensity (heat, redness, brightness, …). The space therefore has a dimension corresponding to each intensity involved (cf. pp. 182ff.). What the singularities associated with the space serve to do, in their virtual aspect, is to determine the geometry of the space. For example, they can determine its limits. An increase in heat and a correlated increase in redness, in the context of a further complex of correlations, will be able to proceed only so far. At the limit it will issue in a singularity that so to speak prevents continuation of the journey. This in turn bears on how the virtual is actualized. If the poker is heated enough, it will start to melt and eventually disintegrate. Again, relatedly, singularities can ensure that the space has certain ‘holes’ that voyagers ‘fall down’. An increase in heat and redness, in the context of other relevant changes in intensity, will eventually be accompanied by a sharp decline in rigidity.

Here we see the way in which singularities shape, fashion, and generally work the virtual. But now recall two cardinal features of Bergson’s account of the virtual: first, that the virtual is continually changing; and second, that the actualization of the virtual can be thought of topologically, as involving processes of blending, stretching, breaking, twisting, piercing, and suchlike. In Deleuze’s account of the virtual, which shares these two features, they can be seen as more or less equivalent to each other. For the continual change of the virtual can be seen as the blending, stretching, and so forth of state spaces of the sort that we have just been considering. A singularity, in the splitting of its virtual aspect from its actual aspect, may ‘dent’ such a space and create a hole into which the relevant virtual tendencies must now descend. Once the poker has disintegrated, for example, further increases in surrounding heat will have new targets and will result in crises of a different kind elsewhere, say the combustion of nearby furniture.

Recall also a cardinal feature of Bergson’s account of the possible, that the possible, no less than the virtual, is continually changing; in particular, that new possibilities are continually coming into existence. This too is an idea that Deleuze embraces. This too is an idea that we can now see anew. We can see it as involving the inception of new connections between intensities, or the inception of new state spaces with extra dimensions. Part of the significance of this is that it signals an extremely important way in which the navigation of these spaces, in the actualization of virtual tendencies, can surmount obstacles. Thus consider a journey along one dimension that leads to some sort of limit. Continuation of the journey along that one dimension seems impossible. But perhaps it is not. Perhaps it is possible by climbing a second dimension and ‘jumping over’ the limit. Thus a substance’s melting point can increase when there is an increase in atmospheric pressure. So too someone’s ability to play the piano can extend beyond previous limits
when accompanied by instances of a hitherto completely absent form of encouragement.

We now begin to get a sense of how discrete individuals are constituted. In the actualization of virtual tendencies various singularities play a more or less direct role. (Note here that any inception of a new connection between intensities of the sort discussed in the previous paragraph is itself a kind of singularity.) The actualization of these tendencies can accordingly be seen as a more or less clear expression of these singularities, which Deleuze likens to the more or less clear expression that obtains between a Leibnizian monad and any given part of the rest of reality (
Logic of Sense
, pp. 110–111). Individuals are constituted as having something like a Leibnizian point of view on reality. (See ibid., 16th Series.)
⁶¹

The account extends to subjects and to features of things (
Logic of Sense
, 16th and 17th Series; see also
Difference and Repetition
, pp. 256ff.). In fact it extends to space and time themselves. Although the endless actualization of virtual tendencies involves the distribution of intensities across extensities, we are not to think of this as occurring within two pre-given containers. ‘Time itself unfolds,’ Deleuze writes, ‘… instead of things unfolding within it’ (p. 88; cf. p. 236).

Let us now retell the story that has just been told, but in different terms, to see better the role that sense plays in it.

The pure events that we considered above are connected in what Deleuze calls ‘the Event’ (
Logic of Sense
, p. 11; see further ibid., 9th and 10th Series). This is the very form of change, on the cusp between the virtual and the actual. Now in the splitting of the virtual from the actual, or in the actualization of the virtual, each of the events involved, as we saw, requires some distribution of further events, each of which in turn requires some distribution of further events, and so on indefinitely. It is through such distributions that the paradoxical element that inheres in all of these events is continually ‘resolved’. Its ‘resolution’ can be thought of as a movement along and between series of events, selecting distributions. The movement never ceases. It cannot. It always involves new pure events in which the paradoxical element inheres. Or rather, it always involves
anew
pure events in which the paradoxical element inheres. The events themselves are not new, inasmuch as, simply
qua
pure events, they must already be connected with all others in the Event. There are thus continual changes in the relations between the events in the Event. And these changes are themselves changes in degree of intensity. For example, a change in heat comes to stand now in a more critical relation to a change of rigidity, now in a much less critical relation to it (as the poker is pulled away from the fire, say).

One model for these continual changes in the relations between events is that of a musical theme and its variations. (The model is especially apt if the variations are thought of as improvised. That avoids undue connotations of stasis.) The theme and its variations have a kind of topological equivalence. Certain elements are invariant from one variation to the next. But relations between them vary, in different kinds of intensity. In one variation, for example, a modulation is accentuated. In another a pause is prolonged. In yet another the original accompaniment becomes the principal melody and vice versa. In a fourth the original principal melody shifts to a new key, with corresponding differences of resonance with respect to the home key. And so on. The changing
sense
of the theme and its variations consists in the changing significance of this nexus of relations, whereby not only can the invariant elements be heard afresh but the theme itself can become an object of renewed (retrospective) attention. This in turn is a model for what Deleuze himself means by sense. As the relations between pure events vary in different degrees of intensity, through the actualization of the virtual, ever new sense is created. And part of what such sense does is to constitute individuals, including subjects, and their various features. Thus the fact that the relation between that change of heat and that change of rigidity becomes more critical in that context is partly constitutive of the identity of that poker. (See e.g.
Logic of Sense
, 14th and 15th Series.)
⁶²