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«Planet M : The intense abstraction of Marilyn Strathern Martin Holbraad and Morten Axel Pedersen Anthropological Theory 2009 9: 371 DOI: ...»

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This is just to say that Strathern’s central paradox regarding the notion of control – the idea that no matter what the scale the degree of complexity stays constant – is integral to this way of thinking of abstraction. Just as ‘isolating’ a particular predicate would suggest a reduction of complexity (a dog is so many things other than a quadruped), so the very same act gives rise to new orders of complexity. But thinking of the paradox in terms of abstraction, we argue, serves to reveal further features of the constancy of complexity that make it seem less than a riot. Two hold particular interest. First, the idea that abstraction entails isolating predicates of objects allows us to emphasize one aspect that Strathern’s characterization tends to leave mute, namely the idea that what she calls scales can be said to originate in the things they serve to compare. Indeed, the manner of the origination is just as interesting as the fact. While the thought of comparing things ‘in terms of ’ or ‘with reference to’ scales conjures a notion of application (as, one might say, a rule applies to instances), the obverse thought of originating abstractions (scales) from more ‘concrete’ objects brings to mind a notion of extraction: to isolate a predicate is to cut it away from the denser mass in which it is initially embroiled, that is, what looks like ‘the thing’. To use the sculptor’s figure/ground reversal, it involves cutting away the mass to make the abstraction appear – a metaphor that is integral to the imagery of ‘Cantor’s dust’, in which scalar effects are replicated by the creation of intermittencies and gaps (Strathern, 2004: xxii–xxiii).

This brings us to a second characteristic of abstraction, which has to do with notions of removal and distance. We have already seen that such notions are foundational to Strathern’s characterization of the metaphysical assumptions of pluralist comparison, since ‘distance’ is precisely what is imagined to separate not only things from each other but also things from the scales that are brought to bear on them. It is just such distances 378

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that images of maps and trees conjure – scaling up or down on an axis proximity and distance, or branches and stems that are related vertically and horizontally by degrees of inclusion and exclusion. For scales to offer a vantage point from which things can be compared they have to be posited as being separate from them – perspective implies distance. Thinking of comparison in the key of abstraction, however, foregrounds movement as a condition for both. If abstraction involves cutting predicates away from the things to which they belong, the distance it achieves can be conceived as the result of an act of removal – a trajectory that cuts open a gap.

Two thoughts about abstraction, then, are embedded in Strathern’s account of the pluralist metaphysic of comparison: the notion that the things can scope their own comparisons by being cut (multiplying their comparative potential, so to speak, by being divided) and the notion that this involves a trajectory of movement. Both of these features carry over to Strathern’s characterization of ‘partial connections’ – i.e. her account of what comparisons involve when one shifts to a postplural metaphysic, in which the distinction between scales and things is collapsed. Indeed, we would argue that they can be used as the basis for a suitably altered conceptualization of the notion of abstraction itself, one which goes to the heart of Strathern’s thinking on comparison.

Postplural abstraction We call the postplural inflection of abstraction that we detect in Strathern’s work ‘abstension’. Abstension is what happens to abstraction when the distinction between abstract and concrete itself is overcome, as it is in Strathern’s postplural universe. We have seen that, as per the Strathernian concept of the relation, the postplural move involves rendering internal to things the differences that scales of comparison would find between them, thus turning things into self-comparisons. Clearly the ordinary associations of abstraction with hierarchically ordered ‘levels’ separated from each other by degrees of distance (the images of maps and trees) have no place here. Nor does the corollary of this way of thinking, according to which abstractions represent things in more ‘general’ terms – as the concept of quadruped stands to any ‘particular’ dog. Indeed, one way of characterizing abstensions would be to say that they are what abstractions become when they are no longer thought of as generalizations, i.e. as concepts that group together in their ‘extension’ things that share a particular feature.

Rather, abstension is what happens to abstraction when it turns intensive, to borrow the Deleuzian terminology (e.g. De Landa, 2002, and see Viveiros de Castro, 2009) – and hence the neologism. Abstension, then, refers to the way in which comparisons are able to transform themselves in particular ways. Considering our rudimentary example once again, abstension is what happens to a dog when it is considered as a quadruped.

That is to say, to think of a dog as a quadruped does not involve positing a relationship between two elements – a dog (deemed as a ‘particular’) that ‘instantiates’, as philosophers sometimes say, the concept of quadrupedness (deemed, in this sense, as a ‘universal’). After all, the distinction between particular things like dogs and universal concepts like quadrupedness is exactly the distinction from which a postplural metaphysic moves us away – just a version, surely, of the distinction between concrete things and abstract scales which renders the world a plural place. Rather, to consider a dog as a quadruped, on the postplural image of abstension, is just to turn it (to scale it) into something different, namely, that thing-cum-scale that one would want to hyphenate 379

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as ‘dog-as-quadruped’. This new ‘third’5 element is a self-comparison in just the sense outlined earlier: it is ‘more than itself ’ because, qua dog-as-quadruped, it is a full-blown dog; and also ‘less than itself ’ because, again qua dog-as-quadruped, it is merely an ‘abstracted’ (though we want to say abstended) quadruped.6 To bring out the peculiar ‘sharpness’ of abstension, we may supplement the range of images that Strathern uses to convey her notion of comparison (the fractal, the cyborg and so on) with what one could claim is their most rudimentary form – the shape of a cone laid on its side (see Figure 1).

Imagining abstensions in this way serves, first of all, to illustrate the crucial differences between postplural abstraction and its plural counterpart, which Strathern depicts with the twin images of the tree and the map. As we have seen, plural comparisons posit distances (or ‘gaps’) that separate both things from one another, and things from the increasingly abstract generalizations in whose ‘extensions’ they are included. Moreover, the latter relationship (i.e. between things and their generalizations) is irreducibly hierarchical or ‘vertical’, since what makes generalizations suitable as scales for comparing things is that they are more abstract than the things compared. As seen in Figure 1, however, abstensions are devoid of both these characteristics of conventional abstractions. What in ‘plural’ abstraction look like extensive gaps ‘between’ things (and between things and scales) in the postplural mode figure as intensive differentiations ‘within’ abstensions, indicated in Figure 1 by the asymmetrical proportions of each of the ‘ends’ of the abstension – the broad ‘thing’-like end and the sharp ‘scale’-like one. Furthermore, this asymmetry on the vertical axis of Figure 1 indicates that hierarchy is absent here.

Laid on its side, as it were, the hierarchical dimension that marks the distances between things and scales dissipates into the internal self-differentiation of abstension.

This correspondence between the ‘verticalization’ of ordinary abstraction and the lateral self-scaling of abstension gives clues as to why Strathernian comparisons are sharper than just ‘relations’. After all, it is the loss of the ordering principles in hierarchies of abstraction (and their corollaries in terms of inclusion and exclusion, connection and disconnection, similarity and difference, and so forth) that critics of the postmodernist penchant for profligate relations lament. So the formal correspondence between hierarchy and self-scaling raises the prospect of retaining, if not a set of ordering

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Figure 1. Abstension Note: The grey penumbra indicates that the correlation between, on the one hand, ‘thing’-likeness and ‘scale’-likeness and, on the other, ‘more’ and ‘less’ can be inverted, as explained in note 6.


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principles as such, then at least a principle of a (no doubt new) kind of order, that may show why Strathern’s postplural universe is more than just a magma of relations (cf.

Scott, 2007: 24–32). Might the asymmetry of self-differentiation do for the postplural world what the symmetry of hierarchy does for the plural one? To see that this is so, we may home in on the questions of ‘cutting’ and ‘removal’ that we introduced earlier.

Plural abstraction, we saw, involves the idea that scales of comparison can be said to be derived from the things they compare in two moves. First, deriving predicates (e.g. ‘quadruped’) from things (e.g. dog) by ‘cutting’ away from them the denser, ‘thingy’ mass in which they are initially embedded. And second, creating a distance between them and the mass from which they are extracted by placing them at a different level of abstraction, thus creating a gap between predicate and thing by a step of ‘removal’. Each of these moves has a direct equivalent in postplural abstension. First, when the difference between thing and scale is ‘internalized’ in the abstension, the latter is still derived from the former. Only now, the sculptor’s figure-ground reversal (viz. cutting the mass of the thing ‘away’ to make the abstract predicate appear) is reversed back: the mass of the thing is retained, but chiselled into a sharper, scale-like shape – still the same mass, that is, but ‘less’ than itself at its scale-like end (to visualize this, imagine how the cone of Figure 1 might be sculpted out of the mass of a right circular cylinder). Second, while this ‘internal derivation’ of the scale from the thing does not involve opening up an (external) distance between the two, it does still turn on an act of removal, namely the ‘internal’ removal of the self-transforming proportions of the cone, as one moves from its broader end to its sharper one (again, to visualize this, imagine the motion of the sculptor’s gouge as it cuts into a cylindrical mass to give it the shape of a cone). So what in the plural image were distances ‘between’ now become formal transformations ‘within’ (trans-formations, to emphasize), that can be conceived as ‘internal motions’ – motions that are perhaps not unlike the ones classicists appreciate in the ‘rhythms’ of ancient columns.

Strathern’s postplural universe of what we have called abstensions, then, presents an image that arguably comes close to what Lévi-Strauss had in mind when he spoke of the ‘science of the concrete’ (1966), provided we remain clear on the essentially oxymoronic character of that phrase, where ‘science’ is meant to have connotations, precisely, of abstraction. And just as Lévi-Strauss argued so forcibly for the irreducible sophistication of this science, albeit ‘savage’, we may note that Strathernian abstensions are in no way inferior to ‘plural’ abstractions when it comes to the sheer agility of the comparisons they furnish. Only now this agility is no longer a matter of adopting different purviews onto things from the vantage points that more abstract scales afford (e.g. grouping cats and dogs together on grounds of their common quadrupedness and then contrasting them, say, from the viewpoint of their locomotion). Rather, the potential for comparison is enhanced by the capacities that what a plural metaphysic would call ‘things’ (e.g. the dog) have to be transformed by being ‘cut’ in particular ways, ‘sharpened’ so as to have particular aspects of themselves revealed (e.g. the dog-as-quadruped).

And the effect of such transformations is to provide, not a point of more general vantage, but rather one of further departure. As thing-like (and scale-like) as the dog from which it was derived, the dog-as-quadruped presents further possibilities for comparative transformation in a whole spectrum of directions – including cats, locomotion, mammals and so on.


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Now this conclusion, itself intensely abstract perhaps, may seem scholastic in its insistence on the contrasting metaphysics of plural and postplural comparison. We would argue, however, that it goes to the heart of one of the most compelling characteristics of Strathern’s manner of conducting comparisons, namely what we have already called its sheer originality. While it goes without saying that one hardly needs to be Strathernian to be original, we would argue that the work of abstension is inherently oriented towards originality. For, one way to express the contrast between plural abstraction and postplural abstension is to say that while the former involves an ‘upward’ (as in the tree) or ‘outward’ (as in the map) move from the particular to the general, the latter moves sideways, as it were, from particular(-cum-universal) to particular(-cum-universal), by means, as we saw, of the peculiar capacities for transformation that it reveals. So comparison is no longer a matter of identifying the general scales that may act as ‘common denominators’ that relate things (as ‘quadruped’ may relate cats and dogs). Rather it is oriented towards revealing ‘uncommon denominators’, if by that one means the peculiar and highly specific capacities for transformation that things(-cum-scales) hold so contingently within themselves.

II Having established, in Part I, the overarching premise of this article – namely that Strathern’s comparative project works according to a logic of ‘intense abstraction’ – we now turn to consider two ‘remainders’ (in her sense) to which this argument gives rise.

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