1.4 ESTRATEGIA
1.6.3 Marco curricular del área de matemática
1.6.3.6 Componentes del área de matemática según el DCBN en EBA
1. Self-falsification.
Let me try to clarify this further. What does it mean for interest to be anterior to both subject and object? First of all, it means that there is interest before there is a subject and an object of interest. This also means that the notions “subject” and “object” somehow arise from interest itself. I believe that the most direct way to clarify this is to have recourse to Nietzsche’s hypothesis of the “will to power.” According to this thought, the essence of the world is “will to power, and that alone.”88 "That alone" and especially not a subject or an object of the will to power.89 As John Richardson rightly emphasises, the will to power has a “telic” and “intentional” structure, it is “end-
88BGE, 36; See also WP, 1059, where the hypothetical nuance is absent: “do you want a name
for this world? A solution for all its riddles? A light for you, too, you best-concealed, strongest, most intrepid, most midnightly men?—This world is the will to power—and nothing besides!
And you yourselves are also this will to power—and nothing besides!” John Richardson remarks that Nietzsche calls the will to power the ‘essence’ of the world, using both Wesen (BGE 259,
GM, II, 12, WP 693 [1888]) and Essenz (BGE 189). See John Richardson, 1996, op. Cit. 18.
89WP 589 [1885-1886] see also WP, 635 [March-June 1888]: “The will to power not a being, not a
becoming, but a pathos—the most elemental fact from which a becoming and effecting first emerge_”
directedness.”90 Seen from a theoretical point of view then, it implies the thought
of an end as a stable and self-identical object of striving. Likewise, it implies the thought of a subject of the will, which remains stable in time. These are as it were “analytically contained” in the concept of the will to power. This is not to say however, that their existence is in anyway affirmed by it.
If we wish to explain how subject and object arise from the non- subjective and the non-objective, it seems we must start here. The difficulty lies in accounting for this theoretical point of view from within the will to power. Indeed, it is only this theoretical point of view which accounts for the objective form of our thought. For Nietzsche, the will to power is essentially the drive to “make equal” (GS 354). In physical terms, it means assimilation in the sense of “digestion.” Nietzsche calls this process “incorporation” [Einverleibung] and I will discuss it in chapter II. However, we should already recall that the will to power is not more physical than it is “spiritual,” its equalising activity is intellectual too because it “posits things” in a predicative way91. Thus, it is plausible that the will to power itself acts as a falsifyer of itself (there is “nothing besides” will to power to falsify): it presents itself in terms of “subjects” and “objects.” For Nietzsche, of course, such oppositions as subject and object are impossible. In reality, drives merely imply a subject and an object by pointing towards them as their regulative horizons perhaps; but at any rate, not as actual realities. There is a gradual continuum that moves towards each pole
90 John Richardson, op. Cit. (1996), 35 ff.
91 “The question is [...] whether this creating, logicising, trimming, falsifying is not itself the best-
guaranteed reality: in short, whether that which ‘posits things’ is not the sole reality” IX, [106] Autumn 1887
tangentially, but this continuum is made of differences of degrees, and refuses any leap: “if we give up the soul, ‘the subject,' there’s no basis for any ‘substance.' One gets degrees of being, one loses being as such.”92 This model has crucial implications for the question of truth. Let me anticipate briefly the rest of the argument. If the will to power is a self-falsifying principle, it means that we have uncovered a certain absolute truth about the will to power (i. e.
Being): it is self-falsifying. More importantly, we may understand better the ontological place of truth or the place of what I have called above, something ‘authentic’ about errors. In this view, truth (as the falsification of experience) names the process by which the will to power falsifies itself. I will discuss this view in more detail later, but let me stress that it necessarily doubles the question of truth. We must ask whether it is indeed true (the traditional question), but also, whether it is real (that is to say, whether it is an essential feature of being as self- falsification). For now, let me return to the question of interest.
2. Reflexivity and Resistance
For Nietzsche, the external world can interest us in two different basic ways: conquest and threat.93 If I apprehend the world as an object of conquest, the object of my interest will be external. If I experience the world as a threat, the object of my interest will be myself. One important implication of this is that interest is essentially bi-directional: it may be directed to the outside world (towards conquest) or to the self (for defense). However, there is a certain
92 X, [19]Autumn 1887
disymetry between these two modes of interest. In common language, interest denotes desire more directly than it does self-defense. This is the case for Nietzsche too. Indeed, we remember that the epistemic and ethical critiques of the notion of subject are intertwined (the concept of subject is false, and it is designed to allows us to assign blame). This is because for Nietzsche, the hostility of the environment is always psychologised by the individual. Hostility is always linked to a deed, and a deed to a “doer.” In fact, then, my interest for self-defense presents itself as a form of desire, namely, the desire expressed by the other person (or personified force).94
This may bring some clarifications on the emergence of the concepts of subject and object. Nietzsche describes self-preservation in terms of “passivity” (or “reactivity”), and conquest in terms of “activity.” This uncovers the intimate relationships of the subject and the object at a deeper level. Their relation is chiasmatic: in “passivity,” the object of interest will be the self and its subject will be the outside world as threat. In “activity” it will be the reverse. It is thus through the notion of activity and passivity that we must understand subject and object: “What do active and passive mean? Is it not becoming master and being
defeated? and subject and object?”95 This indicates that the notions of subject and object do not arise from the experience of the separation of self and world, but rather it emerges from the experience of their contact. This relationship is therefore reversible insofar as any act of will implies both activity and passivity.
94 See WP, 775 [Spring-Fall 1887] 95 VII, [48] Late 1886-Spring 1887
Consider the following two contemporaneous claims. Firstly: “What is ‘passive’? resisting and reacting. Being hindered in one’s forward-reaching movement: thus an act of resistance and reaction [.] What is ‘active’? Reaching out for power.”96 Secondly: “The will to power can only express itself against resistances; it seeks what will resist it—this is the original tendency of protoplasm in sending out pseudopodia and feeling its way.”97 In the experience of reality, the two opposing drives are almost simultaneously subject and object for each other, because they
resist each other. As a result, we obtain a line of contact across which subject and object of interest indefinitely alternate: the conqueror (subject) is opposed some resistance and thereby becomes object of the resistance imposed to it by the resisting object of the conquest. Conversely, this object, by virtue of its own resistance, becomes subject.98 For Nietzsche, this ‘line of contact’ is the basis upon which we build the concepts of inside and outside, and further, of subject and object. Even though Nietzsche presents this process as essentially a hostile encounter, it also involves and informs the structure of perception. Indeed, Nietzsche regards perception as a function of the drives’ resistance-seeking (recall the identity of increase-seeking and perception in the case of the
96 V, [64] Summer 1886-Autumn 1887 97 IX [151] Autumn 1887 my emphasis
98 This line obviously, is not a place of stability insofar as total conquest is eventually possible.
However, any process of subjection is always identical with a resistance. The disparition of a resistance is the end of the process, and the apparition of a new resistance, since the will to power is defined by its discharge and that discharge can only take place against resistance. See WP, 650 [1885-1886] and 634 [March-June 1888]
protoplasm99). As I will discuss in chapter VI, Merleau-Ponty too encounters this chiasma and this reversibility between subject and object as the structure of perception and like Nietzsche, he will hold that this coincidence of perception and, the will to increase is correlative to the coincidence of activity and passivity.100
These unions of opposites are occasioned by the experience of a resistance. Here, we arrive at the question of externality. A resistance is the experience of the externality of the world. Nietzsche also claims that resistances lead to self-consciousness: if this resistance becomes “master” over me, I become “object” for myself. Let me emphasise this point which is essential to most of Nietzsche’s later worldview: consciousness is always an act of subjection, it involves a tension between the subject and the object of consciousness. Here, we understand in what sense Nietzsche thinks that consciousness is a “disease”101: “conscious thought,” Nietzsche writes, “is nothing but a certain behaviour of the instincts towards one another.”102 Here, we encounter the unity of “consciousness” as described in GS, 354 and the “bad conscience” of GM, II, 16. In both cases, it is a question of opposing drives.103
99 See also WP 702 [March-June 1888]
100 For the identity of perception and passivity, see WP, 611 [1883-1887] 101GS, 354
102GS, 333, the same idea appears in BGE 36. See Graham Parkes, Composing the Soul,
Chicago, University of Chicago Press, 1996 353; Leslie Thiele, Nietzsche and the politics of the soul, Princeton, Princeton University Press, 1990, 51, ff.
103 Indeed, as early as 1881, when Nietzsche still seeks to draw the living from the inert matter,
This is the structure that underlies the metaphor of the inner world mentioned in GM, II, 16. It is worth citing again:
“the whole inner world, originally stretched thinly as though between two layers of skin [zwei Häute], was expanded and extended itself and gained depth, breadth and height in proportion to the degree that the external discharge of man’s instincts was obstructed.”
Here, Nietzsche describes the originary inner world as the origin of the reflexivity of interest: because there is a (ever-so-small) gap within the individual, her drives have the ability be re-directed towards her other ‘half”: the self is structured in such a way that there is a potential object of domination
within it. This setup allows for an inner relation of forces of the same type as the
external one: there is externality within the self. This is made possible by the gap between the two “layers of skin,” allowing for passivity and activity within the self, and thereby allowing for aggressivity against oneself, which is what Nietzsche describes in the rest of GM, II, 16. Although the metaphor does not return in Nietzsche’s writings, he maintains in several instances that the rules that apply in external relations of power apply internally as well: “I maintain the phenomenality of the inner world too: [...]The ‘apparent inner world’ is governed by just the same forms and procedures as the ‘outer’ world.”104 This setup which shows the interconnection of consciousness (external interest) and self- consciousness (internal interest) is similar to the “animal consciousness”
with itself: self-differentiation: “let us not think of the return to non-perception as a retrogression! We become completely true, we are perfected. Death must be reinterpreted! We thus are
reconciled with reality, i. e. with the dead world”11[70] (Spring-Fall 1881).
described in GS 354, where consciousness and self-consciousness are not distinct.105
Let us recall that for Nietzsche, basic consciousness is originary. It is not derived from anything else. This characterisation of the human’s originary inner world (“animal consciousness” or “soul”) will have great consequences for Nietzsche’s ontology and cosmology. This is because, in my reading, Nietzsche’s positing of this internal separation within the individual, and his subsequent relativisation of the notions of internality and externality commit him to a worldview determined by self-differentiation. In what follows, I shall mean ‘self-differentiation’ in the sense of the always-already present ability for one to be an object for oneself. In line with the above discussion, this involves (among other things) the primacy of intentionality over and above intentional poles like subject and object, and the reversibility of this intentionality. For Nietzsche, self- identity is impossible precisely by virtue of the tangentiality of intentionality106:
105 In the first paragraph of the aphorism, Nietzsche describes “consciousness” as a “mirror.” In
the third one, he writes: “[man] needed ‘consciousness,' first of all, he needed to ‘know’ himself what distressed him, he needed to ‘know’ how he felt, he needed to ‘know’ what he thought.” All features of what we would usually call “self-consciousness.” The conflation is of course,
purposeful on Nietzsche’s part, it is the same need (arising from the hostility of the environment) which gave rise to both consciousness and self-consciousness.
106In the whole of this thesis, I lay great emphasis on the notion of tangentiality. I mean
tangentiality in the senseinherited from the Leibnizian infinitesimal calculus. It denotes a linear movement, structured by two end points which it never reaches but approaches indefinitely. In this sense, tangentiality qualifies Being qua becoming. The tangentiality of becoming expresses the tangentiality of intentionality in Merleau-Ponty (the two end points being the subjective and objective poles) and the tangentiality of self-becoming (the healthy
“If we give up the effecting subject, then also the object on which effects are exerted. Duration, conformity with itself, being, inhere neither in what is called subject nor in what is called object. [...] All these are oppositions which don’t exist in themselves and in fact only express differences of degree that look like oppositions when viewed through a particular prism.”107