Derrida and The Origin of Geometry.

“We stand, then, within the historical horizon in which everything is historical, even though we may know very little about it in a definite way. But it has its essential structure that can be revealed through methodical inquiry.” (172).
“Making geometry self-evident, then, whether one is clear about this or not, is the disclosure of its historical tradition” (173).
The following examination will attempt to deal with certain key moves which are made within the Origin of Geometry, by both Derrida and Husserl, which seem to merit our attentiveness. The exemplarity of Husserl’s Origin lies in a ‘revolution’[1] in the manner of proceeding historically in order to “take possession of the meaning, method and beginning of philosophy, the one philosophy to which our life seeks and ought to be devoted” (157).[2] The Origin must be viewed as an attempt to respond to, or address, a perceived Crises in the sciences. The need for proper contextualization seems to be of paramount importance to any proper reading of the text. The moves made by Husserl are informed by the Crises, which is of a science completely given over to its own logical activity; a science completely given over to its own abstractions, informed by the “success of its practical application,” but not given to any “actual insight” (169) ‘Geometry,’ as an exemplary instance of mathematics, as the science of shapes existing in space-time, exists as a kind of ‘tradition.’ The ‘tradition’ of ‘geometry’ had already been emptied of its sense, or its “truth-meaning’ when it was received by Galileo. Thus, it becomes necessary for Husserl, in order to halt the mechanical advance of a science completely given over to its own abstractions, to demonstrate that the constitution of ‘geometry,’ and hence of science in general, was do to the creative acts of the human animal. This can only be seen as a need for re-awakening, the need for the return inquiry, or Ruckfrage, in order to unearth the original, or originary sense, buried under the various ‘sedimentations’ of ‘tradition.’ The examination that follows will engage with the ‘method’ illuminated in the Origin, which is the ‘what,’ of its exemplarity, and the ‘how’ of its procession. The following engagement will necessarily be mediated, and perhaps even ‘supplemented,’ by Derrida’s Introduction.
It seems apparent that every significant move within the origin is also a site of a kind of privilege, or perhaps a choice, which is at the same time not a choice but a necessary manoeuvre within the purview, or ‘horizon’ of phenomenology.[3] The privileged case of writing,[4] as the “infinitization” of absolute ideal objectivity, at once liberates, or ‘frees’ the ideal objectivity from the ‘finite’ community of speakers, while at the same time opening a ‘transcendental field’ which assures its transmission, but empties the sense of origin from the absolute ideality. Transcendental historicity, is nothing other than the eidos of historicity as the constituting activity of all the eidetic sciences. Through this move we are placed in a ‘horizon,’ which is the site of an irreducible tension, or an essential structural relation. The transcendental subjectivity, becomes responsible for the sense, or the possible reactivation of the sense which is carried with every subsequent ‘sedimentation.’ However, as inscribed, the ideal object is once again ‘fallen’ into linguistic expression, which is necessarily ‘equivocal.’[5] At the same time, however, language can neither be singularly ‘equivocal;”[6] nor ‘univocal,’[7] rather, it is the case, as Husserl maintains, that the possibility of univocity is precisely that which informs the intentional content of the equivocal embodiment. Thus, univocity, the possibility for reactivation of the original sense, functions as the telos, or the absolute ‘horizon,’ of the equivocal (104). The univocal becomes what Derrida will call the “Idea in the Kantian sense.”[8] Furthermore the movement within the structure is necessarily temporal, thus we will examine the relation between the “Idea” and the “Living Present.”
We turn now to the sight of another privileged movement the privilege of the ‘Now’ of the ‘Living Present.’ Perhaps, it is necessary to turn back to the series of quotes which opened, and have guided, the current examination. Firstly, that we are always in the midst of a ‘historical horizon,’ and that all traditional objects of ‘geometry,’ or of science in general, encountered therein bring with them their intrinsic history. As Derrida states it “…we know a priori that every cultural present, therefore every scientific present, implicates in its totality the totality of the past” (109). Grounded in the “Living Present” of the particular egological consciousness, this space is where the entirety of the past ‘interweaves’ with a constituting cultural present, is the “historical Present,” or the “historical absolute.[9]”
“”…this historical present has its historical past behind it, that it has developed out of them, that the historical past is a continuity of pasts which proceed from one another, each, as a past present, being a tradition producing tradition out of itself” (176).
Any factual investigation into the sense of historicity, must therefore begin from the “a priori intrinsic historicity of sense.” Historicity, which is nothing other than sense-history, as ‘horizonal,’ is made possible by ideal objects, of which ‘geometry’ is one. Historicity is, thereby, uncovered as ‘circular’ in structure, the possibility of ‘repetition,’ or a ‘reactivation’ of self-evidences resides in the possibility of uncovering a universal a priori historical ‘world.’ Husserl, through the method of “free variation,”[10] which Derrida characterises, as a “zigzag,” “forward and backward,” uncovers the apodictic of universal historicity. Properly understood as a method, Derrida is careful to point out that ‘variation’ does not seek to “deduce factuality a priori,” but rather removes “every bond to the factually valid historical world”(112-113). By removing all facticity, Husserl uncovers what is historically universal and necessary a priori.
The ‘ideality,’ called ‘geometry,’ was constituted by Euclid[11], although it predates him, continued onward through Galileo[12], and subsequently Newton, and will doubtlessly continue through countless possible futural modifications and ‘sedimentations’, all the while remaining this ideality called ‘geometry.’ Thus, as Derrida remarks, Euclid’s ‘geometry’ marks the ‘infinitization’ of the initial ‘finite a priori system’ (130).[13] It therefore, seems to be the case that ‘geometry’ is not yet at its origins but rather in a process of proceeding toward it. We have discussed this movement before in our treatment of the ‘equivocal’ and the ‘univocal.’ The original ‘geometric’ ideation, therefore announced its completion at the onset, but its completion is continually ‘deferred.’ ‘Geometry,’ therefore, can see its unity in the ‘Now’ of the ‘interweaving’ between the ‘historical present’ and the ‘Living Present, where the ‘phenomena’ and ‘idea’ momentarily reside in a kind of ‘dialectic.’ The “Idea,” is therefore a kind of mediation between consciousness and history, however, the ‘Idea’ is such that it never phenomenalizes itself.[14] It seems to be the case therefore that the ‘Idea’ is both the possibility of something like the absolute ground of the ‘Now’ of the ‘Living Present,’ as the site of “interweaving,” yet at the same time ‘defers’ its appearing to the ‘gaze’ of phenomenological sight.
Finally, let us turn to what might be seen as the announcement of Derrida, of a Derridian trajectory at the limits of phenomenology. If we return to what was declared to be at stake in Husserl’s Origin of Geometry, namely the possibility of possessing “the meaning, method and beginning of philosophy,” what has become the status of the Husserlian project? The ‘Idea,’ which makes possible something like a project of phenomenology, which ultimately seeks ‘the thing in itself,’ is hence seen to be as Derrida states it:
“…stretched between the finitizing consciousness of its principle and the infinitizing consciousness of its institution, the Endstiftung indefinitely deferred [differee] in its content but always evident in its regulative value” (138).
The marked absence of a phenomenology of the ‘idea,’ evidences the inability of phenomenology to endeavour to undertake a phenomenology of phenomenology. The ‘Idea’ seems to take the place of that which it is the ‘Idea’ ‘of,’ but the ‘of’ is never given in itself. The Idea, therefore, “reveals the being of the intention: intentionality itself” (139). The result is that phenomenology cannot ground itself in this space between the ‘Idea’ and what it is an ‘Idea’ of, this space which points toward a telos, or the possibility of a unity, but which is never a unity but rather an infinite ‘horizon.’ This space is always an anticipation of meaning but can never grasp the ‘meaning’ of a philosophy whose meaning will always be differed. Thus, it would seem, that the use of ‘transcendence,’ has always marked the site the ‘delay,’ or ‘deferral,’ which seems necessary for the existence of anything historical.
Throughout my reading of Derrida’s Introduction to the Origin of Geometry, I have attempted to retain a sense of the specificity involved in Husserl’s work. Perhaps, it may be remarked, that this site has been a rather complex one, and perhaps it may be further remarked that I may not have been able to express anything beyond some provisional understanding. The current exercise, has itself, been a process,[15] albeit an incredibly messy one, of working within the limits of the‘horizon’ of phenomenology.

[1] What makes Galilean geometry exemplary? Is it proper to speak of a ‘revolution?’ Can we speak of something like a ‘revolution’ as a characteristic of Galilean geometry? If we decide to maintain that indeed a ‘revolution’ is what we are dealing with, what is at stake in such an utterance? Do we place at risk the sense we are intending? If we invoke the notion of ‘revolution,’ do we not import a certain sense of movement? Perhaps the movement is of a political nature as in the overturning, or alteration, of a governing body, or of a point of view. Perhaps, even further, the movement implied by ‘revolution’ is of a circular nature, of a return to the point of origin?
[2] It should, perhaps, be noted, or remarked that the ‘first philosophy’ within which might be able to ground the historical project of science is Greek, and hence European, in origin.
[3] If phenomenology is to be able to possess ‘this first philosophy’ it must come to possess it in its sense. This initial statement is perhaps the statement of a limit which will, perhaps, become clearer as we continue.
[4]“The possibility of writing will assure the absolute traditionalization of the object, in its absolute ideal Objectivity” Writing ‘frees’ the ‘bound’ ideality from the synchronic exchange within the institutive community; thereby opening the ‘transcendental field’ wherein all factual subjectivities may be absent. At the same time, however, the absolute Objectivity, as a kind of assertion, remains in the legitimate purview of a transcendental subjectivity and retains within itself its essential historicity. The space of transcendental history has, through this movement been illuminated (77).
[5] ‘Equivocal,’ in the sense that any singular sign can have a plurality of possible significations, thus the ‘sign’ which stand in for the ideal object, is no the object itself, but rather, its worldly manifestation.
[6] Pure ‘equivocity’ would ‘bound’ every ideality to its linguistic embodiment.
[7] Pure Univocity would make the linguistic embodiment equivalent to the thing-itself and hence eliminate the possibility of history altogether.
[8] The “Idea in the Kantian sense” expresses both its origin, and its content, however is never given to intuition as such, but rather serve as the promise, or announcement of a future unity.
[9] “The Living Present,” as the ground of the “historic Present,” as the primordial absolute of temporality,” as the space which maintains the distinction, or a Derrida terms it the ‘dialectic’ between ‘retention’ and ‘protention’ and which constitutes the ‘now’ only in ‘recollection’ (58)
[10] “…free variation, and in running through the conceivable possibilities for the life-world, there arises, with apodictic self-evidence, an essentially general set of elements going through all the variants; and of this we can convince ourselves with truly apodictic certainty.”(177)
[11] Euclid, marks the site of the “primordial” “inaugural infinitization” which opens up a mathematical field, or the “possibility of mathematical a priori.”(128) Euclid, is the spatio-temporal location of the axiomatization of an idealized geometry, which once inscribed, becomes the omni-temporal virtualization of an ideal objectivity; which might otherwise have remained “bound” within the ‘finite’ egological community of the originary Greek geometers.
[12] Galileo, as the site, or ‘moment’ of the taking up of the constituted geometric ideality of Euclid, or the possibility of mathematics in general, and projecting it, along with ideal notions of “motion,” “time” and “matter,” and thereby opening up a new “infinity” and expanding the a priori system initially constituted by Euclid. Galileo is both the site of a ‘revolution,’ a ‘sedimentation and hence a kind of rebirth.
[13] Although it happens to be the case that for Euclid himself ‘geometry’ remained a closed apriori system.
[14] If we are attentive to this reflection, it seems to pertain to every movement through the “Now” of the living present, which itself becomes an “Idea” which can only be ‘recollected.’ Through the movement of ‘retention’ and ‘protention’ it becomes clear that the ‘retention’ is not truly the thing itself, and the ‘protention’ is but the projection, or the bringing forward, of the Idea of the ‘Now’ which hold the promise of ‘Now’s’ to come.
[15] Perhaps, what has occurred presently may loosely be called a process of some sort. A process of losing one’s way, within the ways of another, in an attempt at the ‘reactivation’ of a ‘sense’ ‘constituted’ by Derrida; a ‘sense’ which seems to both go beyond, and come before the name Derrida.