I

The mathematical object seems to be the privileged example and most permanent thread guiding Husserl’s reflection. This is because the mathematical object is ideal. Its being is thoroughly transparent and exhausted by its phenomenality. Absolutely objective, i.e., totally rid of emparical subjectivity, it nevertheless is only what it appears to be. Therefore, it is always already reduced to its phenomenal sense, and its being is, from the outset, to be an object of a pure consciousness.

The Philosophy of Arithmetic, Husserl’s first important work, could have been entitled The Origin of Arithmetic.

In 1887-91, the origin of artithmetic was described in terms of psychological genesis. In The Origin of Geometry, after fifty years of meditation, Husserl repeats the same project under the species of a phenomenological history.

[…] when, in the period of the Crisis, history itself breaks through into phenomenology, a new space of questioning is opened, one that will be difficult to maintain in the regional limits which were so long prescribed for it. [29]

While constantly practiced in the Crisis itself, this new access to history is never made a problem. At least not directly as such.

Neither the structures of historicity in general, nor the methods of the phenomenology of history were made the objects of specific, original questions.

 

Now geometry is a mathematical ontology whose object is determined as the spatiality of the thin belonging to Nature.

 

II

For Galileo – whose name here is the exemplary index of an attitude and a moment, rather than a proper name – was already an inheritor of geometry. [35]

If, in the Crisis, a very important place is reserved for Galileo and his revolution (which Husserl situates at the origin of the modern spirit’s perils) […]

[NB. the position of Dee with respect to this particular revolution]

[…] here the radicalist demand wants to undo the sedimentations upon which the enterprise of an infinite mathematization was based. We must reduce the very remarkableness of the Galilean naivete to free the question as to the origin of geometry. [36]

In the Crisis, while invoking Galileo’s blindness to the traditoonal space of his own adventure and designating his ‘fateful ommission’, [not to enquire in return as to the original sense-bestowing production which, as an idelisation prracticed on the original ground of all theoretical and practical life […] resulted in the geometrical ideal formations] Husserl announces very precisely the task that he will undertake a little later on in the Origin: ‘For Galileo, then, [pure geometry as tradition] was given – and of course he, quite understandably, did not feel the need to go into the manner in which the accomplishment of idealization originally arose (i.e. how it grew on the underlying basis of the pre-geometrical, sensible world and its practical arts) or to occupy himself with questions about the origins of apodictic, mathematical self-evidence’. [37]

‘It did not enter the mind of a Galileo that it would ever become relevant, indeed of fundamental imprtance, to geometry, as a branch of a universal knowledge of what is (philosophy), to make geometrical self-evidence – the ‘how’ of its origin – into a problem. For us, proceeding beyond Galileo in our historical reflections, it will be of considerable interest to see how a shift of focus became urgent and how the ‘origin’ of knowledge had to become a major problem’.[37]

[…] if one must return to the instituting sense of first acts, it is not at all a question of determining what in fact were the first acts, the first experiences, the first geometers who were in fact responsible for the advent of geometry. […] even if, at its limit, this determination would embrace all the historical facts that have constituted the emperical milieu of truth’s founding, it would still leave us blind about the very sense of such a founding: a sense that is necessary and compared to which these facts have at best only an exemplary signification.

The juridical priority of the question of phenomenological origin is therefore absolute. [38]

[…] although it only has for its content ideal essences, ready-made geometry holds here in bulk the status of a fact which must be reduced in its factuality so that its sense can be read.

In a historical retrospection towards origins, Kant also evokes this mutation or transformation, this ‘revolution‘ which gave birth to mathematics out of some emperical ‘gropings’ in the Egyptian tradition.

‘The history of this revolution’, attributed to the ‘happy thought of a single man’ in ‘an experiment from which the path had to be taken must no longer be missed and from which the sure way of science was opened and prescribed for all times and in endless expansion‘, was more ‘decisive’ than the emperical discovery ‘of the path around the famous Cape [of Good Hope]’.

Thusk, like Husserl, Kant is attentive to the historical dimension of apriori possibilities and to the original genesis of a truth, whose birth (or birth certificate) inscribes and prescribes omnitemporality and universality – not only for the opening of its possibility, but also for each of its developments and for the totality of its becoming. [As with Husserl] the sense of the first demonstration can be rigorously grasped, even though we know nothing of the first factual experience or the first geometer […] [39]

Nevertheless, Kant’s indifference to the factual origin is more immediately legitimate than Husserl’s. For the inaugural mutation which interests Kant hands over geometry rather than creates it; it sets free a possibility, which is nothing less than historical, in order to hand it to us. At first this ‘revolution’ is only a ‘revelation for’ the first geometer. It is not produced by him. [40]

Undoubtedly, Husserl’s production (Leistung) also involves a stratum of receptive intuition. But what matters here is that this Husserlian intuition, as it concerns the ideal objects of mathematics, is absolutely constitutive and creative: the objects or objectivities that it intends did not exist before it; and this ‘before’ of the ideal objectivity marks more than the chronological eve of a fact: it marks a transcendental prehistory. [40]

kantian revelation

For the Kantian revelation, on the contrary, the first geometer merely becomes conscious that it suffices for his mathematical activity to remain within a concept that it already possesses. The ‘construction’ to which he gives himself, then, is only the explication of an already constituted concept that he encounters, as it were, in himself – a description whcih no doubt for Husserl as well would be true of every noncreative geometical act, and which teaches us about the sense of ready-made geometry as such, but not about geometry in the act of being instituted.

Contrary to ots synthetic explication, the concept itself, as a structure of apriori prescription, could not be historical, because it is not, as such, produced and grounded by the act of a concrete subject. Here all history can only be emperical. And if there is a birth of geometry for Kant, it seems only the extrinsic circumstance for the emergence of a truth (which is itself always already constituted for any factual consciousness).

Thus the spontaneous eidictic reduction which frees the geometrical essence from all emperical reality – that of sensible figuration as well as from the geometer’s psychological lived experience – is for Kant always already done [JD note – this seems true, furthermore, of the whole of Kant’s transcendental analysis].[41]

Strictly speaking, the reduction is not for or by a subject who makes himself responsible for it in a transcendental adventure, a protogeometer or philosopher reflecting on protogeometry; it is always already made possible and necessary by the nature of geometrcal space and the geometrical object.

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[there is no opening here for anything to affect the nature of this space. Does Husserl open the possibility of an originary technicity that will mean that this Kantian aesthetic form along with its temporal twin, is actually open to its own transformation? let’s see..]

the hidden history

Barring a ‘scarcely altered’ conventional Platonism, Kant’s indifference to emperical history is only legitimated from the moment that a more profound history has already created nonemperical objects. This history remains hidden for Kant.

Can we not say here that the theory of ideal space and time both requires and suppresses the bringing to light of an intrinsic and nonemperical historicity of the sciences of space and motion? If space and time were transcendental realities, a way would be opened for an ahistorical metaphysics and for a historicist emperical science, two interrelated possibilities that Kant always denounced in one and the same move. [42]

But to avoid empericism from the start and at any price, Kant had to confine his transcendental discourse to a world of ideal constituted objects, whose corrolate was therefore itself a constituted subject.

This notion of a protohistory, which the whole of Kantian philosophy seems to make contradictory even while invoking it, becomes Husserl’s theme.

In fact, we now wonder about the sense of the production of geometrical concepts before and this side of the Kantian ‘revelation’, before and this side of the constitution of an ideally pure and exact space and time.

[JD note – For Descartes , only after this phenomenology of mathematical evidence and with the hypothesis of the Evil Demon will the critical or juridical question be posed of the ground that guarantees the truth of naive evidence. The description itself and the ‘natural’ validity of this truth, moreover, will never be put into question on their own specific level. The priomordial ground of these constituted truths, whose mode of appearing is thus clearly recognised, will be delegated to a veracious God who is also the creator of eternal truths […]. In this respect, Descartes’ God, like that of the great classic rationalists, would only be the name given to a hidden history and ‘would function’ as the necessary reduction of emperical history and the natural world, a reduction which pertains to the sense of these sciences.]

[…] if, on the other hand, the eidos and the ideal object do not preexist every subjective act, as in a [conventional] Platonism; if then they have a history, they must be related to, i.e., they must be primordially grounded in, the protoidealisations based on the substrate of an actually perceived real world. But they must do this through the element of an original history. [45]

To proceed to the ground and primordial constitution of truth, we must return, starting from the real world, to a creative experience.

Even were it unique and buried, this expereince remains, de jure as well as de facto, first.

History as institutive would be the profound area where sense is indisociabel from being, where the de facto is indissociable from the de jure.

[…] the here and now of the ‘first time’ is institutive and creative.

Is this to say that this inseperability of fact and sense in the oneness of an instituting act precludes access for phenomenology to all history and to the pure eidos of a forever submerged origin?

Not at all. The indissociability itself has a rigorous determinable phenomenological sense. The imaginary variation of static phenomenology simply supposed a type of reduction whose style will have to be renewed in a historical phenomenology. [47]

The historical reduction […] will be reactivating and noetic. Instead of repeating the constituted sense of an ideal object, one will have to reawaken the dependence of sense with respect to an inaugural and institutive act concealed under secondary passivities and infinite sedementations – a primordial act which created the object whose eidos is determined by the iterative reduction.

 

The singularity of the invariable first time already has a necessity whose eidetic fund is indeed rather complex: [48]

1. there is an essence-of-the-first-time in general, an Erstmaligkeit, an inaugural signification that is always reproducible, whatever its de facto example may be. Whatever were the emperical contents of the origin, it is apodictically and a priori necessary that geometry has had an origin and thus appeared a first time. […] Their historicity then is one of their eidetic components.

Husserl: ‘our interest shall be  the inquiry back into the most original sense in which geometry once arose, was present as the traditoion of millenia… we inquire into that sense in which it appeared in history for the first time – in which it must have appeared, even though we know nothing of the first creators and are not even asking after them.’

Here the ‘in whihc it must have appeared‘ clearly reveals Husserl’s intention and sums up the sense of every reduction. This ‘must‘ (have appeared) marks the necessity now recognised ans timelessly assigned to a past fact of an eidetic pre-scription and of an apriory norm. I can state this value of necessity independently of all factual cognition. Moreover, it is a double necessity […] of having had a historical origin and of having had such an origin, such a sense of origin.

But an irreducible historicity is recognised in that this ‘must’ is announced only after the fact of the event. [49]

2. whatever in fact the first produced or discovered geometrical idealities were, it is a priori necessary that they followed from a sort of non-geometry, that they sprang from the soil of a pre-geometrical experience.

3. whoever in fact the first geometers were, and whatever in fact the emperical content of their acts was, it is a priori necessary that the establishing gestures had a sense, such that geometry issued from them with the sense as we now know it. […] This means – by a necessity which is no less than an accidental exterior fate – that I must start with ready-made geometry, such as it is now in circulation and whjich I can always phenomenologically read, in order to go back through it ans question the sense of its origin. 

Husserl here speaks of Ruckfrage, a notion no doubt current enough, but which now takes on a sharp and precise sense. We have translated it by return inquiry (question en retour). Like its German synonym, return inquiry (and question en retour as well) is marked by the postal and epistolary reference or resonance of a communication from a distance. Like Ruckfrage, return enquiry is asked on the basis of a first posting. From a recieved and already readable document, the possibility is offered me of asking again,a dn in return, about the primordial and final intention of what has been given me by tradition. The latter, which is only mediacy itself and openness to a telecommunication in general, is then, as Husserl says, ‘open… to continued enquiry’.

These analogies, the metaphorical focus of our text, confirm ast what point is required the ‘zigza‘ way of proceeding – a procedure that the Crisis proposes as a sort of necessary ‘circle‘ and which is only the pure form of every historical experience. [51]

[Adding scan from book. Seems that this is an important passage for a lot of Derrida’s subsequent work on postal systems and metaphor. White mythologies as worn metaphors whose origins are lost, etc. etc. ]

 

 

III

‘This return inquiry unavoidably remains within the sphere of generalities, but, as we shall soon see, these are generalities that can be richly explicated…’ (Husserl)

The first of these radical generalities is precisely that which authorises the return inquiry: the unity os geometry’s sense is that of a tradition. Geometry’s development is a history only because it is a history. However far its building up progresses, however generous the proliferation of its forms and metamorphoses may be, they do not call again into question the unified sense of what, in this development, is to be thought of as the geometrical science. The ground of this unity is the world itself: not as the finite totality of sentient beings, but as the infinite totality of possible experiences in space in general. The unity of the geometrical science, which is also its oneness, is not confined to the systematic coherence of a geometry whose axioms are already constituted; its unity is that of a traditional geometrical sense infinitely open to all its own revolutions.

[the future developments of geometry are implied in this unity – questions around the priority of the form of spatiality with respect to geometry (the degree to which geometry precedes spatiality) and then as to the technicity of its origin (does a certain technics (geodesy/horology) intervene?)]

To pose the question of this traditional unity is to ask oneself: how, historically, have all geometries been, or will they be, geometries?

Furthermore, this unity of geometry’s sense, such as it is announced in the Origin, is not a general concept that is extracted or abstracted from various known geometries. On the contrary, it is the primordial concrete essence of geometry that makes such a generalising operation possible.

behind the axioms of mathematics

[…] if the primordial act of grounding that Husserl wishes to elicit here was the institution of axiomatics and the ideal of deductivity in general – and if this institution was described as that of mathematics itself – then the Husserlian project would be seriously threatened by the evolution of axiomatization towards total formalisation within which one necessarily comes up against the limits stated by Godel’s theorum […]

But that is not so!

[…] there is no doubt […] that the kinds of primordial evidence he investigates here are for him prior to those axioms and serve as their ground. (husserl: ‘Primordial evidence must not be confused with the evidence of ‘axioms’; for axioms are in principle the results of primordial sense-fashioning and always have this behind them‘.)

Axiomatics in general (from which alone every ideal of exhaustive and exact deductivity can then spring) already supposes, therefore, a sedimentation of sense: i.e., axiomatics supposes a primordial evidence, a radical ground which is already past. It is then already exiled from the origins to which Husserl now wishes to return. [55]

[…] as soon as the question of origins arises, geometrical determinability seems indeed to have the sense of geometrical determinability in general, as the infinite horizon of a science, whatever future forms develop.

When Hursell speaks in the Origin of a ‘horizon of geometrical future in precisely this style’, this style os not that of deductivity, but of geometrly or mathematics in general, from which as yet and always the undecidables or any other future mathematical formations will stem.

The unity of geometrical truth’s primordial sense, that unity which orients the Origin, could then be posed in a question of this kind: what is mathematical determiniability in general, if the undecidability of a proposition, for example, is still a mathematical determination? Essentially, such a question cannot expect a determined response, it should only indicate the pure openness and unity of an infinite horizon. [56]

science as Weltanschauung

As cultural form, the idea of science is undoubtedly also part of the Weltanschauung, and the content of science and philosophy is undoubtedly transmitted according to the same process as all other forms of culture and tradition in general. The process is analogous, if not identical, to that of internal time-consciousness described from the noematic viewpoint in the 1904-10 lectures. The present appears neither as the rupture nor the effect of a past, but as the retention oaf a present past, i.e., as the retention of a retention, and so forth. Since the retentional power of living consciousness is finite, this consciousness preserves significations, values, and past acts as habitualities (habuitus) and sedimentaitons. Traditional sedimentations in the communal world will have the function of going beyond the retentional finitude of individual consciousness. Of course, sedimentary retenion is not only the condition for the possibility of protention: it also belongs essentially to the general form of protention, which is itself conceived under the absolutely unique and universal form of the Living Present.

The latter, which is the primordial absolute of temporality, is only the maintenance of what indeed must be called the dialectic of protention and retention, despite Husserl’s repugnance for that word.

In the movement of protention, the present is retained and gone beyond as past present, in order to constitute another primordial and original Absolute, another Living Present.

Without this extraordinary absolute alteration of what always remains in the concrete and lived form of an absolute Present, wihtout this always renewed originality of an absolute primordiality, always present and always lived as such, no history would be possible. [58]

But at other times, on the contrary, Husserl describes science as a unique and archetypal form of traditional culture. Besides all the characteristiocs that it has in common with other cultural formations, science claims an essential privilege: it does not permit itself to be enclosed in any historeically determined culture as such, for it has the universal validity of truth. As a cultural form which is not proper to any de facto culture, the idea of science is the index of a pure culture in general; it designates culture’s eidos par excellence.

In this sense, the cultural form ‘science’ (of which geometry is one example) is itself ‘exemplary’ in the double sense of this word, eidetic and teleological: it is the particular example whcih guides the eidetic reduction and intuition, but it also is the example and model which must orient culture as its ideal.

[…] on the one hand, the culture of truth is the highest and most irreducible possibility of emperical culture; on the other hand, the culture of truth is itself only the possibility of a reduction of emperical culture and is manifested to itself only through such a reduction, a reduction which has become possible by an irruption of the infinite as a revolution within emperical culture.

[David Deutch on the Beginning of Infinity]

At the same time, the culture and traditoion of the truth are characterised by a paradoxical historicity. In one sense, they can appear disengaged from all history, since they are not intrinsically affected by the emperical content of real history and by determined cultural interconnections. This emancipation can be confused with a brewaking from history in general. For those who confine themselves to historical factuality, as well as for those who enclose themselves in the ideality of validity, the narration of truth can only have the historic originality of myth. [59]

But in another sense, one that corresponds to Husserls’s intention, the tradition of truth is the most profound and puriest history.

As soon as phenomenology breaks from both conventional Platonism and historicist empericism, the movement of truth that it wishes to describe is really that of a concrete and specific history – the foundations of which are a temporal and creative subjectiviry’s acts based on the sensible world and the life-world as cultural world.

This progress is brought about by the permanent totalisation and repetition of its acquisitions.

Only a communal subjectivity can produce the historical system of truth and be wholly responsible for it.

The irreducibel historicity of geometrical becoming is characterised by the fact that ‘the total sense of geometry'(and it necessary noetic correlate, total subjectivity) ‘could not have been present as a project and then as mobile fulfillment at the beginning’. If the history of geometry were only the development of a purpose wholly present from the beginning, we would have to deal only with an explication or a quasi-creation. We would have on one side a sychronous or timeless ground and, on the other side, a purely emperical diachrony with its indicative function but wihotu any proper unity of its own. Neither pure diachrony nor pure synchrony make a history.

 

IV

Husserl: ‘Geometrical existence is not psychic existence; it does not exist as something personal within the personal sphere of consciousness; it is the existence of what is Objectively there for ‘everyone’ (for actual and possible geometers, or those who understand geometry). Indeed, it has, from its primal institution, an existence which is peculiarly supratemporal and which – of this we are certain – is accessible to all men, first of all to the actual and possible mathematicians of all peoples, all ages; and this is true of all ist particular forms’.

The language of genesis could well seem fictive as this point: the description of any real development (neutralised in principle) would not call for it, but bringing to light the forma conditions of possibility, the de jure implications, and eidetic stratifications does.

Undoubtedly there is not in this account the least grain of history if we understand byt that the factual content of development. BUt the annoyed letdown of those who would expect Husserl to tell them what really happened, to tell them a story, can be sharp and easlily imaginable: however, this disappointment is illegitimate. [65]

Husserl only wished to decipher in advance the text hidden under every empirical story about which we would be curious.

Pure-interconnections-of history, apriori-thouth-of history, does this not mean that these possibilities are not in themselves historical? Not at all, for they are nothin but the possibilities of the appearance of history as such, outside of whihc there is nothing. History itself establishes the possibility of its own appearing. [66]

 

V

This possibility is first called ‘language‘.

If we ask ourselves about the manner in which the subjective evidence of geometrical sense gains its ideal Objectivity, we must first note that ideal Objectivity not only characterises geometrical and scientific truths; it is the element of language in general.

In an important note, Husserl specifies that ‘the broadest concept of literature’ comprises all ideal formations, since, in order to be such, they must always be capable of being expressibel in discourse and treanslatbale, directly or not, from one language into another. In other words, ideal formatioons are rooted only in language in general, not in the factuality of languages and their particular linguistic incarnations.

It is through these themes […] that the very subtle and specifig character of the Husserlian question appears.

The ideal object is the absolute model for any object whatever, for objects in general. It is always more objective than the real object, than the natural existent.

[…] the real object can never attain that absolute Objectivity which can be proposed for all subjectivity in general in the intangible identity of its sense.

The question ‘how is any object in general possible?‘ assumes its sharpest and most adequate form, then, in the Origin, when Husserl wonders: ‘How is ideal Objectivity possible?’

The ideal Objectivity of geometry is absolute and without any kind os limit. Its ideality – tertiary – is no longer only that of the expression [intra linguistic] or intentional content [inter linguistic]; it is that of the object itself. 

All adhearance to any real contingency is removes. The possibility of translation, which is identical with that of traditioon, is opened as infinitum: ‘The Pythagorean theorum, indeed all of geometry, exists only once, no matter how often or even in what langage it may be expressed. It is identically the same in the ‘original language’ of Euclid and in all ‘translations’ ; and within each language it is again the same, no matter how many times it has been sensibly uttererd, from the original expression and writing-down to the innumerable oral utterances or written and other documentations.

Husserl: ‘But the idealities of geometrical words, sentences theories – considered purely as linguistic formations – are not the idealities that make up what is expressed and brought to validity as truth in geometry; the latter are ideal geometrical objects, states of affairs, etc. Wherever something is asserted, one can distinguish what is thematic, that about which it is said (its sense), from the assertion, which itself, during the asserting, is never and can never be thematic. And the theme here is precisely ideal objectivities, and quite different ones from those coming under the concept of language.’

For the first time, wiht the absolute ideality of an object – the geometrical object which is through and through only the unity of its true sense – we pass beyond or rid ourselves of the ideal, but still bound, Objectivity of language. [75]

We simultaenously reach an Objectivity that is absolutely free with respect to all factual subjectivity.

That is why the exemplary queston of the origin of Objectivity cvoiuld not be asked apropos linguistic ideality as such, but apropos what is intended across and on the other side of this ideality.

But as the absolute ideal objectivity does not live in a topos ouranios, it follows that:

1. its freedom with respect to all factual subjectivity has only laid bare ist lrgitimate [de dropit] ties with a transcendental subjectivity;
2. its historicity is intrinsic and essential.

Thus the space for a transcendental historicity is prescribed in all its enigmatic depth.

‘Our problem now concerns precisley the ideal objectivities which are thematic in geometry: how does geometrical ideality (just like that of all sciences) proceed from its primary intrapersonal origin, where it is a formation produced within the conscious space of the first inventor’s soul, to its ideal Objectivity.’

 

VI

Husserl’s response is direct and comes very quickly. It has the style of a turnabout […]. Ideality comes to its Objectivity ‘by means of language, through which it recieves, so to speak, its linguistic flesh’.

‘[…] how does linguistic incarnation make out of the merely intrasubjective formaiton the Objective, that which, for example, as geometrical concept or state of affairs, is in actual fact present, intelligible for all, now and always, already being valid in its linguistic expression as geometrical discourse, as geometrical proposition in its geometrical ideal sense?’

We might be surprised.

transcendental language

After having so patiently extracted […] thematic truth from linguistic ideality and from all ‘bound’ idealities, Husserl then seems to redescend toward language as the indispensible medium and condition of possibility for ideal Objectiviry, for truth itself, which would be what it is ojnly through its historical and intersubjective circulation. [76]

Thus, does Husserl not come back to language, culture, and history, all of which he reduced in order to have the pure possibility of truth emerge [unbound]? Is he not ‘bound’ again to lead into history that whose absolute ‘freedom’ he just described? From then on, will he not be compelled to remove all the reductions step by step, in order to recover finally the real text of historical expereince?

In reality – and we think this is the most interesting difficulty of this text – Husserl does exactly the opposite.

This return to language, as a return home to culture and history in general, brings to its final completion the purpose of the reduction itself.Going beyond ‘bound idealities’ toward the theme of truth itself is a reduction which makes the independence of truth appear with respect to all de facto culture and language in general. But once more it is only a question of disclosing a juridical and transcendental dependence.

No doubt geometrical truth is beyond every particular and factual linguistic hold as such, one for which every subject speaking a determined language and belonging to a determined cultural community is in fact responsibel. But the Objectivity of this truth could not be constituted without the pure possibility of an inquiry into a pure language in general.

Without this pure and essential possibility, the geometrical formation would remain ineffable and solitary.

Then it would be absolutely bound to the psychological life of a factual individual, to that of a factual community, indeed to a particular moment of that life.

It would become neither omnitemporal, nor intelligible for all: it would not be what it is.

[JD note: Here we are speaking of transcendental language insofar as, on the one hand, the latter is ‘constituting‘ compared with ideal Objectivity, and, on the other, insofar as it is not confused in its pure possibility with any de facto emperical language]

[does this notion of a transcendental language open the possibility of a transformation of the aesthetic? – with ref to the questions posed above]

Whether geometry can be spoken about is not, then, the extrinsic and accidental possibility of a fall into the body of speech or a slip into a historical movement. Speech is no longer simply the expression (Ausserung) of what, without it, would already be an object: caught again in its primordial purity, speech constitutes the object and is a concrete juridical condition of truth.

The paradox is that, without the apparent fall back into language and thereby into history, a fall which would alienate the ideal purity of sense, sense would remain an emperical formation imprisoned as fact in a psychological subjectivity – in the inventor’s head.

Historical incarnation sets free the transcendental, instead of binding it. This last notion, the transcendental, must be rethought.

Does this ultimate reduction, which opens onto a transcendental language, revolutionise Husserl’s thought? Does this return to a speaking subject as what constitutes the ideal object, and then absolute Objectivity, proceed to contradict a previous philosophy of language?

[…] the return to the primordiality of the speaking subject is no more in contrast with [the] first approach to language than the ‘idealism’ of Ideas I is, as was thought, with the apparent ‘logicism’ or ‘realism’ of the logical Investigations. The question is simply to parenthesise constituted language, which is what Husserl continues to do in Formal and Transcendental Logic and in the Origin, in order, subsequently, to let the originality of constitutive language come to light. [78]

[…] is the recognition in language of what constitutes absolute ideal Objectivity, as far as it states this Objectivity, not just another way of announcing or repeating that transcendental intersubjectivity is the conditioon of Objectivity?

At bottom, the problem of geometry’s origin puts the problem of the constitution of intersubjectivity on a par with that of the phenomenological origin of language.

For the moment it suffices to know, if not how, at least that language and consciousness of fellow humanity are interrelated possibilities and already given the moment the possibility of science is established.

The horizon of fellow mankind supposes the horizon of the world: it stands out and articulates its unity against the unity of the world.

Of course, the world and fellow mankind here designate the all-inclusive, but infinitely open, unity of possible experiences and not this world right here, whose factuality for husserl is never anything but a variable example.

Consciousness of being-in-community in one and the same world establishes the possibility of a universal language. Mankind is first conscious of itself ‘as an immediate and mediate linguistic community.’

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[

additional reflections on the below here

 

nb. thinking of radical title in Schmitt. where land appropriation is the originary gesture of the group – the appropriation of land is the logical root of law, and the founding gesture of the community, but here, in Husserl, language [let’s jump ahead and say technics] is co-originary. for Schmitt it founds the spatial [geometric] order. some kind of measure makes this possible – technicity is in the origin]

On this, see A History of Mathematics (Boyer) (p16). ‘The Greek historian Heroditus tells us that the obliteration of boundaries in the overflow of the Nile emphasised the need for surveyors. The accomplishments to the ‘rope-stretchers’ of Egypt evidently were admired by Democritus, an accomplished mathematician and one of the founders of an atomic theory […].  And on p6 (section titled ‘Origin of Geometry’): Heroditus held that geometry had originated in Egypt, for he believed that the subject had arisen there from the practical needs for resurveying after the annual flooding of the river valley. Aristotle argued that it was the existence of a priestly leisure class in Egypt that had prompted the pursuit of geometry. We can look upon the views of Heroditus and Aristotle as representing two opposing theories of the beginnings of mathematics, one holding to an origin in practical necessity, the other to an origin in priestly leisure and ritual. The fact that the Egyptian geometers sometimes were referred to as ‘rope-stretchers’ (or surveyers) can be used in support of either theory, for ropes undoubtedly were both used in the laying out of temples and in realigning the oblitrated boundaries.

Boyer notes that both these theories underestimate the age of the foundation of mathematics. Of interest here: for Heroditus it is clear that Geometry, Technics (of surveying), and Nomos are coimplicated in the origin of each. No Nomos without a technics (for measuring) and a geometry (for calculating). Geometry originates in the nees for borders, for the spatial organisation of the land (Nomos), and requires a Technics to be realised in the world, etc. 

‘Thus, in some form, the constitutive process of a land-appropriation is found at the beginning of the history of every settled people, every commonwealth, every empire. This is true as well for the beginning of every historical epoch. Not only logically, but also historically, land appropriation precedes the order that follows from it. It constitutes the original spatial order, the source of all further concrete order and all further law. It is the reproductive root in the normative order of history. All further property relations – communal or individual, public or private property, and all forms of possession and use in society and in international law – are derived from this radical title. All subsequent law and everything promulgated and enacted thereafter as decrees and commands are nourished, to use Heraclitus’ word, by this source.’ [NOMOS, p. 48]

See also Stiegler Technics & Time 1 (p. 143 in Fr Fayard edition). Reading of Rousseau: ”grouping’ is not originary’. At his origin, man is not in society (he is ‘entirely with himself’). He has no need for prostheses. His body being the only instrument he know, he employs it for different uses. Everything is inside, the origin is the interior. The fall (la chute) is exteriorisation. [the question here is to what extent this exterieorisation is in fact primary, originary. Man prior to this is mythological. Most interesting though: for Schmitt, radical title founds the spatial order, and the social order. The social/spatial order is made possible through land appropriation. In the above from Derrida, intersubjectivity, language, technics, spatiality (via gemoetry) are all in play in the origin.]

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In connection with this we need to note three important points:

1. Within the horizon of this consciousness of fellow mankind, it is ‘mature, normal’ mankind that is ‘privileged’, both ‘as the horizon of civilisation and as the linguistic community’. The theme of adult normality, which took up more and more room in Husserl’s analyses, is here treated as a matter of course. […] To have access to the eidos of mankind and of language, certain men and certain speaking subjects – madmen and children – are not good examples.
2. The possibility of a mediate or immediate horizon of universal language risks running into essential difficulties and limits. 1. it presupposes the hazardous problem concerning the possibility os a ‘pure grammar’ and ‘a priori norms’ of language is resolved; 2. it presupposes that as heterogeneous as the essential structures of several languages may be, translaiton is an always possible task: two normal men will always have an a priori  consciousness of their belonging together to one and the same humanity, living in one and the same world. […] For Husserl, the model of language is the objective language od science. A poetic language, whose significations would not be objects, will never have any transcendental value for him.
3. As the infinite horizon of every possible expereince, the world is consequently ‘the universe of Objects which is linguistically expressible in its being and its being-such’. […] The world, therefore, is essentially determined by the dative and horizontal dimension of being percieved. […] Despite all the antagonistic motifs which animate phenomenology, space’s privilege therein is in certain respects remarkable. […] Geometry, in effect, is the science of what is absolutely objective – i.e. spatiality – in the objects that the Earth, our common place, can indefinitely furnish as our common ground with other men. But if an objective science of earthly things is possible, an objective science of the Earth itself, the ground and foundation of these objects, is as radically impossible as that of transcendental subjectivity. The transcendental Eaeth is not an object and can never become one. And the possibility of a geometry strictly complements the impossibility of what could be called a ‘geo-logy’, the objective science of the Earth itself. This is the sense of the fragment* which reduces, rather than ‘refutes’, the Copernican naivete and shows that the Earth in its protoprimordiality does not move. […] Primordially, the earth moves no more than our body moves. […] The Earth therefore knows the rest of an absolute here […] Rest starting from which motion and rest can appear and be thought as such, the Rest of a ground and a horizon in thier common origin and end.

[*NB JD note on this: This Fragment [‘Fundamental Investigations on the Phenomenological Origin of the Spatiality of nature’], dated May 1934.From the perspective of the science of space, it sketches a movement analogous to that of the Origin, but directed toward kinematics. In a certain sense, it completes the origin, although in the Origin Husserl clealry specifies that geometry is only a title for all mathematics of pure spatiotemporality.

Husserl: ‘We Copernicans, we men of modern time, we say: the earth is not ‘the whole of Nature’, it is one of the planets, in the infinite space of the world. The earth is a spherical body which certainly is not perceptible as a whole, by a single person and all at once, but in a primordial synthesis as the unity of singular experiences bound to each other.’ […]]

 

If the possibility of language is already given to the primally instituting geometer, it suffices that the latter has produced in himself the identity and the ideal permanence of an object in order to be able to communicate it. Before the ‘same’ is recognised and communicated among several individuals, it is recognised anjd communicated within the individual consciousness […]. Thus, before being the ideality of an ideal object for other subjects, sense is this ideality for other moments of the same subject. In a certain way, therefore, intersubjectivity is first the nonemperical relation fo Ego to Ego, of my present present to other presents as such; i.e., as others and as presents (as past presents). […] The Living Present constitutes the other as other in itself and the same as same in the other. [86]

 

VII

writing

A decisive step remains to be taken. By itself the speaking subject, in the strict sense of the term, is incapable of absolutely grounding the ideal Objectivity of sense. Oral communication (i.e., present, immediate, and synchronous communication) among the protogeometers is not sufficient to give ideal objectivities their ‘continuing to be’ and ‘persisting factual existence‘, thanks to which they perdure ‘even during periods in which the inventor and his fellows are no longer awake to such an exchange or even, more universally, no longer alive.’

To be absolutely ideal, the object must still be freed of every tie with an actually present subjectivity in general. Therefore, it mus perdure ‘even when no one has actualised it in evidence’. Speech has freed the object of individual subjectivity but leaves it bound to its beginning and to the synchrony of an exchange within the institutive community.

The possibility of writing will assure the absolute traditionalisation of the object, its absolute ideal Objectivity – i.e., the purity of its relation to a universal transcendental subjectivity. Writing will do this by emancipating sense from its actually present evidence for a real subject and from its present circulation within a determined community. ‘The decisive function of written expression, of expression which documents, is that it makes communication possible without immediate or mediate address; it is, so to speak, communication become virtual’.

That virtuality, moreover, is an ambiguous value: it simultaneously makes passivity, forgetfulness, and all the phenomena of crisis possible. [87]

Without the ultimate objectificaiton that writing permits, all language would as yet remain captive of the de facto and actual intentionality of a speaking subject or community of speaking subjects. By absolutely virtualising dialogue, writing creates a kind of autonomous transcendental field from which every present subject can be absent.

Thus a subjectless transcendental field is one of the ‘conditions’ of transcendental subjectivity.

When considering the de jure purity of intentional animation, Husserl always says that the linguistic or graphic body is a flesh, a proper body (Leib), or a spiritual corporeality […]. From then on, writing is no longer only the worldly mnemotechnical aid to a truth whose own being-sense would dispense with all writing-down. The possibility or necessity of being incarnated in a graphic sign is no longer simply extrinsic and factual in comparison with ideal Objectivity: it is the sine qua non condition of Objectivity’s internal completion.

As long as ideal Objectivity is not, or rather, can not be engraved in the world – as long as ideal Objectivity is not in a position to be party to an incarnation (which, in the purity of its sense, is more than a system of signals [signalisation] or an outer garment) – then ideal Objectivity is not fully constituted. Therefore, the act of writing is the highest possibility of all ‘constitution‘, a fact against which the transcendental depth of ideal Objectivity’s historicity is measured.

What Fink writes about speech in his excellent transcript of the Origin  is a fortiori true for writing: ‘In sensible embodiment occurs the ‘localisation’ and the ‘temporalisation’ of what is, by its being-sense, unlocated and untemporal.’

But does this formulation not permit linguistic embodiment to be understood as taking place outside the being-sense of ideal objectivity? As ‘occurring’ or ‘unexpectedly happening’ in addition to the being-sense? Does not this formulation give the impression that ideal objectivity is fully constituted as such before and independently of its embodiment, or rather, before and independently of its ability to be embodied?

But Husserl insists that truth is not fully objective, i.e., ideal, intelligible for everyone and indefinitely perdurable, as long as it cannot be said and written.

Undoubtedly, truth never keeps the ideal Objectivity or identity of any of its particular de facto incarnations; and compared to all linguistic factuality it remains ‘free’. But this freedom is only possible precisely from the moment truth can in general be said or written, i.e., on condition that this can be done.

Paradoxically, the possibility of being written [possibilite graphique] permits the ultimate freeing of ideality.

Therefore, we could all but reverse the terms of Fink’s formula: the ability of sense to be linguistically embodied is the only means by which sense becomes nonspatiotemporal.[90]

From then on, in effect, as is prescribed for it, sense is gathered into a sign, and the sign becomes the worldly  and exposed residence of an unthought truth. We have previously seen that truth can perdure in this way without being thought in act or in fact – and that is what radically emancipates truth from all empirical subjectivity, all factual life, and the whole real world.

At the same time, man’s communal being ‘is lifted to a new level’: it can appear, in effect, as a transcendental community.

The authentic act of writing is a transcendental reduction performed by and towards the we.

But since, in order to escape worldliness, sense must first be able to be set down in the world and be deposited in sensible spatiotemporality, it must put its pure intentional ideality, i.e., its truth-sense, in danger.

the disappearance of truth

Thus a possibility, which even here accords only with empiricism and nonphilosoiphy, appears in a philosophy which is (at least because of certain motifs) the contrary of empiricism: the possibility of truth’s disappearance. [93]

What disappears is what is annihilated, but also what ceases, intermittently or definitely, to appear in fact […].

To determine the sense of this ‘disappearance’ of truth is the most difficult problem posed by the origin and all of Husserl’s philosophy of history.

Furthermore, we were unable to find in Husserl an unequivocal response to a question which only makes that of phenomenology iteslf return: what is the sense of its appearing? That equivocation will presently reveal both how much the author of the Crisis was a stranger to history or how fundamentally incapable he was of taking it seriously, and at what point (in the same moment) he strives to respect historicity’s own peculiar signification and possibility and truly to penetrate them.

What, then, is this possibility of disappearance?

1. let us rule out the possibility fo a death of sense in general within the individual consciousenss. Husserl clealry specifies in the Origin and elsewhere that, once sense appeared in egological consciousenss, its total annihilaiton becomes impossible.
2. The graphic sign, the guarantee of Objectivity, can also in fact be destroyed. This danger is inherent in the factual worldliness of inscription itself, and nothing can definitively protect inscription from this. […] Such a forgetfulness would not only suppress this sense but would annihilate it in the specific being-in-the-world to which its Objectivity is entrusted. For Husserl clearly said this: insofar signs can be immediately perceptible by everyone in their corporeality; insofar as their bodies and corporeal foms are always already in an intersubjective horizon, then sense can be deposited there and communalised. Corporeal exteriority undoubtedly does not constitute the sign as such but, ins a sense that we must make clear, is indispensible to it. […] All factual writings, in which truth could be sedimented, will never be anything in themselves but sensible ‘exemlars’, individual events in space and time […] Since truth does not essentially depend on any of them, they could all  be destroyed without overtaking the very sense of absolute ideality. Undoubtedly, absolute ideality would be changed, mutilated, and overthrown in fact; perhaps it would disappear in fact from the surface of the world, but its sense-of-being as truth, which is not in the world – neither in our world here, nor any other – would remain intact in itself. Its being-sense would preserve its own intrinsic  historicity, its own interconnections, and the catastrophy of worldly history would remain exterior  to it.  […] Since transcendental consciousness can always and with complete freedom modify or suspend the thesis of each (therefore all) contingent existence and of each (therefore all) transcendence, its very sense is de jure and absolutely independent of the whole world. The situation of truth, particulalry of geometrical truth, is analogous. […] since the interconnections and sedimentations of geometrical truth are free of all factuality, no worldly catastrophe can put truth itself in danger. All factual peril, therefore, stops at the threshold of its internal historicity.
3. We would be fully convinced if ther[…] Husserl had considered writing to be a sensible phenomenon. But did we not just find out that writing, insasmuch as it was grounding (or contributing to the grounding of) truth’s absolute Objectivity, was not merely a constituted sensible body (Korper), but was also a properly constituting body (Leib) – the intentional primordiality of a Here-and-Now of truth?

If writing is both a factual event and the uprising of sense, if it is both Korper and Leib, how would writing preserve its Leiblichkeit from corporeal disaster?

Husserl is not going to immobilize his analysis within this ambiguity, which for him is only a provisoional and factual confusion of regions.