Mathesis, Science and Philosophy

  • Posted on: 1 August 2010
  • By: worker

<table><tr><td>From <a href="http://www.gold.ac.uk/history/news-events/mathesis/">Goldsmiths</a>

<p>From an introduction by Gilles Deleuze to, La Math&eacute;se ou Anarchie et Hi&eacute;rarchie de la Science, by Jean Malfatti de Montereggio [1]. Translated from the French by David Reggio, Goldsmiths College, Department of History.</p>

<p>It is interesting to define mathesis in its dealings with science and philosophy. Such a definition inevitably remains exterior to mathesis itself – it is simple, provisional, and tends only to show that independently of all historical moments, mathesis characterises one of the great attitudes of mind always present. This is to say that here we will find only one critique of the arguments that scholars and philosophers have a tendency to invoke against mathesis.</p>

<p>The word 'initiated' and as to what it signifies needs to be addressed. It is also essential that we do not forget the landscape of the Indian civilisation within which mathesis was deployed, for we cannot say that mathesis is an abstraction of this civilisation, but only that our occidental mentality can grasp certain fundamental aspects. Indeed, mathesis, as a form of introduction, as a preface to itself, is already satisfactory and it is with this viewpoint that Dr. Malfatti's book presents a capital interest. Other works have no doubt since appeared that delve further into the Indian consciousness, yet there aren't many that venture, more than this, to introduce the notion of mathesis in-itself vis-&aacute;-vis science and philosophy.</p></td><td><img title="recursion is hot!" src="files/pictures/2009/fuckscience.jpg"></td></tr></table><!--break-->

<p>It is not easy to understand the exact sense of the discussions that periodically oppose philosophers and scholars because they do not speak the same language. Science installs itself within the object, it even reconstructs and uncovers the reality at the level of the object of thought without ever posing the problem of the conditions of possibility. The philosopher, however, situates the object as a representation in relation to the knowing subject. It matters little to him, asserts M. Alqui&eacute; [2], to know what is finally material or atoms, since these like all other representations only have philosophical status in terms of the mind which represents them. And we have yet to see the changes that the latest discoveries in modern physics can bring to the conceptions of Berkeley for example, dating from the 18th century!</p>

<p>There is a fundamental dualism in the knowledge of Science and Philosophy – an anarchic principle. At root, it is the Cartesian opposition between an extended substance and a thinking substance. The Cartesian example is especially interesting since Descartes never renounced it to the unity of knowledge, that is, to the mathesis universalis. It is also intriguing to see how this argument is situated on the theoretical plane where the knowing mind, in-itself so distinct from the extension with which it strictly appears to have nothing in common, deploys the order of things in as much as it thinks the order of its representations. Here, there is rupture and destruction as soon as there is unity. Descartes further asserted that with this rupture, unity finds its true sense in re-forming upon another plane. But in the same stroke where the theoretical disunion of thought and extension is affirmed, so too affirmed is the event of their union as a definition of life. This unity is not said of an abstract God transcending humanity, but rather of concrete life itself.</p>

<p>The tree of knowledge is not a simple image. The unity, the hierarchy beyond all anarchic duality, is the very unity of life, delineating a third order, irreducible to science and philosophy. Life is the unity of soul as the idea of the body and of body as the extension of soul. The two other orders, science and philosophy, physiology and psychology, tend to rediscover their lost unity at the level of living man. Beyond a disincarnated psychology within thought or a mineralised physiology within matter, mathesis finds its end through a true medicine where life defines itself as knowledge of life and knowledge as life of knowledge. The axiom is thus, “Scientia vitae in vita scientiae” and with it comes a triple consequence.</p>

<p>To believe that mathesis is merely a mystic thought, inaccessible and beyond human, is a complete error. This is nothing other than a misunderstanding of the word 'initiated' because the mathesis unravels itself at the level of life, of living man, where it is before all thought of incarnation and individuality. Essentially, mathesis wants to be the exact description of human nature. Yet does mathesis in fact surpass this living human nature?</p>

<p>Mathesis defines itself effectively as a collective and supreme knowledge, a universal synthesis, &quot;a living unity incorrectly deemed human&quot;. We must understand that such a definition is not immediate but eventual and that a particular sense prefigures the relations between man and the infinite where the natural relation unites the living with life. Life, in the first instance, seemingly exists in terms of the living, within the living organism that puts it into action. Life exists only by its fragmentary and closed assumptions, with each person realising it for his own purpose within a solitude. This is to say that universality, the community of life, is born unto itself, it is given to each person as a simple outside, as an exteriority that remains foreign, an Other.</p>

<p>There is indeed a plurality of men yet each person who needs to commonly assume his life for himself rightly does so without a common measure with others. With this, the universal is immediately recuperated and life is defined as complicity rather than a team. The team is, in effect, the realisation of a common world whose universality is either compromised or fragmented, so much so that in the course of this realisation the substitution of members becomes a possible and indifferent thing. Such is science, on the side of the object of thought, or philosophy, on the side of the thinking subject. In both cases we have a dead team, theoretical, non-practical and speculative. The only living Team is that of God, and this because there is only one God, symbolised within the circle, the perfect figure, indifferent, where all points are at an equal distance to the centre. With complicity, on the contrary, there is a common world where the community comes into effect through each member realising it for himself without a common measure with others, and without the possibility of substitution.</p>

<p>The principle human realities of birth, love, language, or death clearly appeal to this very design. Under the sign of death, each person exists as non-substitutable and we cannot be replaced. It is precisely here that the universal and its negation create only one. More importantly, the trait of complicity is that it can be ignored, denied and betrayed. So well does the term &quot;each one&quot; deny the universal the very moment it affirms it that we can only be sensitive to this negative aspect! The human problem consists of passing from a state of latent ignorant complicity to an affirmative complicity. This is certainly not the point where one loves as one and all but where one and all love as one, and it is the very moment where the living persisted in its individuality, where it was affirmed as universal. At the moment where the living closed upon itself, in defining the universality of life as an outside, it was unable to see that the universal had been interiorised – man realised the universal for himself and defined it as a microcosm. The first goal of mathesis, therefore, is to assure this awareness of the living in its relation to life and to establish the possibility of a knowledge of individual destiny.</p>

<p>From a purely natural and unconscious complicity where each individual opposes others, and more generally the universal, he passes to a complicity that knows where each person is grasped as &quot;pars totalis&quot; within a universe that has already constituted him. This is, in other words, the federation. Ostrowski, the translator of this work, described the federation in a most curious fashion as being, &quot;The moment where Germanic antiquity searches to reconstruct its federative unity (1849), lost for centuries, and which will probably finish by rediscovering itself within our own. It would not be without interest to examine the efforts undertaken by this population of bold thinkers, to bring science to the unity as its original departure, to its common centre.&quot;</p>

<p>We see that the federation is a definition of life and not a unity founded upon a cult of force. Unity comes about at the level of concrete man and very far from transcending the human condition, it is its exact description, one that simply needs to position man within his relation to the infinite, to the universal. Each individual exists by virtue of denying the universal, but in the same stroke as man’s existence refers to a plurality the negation functions universally under the exhaustive form of each and every person. This is the only human way of affirming what existence denies.</p>

<p>Complicity is consciousness and initiation is nothing else but this. Initiation is not mystical because it is the thought of life and the only possible way of thinking life. Initiation is mysterious by virtue of the knowledge it represents where each person need acquire it for himself. The initiated, is living man in his relation to the infinite and the key notion of mathesis is that between the living and life one finds the same relation as between life as species and divinity. Mathesis is not in the least mysterious because individuality never separates from the universal and the multiplicity of living beings refers to the unity that it designs in-depth. An example is the simple design of the circle by the ellipsis, and this is why we need to take the word of Malfatti literally in reminding us that the circle, the wheel, represents God: &quot;mathesis would be for man in his relation to the infinite, that which is the locomotion of space.&quot; </p>

<p>Mathesis is a knowledge of life. It is neither a science, nor a philosophy, it is not the study of being, nor the analysis of thought. Indeed, a particular method must reply to its particular object, and for Malfatti, the cogito of mathesis announces: sum, ergo cogito; sum, ergo genero, namely, that the method unique to mathesis will be neither scientific nor philosophical. The opposition of thought and being, of philosophy and science, matters little for mathesis because this opposition is an illusory and false alternative. Mathesis situates itself upon a horizon where the life of knowledge identifies itself with the knowledge of life, where it is simply an awareness of life.</p>

<p>Scientific method is explanation. To explain is to realise a thing through something other than itself. Heat is movement, water is composed of H2O, but movement as the object of thought is only constituted by negating that which it explains - heat - in terms of a system of sensible qualities. Much in the same way, when we arrive at H2O water no longer exists. These sensible qualities, which we can also call appearances, are no more than the very definition of appearance without seeming to be so. At the other extreme, philosophical method is largely in the direction of description, it is a reflexive analysis where the sensible world is described as the representation of the knowing subject. Here again, it receives its status from something other than itself, and in the two cases of scientific and philosophical method we discover a new opposition, that of thought and the sensible.</p>

<p>We have defined the object of mathesis in terms of the science/philosophy opposition, the object of the thinking thought-subject [3]. But here there is merely a primary aspect of anarchy. A new depth to the opposition is seen with the object of thought not merely &quot;thought&quot; as the thinking subject, but also being &quot;object&quot; as the sensible object. Everyday life traces its path in the objectivity of the sensible where objects are outside of us as their own proper signification to which we owe nothing. It is philosophically that colour is a secondary quality, a representation of the knowing mind, and it is scientifically that colour is reduced to the object of thought, a &quot;vibration&quot;, the very last word of reality. But it is no less certain that colour can be represented in-itself to the individual without reference to another thing other than itself – the individual knows well that things haven't waited for him to exist.</p>

<p>The object delivers itself to the observer in accordance with one’s point of observation. This event is not a sign of the object's dependency, but on the contrary, it is the manifestation of its total objectivity. It is well known that the contemplated object is detached from a ground constituted by the ensemble of other objects. Yet the object could not sustain the slightest relationship with others if this relation remained exterior. For an object to detach itself as a form upon a ground of other objects it first needs to have established itself on its own proper ground. Such are the 3 sides upon which the cube is always modelled - 3 sides and no more - and for it to be 6 sides the cube needs to have already been its own ground. This phenomenon returns the object to itself and not to the perceiving subject. In saying that 3 sides are already 6 is to postulate the identity of extension (3) and comprehension (6) within the sensible object. Why this identity? Why do the six sides present themselves as 3? It is simply because everyday space is of 3 dimensions. In taking a moment to reflect, one will see that 6 sides only have reference to a plane [4]. The only way for 6 sides to exist as a whole in a space of 3 dimensions is to present 3. The identity of extension and comprehension therefore simply defines space where the sensible object in general is the perfect concept, and where the word &quot;concept&quot; no longer signifies the &quot;object of thought&quot;.</p>

<p>This is but one moment within the number theory of mathesis, another being the number 7. As Malfatti shows, 7, is represented by means of straight lines and never by curved lines. It has the appearance of 3 dimensions indicating the truth that the whole body (individual) can be considered as the extension of surface (4), working in 3 directions, length, breadth and depth. Secondly, 7 is a concept that it is yet to represent the individual having become real [5], it is, &quot;the multiple development of the universal in innumerable individualities. It is the father of time and its image before divisible time that rolls within space upon the undulating images of appearance... it moves above the appearance.&quot; A philosophical or scientific critique of this conception would surely lead to error because it is not of the same domain, nor of the same method.</p>

<p>We saw that the method of mathesis found itself before an opposition to be surpassed, that of the object of thought and the sensible object. Science effectively explains the sensible object by something other than itself, by the object of thought. In delivering this object of thought to the sensible a new duality of reducing the quantity to the quality is introduced, where one can say that this reduction is the very reduction at work within the symbol. The most simple of examples will suffice to show this. When I say that the flag is a symbol of the homeland, I essentially present a sensible object as an incarnation of the object of thought, of a knowledge. What's more, this sensible object is the very knowledge that it incarnates. Earlier, in terms of explanation, the object of thought was the explanatory agent (l'expliquant) qualified through the negation of the sensible object it sought to explain. Contrastingly, the symbol is where the symbolising agent (symbolisant) becomes the sensible object to which the symbolised knowledge completely identifies.</p>

<p>Mallarm&eacute;'s Fan, is a poem which essentially depicts this. The subject is movement in-itself, a pure object of thought, beyond all sensible manifestation, where it both moves above appearance and keeps it at a respectful distance. As he writes:</p>

<blockquote>“Whose imprisoned stroke thrusts back The horizon delicately”</blockquote>
<p>The entire development of the poem consists of incarnating a sensible object with the thought of movement, to transform it within this object, within a fan as a thing, the closed fan and not only within the open fan which finds its profound mortification within sensible matter. Mallarm&eacute; further indicates this passage from the opening to the closed in writing of, &quot;The sceptre of pink shores&quot; and, &quot;This closed white wing you place&quot;.</p>

<p>This is one mere example which highlights the general sense of the symbol, the incarnation of a knowledge, the movement of mathesis. Contrary to scientific explanation, the symbol is identity, it is the encounter between the sensible object and the object of thought. The sensible object is said of the symbol, and the object of thought, in loosing all scientific signification, is a hieroglyph, a numeral. In their identity, they form the concept. The symbol is extension, the hieroglyph comprehension. According to Malfatti, since the word &quot;initiated&quot; discovers its full sense the mysterious character of mathesis is not directed toward the uninitiated (profanes) in an exclusively mystical sense, but underlies the necessity to grasp the concept in the minimum of time, and that physical incarnations take place in the smallest possible space – unity within diversity, general life within particular life.</p>
<p>We could even say that the notion of the initiated is rationalised to the extreme. If the work defines itself as the creation of a sensible object as the outcome of a knowledge, mathesis, while it is the living art of medicine, is the work par excellence, the work of works, where it is knowledge itself that is transformed into the sensible object. It is throughout Malfatti’s study, that we see mathesis insist upon the correspondences between material and spiritual creation.</p>

<p>Let us apply this symbolic movement to man. Thought, namely comprehension, defines the human condition as an existence separated from its essence. In saying that essence and existence are dissociated within man is to say that there are several men (extension). In effect, &quot;if, for example, there are twenty men within nature, it would not suffice to know the cause of human nature in general&quot; (Spinoza), that is, each existence finds its proper essence outside of itself, within the Other, where man is not only mortal but &quot;natal&quot;. And if the parents bestow their essence upon their child at his disposal, does the child in turn see in his parents the very principle of his intelligibility? In the same stroke where human comprehension is defined by the separation of existence and essence, the extension to which it is correlative, identical even, refers to sexuality: &quot;man and woman exist in two separate bodies, each one possessing the body of the other within it&quot;. We now see that it is through man that the concept as the identity of extension and comprehension comes into the world. In other words, it is sexuality that establishes sexual qualities. Here, Malfatti cites the words of Hippocritus, &quot;Man is a duality, and if he were not a duality, he would not feel it as so.&quot; But we have seen that sensation refers to three dimensions. Is it not also a sexual duality that one must observe as the triadic character of love, &quot;What would individual life be without the love of the self, which alone can lead it to the life of the species, in reproducing it as eternal being, infinite, within space? Dualism does not contain real life. Sexual love conciliates the other two, egoism and heroism.&quot; The life of the world is established under the compound sign: becoming (as addition; namely birth), duration (as the multiplication through which the act of becoming is conserved), and destruction or subtraction.</p>

<p>What will be the human concept par excellence? God, unity of essence and existence, is conceptualised by the circle (equivalence and rest, indifference of the interfocal zone and pregenethetic life). With the ellipsis however (or rather the ellipsoid always in movement), we rediscover the separation, the duality, the sexual antithesis of families. This is where three dimensions are born. We can define this journey as the birth of the equivocal where the ellipsis is defined by an equivocal circle. We recall how even the object of mathesis found itself before the problem of life, of complicity, &quot;it is at the same moment,&quot; says Malfatti, &quot;where the individual momentarily places himself in the place of nature, that he returns his life to the life of nature&quot;. In this sense, sexual love is at the same time love of the self and love of the species, man-having-become-interior and man-becoming-exterior. Let us recall the other part to the correspondence that presides over relations, namely, living being/universal life, and, universal life as species/divinity. One will also see Malfatti insist that the genethetic and the pregenethetic are inseparable because one designs the other in depth: &quot;Before I was round. Now, I am extended in the form of an egg.&quot; Through engenderment humanity pursues its own immortality where time is constituted as the mobile image of the eternal search for the completion of the ellipsis within the circle. Ecstasy is merely the act by which the individual is raised to the level of species. The species, in effect, allows itself to think the limits of the circle – before the sin Adam existed as humanitas.</p>

<p>It comes as no surprise that method rejoins the object of mathesis. It is through the same action that mathesis is situated beyond the opposition of the thinking subject /object of thought, and also beyond the other opposition we saw to be the object of thought /sensible object. We again see this more clearly with the problem of numbers. On the one hand, the number exists only within the decade, that is to say, within numeration. A number appears to be constructed by an act of mind, transparent to itself, where we are content with adding the unity to the preceding number. In this way, the number appears on the side of the thinking subject yet the object of thought, is on the contrary, revealed as opacity, endowed with unforeseeable property to the point where the transparent mind engenders veritable natures. We will see that Mathesis privileges the number and that the symbol is in fact the number that has become a sensible object/ </p>

<p>It is also interesting to see how Malfatti reproaches the analogical studies of the Greeks. Their error was to have searched for the signification of the number in terms of a purely geometrical relation and in doing so they confined mathesis to the object of thought. Yet it is the symbol in its full sense that needs to be extricated from the number. The decade begins with 0, the hieroglyph of man and the world, and finishes with 10 which is the realised unity within a complete spiritual and corporeal organism. Malfatti thus writes that 10, &quot;neither tires with the action of entering nor that of leaving. He is the sovereign of a small world (microcosm) within man.&quot;</p>

<p>Our definition of mathesis was double. In its object, in relation to the thinking subject/object of thought duality, in its method, in relation to the other duality of the object of thought/sensible object. We reach a point where the two themes incessantly support and identify one another. The first encouraged us to lay down a system of correspondences between the individual (microcosm) and the universal, the second, between the corporeal and the spiritual. Thus we do not seek a philosophical &quot;explanation&quot; for the union of the soul and the body, and we no longer attempt to scientifically critique the correspondences established between the individual and the universe, under the grand themes of fire, of fermentation...etc [6]. </p>

<p>Mathesis evolves in another domain. In the double depth (&eacute;paisseur) of the symbol, it finds its end as the living art of medicine, incessantly establishing a system of increasingly intimate correspondences, where closely knit individual realities are to be found.</p>

<hr />
<p><strong>Footnotes<br /></strong>
[1] <em>Jean Malfatti de Montereggio, La Math&eacute;se ou anarchie et hi&eacute;rarchie de la science. Editions Du Griffon D’Or, Paris 1946.<br /></em>
[2] <em>Deleuze, whilst studying for his agr&eacute;gation at the Sorbonne, was under the supervision of three eminent scholars: Jean Hyppolite, Georges Canguilhem and Ferdinand Alqui&eacute; – the latter being the foremost commentator on Descartes, (trans.)<br /></em>
[3] <em>Written in the French as, ‘Objet de pens&eacute;e-sujet pensant’ as (trans).</em> <br />
[4] <em>We translate ‘plan’ in purely geometrical terms as ‘Plane’ (trans).<br /></em>
[5] <em>Written in the French as ‘Il ne repr&eacute;sente pas encore l’individu devenu r&eacute;el’ (trans).</em> <br />
[6] <em>Similarly, it would be pointless to want to refute the physiological conceptions put forward for example, in the Third Study: they belong elsewhere, to “romantic medicine” and to “natural philosophy”. The scientific elements thus drawn upon by Dr. Malfatti de Montereggio were very much fragmentary to be sufficient enough for a complete construction. The author therefore fills the voids with bold teleological hypotheses. It is his weakness, but it is also the inevitable fate of each a priori synthesis.</em></p>

<h2>Working Papers on Cultural History and Contemporary Thought</h2>

<h3>Mathesis, Science and Philosophy (1946)</h3> <p><strong>David Reggio (Department of History, Goldsmiths)</strong></p>

Comments

So is this any different than Crowley's work "The Book of Thoth" - or many other numerological texts on the meaning of base 10 numbers? I'm not even sure how to understand this in it's own context. It seems like the conclusion or introduction to a complete exploration of mathesis - is it? Foucault's "the Order of Things" has at least a bit more elaboration on mathesis... but is especially more applied in it's exploration of the changes in different knowledge-systems of the function mathesis serves (the episteme). Can you maybe elaborate on this a bit? Sorry, but the content seems quite "condensed" to me.

-Squee

I ain't gonna talk to a scientist, ya'll mothafuckas lyin and gettin me pissed!