The Third Mind: Alain Badiou on Duchamp

On the question of relationship between art and number, we can see that the fatal number, for Duchamp, is the 3. “The number three as three, for me is neither unity nor duality, the three is everything, the final end of numeration”. Or again: “One is unity, two is the double, and three is the rest”. Duchamp works on the relation between the infinite and space or spaces, that is to say dimensions. But the final space is always tridimensional. This is why he can say “millions do not count, the three fills the same role for me.”

— Alain Badiou (2008)

Figure 1. The Bride Stripped Bare by Her Bachelors, Even (The Large Glass);

The autonomy of number as an ontology of wholeness requires an occult deconstruction of Alain Badiou’s numerical contribution to continental astrology. The wedding of opposites crucial to alchemy and the occult sciences is achieved via the autonomous number as the integration of quality (feminine) and quantity (masculine).

This autonomy is crucial to our radically revised portrait of the Übermensch; in this term, the archeology is imbedded in the two distinct making up the term: Uber (over) mensch (person). Over person is also, in terms of number, two parts making up a Third entity. The two parts are quantitative and the Third is qualitative, a new Being. Together is the marriage of quality (the feminine) and quantity (the masculine), a nuance in which Deleuze accounts for “difference.”

The study of qualitative number is numerology, the occult science practiced by astrologers, numerologists and perhaps Satanists. Yet, the autonomy of number, unified by the integration of quality and quantity, is also crucial to sacred geometry. This is why the Masonic Guilds were the organizations putting occult knowledge into daily practice through their allegorical rites of Hiram made evident in their building constructions.

Due to Badiou’s scholarship, number is now safely within the borders of continental philosophy. Trained as a mathematician who revolutionized philosophy by bringing in the ontology of number, the French philosopher’s qualitative application of number is to be discovered in his intuitive (i.e. feminine) manner of organizing texts.

For example, in Existence Short Treatise Transitory Ontology (Badiou, 2006, p.79) the philosopher cites three factors (whether they be highlights, points or features) a total of seventeen times. In this key “transition” text, groupings of three also give birth to new concepts of three. For example, in a passage on Lucretius’s double expression of a singular idea, he cites: “a mode of extension and the idea of that mode are one and the same thing, but expressed in two ways.” He then goes on to make three points, the second of which, like the Mobius strip or, the Slavoj Žižek double negative, itself contains three: “Second, that there is not only a single fundamental relation, causality, but at least three, which apart from causality I call “coupling” and “inclusion” (Badiou 2006, p. 143).

Yet, no writing of Badiou has revealed a stronger unconscious intent to bring the bipolar universe into consciousness than his Duchamp essay ostensibly investigating the qualitative aspects of number. In this essay, autonomy of the three is established by means of the artist who bears the distinction as the visionary forerunner of a twenty-first century modernism.

Autonomous number in Duchamp’s The Large Glass heralds the return of the lost feminine as Bride. The self-generating bipolar Sky Goddess propels her suitors into rotation (the chocolate grinder) by means of her creativity powered by the three empty panels of her wing. These framed negative spaces represent the empty vessel of the feminine filled through the creative spirit.

As prelude, Duchamp created a series of four small-scale “erotic objects”, including the evocative Female Fig Leaf and the phallic Dart Object. These objects were the externalizations of his internal embodiment of gender opposites into the hieros gamos, externalized in his marriage to Tini Matisse, born under the sign of Aquarius, in opposition to his Leo signature.

In keeping with the phenomenology of the “set” mirror, Badiou’s writing on Duchamp’s relationship with the number three reflects the artist’s pursuit of the wedding of form and content. To repeat Badiou: “But the final space is always tridimensional.”

We will now investigate how the symmetry of “the final solution” between French philosopher and artist is the in-between space of the hieros gamos. In a magical flourish, the philosopher ends his Duchamp essay emphasizing three points (bold is mine):

But everything must be taken up again starting from three points, which are quite singular: These points work against the anonymous and democratic concept of the work of art. These three points open the door, for a new aristocratic and self-expressive notion of modern art (Badiou 2008, para. 22).

Again, Badiou breaks down Duchamp by thirds. This time it is three functions detailed below:

1). The decisive function of the refusal opposed to his work in Duchamp’s destiny. First, in 1912, the refusal of the great cubist canvas “Nude descending a stairway” by the Salon des Independents. This was the French refusal. Then, in 1917, the refusal or the dissimulation of the urinal entitled “Fountain” and signed R. Mutt, by the counsel of The Society of Independent Artists. This was the American refusal. These are crucial episodes. In 1968, Duchamp was an artist practically idolized by his peers and by the vanguard youth. But his rancor is still felt, when he declares: “Don’t forget that I never had any success until recently, very recently.”

Behind his provocative and accomplished vision, Duchamp is a man (para. 23).

In the second point, the content of the three appears again in the second listing of Duchamp’s works after the word “even”. In mathematics, the word is applied to numbers that can be divided into equal proportions, which is distinct from the indivisibility of the three as prime number. The list of the “ordinary objects” with “redundant names” relate to “even”, the masculine rationality for which Duchamp is known as the Father of Conceptualism. But these two works are separated from the list of the three listed “complex compositions” which encompass in content the prime number of the three, related to quality/the feminine. Badiou qualifies the right brain compensation through number with the final two sentences as the second function:

2). The function, not only of his signature, now unfailing even for copies very far off. But inscriptions or legends affected to ordinary objects as to complex compositions, in vivid contrast with the redundant names of the type “Bottle Stand” or “Bicycle Wheel” or even “The Big Glass”….”Why not Sneeze Rose Selavy,” “In Advance of the Broken Arm”, and many others.

All that is not at all abstract art. He projects the singularity of an art of poetic writing (para. 25).

In his presentation of the second function, Badiou mirrors Duchamp’s creative process (contained in his final sentence) with his own projection into the Third via his own “poetic writing” presenting the philosopher’s “art” regarding the autonomy of number. This is confirmed in the Third and final function, eroticism. This section contains the three as autonomous content, first as quantity (three), then as quality with his poetic composition of the list of three (works) enclosing the gender balance of Duchamp’s hermetic punning. The self-contained autoeroticism can be found in Duchamp’s famous transgender 1919 icon establishing him firmly on the path of a unifying erotic art. The mustached Mona Lisa entitled L.H.O.O.Q. is a hand colored collotype representing the “sacred marriage” of gender opposites.

Figure 2. Portrait of Marcel Duchamp with his work L.H.O.O.Q., Paris, 1965.

Now, we arrive at Badiou’s third function (bold is mine):

3). The function of eroticism, absolutely original and constant. The word “naked” is found everywhere. Or the thing… the three great works, but also a great many other works. As well as the Virgin, the roguish puns (LHOOQ), the use of sperm, etc. (para. 28).

The French philosopher is taking on the “mirroring set” function of his numbers in righting the compensation of his logos left-brain knowledge. The three Badiou functions reflect Duchamp’s allegiance to the autonomy of the three, both in quantity (3) and quality, identified by the contents of a set (the Virgin, the roguish puns (LHOOQ), the use of sperm) which has not been identified as such.

In his modestly titled “Some Remarks on Marcel Duchamp” the French philosopher has resurrected the hermeneutics of the creative power of the three (Streitfeld, 2014). The autonomy of this prime number, which symbolizes the creative passage into the Third, defeats any scientific attempt to reduce number to instrument. With this essay taking him into the terrain of the hermetic, Badiou mirrors Duchamp as a pioneer, not simply of a twentieth century conceptual art, but a twenty-first century neo-conceptual (neo-modernist) art integrating intuition from the right hemisphere of the brain, with logos from the left brain.

What is the ontology by which this has been achieved? It begins and ends with the specific quality of the three. Three is the only number capable of being the quantitative sum of its chronological placement. The count of three makes the same number both in linear progression (1,2,3) and mathematically (1+2=3).

The figuration of this holistic autonomy is contained within the structure of the equilateral triangle. Three identical lines intersect at three angles. Inherent in this structure is the trisection of the 180-degree tension of opposites: the straight line between two points, and further, the composition of two triangles with points facing opposite directions is the square. The quaternity brings us back to Duchamp’s The Large Glass, in which Badiou assesses in his conclusion:

These three questions seem to converge towards something else that would be that any framing is polarized by a fantasized framing. And that eroticism is of the order of art, as the necessary other side of calculation (para. 29).

Therefore, “Some Remarks Concerning Marcel Duchamp” concludes with a bold new beginning overlooked by art theorists. By this, I mean that the philosopher who brought mathematics back into Western philosophy brings the autonomy of the three “towards something else that would be that any framing is polarized by a fantasized framing”. The “framing” that Badiou refers to as “polarized by a fantasized framing” is present in the three sequences of the three (described above) made material in the artist’s last greatest work (Fig. 10), in which a “set” of three framed negative spaces of the Bride’s “wing.”

When we view the Duchamp parting narrative revealing the distance between the bride and her suitors from the Third realm of the artist’s playful merging of gender opposites, we add a new dimension to Badiou’s reintroduction of mathematics into western philosophy. The Bride Stripped Bare by her Bachelors, Even is summed up on the right side of the comma: Even. The balance of opposites represented by the “even” number embodies a Badiousian neo-modernism in the Duchamp marriage of logos (the conceptual via his invention of the “readymade”) and erotic consciousness:

The story—in the work of Duchamp—of the struggle between the abstraction of indifferent choice and the seduction of desire and images. But it is probably the contradictory destiny of the most important part of modern art (para. 29).

In the final sentence of his remarks, Badiou states the problem and becomes the solution. In pointing out the contradiction between the subjectivity of Eros and the objectification of abstraction, Duchamp was summing up the subject/object dilemma riddling the art critic. Even the philosopher introducing number into continental philosophy is hampered with the binary unresolved by the masculine left brain domination of western culture.

–Lisa Paul Streitfeld, Ph.D.


Badiou, Alain (2008). Some Remarks on Marcel Duchamp. The Symptom 9. Retrieved from: June 10, 2008. Accessed February 3,2013.

Badiou, Alain (2006). Briefings on Existence: A Short Treatise on Transitory Ontology: Transl. Norman Madarasz. SUNY Series, Intersections: Philosophy and Critical Theory. Albany: State University of New York Press.

Streitfeld, Lisa (2014) Hermeneutics of New Modernism (2014). New York/Leipzig: Atropos Press.