ブルース・フィンクによる比較的評判の高い英訳『ラカンセミネールⅩⅩ（アンコール）』の翻訳者注にはこうある。
ここではpure differenceに注目しよう。the One of "pure difference"、すなわち“純粋差異”の〈一〉とある。このおそらくドゥルーズの『差異と反復』を念頭において使用されたのだろう「純粋差異」とは、何だったか。ドゥルーズは、差異が可能になる条件を純粋差異と呼んだ。とすれば、〈一〉が可能になる条件がYa d' l'Unなのだろうか。
以下に、主にラカンの Y a d'l'Unをめぐる叙述を、ジジェクの『LESS THAN NOTHING』2012から抜き出すが、このジジェクの解釈が標準的なものなのかどうかは知るところではない（ラカンの解説書のなかでも、すくなくとも英語圏の論文では、Y a d'l'Un をめぐる叙述はすこぶる少ないーーもちろんわたくしの気づく範囲では、ということだが）。
Ya d' l'Un is by no means an immediately comprehensible expression, even to the French ear, but the first sense seems to be "There's such a thing as One" (or "the One") or "There's something like One" (or "the One"); in neither case is the emphasis on the "thing" or on quantity. "The One happens," we might even say. A detailed discussion of Seminar XIX would be required to justify the translation I've provided here, but at least two things should be briefly pointed out: Y a d' l'Un must be juxtaposed with II n y a pas de rapport sexuel, there's no such thing as a sexual relationship (see Seminar XIX, May 17, 1972); and Lacan is not saying "there's some One" (in the sense of some quantity of One) since he is talking about the One of "pure difference" (see Seminar XIX, June 1, 1972).
ここではpure differenceに注目しよう。the One of "pure difference"、すなわち“純粋差異”の〈一〉とある。このおそらくドゥルーズの『差異と反復』を念頭において使用されたのだろう「純粋差異」とは、何だったか。ドゥルーズは、差異が可能になる条件を純粋差異と呼んだ。とすれば、〈一〉が可能になる条件がYa d' l'Unなのだろうか。
以下に、主にラカンの Y a d'l'Unをめぐる叙述を、ジジェクの『LESS THAN NOTHING』2012から抜き出すが、このジジェクの解釈が標準的なものなのかどうかは知るところではない（ラカンの解説書のなかでも、すくなくとも英語圏の論文では、Y a d'l'Un をめぐる叙述はすこぶる少ないーーもちろんわたくしの気づく範囲では、ということだが）。
ラカンの「〈他者〉は無い il n'y a pas de l'Autre」は、彼の Y a d'l'Un、つまり「〈一〉の何かが有る there is something of the One」と厳密な相関関係がある。Y a d'l'Un の〈一〉Unが「分割できない残余indivisible remainder」、性関係を存在しないものとする限りにおいて、Y a d'l'Unは「性関係は無い il n'y a pas de rapport sexuel」とも厳密に相関関係がある。それは、この関係のまさに対象-障害object‐obstacleである。Y a d'l'Un の〈一〉 は元来、神話的なすべてを包括する〈一〉ではない。フロイトが嘲弄した悪評高い「大洋的感情oceanic feeling」ではない。そうではなく、〈二〉Twoのハーモニーをかき乱す「現実界の破片little piece of the real」、糞便のような残余である。
この決定的な区別を明瞭化するために、Le Gaufeyは後期ラカンの微妙な一節に注意を促している。それは、“il n'y a pas de rapport sexuel 性関係は無い” から “il y a du non‐rapport (sexuel)(性の)無-関係は有る”である。この移行は、まさにカントの区別、否定判断(述語の否定)と無限判断(非-述語の肯定)のあいだの区別に合致する。
「性関係は無い」はいまだ二つの性のあいだの永遠の相克という古臭いモティーフにおける変奏の一つとして読みうる。「無-関係は有る」は遙かにラディカルな何かを意味する。すなわち、逆説的な「超-有限の」対象ーーそれ自身の欠如と重なり合う、あるいはそれ自身に関する過剰ーーにおける性関係の不可能性のポジティヴ化positivizationである。
この意味は、男性masculineと女性feminineは、単純に二つの「ズレた存在out‐of‐sync entities」ではなく、ある意味で、性差は二つの性(二つの性の差異のあること)に先行しているということだ。二つの性はどういわけか(論理的には)後に来る。二つの性は〈差異〉の袋小路に反応し、解消もしくは象徴化しようと努めるのだ。この袋小路は、対象aと呼ばれる疑似対象に具現化される。
この理由で、我々は対象aのことを単純に性的sexualでないと言うべきではない。それは、不-性的un‐sexualなのである、吸血鬼が不死undeadであるというときとまさに同じ意味で、不-性的un‐sexualなのだ。「不死」とは、生きているのでも死んでいるのでもなく、怪物的な生ける死である。同様に、対象aは、性的でも非性的non‐sexualでもなく「性的に無性的sexually asexual」であり、二つの性のいずれにも等しくないが、それにもかかわらずいまだ性的なのである。ラカンが指摘したように、ここで問題になっているのは、「すべての原理の原理principle of all principles」における変化以外のなにものでもない。それは、無矛盾の存在論の原理から性関係は無いという原理への変化である。
「性関係は無いthere is no relationship」から「無-関係は有るthere is a non‐relationship」への移行いかにカントの否定判断から無限判断への移行をもたらすかは容易に見てとれる。「彼は死なない」は「彼は不死である」と同じではない。それは「性関係は無い」が「無-関係は有る」と同じではないのと同様である。性差に関するこの移行の重要性は次のことにある。もし我々の究極的な地平として「性関係は無い」に留まってしまえば、我々は二つの性のあいだの永遠の闘争という伝統的な空間に居残ったままだということだ。
ジャック=アラン・ミレールでさえ時にこのように見えることがある。例えば、 彼が「性関係は無い」を、「女に関して男は、その錠に合う鍵のようなものではない」という線で読むとき。これでは調和harmonyに対照させた非調和disharmonyの単純な主張にすぎない。一旦、我々が「無-関係は有る」に移行するとき、ヘラクレイトス的な「相克における統合／調和」の類さえ置き去りにする。というのは男性と女性はもはや左右対称の相反する軸ではないからだ。二つのうちの一つ(女性)はそれ自身の否定を含んでいる。そのため相反性の領野から抜け出す。ーー非-女は男ではなく、女性性内部の非-女という深い裂け目である。不死が死の領域内部にある(生ける死として)のと同様である。（ZIZEK,LESS THAN NOTHING,2012、私訳 強調は訳者による）
※カントの否定判断と無限判断については、「「沖合いはるかな遠い未来のなか」へ送りだされたラカン理論」の後半を見よ。
ここでは、《非-女は男ではなく、女性性内部の非-女という深い裂け目である》についてのみ捕捉しよう。
ーー《女は非-全体（無限集合）なのだから、女でない全てがどうして男だというんだね？》
ここでは、《非-女は男ではなく、女性性内部の非-女という深い裂け目である》についてのみ捕捉しよう。
“since woman is ‘non‐all,’ why should all that is not woman be man?” (Lacan,S.ⅩⅨ）
ーー《女は非-全体（無限集合）なのだから、女でない全てがどうして男だというんだね？》
排中律とは、「Aであるか、Aでないか、そのいずれかが成り立つ」というものである。それは、「Aでない」と仮定して、それが背理に陥るならば、「Aである」ことが帰結するというような証明として用いられている。ところが、有限である場合はそれを確かめられるが、無限集合の場合はそれができない。ブローウェルは、無限集合をあつかった時に生じるパラドックスは、この排中律を濫用するからだと考える。（柄谷行人『トランスクリティーク』）
…………
・我々の「抹消されたファロス」の学素 φ barréは，「性関係は無い」を形式化する学素です．
・Ⱥ は，他 A のなかの欠如と定義されていますが，それは，il n'y a pas d'Autre de l'Autre［他 A の他 A は無い］の学素でもあります．
ここにみられるように、この箇所においては上のジジェク解釈とほぼ等しい。再掲するなら、
ラカンの「〈他者〉は無い il n'y a pas de l'Autre」は、彼の Y a d'l'Un、つまり「〈一〉の何かが有る there is something of the One」と厳密な相関関係がある。Y a d'l'Un の〈一〉Unが「分割できない残余indivisible remainder」、性関係を存在しないものとする限りにおいて、Y a d'l'Unは「性関係は無い il n'y a pas de rapport sexuel」とも厳密に相関関係がある。（ジジェク）
すなわち il n'y a pas de l'Autre＝Ⱥと il n'y a pas de rapport sexuelはY a d'l'Un とのあいだに相関関係があるとなっている。
これらから判断できるように、以下の文に現われる小笠原マテームはφ barré、「性関係は無い」、あるいはȺを代入して読んでもよいだろう。くり返せば、以下の文は、いささかの齟齬があるように思える部分や小笠原氏の独自のマテーム使用を除けば、Y a d'l'Unの説明としてとても分かりやすい。
※ex-sistenceについては、「〈他者〉の〈他者〉は外-存在する」（ジジェク＝ラカン）を参照のこと。
鈴木晶氏の訳では〈一者〉となっているが、これは原文ではthe Oneである。
続きを邦訳のみいくらか附記しておく。
さて、ふたたびLESS THAN NOTHING(2012)に戻って、パルメニデスと〈一〉にかかわる箇所を原文のまま掲げる(パルメニデス理解のさわりとしては、「プラトンの『パルメニデス篇』における「第一の仮定」」（岡崎文明）にパルメニデスの〈一〉の八つの仮定がまとめられてある）。
※注
40 Dolar, “In Parmenidem Parvi Commentarii,” p. 67.
41 Ibid., p. 81.
42 Ibid., p. 82.
43 Armand Zaloszyc, “Y a d'l'Un,” intervention at the Congress of the World Association of Psychoanalysis, Rome, July 13–16, 2006.
44 Ibid.
45 This translation probably relies on Meister Eckhart, who had already coined “Ichts” as a positive version of “Nichts,” i.e., the void in its positive/generating dimension—the nihil out of which every creation proceeds. What Eckhart saw was the link between the subject and negativity.
46 Not to mention the weird fact that, in English, den means “cave, hideout, nest, safe place.”
47 Lacan, The Four Fundamental Concepts of Psycho‐Analysis, p. 62.
48 Alain Badiou and Barbara Cassin, Il n'y a pas de rapport sexuel, Paris: Fayard 2010, p. 82.
49 Jacques Lacan, “L'Étourdit,” Scilicet 4, Paris: Seuil 1973, p. 51.
50 Ibid.
一，Un について，この等価性を措定することができます：
Un ≡ φ barré
一，Un について，Lacan は Séminaire XIX ...ou pire でこの命題を提示します：
Y a d'l'Un.
Y a d'l'Un は，il y a de l'Un という文を日常会話における発音のしかたで発音した音をそのまま表記したものです．代名詞 il が省略されてしまい，また，de の母音が飲み込まれてしまいます．
il y a は存在を差し徴す表現です．英語の there is, ドイツ語の es gibt に相当します．
Y a d'l'Un は，日本語では「一が有る」と訳すしかありませんが，それでは重要な点が抜け落ちてしまいます．それは，de と定冠詞から成る部分冠詞の意義です．
部分冠詞は，非可算名詞に関してその何らかの量を差し徴します．たとえば英語で would you like some coffee ? と言うときの some に相当します．
フランス語では voulez-vous du café ? du は de と le の縮合です．
では，φ barré としての一，Un に部分冠詞が付されるのは，如何なることか？
存在の真理の現象学的構造 a/ φ barré に即して考えてみましょう．ちょうど昨日の東京ラカン塾精神分析セミネールで読解した Encore p.47 の一節で Lacan はこう言っています：
l'inadéquat du rapport de l'Un à l'autre.
一と autre (つまり，petit a) との関係の非十全適合．
signifiant a は Un に対して十全適合的ではない．そも，signifiant a は Un を代表する仮象にすぎません．
« y a d'l'Un » の部分冠詞は，signifiant の実在に対するこの非十全適合性を差し徴しています．
一，Un は，ひとつ，ふたつと数える際の単位ではなく，「すべて」のことです．「すべて」である Un という signifiant を以て存在事象そのもの全体を差し徴すと考えるなら，部分冠詞は必要なく，l'Un est ないし il est l'Un と言ってもよいでしょう．
しかし，Lacan が考えている Un は，存在事象ではなく，而して，存在φbarréです．
signifiant Un を「すべて」として措定するとき，必ずそれに対して解脱的である何か，それに対して ex-sister する何かが存有します．「すべて」であるはずの Un は，実は「すべて」ではなく，ex-sistence を考慮に入れるなら，部分にすぎないのです．
かくして，« y a d'l'Un » の部分冠詞は，間接的に ex-sistence を指しているのだ，と読解することができます．
ジジェクはほかにY a d'l'Unをめぐって、同じ書の「FROM THE ONE TO DEN」という節にて、プラトンの「パルメニデス篇における八つの〈一〉の仮定」を引用しつつ叙している。この箇所は、わたくしには難解で訳す気にもならないが、ここでは英文のまま後学？のために貼り付けておく。この箇所には、LESS THAN NOTHINGという表現が出て来ているように、おそらくこの膨大な著書の核心箇所のひとつであるだろう。以下の文で当面、注目すべきなのは（わたくしにとって）、〈一〉をサントームであると、ジジェクは記している箇所である。そしてここでのサントームは次ぎの意味と捉え得る。
小笠原晋也氏が《Un は，存在事象ではなく，而して，存在 φbarréです》、もしくはȺとしていることにも再注目しておこう。ここでのジジェクと小笠原晋也氏の見解は等しいとは言いがたいながら、限りなく近い。
もっとも、ジジェク自身、〈一〉がサントームであると、90年代初頭からすでにくり返している。ここで厄介なのはサントーム概念そのものの捉え方が二種類あるようにみえることなのだが（参照：ラカン派の二種類のサントーム・症状）。すなわち現実界の症状の核という意味と、その核と同一化しつつも距離をとるために発明される父の名の代替物の新しいシニフィアンという意味があるように思える。
ーー《なぜ我々は新しいシニフィアンを発明しないのか？ たとえば、それはちょうど現実界のように、全く無意味のシニフィアンを》とでも訳せる文だが、この新しいシニフィアンがまたサントームであるのだ。
このあたりが、上にジジェクと小笠原見解が等しいとは言いがたいと口を濁した理由である。いずれにせよ。初期ジジェクの論では症状の現実界の核ばかりが強調されている。以下、1991年に上梓された『斜めから見る』から引用するが、ここでの見解は、現在そのまま通用するとは思われない。ただしサントームにをめぐる箇所は、2012年段階と同様な見解を示している。
症状が、解釈を通して解消される無意識の形成物であるなら、サントームは、"分割不能な残余"であり、それは解釈と解釈による溶解に抵抗する。サントームとは、最小限の形象あるいは瘤であり、主体のユニークな享楽形態なのである。このようにして、分析の終点は"症状との同一化"として再構成される。（ジジェク『LESS THAN NOTHING』2012 私訳）
小笠原晋也氏が《Un は，存在事象ではなく，而して，
sinthome ……それは，存在の真理 φ barré を，仮象で覆うことなく，そのままに ex-sister させることです．（小笠原晋也 ツイッターセミネールより）
もっとも、ジジェク自身、〈一〉がサントームであると、90年代初頭からすでにくり返している。ここで厄介なのはサントーム概念そのものの捉え方が二種類あるようにみえることなのだが（参照：ラカン派の二種類のサントーム・症状）。すなわち現実界の症状の核という意味と、その核と同一化しつつも距離をとるために発明される父の名の代替物の新しいシニフィアンという意味があるように思える。
Pourquoi est-ce qu'on n'inventerait pas un signifiant nouveau? Un signifiant par exemple qui n'aurait, comme le réel, aucune espèce de sens?” （ J. Lacan, Le Séminaire XXIV, L'insu que sait de l'une bévue, s'aile a mourre, Ornicar ?, 17/18, 1979, p. 21）
ーー《なぜ我々は新しいシニフィアンを発明しないのか？ たとえば、それはちょうど現実界のように、全く無意味のシニフィアンを》とでも訳せる文だが、この新しいシニフィアンがまたサントームであるのだ。
ラカンはこの自己によって創造されるフィクションを、サントームと呼んだ。…新しいシニフィアン或いはサントームの創造の文脈における創造とは、〈大他者〉の欠如の上に築き上げられるものである。すなわちcreatio ex nihilo無からの創造においてのみ。（Paul Verhaeghe and Declercq"Lacan's goal of analysis: Le Sinthome or the feminine way"2002.）
このあたりが、上にジジェクと小笠原見解が等しいとは言いがたいと口を濁した理由である。いずれにせよ。初期ジジェクの論では症状の現実界の核ばかりが強調されている。以下、1991年に上梓された『斜めから見る』から引用するが、ここでの見解は、現在そのまま通用するとは思われない。ただしサントームにをめぐる箇所は、2012年段階と同様な見解を示している。
……このことは、ラカンの『セミネールⅩⅩ』に見出されるもう一つの予期せぬ特徴を説明するのに役立つ。その予期せぬ特徴とは、シニフィアンからシーニュ（記号）への移行と同様の、〈他者〉から〈一者〉への移行である。晩年にいたるまでラカンの努力はすべて、〈一者〉に先行するある他者性の輪郭を描くことに向けられていた。まず最初に、シニフィアンの領域における異物として、すべての〈一者〉はその〈他者〉との差異関係の束によって定義される。つまり、すべての〈一者〉は前もって「他の中の一つ」として捉えられる。次に、偉大な〈他者〉（象徴的秩序）の領域それ自体の中で、ラカン派その〈疎遠なるもの ex-time〉、すなわちその不可能で現実界的な核を、「分離」し抽出しようと試みた（〈対象a〉はある意味で「〈他者〉そのものの真ん中にいる他者」であり、そのいちばん中心にある異物である）。だが『セミネールⅩⅩ』において、われわれは突然、ある〈一者〉と遭遇する(『〈一者〉がいるThere Is One, Y a d'l'Un』から）。この〈一者〉は他の中の一つではなく、〈他者〉の秩序に固有の分節にまだ参加していない。この〈一者〉はいうまでもなく意味-の-享楽の〈一者〉、まだ鎖に繋がれておらず、享楽にたっぷり浸って自由に浮遊しているシニフィアンの〈一者〉にほからない。この享楽が、シニフィアンが鎖の一つへと分節されるのを阻止している。この〈一者〉の次元をあらわすために、ラカンはサントーム le sinthome という新語をつくった。(ジジェク『斜めから見る』1991鈴木晶訳、p247）
鈴木晶氏の訳では〈一者〉となっているが、これは原文ではthe Oneである。
This helps us to explain another unexpected feature of Lacan's Seminar XX (Encore): a shift, homologous to that from signifier to sign, from the Other to the One. Up to his last years, all Lacan's effort was directed toward delineating a certain otherness preceding the One: first, in the field of the signifier as differential, every One is defined by the bundle of its differential relations to its Other, i.e., every One is in advance conceived as "one-among-the-others"; then, in the very domain of the great Other (the symbolic order), Lacan tried to isolate, to "separate" its ex-time, its impossible-real kernel (the objet petit a is in a way "the other in the midst of the Other itself," a foreign body in its very heart). But all of a sudden, in Seminar XX, we stumble upon a certain One (from There Is One, Y a d'l'Un) that is not one-among-the-others, that does not yet partake of the articulation proper to the order of the Other. This One' is of course precisely the One of Jouis-sense, of the signifier insofar as it is not yet enchained but rather freely floating, permeated with enjoyment: it is this enjoyment that prevents it from being articulated into a chain. To indicate the dimension of this One, Lacan coined the neologism le sinthome.
続きを邦訳のみいくらか附記しておく。
この点は、主体の整合性の究極の支えとして機能する。それは、「汝はそれである thou art that」の点、「主体の中にあって主体以上のもの」、したがって主体が「自分自身以上に愛している」ものの次元を示す点であり、それにもかかわらず症状でもなければ、幻想でもない（症状とは暗号化されたメッセージである。主体はそこにおいて、〈他者〉から自分自身のメッセージを裏返しの形で受け取る。幻想とは想像のシナリオで、それはその魅惑的な現前によって、〈他者〉、すなわち象徴的秩序における欠如、その非整合性、すなわち象徴化の行為そのものに含まれた根本的不可能性、「性的関係の不可能性」を隠蔽する）。（ジジェク『斜めから見る』pp.246-248）
さて、ふたたびLESS THAN NOTHING(2012)に戻って、パルメニデスと〈一〉にかかわる箇所を原文のまま掲げる(パルメニデス理解のさわりとしては、「プラトンの『パルメニデス篇』における「第一の仮定」」（岡崎文明）にパルメニデスの〈一〉の八つの仮定がまとめられてある）。
Parmenides's dialectical exercise is divided into eight parts: apropos of each of the two basic hypotheses—if the One is and if the One is not—he examines the consequences for the One, and the consequences for the Others; plus he adds a subtle but crucial distinction between the One which has being and the bare One, so that altogether we get eight hypotheses:
In the case of hypotheses 2, 3, 5, and 7, which predicate being (or non‐being) of the One, the result is positive: predication is possible; that is, positive statements can be made of the One (or of the not One). In the case of hypotheses 1, 4, 6, and 8, which put the One out of the sphere of being (or non‐being), the result is negative: predication is not possible; that is, nothing can be asserted of the One (or of the not One):
(1) “There is One,” but a totally ineffable‐unpredictable One without Being, a One which is neither true nor false—Dolar is right to point out that this One is not the non‐symbolic Real, but the lack of a signifier, the “barred” signifier ($), which is as such still inherent to the order of the signifier.40
(2) One with Being, “One is”: we can predicate it, we are dealing with One which is; but crucial here is the implied difference between One and Being: “If one is, it participates in being, and is therefore something different from being, for otherwise it would make no sense to assert that one is.”41
But the moment we concede this difference, we are compelled to repeat it indefinitely, i.e., within each of its poles: every One again is and is One, every being is and is one, etc.: “‘The one that is' falls apart into one and being, but in such a way that each part includes the other as its part. This inner division, once it has started, cannot be stopped: the moment we have two parts, we have infinitely many of them.”
Or, to put it in Hegelese, each term has two species, itself and the other term; each term is the encompassing unity of itself and its other. We enter thereby the problematic space of self‐referential paradoxes: “One is now at one and the same time the whole and the part, and so into infinity, it is both limited and unlimited, it both moves and stands still, it is both identical and different, like and unlike itself and others, both equal and unequal to itself and to others etc.”
If the result of the first hypothesis is that we cannot predicate anything of the One, the result of the second hypothesis is that “anything goes,” we can predicate all possible, even mutually exclusive, predicates. Dolar draws here exactly the opposite conclusion to Armand Zaloszyc: Lacan's Y a d'l'Un is a paraphrase not of the first, but of the second of Parmenides's hypotheses:
Lacan's famous dictum Y a d'l'Un can be read as a paraphrase of this second hypothesis. Translating it simply by “There is One” one loses the paradox of the French formulation, where the partitive article (de) treats the one as an indefinite quantity (as in Il y a de l'eau, “There is water,” i.e. an indefinite quantity of it), implying, first, that there can be an immeasurable quantity of one, i.e. of what is itself the basis of any measuring, and second, if the quantity is indefinite, then it is divisible (like water)—but into what, if one is the minimal unity?42
But does this weird immeasurable quantity not mean that the One of the second hypothesis should not be linked to Lacan's Y a d'l'Un, that the “One which is,” the unary signifier, S1, should rather be opposed to the immeasurable “there is (something of the) One,” which is characterized by a divisibility and thus a multiplicity not composed of Ones?
The paradox is here a very elegant Hegelian one: although Plato is the philosopher of the One, what he is unable to think (as opposed to just “represent”) is precisely the One as a concept. To do this, one needs not only a self‐relating reflexive predication (the One is a “one One,” an x which partakes of the Idea of One with regard to Oneness itself)—which Plato possesses—but also the positive concept of zero (which Plato does not possess): to get a pure concept of the One, not just the notion of one thing, the x which “partakes of the idea of One with regard to Oneness itself” has to be zero, a void, devoid of all content. Or, to put it in a more descriptive way: being‐a‐One adds nothing to the content of an object; its only content is the form of self‐identity itself.
In Dolar's reading, the first two hypotheses are two circles which partially intersect, so that the first hypothesis stands for the One without Being, that is, the One from which the part of it which intersects with Being is subtracted, and the second hypothesis stands for the narrow intersection of the two circles of One and Being.
(3) One with Being does not preclude Others with Being: there can be Others with predicates.
(4) One without Being precludes Others and thus also their predication.
(5) It concerns a One, something that is an entity, but which does not exist, i.e., does not have Being. Even if One is not, we can still predicate it, i.e., negative predication is possible, we know what we are saying when we negate a predicate.
(6) The One is here not only deprived of Being, but deprived of its very character of One: it is no longer a non‐existent entity, but a nonentity—and, as such, cannot be predicated.
(7) What does the fact that the One is a non‐existing entity mean for Others? As in the case of the hypothesis 5, Others can be predicated.
(8) If, however, One is not only a non‐existent entity, but a nonentity, then there are also no Others, existing or non‐existing—there is nothing at all.
To account for the difference between hypothesis 5—one can talk (make propositions, say true things) about non‐being; truth has a structure of (symbolic) fiction—and hypothesis 7—everything is a fluid appearance—we must introduce a tripartite distinction between symbolic fiction, imaginary illusion, and the appearance of the Real: the One of hypothesis 5, the One that does not exist, but which we can talk about, is the symbolic fiction; the dispersed not‐One of hypothesis 7 is that of imaginary illusion; and, we may add, the One that is not One of hypothesis 8 is the Real as impossible.
Radically opposed to Dolar's reading of Parmenides is that of Armand Zaloszyc, according to whom “Y a d'l'Un” is the formula for the pure jouissance‐One, that is, a jouissance not yet mediated by the Other, the symbolic order, not yet “departmentalized,” accountable. The missing link which legitimizes us in establishing a connection between this thesis of Lacan and the first hypothesis of Plato's Parmenides (which asserts the One totally external to Being, with no relation to or participation in Being) is provided by the Neoplatonist “mysticism” of Plotinus—recall that, for Lacan, the mystical ex‐stasis is the paradigmatic example of the jouissance‐One. Parmenides was the Neoplatonists' favorite of Plato's texts, and they read it as a powerful assertion of the ineffability of the One with which the mystical experience reunites us:
The demonstration of the first hypothesis of the Parmenides leads to the conclusion that it is impossible that the One exists. So it is, the One of this first hypothesis, being one by definition, could neither have parts nor be a whole. Therefore, it will have neither beginning, nor end, nor limits. For the same reason, it will not participate in time. It will therefore have no being since to be implies the participation in a time. And, if it is not at all, then can it have something that belongs to it or comes from it? Most certainly not. Therefore it has no name; there is no definition, no perception, and no knowledge of it. Is it possible that this be so of the One? No. From this demonstration of impossibility it can surely be legitimately introduced that “since the One in no way participates with being,” it does not exist, that there is nothing beyond being, that being is therefore all. The Neoplatonists chose to read the Parmenides demonstration of impossibility differently. They agreed that there is an incompatibility between the One and being, but rather than deducing that the One does not exist, they concluded that no doubt the One did not exist in terms of being, but that beyond being, there is the One, that the One ex‐sists from being.
In this way, “there is the One” constitutes a formula that opposes ontology and leads towards the notion of the not‐all of a radical Other, in terms of the otherness with which there is no relation, where emerges the logic of the Parmenides demonstration. Being on one side, and on the other, the there is—they are incompatible. Being on one side, the real on the other. We immediately see that this opposition is the one at work in negative theologies, in the pursuit of a non‐knowledge that equals itself to learned ignorance, in the accounts given by the great Christian mystics of their experience, using oxymorons drawn from The Mystic Theology of Pseudo‐Dionysius the Aeropagite.43
There are two arguments for this reading. When Lacan talks about jouissance feminine, he always qualifies it—“if a thing like that were to exist (but it does not)”—thereby confirming its incommensurability with the order of being (existence). Plus, his formula is Y a d'l'Un, and the impersonal il y a is, like the German es gibt which plays such a key role in late Heidegger, clearly opposed to being (in English, this distinction gets blurred, since one cannot avoid the verb “to be” in translation). There is, however, one conclusive counter‐argument which pretty much ruins the case: Zaloszyc refers to the Neoplatonic mystics as the missing link between Plato and Lacan, yet, as we have already seen, Lacan explicitly rejects the Neoplatonist reading of Parmenides. It thus seems that Dolar's opposed reading—wherein the One versus Being is, in Lacanese, the symbolic versus the Real—is much more convincing. But let us see where Zaloszyc's reading leads him:
The One that there is, is the one of the jouissance One, that is, the jouissance designated in the terms of the first hypothesis of the Parmenides … it is opposed to a jouissance developed partes extra partes that is consequentially accountable and numerable according to the measurements of the signifier. If we think about it, the being itself is only determined by meaningfulness, whereas we refer the jouissance One to the real. The real as impossible, as we have already seen.
So there is a jouissance that is not without a relation to the Other of the signifier (that is alienated to the signifier), and there is an autistic jouissance, separated from the signifier and separated from the Other, for which the paradigm is the non‐relation. That is the jouissance One. From there, there are two ways to go: either maintain that there is no other being than being, with the will to foreclose the jouissance One, or support the idea that there is the One that exists apart from being, in which case the demonstration of impossibility takes into account the trace that this One leaves in the Other, in the form of “there is no sexual relation” …
The passage from the jouissance One to the Name‐of‐the‐Father is the passage from the not‐all to an all, but this passage leaves an un‐sublated remainder/excess, the trace that the jouissance One will leave there. One of the forms of this excess is jouissance feminine, the other is the Freudian Ur‐Vater, the one who enjoys all the women.44
Insofar as, for Lacan, this One is (also) an “indivisible remainder” which makes the sexual relationship inexistent, one can understand how Y a d'l'Un is strictly correlative to il n'y a pas de rapport sexuel: it is the very object‐obstacle to it; it is not primarily the mystical all‐encompassing One of the infamous “oceanic feeling” derided by Freud, but a “little piece of the Real,” the excremental remainder which disturbs the harmony of the Two. The equation of the two excesses (jouissance feminine and Ur‐Vater) also makes sense: it points towards Lacan's statement that “woman is one of the names of the father.”
What makes Zaloszyc's solution problematic is that it is ultimately incompatible with the very logic of the non‐All to which it refers: it reduces it to the “masculine” logic of exception; symptomatically, Zaloszyc himself uses the term “exception” to designate the feminine position: “The feminine side of sexuation will present itself, not without a tie to the phallic signifier, but also not without having preserved a relation with the jouissance One”; this is what “makes a woman an exception,” namely an exception to the phallic‐symbolic order.
How are we to relate the One of Y a d'l'Un (“there is [some] One, something of a One,” developed by Lacan in Seminar XX [Encore]) to the series of unary signifiers, prior to their unification through a phallic Master‐Signifier—the infinitely self‐divisible series of S1 (S1 (S1 (S1…))), which also replicates the frame of the materialist ontology of multiplicities and Void? There is a good reason Lacan uses the common French expression Y a d'l'Un, which is as far as possible from the elevated mystical assertion of the One beyond all being(s), epekeina tes ousias (like “there is water there”—an unspecified quantum). However, the One of Y a d'l'Un is not yet the One of counting: the diffuse “there is something of the One” precisely prevents the fixation of limits which would render possible the counting of Ones. What if one reads Lacan's Y a d'l'Un as the formula of the minimal libidinal fixation (on some One) constitutive of drive, as the moment of the emergence of drive from the pre‐evental One‐less multiplicity?
As such, this One is a “sinthome,” a kind of “atom of enjoyment,” the minimal synthesis of language and enjoyment, a unit of signs permeated with enjoyment (like a tic we compulsively repeat). Are such Ones not quanta of enjoyment, its smallest, most elementary packages?
Obscurantist idealists like to vary the motif of “almost nothing”: a minimum of being which nonetheless bears witness to divinity (“God is also present in the tiniest speck of dust …”). The materialist answer to this is the less than nothing. The first to propose this answer was Democritus, the father of Ancient Greek materialism (and also, incidentally, one of the first to formulate the principle of equality—“Equality is everywhere noble,” as he put it). To express this “less than nothing,” Democritus took recourse to a wonderful neologism den (first coined by the sixth‐century‐BC poet Alcaeus), so the basic axiom of his ontology is: “Nothing is no less than Othing,” or, as the German translation goes, “Das Nichts existiert ebenso sehr wie das Ichts.”45
It is crucial to note how, contrary to the late Wittgensteinian thrust towards ordinary language, towards language as part of a life world, materialism begins by violating the rules of ordinary language, by thinking against language. (Since med'hen does not literally mean “nothing,” but rather “not‐one,” a more adequate transposition of den into English would have been something like “otone” or even “tone.”46)
The Ancient Greeks had two words for nothing, meden and ouden, which stand for two types of negation: ouden is a factual negation, something that is not but could have been; meden is, on the contrary, something that in principle cannot be. From meden we get to den not simply by negating the negation in meden, but by displacing negation, or, rather, by supplementing negation with a subtraction. That is to say, we arrive at den when we take away from meden not the whole negating prefix, but only its first two letters: meden is med'hen, the negation of hen (one): not‐one.
Democritus arrives at den by leaving out only me and thus creating a totally artificial word den. Den is thus not nothing without “no,” not a thing, but an othing, a something but still within the domain of nothing, like an ontological living dead, a spectral nothing‐appearing‐as‐something.
Or, as Lacan put it: “Nothing, perhaps? No—perhaps nothing, but not nothing”;47 to which Cassin adds: “I would love to make him say: Pas rien, mais moins que rien (Not nothing, but less than nothing)”48—den is a “blind passenger” of every ontology.49 As such, it is “the radical real,” and Democritus is a true materialist: “No more materialist in this matter than anyone with his senses, than me or than Marx, for example. But I cannot swear that this also holds for Freud”—Lacan suspects Freud's link to kabbala obscurantism.50
In characterizing den as the result of “subtraction after negation” (something—nothing—othing), Cassin, of course, cannot resist the temptation to have a stab at Hegel: “It cannot be dialecticized precisely insofar as it is not an assumed and sublated negation of negation, but a subtraction after negation.”51 The rise of den is thus strictly homologous to that of objet a which, according to Lacan, emerges when the two lacks (of the subject and of the Other) coincide, that is, when alienation is followed by separation: den is the “indivisible remainder” of the signifying process of double negation—something like Sygne de Coûfontaine's tic, this minimal eppur si muove which survives her utter Versagung (renunciation). The later reception of Democritus, of course, immediately “renormalized” den by way of ontologizing it: den becomes a positive One, atoms are now entities in the empty space, no longer spectral “othings”(less‐than‐nothings).
The neologism den evokes density and thus points towards the primordial, pre‐ontological, contraction: den is, arguably, the first name for Lacan's Y a d'l'Un—there are ones, minimal points of contraction, of ens which is not yet the ontologically constituted One. Perhaps, an anachronistic reference to Kant can nonetheless be of some help here: meden follows the logic of negative judgment, it negates being as a predicate, while den asserts non‐being as a (positive) predicate—den is nothingness (the void) which somehow “is” in itself, not only as a negation of (another) being. In other words, den is the space of indistinction between being and non‐being, “a thing of nothing,” as the “undead” are the living dead. (The well‐known “Panta rei, ouden menei” of Heraclitus can thus be read as: “everything flows, nothing remains”—“nothing” as the very space of indistinction of things and no‐thing.)
Predictably, the Eleatic Melissus, in his critique of Democritus, dismissed den with the scathing remark that “far from being a necessary existent, [it] is not even a word.” In a way, he is right: we need a non‐word to designate something that, precisely, does not yet exist (as a thing)—den lies outside the scope of the unity of logos and being. Democritean atomism is thus the first materialist answer to Eleatic idealism: Eleatics argue from the logical impossibility of the void to the impossibility of motion; Democritean atomists seem to reason in reverse, deducing from the fact that motion exists the necessity that the void (empty space) exists. The ultimate divide between idealism and materialism does not concern the materiality of existence (“only material things really exist”), but the “existence” of nothingness/the void: the fundamental axiom of materialism is that the void/nothingness is (the only ultimate) real, i.e., there is an indistinction of being and the void. If, for Parmenides, only being is, for Democritus, nothing is as much as being. In order to get from nothing to something, we do not have to add something to the void; on the contrary, we have to subtract, take away, something from nothing. Nothing and othing are thus not simply the same: “Nothing” is the generative void out of which othings, primordially contracted pre‐ontological entities, emerge—at this level, nothing is more than othing, negative is more than positive. Once we enter the ontologically fully constituted reality, however, the relationship is reversed: something is more than nothing, in other words, nothing is purely negative, a privation of something.
This, perhaps, is how one can imagine the zero‐level of creation: a red dividing line cuts through the thick darkness of the void, and on this line, a fuzzy something appears, the object‐cause of desire—perhaps, for some, a woman's naked body (as on the cover of this book). Does this image not supply the minimal coordinates of the subject‐object axis, the truly primordial axis of evil: the red line which cuts through the darkness is the subject, and the body its object?
※注
40 Dolar, “In Parmenidem Parvi Commentarii,” p. 67.
41 Ibid., p. 81.
42 Ibid., p. 82.
43 Armand Zaloszyc, “Y a d'l'Un,” intervention at the Congress of the World Association of Psychoanalysis, Rome, July 13–16, 2006.
44 Ibid.
45 This translation probably relies on Meister Eckhart, who had already coined “Ichts” as a positive version of “Nichts,” i.e., the void in its positive/generating dimension—the nihil out of which every creation proceeds. What Eckhart saw was the link between the subject and negativity.
46 Not to mention the weird fact that, in English, den means “cave, hideout, nest, safe place.”
47 Lacan, The Four Fundamental Concepts of Psycho‐Analysis, p. 62.
48 Alain Badiou and Barbara Cassin, Il n'y a pas de rapport sexuel, Paris: Fayard 2010, p. 82.
49 Jacques Lacan, “L'Étourdit,” Scilicet 4, Paris: Seuil 1973, p. 51.
50 Ibid.
