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ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ ΜΕ ΘΕΜΑ «Η φιλοσοφία του Alain Badiou στα Μαθηματικά και τη Φιλοσοφία. Το ένα και το πολλαπλό» ΝΑΝΟΠΟΥΛΟΥ ΒΑΣΙΛΙΚΗ (Α.Μ.: Δ200921) ΕΠΙΒΛΕΠΩΝ ΚΑΘΗΓΗΤΗΣ: ΣΠΥΡΟΥ ΠΑΝΑΓΙΩΤΗΣ ΑΘΗΝΑ, ΝΟΕΜΒΡΙΟΣ 2013

Η φιλοσοφία του Alain Badiou στη Φιλοσοφία και τα Μαθηματικά

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  • Alain Badiou .

    (..: 200921)

    :

    , 2013

  • 2

    :

    1) ( )

    2)

    ....

    3)

    ....

  • 3

  • 4

    , , ,

    ,

    ,

    , .

  • 5

    Badiou

    Being and Event ( ) (1988). Badiou

    , 1988,

    . Heidegger

    .

    Alain

    Badiou,

    .

    , , ,

    . ,

    . ,

    .

    .

    , , .

    , .

    ,

    . ,

    (

    ),

    .

    , .

    the event ( ). ,

    (, , .),

    .

    ,

    .

    .

    .

    , . ,

    . -,

    , .

  • 6

    , ,

    (generic). , ,

    ,

    . ,

    . ,

    , . (

    )

    .

    . ,

    .

    Cantor.

    Gdel, Cohen

    .

    :

    , , , , , . (A. Badiou, 2005)

    : /, , , , , , ,

  • 7

    Abstract

    In the present paper we will focus on the presentation of Badious work with title

    Being and Event (1988) which was considered as a station in the history of

    philosophy. We will have to look at Heideggers Being and Time to find such a

    new and synthetic philosophical work.

    According to Alain Badious particular philosophical thought, we meet four basic

    affirmations that went entirely against the flow of this ordinary philosophy.

    Firstly, situations are nothing more, in their being, than pure indifferent multiplicities.

    Consequently it is pointless to search amongst differences for anything that might

    play a normative role. If truths exist, they are certainly indifferent to differences.

    Cultural relativism cannot go beyond the trivial statement that different situations

    exist. It does not tell us anything about what, among the differences, legitimately

    matters to subjects.

    The structure of situations does not, in itself, deliver any truths. By consequence,

    nothing normative can be drawn from the simple realist examination of the becoming

    of things. In particular, the victory of the market economy over planned economies,

    and the progression of parliamentarism (which in fact is quite minor, and often

    achieved by violent and artificial means), do not constitute arguments in favor of one

    or the other. A truth is solely constituted by rupturing with the order which supports

    it, never as an effect of that order. He has named this type of rupture which opens up

    truths the event. Authentic philosophy begins, not in structural facts (cultural,

    linguistic, constitutional, etc), but uniquely in what takes place and what remains in

    the form of a strictly incalculable emergence.

    A subject is nothing other than an active fidelity to the event of truth. He

    philosophically found the notion of militant at a time when the consensus was that

    any engagement of this type was archaic. Not only did he found this notion, but he

    considerably enlarged it. The militant of a truth is not only the political militant

    working for the emancipation of humanity in its entirety. He or she is also the artist-

    creator, the scientist who opens up a new theoretical field, or the lover whose world is

    enchanted.

    The being of a truth, proving itself an exception to any pre-constituted predicate of

    the situation in which that truth is deployed, is to be called generic. In other words,

    although it is situated in a world, a truth does not retain anything expressible from

  • 8

    that situation. A truth concerns everyone inasmuch as it is a multiplicity that no

    particular predicate can circumscribe. The infinite work of a truth is thus that of a

    generic procedure. And to be a Subject (and not a simple individual animal) is to be

    a local active dimension of such a procedure.

    The writer attempted to argue for these theses and link them together in a coherent

    manner. What is more, he placed a rather sophisticated mathematical apparatus at

    their service. To think the generic character of truths he turned to Gdel and Cohens

    profound thinking of what a part of a multiple is. And he supported this intervention

    of mathematical formalism with a radical thesis:

    Insofar as being, qua being, is nothing other than pure multiplicity, it is legitimate to say that ontology, the science of being qua being, is nothing other than mathematics itself. (A. Badiou, 2005)

    Key words: being/existents, being qua being, event, subject, multiplicity, generic truth procedure, situation, set theory

  • 9

    ...10

    ... ...12

    1:

    1.1. .....16

    1.2. ...18

    1.3. ...22

    1.4. ...........24

    2: Alain Badiou

    2.1. Alain Badiou...............................................29

    2.2 Badiou....33

    2.3. : ......42

    2.4. : a priori ...44

    2.5. . .....53

    2.6 .....58

    2.7. Badiou .60

    2.8

    . .......64

    . .......76

    .....78

    Badiou...81

    2.9. Badiou ....86

    2.10. Alain Badiou.......92

    .....95

    Alain Badiou...96

    ........99

  • 10

    Alain Badiou .

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    Spinoza, Hegel, Mallarm, Pascal, Hlderlin, Leibniz, Rousseau, Descartes

  • 11

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  • 12

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  • 13

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  • 14

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  • 15

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  • 16

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  • 17

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  • 18

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  • 19

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  • 20

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  • 21

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  • 22

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  • 23

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  • 24

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  • 25

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  • 26

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  • 27

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  • 28

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    status .

    , Alain Badiou

    ,

    .

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    . (Alfred North Whitehead, 1861-1947,

    , 1929, . 1979)

  • 29

    2

    Alain Badiou

    2.1 Alain Badiou

    Being and Event ( ), Badiou

    ,

    :

    1. Heidegger .

    2.

    , Russell

    ,

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  • 30

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  • 31

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  • 32

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  • 33

    2.2 Badiou

    ,

    Badiou,

    :

    .

    .

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    :

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    , .

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  • 34

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    ).

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  • 35

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  • 36

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    - .

    ( Kant)

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    , .

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    ,

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    - . 1902, Bertrand Russell

    :

  • 37

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    .

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  • 38

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  • 39

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  • 40

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  • 41

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  • 42

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  • 43

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    (count-

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  • 44

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    Cantor

    Zermelo, Fraenkel Gdel

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  • 45

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  • 46

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  • 47

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  • 48

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  • 49

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  • 50

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  • 51

    priori

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    de facto

    de fcto

  • 52

    .

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  • 53

    2.5 (generic truth procedure)

    Badiou,

    (generic).

    Paul Cohen 1963.

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    , ,

    . ,

    ,

  • 54

    Picasso .

    , ,

    . Badiou - -

    Heidegger, .

    , - ,

    , .

    , ,

    , ,

    .

    -,

    ;- . , ',

    , , , ,

    . ,

    , ,

    ,

    :

    .

    ,

    , Badiou,

    . generic

    (, , , ,)

    ( , , , ,).

    . ,

    , , . (

    ) ,

    -. ,

    Badiou.

    Badiou

    - -

    : , ,

    . ,

    , ,

  • 55

    .

    ,

    (generic) (forcing).

    , ,

    - ,

    .

    , .

    -, , ,

    .

    ,

    , .

    (mathme) ,

    , ( )

    ,

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    ,

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    .

    ; Badiou

    ,

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    , ,

    (vridicit).

    . , ,

    () ( ),

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    , ,

    - :

    , .

    ( ,

    , ) (

    , , ...).

  • 56

    .

    .

    ,

    .

    ,

    , . -

    -

    (savoir), .

    ,

    .

    . , ,

    , , ,

    .

    .

    .

    ,

    . ,

    ,

    (- ).

    , ,

    . :

    .

    . ,

    , .

    , . (Badiou, 2006, 24).

  • 57

    , , ,

    ,

    , , .

    :

    - (compossibility)

    : ,

    :

    .

    .

    .

    , ,

    ...

    , ,

    , . (Badiou, 2006, 25).

    ,

    - ,

    (Badiou, 2006, 28).

    : (

    , ), (

    , ), (

    ) (

    ).

    ( ).

  • 58

    2.6

    ,

    ,

    , .

    ,

    .

    .

    , ,

    .

    - -

    .

    . ,

    .

    , .

    . , ,

    . ,

    , .

    Badiou ,

  • 59

    ,

    , (., .125-136)

    (Badiou)

    -

    . ,

    ,

    (Badiou).

    Badiou -

    , ,

    .

    :

    , -

    . ,

    .

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    (

    ).

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    .

    , , .

    : , ,

  • 60

    .

    : ,

    ,

    . ,

    .

    : , ,

    . , ,

    , .

    2.7 Badiou

    , , .

    ,

    ( ).

    , Heidegger

    . Badiou

    (Lacan)

    .

    :

    ,

    , ,

    , Husserl

    (Badiou, 2006, 32).

    Heidegger, Badiou :

    Heidegger : ,

    (Badiou, 2006,

    61).

  • 61

    (disaster).

    , Badiou,

    : ,

    ,

    ,

    . (suture)

    ,

    , .

    . (

    )

    -

    .

    ,

    Heidegger

    ,

    .

    .

    Badiou

    .

    Badiou,

    .

    o Heiner Mller,

    , .

    Badiou,

    . , ,

    ,

    - .

    .

  • 62

    Badiou ,

    . Thorie du sujet (1982),

    Mao, Mallarm Lacan.

    ,

    Badiou,

    - .

    Being and Event,

    . , ,

    , Badiou,

    .

    ,

    Badiou .

    , Badiou

    .

    , , :

    ,

    (Badiou, 2006, 52).

    Badiou , ,

    :

    )

    , ,

    ' ,

    )

    , ,

    (Badiou, 2006, 52-53).

  • 63

    2.8

    Being and Event, Badiou Zermelo-Fraenkel

    -

    Cantor. .

    Badiou .

    - ,

    ,

    , .

    ,

    - .

    -

    - (impasse of formalization).

    . ,

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    , .

    .

    ,

    .

    .

    , . ,

    , ,

    , --

    ,

    ( ).

    Hegel , ,

    , .

  • 64

    ,

    . , ,

    , ,

    ( : ). ,

    , .

    , ,

    ( , 1, .27)

    -

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    .

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    ,

    , .

    Badiou

    :

    ,

    .

    , ,

    ,

    Badiou .

    .

    Badiou,

    .

  • 65

    Cantor Zermelo,

    Fraenkel. ,

    (conditioning),

    .

    Badiou,

    , , .

    . ,

    .

    . , .

    ,

    , ,

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    ,

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    . ,

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  • 66

    ,

    . , .

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    Kant.

    ;

    , ; -,

    Kant.

    .

    . ,

    Kant

    . , , .

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    Cantor. ,

    .

    . ,

    . ,

    .

    Cantor

    . : .

    :

    ;

    Einstein .

    - , ,

    -

    ;

    '

    ( ) ;

  • 67

    ,

    .

    .

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    .

    , .

    .

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    .

  • 68

    . ,

    .

    .

    .

    , , .

    ,

    (integral) (differential) (calculus),

    . .

    ,

    . , ,

    .

    : ;

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    ;

    .

    ,

    .

    . .

    ,

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    .

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    . .

  • 69

    ,

    . ,

    , Badiou ,

    .

    , :

    , ,

    , ,

    Badiou, .

    , :

    , . ,

    , .

    Badiou

    , ,

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    ,

    :

    , , ,

    .

    ,

    ,

    :

    . ,

    , : -

    Russell-

    , ,

    Being and Event.

  • 70

    Badiou

    . Deleuze, ,

    Badiou : ,

    ,

    . Badiou

    ,

    Badiou . ,

    -Ph1:Ph2=a1:Ma2- Badiou ,

    ,

    , , .

    ,

    ,

    ,

    Badiou forcing Cohen.

    ,

    Badiou,

    ,

    , Cantor

    Mallarm. , ,

    .

    ,

    , ,

    . ,

    , . Badiou,

    , ,

    .

    ( ),

    , .

    Badiou

    -,

  • 71

    . , , ,

    Zermelo-Fraenkel ,

    . ,

    Easton,

    . Badiou

    ,

    , ,

    : , , .

    Badiou ,

    Marx Freud:

    ,

    ,

    .

    ,

    , . , ,

    . , ,

    ,

    -

    .

    , .

    ,

    ,

    , , . ,

    ,

    :

    .

    (encounter),

    . ,

    (One Eternal

    Necessity), , .

    .

  • 72

    , ,

    . Badiou Lear ,

    Lear ,

    , ,

    .

    , ,

    , ,

    .

    , ;

    . ,

    .

    -. ,

    .

    ,

    --.

    Badiou Cantor

    Zermelo-Fraenkel

    . , -,

    :

    ,

    : , ,

    . Badiou

    . .

    , -

    -

  • 73

    -

    . , , , ,

    ,

    . Badiou

    , ,

    : .

    - ,

    , . ,

    ,

    . ,

    Zermelo-Fraenkel.

    Robert Blanch,

    .

    -

    :

    Peirce ,

    ,

    , . ,

    .

    ,

    ,

    , ,

    - (presented-being).

    ,

    ,

    , .

  • 74

    , Badiou ,

    , .

    Badiou :

    , , , .

    . ,

    :

    ,

    , , -. ,

    Derrida ,

    , Hegel,

    , , , ,

    Deleuze ,

    ,

    : ,

    . : ,

    Gdel,

    , . ,

    ,

    , ,

    : .

    .

    -

    , Badiou :

    , -

    . Badiou - ,

    .

    , .

    (being fleshed out): (fleshing out)

  • 75

    . ,

    Badiou, , -

    .

    .

    (evental sites) ,

    . , Badiou

    .

    .

    , , .

    .

    , ..

    ,

    .

    : ,

    , ,

    ,

    , , .

    ,

    ,

    .

    .

    Badiou

    -

    - . ,

    , ,

    -

  • 76

    .

    :

    ,

    .

    :

    ( ), (

    avant-garde), ( ).

    Badiou,

    .

    . , .

    .

    ,

    ,

    . ,

    .

    Badiou, : ,

    , ,

    (what-is-not-being-qua-being).

    :

    .

    Badiou, ,

    . ,

    Badiou. ,

    ,

    Bachelard, Koyr, Canguilheim Foucault.

    . ,

  • 77

    :

    , .

    , Being and Event

    . , Badiou

    Mallarm.

    Cast f Dice...,

    : .

    , , ,

    , , ,

    : , .

    .

    , , Badiou

    avant-garde status quo.

    : . ,

    Badiou

    . ,

    . ,

    ,

    : ,

    . , ,

    , ,

    ,

    .

    - , -

    , .

    Badiou , :

    ,

    , , .

  • 78

    Badiou .

    ,

    . Derrida

    , Jean-LucNancy

    , Foucault .

    Badiou

    .

    Badiou

    : ,

    ,

    , ,

    , , , ,

    . , ,

    Badiou

    -

    : (

    ), ( ),

    (

    ). :

    ,

    . ,

    . ,

    .

    .

    Badiou.

    --

    . Badiou,

    ,

    .

  • 79

    ,

    ,

    .

    . Badiou ,

    , .

    Badiou ,

    - - . ,

    Badiou,

    , :

    ,

    ,

    . , Badiou

    ,

    .

    - -

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    ,

    . ,

    : ,

    .

    ,

    .

    .

    .

    , Slavoj

    Zizek, Lacan, .

    Badiou,

  • 80

    ,

    .

    , ,

    .

    ,

    ,

    .

    Badiou,

    . Badiou ,

    ,

    . Badiou

    - , ,

    , Badiou

    . - -

    Paul Cohen ,

    . , Cohen

    , , .

    , .

    Badiou

    - ,

    , -

    Badiou

    :

    .

    Badiou

    .

    Badiou,

    , Being and Event.

    , ,

    . Badiou

    forcing, , Paul Cohen.

  • 81

    , Badiou

    : .

    Badiou

    . ,

    , ,

    -

    .

    Badiou

    Badiou

    , ,

    , .

    Badiou (state)

    , (). (

    .)

    , , ,

    .

    , .

    . Badiou

    ( ) ,

    .

    :

    , .

    .

    .

    , , ,

    , . .

  • 82

    . Badiou

    , (savoir)

    (sens)

    .

    ,

    ()

    .

    , Badiou

    . , ,

    , .

    , .

    .

    ,

    , ,

    . ,

    ,

    . cogito.

    Kant,

    ,

    , ,

    .

    (operateur),

    .

    , ,

    , .

    .

    , .

    .

    Sartre. .

    Hegel.

    .

    Sartre .

  • 83

    . ,

    , .

    ,

    cogito , , , .

    ( )

    , ,

    ,

    ' . ,

    ,

    ,

    .

    - -

    .

    .

    .

    Marx Freud,

    .

    .

    , , -- ,

    ,

    -

    , .

    () ()

    .

    ,

    , ,

    .

    .

    ,

  • 84

    :

    .

    Badiou :

    ?

    Badiou

    - ,

    , .

    ,

    (identity) (agency).

    ,

    . ,

    . ,

    .

    .

    Badiou.

    ,

    . , ,

    . (

    )

    .

    , - -

    .

    Badiou

    . , ,

    ,

    ,

    . , ,

  • 85

    , .

    , ,

    . ,

    .

    , ,

    .

    ; , ,

    , . . ,

    , Badiou.

    . .

    . . ,

    .

    , ,

    .

    ,

    . ,

    ,

    .

    - ,

    Badiou,

    .

    .

    . ,

    ,

    .

  • 86

    , .

    Badiou.

    Badiou

    ,

    .

    2.9 Badiou

    Alain Badiou

    .

    . , :

    ,

    , , ,

    , ,

    (Badiou, 2006, 90).

    Nietzsche.

    . ,

    .

    .

    , ,

    . ,

    , (Badiou, 2006, 96).

  • 87

    Badiou -

    -. ,

    - , ,

    ...

    ,

    (Badiou 2006: 95-96).

    Badiou

    (, - -

    , , )

    ,

    :

    , , .

    - .

    ,

    .

    (Badiou 2009b: 23).

    - .

    ,

    ,

    .

    , ,

    , , ,

    .

    - Badiou- Slavoj Zizek,

  • 88

    , ,

    ...

    ... ,

    ()... ,

    (

    ).

    , ,

    .

    Badiou .

    ,

    , ,

    ,

    .

    Alain Badiou :

    - ( - ).

    (

    , ).

    - (

    , ) ,

    ( ) ( ).

    .

    -- ( )

    . ,

    - ,

    .

    ,

    , ,

    ,

    .

  • 89

    , :

    ,

    -- ( ). -

    , ,

    - . , -

    - -

    . , ,

    - . , ,

    -- ( ).

    , .

    :

    ,

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    ,

    .

    - .

    ,

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    .

    .

    .

    --,

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  • 90

    . ,

    .

    , ( )

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    .

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    .

    .

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    , .

  • 91

    , . ,

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    , .

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  • 92

    ,

    . , , ,

    . , - . ,

    , , ,

    .

    , , .

    , , ,

    ,

    , , , -

    - -

    .

    2.10 Alain Badiou

    , Badiou

    ,

    '60,

    Heidegger.

    , Badiou,

    .

    Peter Hallward,

    ,

    . ,

    - -

    (generic) .

    ,

    .

    Badiou.

    , Heidegger,

  • 93

    Deleuze, , Stalin,

    Foucault, ,

    , .

    . Badiou

    , , -

    -

    .

    ,

    (adequation,

    , , ),

    ,

    . ' ,

    , ,

    .

    ,

    Badiou

    ()

    :

    ().

    , Badiou

    (

    )

    , ,

    , Deleuze,

    .

    , , ,

    Badiou,

    ,

  • 94

    ,

    (

    Hegel, Marx, Bergson, Heidegger, Sartre) Alain Badiou;

    ,

    20 ; ,

    ,

    ( ,

    ),

    - ,

    - ,

    , ..,

    ,

    : ,

    , -,

    , ! :

    ;

    ,

    ( Sartre -

    , - Badiou

    ,

    ) , ,

    ,

    , Badiou, ,

    ' !

  • 95

    ,

    Alain Badiou

    . ,

    .

    ,

    (generic),

    (forcing) . .

    ,

    .

    Badiou .

    , ,

    .

    ( )

    ,

    .

    (),

    .

    Badiou,

    , ,

    . ,

    , .

    ,

    .

  • 96

    Alain Badiou

    Alain Badiou (17/01/1937-), , , , , . , .

    . Lyce Louis-le-Grand Ecole Normale Suprieure (1957-1961). Reims 1963, ( ) Franois Regnault, . . "" . . VIII (Vincennes-Saint Denis) 1969 30 ( '68) cole Normale.

    , (PSU), - . , Almagestes , 1964. 1967 Louis Althusser, Jacques Lacan Cahiers pour l'Analyse. ( ), , . . '68, , .

  • 97

    , Badiou Paris VIII/Vincennes-Saint Denis - . Gilles Deleuze Jean-Franois Lyotard.. 1980, , Badiou , Thorie du sujet (1982), magnum opus , Being and Event ( ) (1988). , Badiou Althusser Lacan, ( Petit panthon portatif/ Pocket Pantheon). ENS 1999. , , Collge International de Philosophie. "L'Organisation Politique, 1985 UCFml, 2007.

    Badiou Ahmed le Subtil. "Rhapsodie pour le theatre" "Beckett, l'increvable desir". College International de Philosophie. T . 1994, "Ahmed le subtil ou Scapin 84", Christian Schiaretti Comedie de Reims. "Ahmed philosophe", "Ahmed se fache" , "Les Citrouilles", "" . 1997 "Calme bloc ici-bas", "" .

    : - "Le Concept de modele", 1969 - "Theorie du sujet", 1982 - "Peut-on penser la politique?", 1985 - "L'etre et l'evenement", 1988 - "Manifeste pour la philosophie", 1989 - "Le nombre des nombres", 1990 - "Conditions", 1992 - "L'ethique. Essai sur la conscience du Mal", 1993 - "Deleuze, la clameur de l'etre", 1997 - "Saint-Paul. La fondation de l'universalisme", 1997 (" ") - "Abrege de metapolitique", 1998 - "Court traite d'ontologie transitoire", 1998 - "Petit manuel d'inesthetique", 1998 - "Le siecle", 2005 - "Logiques des mondes"

    . , , .

  • 98

    . "L'etre et l'evenement" (1988). . Heidegger, Derrida . , Badiou . .

  • 99

    , K., , , , ., , , 2005

    ., , , /, 2000 , ., Wittgenstein Heidegger, , 2003

    , ., , , 2005 , , , . . , , , 1994

    , ., , , , , 2007

    , ., , ,

    , ., - , , 2010-2012

    , ., , , 2010 , ., ., , , 2004 , ., , , , 2009

    , ., , , 2009-10

    Badiou A., , , , 2009 Badiou A., , , , 2009 Badiou A., , , , 2006 BadiouA., , , ,

    2011 Badiou A., . , Scripta, , 1998

    BadiouA., , , , 2009 Badiou, Alain, Being and Event, by Oliver Feltham, London and New York:

    Continuum, 2005 Badiou, Alain, Infinite thought, truth and the return to philosophy, by Oliver

    Feltham & Justin Clemens, London and New York: Continuum, 2004 Badiou, Alain, Metapolitics, London and New York: Verso, 2006 Badiou, A., Metaphysics and the critique of metaphysics, Pli: the Warwick

    journal of philosophy, n. 10, pp. 174-190, 2000 Badiou A., Of Life as a name of Being, or, Deleuze's vitalist ontology, Pli:

    the Warwick journal of philosophy, 10, pp. 191-199, 2000 Badiou A., Second manifesto for philosophy, by Louise Burchill, Polity

    Press, 2011 Badiou A., The adventure of French philosophy, New Left Review, issue 35,

    2005 Badiou A., Logics of worlds, Continuum, London, 2009 Badiou A., The event in Deleuze, Parrhesia, number 2, pp. 37-44 ( ), 2007

    Bensad, Daniel, Alain Badiou and the miracle of the event, in Hallward (ed.): 94-105, 2004

  • 100

    Bosteels, Bruno, Alain Badiou's Theory of the Subject: Part I. The Recommendation of Dialectical Materialism?,Pli 12, 200-229, 2001

    Hallward, Peter (ed.), Think Again. Alain Badiou and the Future of Philosophy, London and New York: Continuum, 2004

    Hallward, Peter, Badiou: A subject to truth, Minneapolis: University of Minnesota Press, 2003

    Neugebauer, O., , , 2003 Toscano, Alberto, From the State to the World? Badiou and Anti-

    capitalism, Communication & Cognition 37:3-4: 199-224, 2004

    http://en.wikipedia.org/wiki/Alain_Badiou http://el.wikipedia.org/wiki/ http://www.skroutz.gr/books/a.7518.Badiou-Alain.html http://waltendegewalt.wordpress.com/tag/badiou/ http://www.filosofia.gr/forum/viewtopic.php?p=105875 http://symvanta.blogspot.gr/2009/02/alain-badiou_7572.html http://www.theseis.com/index.php?option=com_content&task=view&id=1101&Itemid=29