Reading Summary of Meditation 6 -
What Badiou is venturing to do with Aristotle in Meditation Six is to use Aristotle's refutation of the void as "thinking" the void as inconsistent multiplicity. In Meditation Five, you may remember, Badiou terms the void, inconsistency as such. Though the point of Aristotle's refutation is to say that a void or a vacuum cannot occur in nature--that it is not a being--Badiou charges ahead by arguing essentially that Aristotle's demonstration of the epistemological, metaphysical, and ontological problems of thinking the void within nature--or in situation--in fact illuminates Badiou's own thesis of the void as inconsistency. That is, Badiou affirms the general line of ontological argumentation but takes issue with the conclusion that Aristotle draws--namely, the absurdity of the possibility of the void. Furthermore, Badiou takes time to distance modern physics from the ontological categories of Aristotle's thought, being that in fact vacuum's can be created within the realm of experimentation. Badiou writes, "For the Greek, the void is not an experimental difference but rather an ontological category, a supposition relative to what naturally proliferates as figures of being" (p71). Therefore, "In this logic, the artificial production of a void is not an adequate response to the question of whether nature allows, according to its own opening forth, 'a place where nothing is' to occur, because such is the Aristotelian definition of the void..." (p71).
Nature, for Aristotle, is the "being-qua-being of that whose presentation implies movement; it is not the law of movement, it is movement....Physics attempts to think the there-is of movement....physics sets itself the following question: why is there movement rather than absolute immobility?" (p71). But again, for Aristotle, "Nature is the principle, the cause, of self-moving and of being-at-rest, which reside primordially in being-moved or being-at-rest, and this in and for itself and not by accident" (p71-72). Therefore, physical refutation--or experimentation--is "barred to us" in our ontological investigation. Badiou's aim is to "discover the ontological weak point of the apparatus inside which Aristotle causes the void to absolutely in-exist" (p72). Or rather, "the void must be examined in situation" (p72). And in accordance with the project of this meditation, Badiou will utilize Aristotle's own terminology/definitions to examine the void in an Aristotelian situation. Badiou writes:
"The Aristotelian concept of a natural situation is place. Place itself does not exist; it is what envelops an existent insofar as the latter is assigned to a natural site. The void 'in situation' would thus be a place in which there was nothing. The immediate correlation is not that of the void and non-being, it is rather that of the void and the nothing via the mediation--non-being, however natural--of place. But the naturalness of place is that of being the site towards which the body (the being) whose place it is, moves. Every place is that of a body, and what testifies to this is that if one removes a body from its place, it tends to that place. The question of the existence of the void thus comes down to that of its function in respect to self-moving, the polarity of which is place" (p72-73).
"The aim of Aristotle's first major demonstration is to establish that the void excludes movement" via the concepts of difference, unlimitedness (infinity), and incommensurability (p73). Again, Badiou utilizes this to "think" the inconsistency of the void. He writes: "This triple determination specifies the errancy of the void, its subtractive ontological function and its inconsistency with regard to any presented multiple" (p73).
In-Difference: Within nature movement is determined by the differentiation of place. Therefore movement cannot occur within the void, because the void as inconsistency, precedes the count-as-one in ordering the structure of the consistent multiple. Therefore, the void "cannot support difference...and consequently forbids movement" (p73). It is Aristotle's view that movement is presentation itself and therefore "absurd to demand proof of the existence of presentation, since all existence is assured on the basis of presentation" (p73). Badiou's point, as I interpret it, is to illustrate the indifference (argued mathematically in Meditation Five) which is inherent in the void. Remembering however, that this implies for Aristotle that the void is non-being. For Badiou, the void is "in truth the name of being" (p72).
In-Finite: Badiou begins, " For Aristotle there is an intrinsic connection between the void and infinity, and we shall see [in Meditation Thirteen and Meditation Fourteen] that he is entirely correct of this point: the void is the point of being of infinity. Aristotle makes this point according to the subtractive of being, by posing that in-difference is common to the void and infinity as species of both the nothing and non-being..." (p73). Badiou continues his inquiry by exploring the ramifications of thinking the void as infinite and therefore outside of situations. "As such, the void is in excess of being as a thinkable disposition, and especially as natural disposition. It is such in three manners" (p74). First, "one would then have to conceive that bodies are necessarily transported to infinity...since no difference would dictate their coming to a halt" (p74). Second, "given that indifference of the void cannot determine any natural direction for movement, the latter would be 'explosive', which is to say multi-directional; transport would take place 'everywhere' " (p74). Thirdly, "if we suppose that it is a body's internal void which" causes movement, "it would also have to be the latter's goal: the void transporting itself towards its own natural place" (p74). Therefore, a kind of "reduplication" of the void would occur. "Yet the indifference of the void prohibits it from differentiating itself from itself..." (p74)
Un-Measure: "Every movement is measurable in relation to another according to its speed. Or, as Aristotle says, there is always a proportion, a ration between one moment and another, in as much as they are within time, and all time is finite....The void is in-numerable, hence the movement which is supposed therein does not have a thinkable nature, possessing no reason on the basis of which its comparison to another movements could be ensured" (p75).
Badiou summarizes this line of argumentation, "What Aristotle is inviting us to think is the following: every reference to the void produces an excess over the count-as-one, an irruption of inconsistency, which propagates--metaphysically--within the situation at infinite speed. The void is thus incompatible with the slow order in which every situation re-ensures, in their place, the multiples that it presents. It is this triple negative determination (in-difference, in-finite, un-measured) which thus Aristotle to refuse any natural being for the void. Could it, however, be a non-natural being? Three formulas must be interrogated here..." (p75).
Firstly, Badiou recalls what Aristotle had attributed to those defenders of the void he was trying to refute; namely, that the same being "pertains to void, to fullness, and to place, but the same being does not belong to them when they are considered from the standpoint of being" (p75-76). "It is thus imaginable that a situation, conceived as a structured multiplicity simultaneously brings about consistent multiplicity (fullness), inconsistent multiplicity (the void), and itself (place), according to an immediate identity which is that of being-in-totality, the complete domain of experience. But, on the other hand, what can be siad via these three terms of being-qua-being is not identical, since on the side of place we have the one, the law of the count; on the side of fullness the multiple counted-as-one; and of the side of the void, the without-one, the unpresented....Under these conditions, the void would be being as non-being--or un-presentation--fullness, being as being--consistency--and place, being as the non-existing limit of its being--border of the multiple by the one" (p76).
Secondly, the void "could be a name for matter-in-itself" (p76). Moreover, to "admit that the void can be another name for matter is to confer upon it the status of an almost-being" (p76).
Thirdly, Badiou examines the last formula which "evokes a possibility that Aristotle rejects, and this is where we part from him: that the void, once it is unlocalizable (or 'outside situation'), must be thought as a pure point" (p77). For Aristotle, this absurdity is grounded in the inability to "separate the question of the void from that of place" (p77). "It is precisely here that Aristotle's acute thought encounters its own point of impossibility: that it is necessary to think, under the name of the void, the outside-place on the basis of which any place--any situation--maintains itself with respect to its being....It is because the void is the point of being that it is also the almost-being which haunts the situation in which being consists. The insistence of the void in-consists as de-localization" (p77).
What Badiou is venturing to do with Aristotle in Meditation Six is to use Aristotle's refutation of the void as "thinking" the void as inconsistent multiplicity. In Meditation Five, you may remember, Badiou terms the void, inconsistency as such. Though the point of Aristotle's refutation is to say that a void or a vacuum cannot occur in nature--that it is not a being--Badiou charges ahead by arguing essentially that Aristotle's demonstration of the epistemological, metaphysical, and ontological problems of thinking the void within nature--or in situation--in fact illuminates Badiou's own thesis of the void as inconsistency. That is, Badiou affirms the general line of ontological argumentation but takes issue with the conclusion that Aristotle draws--namely, the absurdity of the possibility of the void. Furthermore, Badiou takes time to distance modern physics from the ontological categories of Aristotle's thought, being that in fact vacuum's can be created within the realm of experimentation. Badiou writes, "For the Greek, the void is not an experimental difference but rather an ontological category, a supposition relative to what naturally proliferates as figures of being" (p71). Therefore, "In this logic, the artificial production of a void is not an adequate response to the question of whether nature allows, according to its own opening forth, 'a place where nothing is' to occur, because such is the Aristotelian definition of the void..." (p71).
Nature, for Aristotle, is the "being-qua-being of that whose presentation implies movement; it is not the law of movement, it is movement....Physics attempts to think the there-is of movement....physics sets itself the following question: why is there movement rather than absolute immobility?" (p71). But again, for Aristotle, "Nature is the principle, the cause, of self-moving and of being-at-rest, which reside primordially in being-moved or being-at-rest, and this in and for itself and not by accident" (p71-72). Therefore, physical refutation--or experimentation--is "barred to us" in our ontological investigation. Badiou's aim is to "discover the ontological weak point of the apparatus inside which Aristotle causes the void to absolutely in-exist" (p72). Or rather, "the void must be examined in situation" (p72). And in accordance with the project of this meditation, Badiou will utilize Aristotle's own terminology/definitions to examine the void in an Aristotelian situation. Badiou writes:
"The Aristotelian concept of a natural situation is place. Place itself does not exist; it is what envelops an existent insofar as the latter is assigned to a natural site. The void 'in situation' would thus be a place in which there was nothing. The immediate correlation is not that of the void and non-being, it is rather that of the void and the nothing via the mediation--non-being, however natural--of place. But the naturalness of place is that of being the site towards which the body (the being) whose place it is, moves. Every place is that of a body, and what testifies to this is that if one removes a body from its place, it tends to that place. The question of the existence of the void thus comes down to that of its function in respect to self-moving, the polarity of which is place" (p72-73).
"The aim of Aristotle's first major demonstration is to establish that the void excludes movement" via the concepts of difference, unlimitedness (infinity), and incommensurability (p73). Again, Badiou utilizes this to "think" the inconsistency of the void. He writes: "This triple determination specifies the errancy of the void, its subtractive ontological function and its inconsistency with regard to any presented multiple" (p73).
In-Difference: Within nature movement is determined by the differentiation of place. Therefore movement cannot occur within the void, because the void as inconsistency, precedes the count-as-one in ordering the structure of the consistent multiple. Therefore, the void "cannot support difference...and consequently forbids movement" (p73). It is Aristotle's view that movement is presentation itself and therefore "absurd to demand proof of the existence of presentation, since all existence is assured on the basis of presentation" (p73). Badiou's point, as I interpret it, is to illustrate the indifference (argued mathematically in Meditation Five) which is inherent in the void. Remembering however, that this implies for Aristotle that the void is non-being. For Badiou, the void is "in truth the name of being" (p72).
In-Finite: Badiou begins, " For Aristotle there is an intrinsic connection between the void and infinity, and we shall see [in Meditation Thirteen and Meditation Fourteen] that he is entirely correct of this point: the void is the point of being of infinity. Aristotle makes this point according to the subtractive of being, by posing that in-difference is common to the void and infinity as species of both the nothing and non-being..." (p73). Badiou continues his inquiry by exploring the ramifications of thinking the void as infinite and therefore outside of situations. "As such, the void is in excess of being as a thinkable disposition, and especially as natural disposition. It is such in three manners" (p74). First, "one would then have to conceive that bodies are necessarily transported to infinity...since no difference would dictate their coming to a halt" (p74). Second, "given that indifference of the void cannot determine any natural direction for movement, the latter would be 'explosive', which is to say multi-directional; transport would take place 'everywhere' " (p74). Thirdly, "if we suppose that it is a body's internal void which" causes movement, "it would also have to be the latter's goal: the void transporting itself towards its own natural place" (p74). Therefore, a kind of "reduplication" of the void would occur. "Yet the indifference of the void prohibits it from differentiating itself from itself..." (p74)
Un-Measure: "Every movement is measurable in relation to another according to its speed. Or, as Aristotle says, there is always a proportion, a ration between one moment and another, in as much as they are within time, and all time is finite....The void is in-numerable, hence the movement which is supposed therein does not have a thinkable nature, possessing no reason on the basis of which its comparison to another movements could be ensured" (p75).
Badiou summarizes this line of argumentation, "What Aristotle is inviting us to think is the following: every reference to the void produces an excess over the count-as-one, an irruption of inconsistency, which propagates--metaphysically--within the situation at infinite speed. The void is thus incompatible with the slow order in which every situation re-ensures, in their place, the multiples that it presents. It is this triple negative determination (in-difference, in-finite, un-measured) which thus Aristotle to refuse any natural being for the void. Could it, however, be a non-natural being? Three formulas must be interrogated here..." (p75).
Firstly, Badiou recalls what Aristotle had attributed to those defenders of the void he was trying to refute; namely, that the same being "pertains to void, to fullness, and to place, but the same being does not belong to them when they are considered from the standpoint of being" (p75-76). "It is thus imaginable that a situation, conceived as a structured multiplicity simultaneously brings about consistent multiplicity (fullness), inconsistent multiplicity (the void), and itself (place), according to an immediate identity which is that of being-in-totality, the complete domain of experience. But, on the other hand, what can be siad via these three terms of being-qua-being is not identical, since on the side of place we have the one, the law of the count; on the side of fullness the multiple counted-as-one; and of the side of the void, the without-one, the unpresented....Under these conditions, the void would be being as non-being--or un-presentation--fullness, being as being--consistency--and place, being as the non-existing limit of its being--border of the multiple by the one" (p76).
Secondly, the void "could be a name for matter-in-itself" (p76). Moreover, to "admit that the void can be another name for matter is to confer upon it the status of an almost-being" (p76).
Thirdly, Badiou examines the last formula which "evokes a possibility that Aristotle rejects, and this is where we part from him: that the void, once it is unlocalizable (or 'outside situation'), must be thought as a pure point" (p77). For Aristotle, this absurdity is grounded in the inability to "separate the question of the void from that of place" (p77). "It is precisely here that Aristotle's acute thought encounters its own point of impossibility: that it is necessary to think, under the name of the void, the outside-place on the basis of which any place--any situation--maintains itself with respect to its being....It is because the void is the point of being that it is also the almost-being which haunts the situation in which being consists. The insistence of the void in-consists as de-localization" (p77).
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