NOTES
FROM: Badiou, A (2011) ‘Ontology of
Multiplicity: omega as event’ EGS
video
There is
no ‘one’ as such.Everything finite is a multiplicity.The
finite does not exist inside a One, whether this
is Natureor
God, and nor does it only exist outside
but as dependent upon the One.The
multiplicity is the fundamental term of
ontology.Of
course we need a strict definition, and this is
why we turn to set theory.What
is a set?
Intuitively
a set arises when we put things together, but we
need a more precise definition.A set
is something composed of elements, represented
as X E Y, meaning X is an element of Y.To
exist at all is to belong to a set, to be an
element in a multiplicity.Everything
that exists is an element of something
different.We also have to remember that the names
of sets are not included among the elements of
the set, that X E X is never possible.This
means an ‘obligation of the other’, that the
other is ontologically necessary.
There are
many consequences of this position.Nothing
can exist separately and alone, but is always an
element of something.We
never exist alone, for example.Difference
is integral to existence, and so is a
relationship with something other.There
is no solipsism.There was always an exterior world.So the
ontology of the multiplicity is one of
difference, and never pure identity.In the
political field, we can see that those who
advocate pure identity not difference are nearly
always reactionary, opposed to the other.So
radical rejection of the other is an ontological
fault.This
is an important political issue today.All
attempts to develop a closed identity have led
to terror and the destruction of the other.For
example the ‘Nazi real’ acknowledged the Jews as
others, but saw their destruction as necessary,
and then the same for all others.This
is a negative relation to the other, but there
are positive ones as well.
What we
need to do is develop our experience of the
different rather than just explore our own
identity.This
is an axiom of true politics, to assume there is
an other, to assume difference, to agree that
identity is not the first element of reality.What
is first is a complex of differences, and we
only explore our identity by experiencing
others.
So the
notion of God as the pure One must be excluded
from our analyses of being, since God is pure
identity.Actually,
there are complications, and it might be the
case that God creates the external world and
difference to develop His true identity, that
the external can be seen as the development of
God, a development of the infinite.Alternatively,
God can be seen as the repository of all
differences, as in Spinoza, or even as omega, as
a recapitulation of finite differences, so that
God is the name of differences.
If X is
always an element of Y, it also means that X
must be a multiple, arranged in a
series—something else is an element of X, Y is
an element of something else, and so on.The
series is stopped at either end by infinity and
the void.The
void belongs to a singleton, but nothing belongs
to the void, so the void is between nothing and
something.Further, there is only one void, unlike
infinity, so there is no determination in the void
-- it cannot generate another void.
How can we
explain the difference between two
multiplicities, where X may belong to Y, but is
not be equal to it?X is
different from Y if it contains an element that
Y does not possess—let us call it Z.This
describes the property known as extensionality,
where we can find a single point of difference
in one element in X but not in Y.This
is a particular or local difference, but it can
explain much larger global differences, the
whole of the difference between X and Y.
However
there are other cases, the differences between
colours, for example, where there is no single
distinct element which can act as a point of
difference.We're talking here of qualitative
differences.These are differences outside ontology
[assuming we mean outside set theory and its
version of ontology].For
this reason, qualitative differences have been
seen as quite different differences, not
extensional and localized, but qualitative and
global, different in their totality.And
this has appeared as a basic philosophical
distinction and produced disputes about the
qualitative as the only true difference—this is
the claim of Bergson, Deleuze and Nietzsche who
think that global differences, the quality of
things, is the only proper difference, and they
do not consider extensional or quantitative
differences as being equally important.However,
it might be the case that we can explain the
global from many local differences, which would
render global differences as an illusion.There
may be infinite local differences in one
multiplicity, and only one difference in
another.We
might be able to explain the differences between
yellow and blue in terms of different
wavelengths, for example.[This
seems to be an important insight into Deleuze’s
insistence on the intensive operating at the
virtual, and his more or less total disregard of
any quantitative differences in the empirical,
which he sees as merely non-conceptual, the
province of science and so on.There
also clearly links between the limited otherness
for women in phallogocentrism as opposed to
their virtual otherness, for example in
Irigaray].
Issues
arise with the notion of succession too [see the
earlier lecture].We
have seen that omega emerges as outside finite
succession, but then yields a succession of
omegas.Succession
does not take place only inside the finite and
cannot be used as a definition.All
finite numbers do succeed, but they also have
successors in the infinite, in the new worlds
opened by omega.It follows that the infinite can not be
defined as non-succession, since omega is
succeeded.Omega can be seen as a cut between the
finite and the infinite, it is not produced by
the finite but succeeds it, not as a consequence
of the finite but as a recapitulation of the
world as well as a cut [reminds me of Lyotard’s
definition of the postmodern].Omega
is therefore like an event, something which is
not precisely law governed and which opens a new
sequence.It
can only be calculated afterwards.
In the new
succession after omega, the laws of the world
still apply [the laws of set theory]—the new
world is not an illusion.There
is some repetition inside the new.We
never totally enter into a totally new, and the
laws of succession and so on remain.However,
we are in another dimension.Some
people think this is chaos, but it is a new
world on the other side of a rupture with the
old world.Omega is a good image for this [partial]
rupture.
Omega as a
point distinguishes the finite and the infinite.Omega
is both the successor and a limit.What
is the difference between these terms?Is it
not possible that the true content of the
infinite can be omega itself? [No because] omega
is an absolute particular point that does not
succeed the finite—this is the limit.Even
new worlds can exist inside omega.In
this sense, the infinite is always a limit [of
the finite].However there is another sort of
infinite, not as the limit but as a succession.Are
these identical?Not if there is a major difference
between rupture and succession [some very old
themes in French philosophy here
--epistemological breaks and all that!].This
second distinction is also inside the infinite,
it is a second kind of both successor and limit.
In the
infinite set, succession shares the law of
succession in the finite, it is a kind of memory
of the finite, a repetition of succession.In the
limit though, there really is a new beginning,
and here it is like the void, which does not
succeed.The
void is also a beginning, and omega can be a new
beginning.The differences between succession and
limit are combined.
The homely
analogy refers back to concrete life.We can
experience an omega.We
know it's a beginning, but we also recognize a
certain familiarity in the succession after the
beginning, certain familiar bits reoccur.It's
the same with infinity—there are differences
inside it, familiar bits as well as
revolutionary ones.Only
omega itself is the true change, and after it we
return to common life.There
all sorts of implications for politics here,
such as the routinization that follows the
insurrection as the true political moment.Even
so, we are not returning to the finite and the
old world—it is simply that something must
continue into the new succession.