Running ahead of myself, here’s the question that’s taking shape over Derrida and Badiou…

It seems as if iterability might be a name for the ability of a being to appear in multiple worlds - in other words, we could map “grapheme” to “being” (multiplicity counted-as-one) and “context” to “world”. A context localises a grapheme as a world localises a being appearing in that world: a grapheme “means” in a context as a being “appears” in a world.

Derrida’s argument for the non-totalisability of a context is that the constituents of a context are themselves iterable marks, and can therefore be placed in new contexts in which their unitary identity is “opened out” (in which they turn out to have a decomposable structure after all). A grapheme that in one context is “atomic” (“on the edge of the void”, in Badiou’s terminology) can be cited in another context in which its parts are discernible. There is therefore no “primitive” mark or contextual element that can securely guarantee access to all the others: unitary identity is always established contextually, by the contingent proximity of elements whose own unitary identity is always susceptible to repetition and dissemination.

For Badiou there is a multiplicity that is non-decomposable, and it is the void (the empty set): it has no further structure, being the minimally-structured element in the hierarchy of constructible sets. The “name of the void”, mark of no mark, marks that which cannot be opened out or disseminated. It is indefinitely repeatable but always “the same” in every context, precisely because it has no positive content or identity: its particular property is to have no elements in common with any other set (hence, no other set can distinguish any part of it).

A “world” is a constructible set: every element in it is “guaranteed” by some other element, with the empty set acting as the “initial object” or minimal element on the basis of which other elements are accessible. So while any given being can appear in multiple worlds with varying degrees of intensity, the void appears (if I’m not mistaken, which - caveat lector - I might be) in all worlds with the same (minimal?) intensity (because the empty set is a part of every set, but no set is a part of the empty set).

What this means is that dissemination has a limit (and the axiom of foundation ensures that this limit applies to every well-formed set: even an infinitely-descending epsilon chain must have a minimal element), and that iterability alone is insufficient to displace this limit. Another way to put this: dissemination alone cannot produce novelty