singularity

The critical threshold or division between two states of being, e.g. between boiling and not boiling. At such a point it is impossible to decide whether the object is in one state of being or another---thus, one would have to say it is neither boiling nor not-boiling and in this precise sense it is properly referred to as undecidable. Both Badiou, Alain and Deleuze, Gilles define the event in terms of singularity, substituting it for essence, which they both dismiss as overly Platonic.