The claim that mathematics studies the modal structure of difference itself is far from a trivial claim, and is one whose support I do not think can be established straightforwardly. Rather, it will require the rest of this work to defend. That said, I would here like to offer what I take to be a striking piece of evidence towards this claim: Griss's negationless mathematics. Griss's programme aimed to banish all use of logical negation from mathematical proofs, and to instead formulate such proofs in terms of an explicitly positive notion of difference. Furthermore, Deleuze was aware of Griss's work and cites it in relation to his own account of intensive difference (Deleuze 1994: 234 and 330 n.11). Here, then, I would like to give a brief overview of Griss's motivation and a brief example of a definition and sketch of a proof that makes use of difference rather than negation.

Griss can be seen as a sort of hyper-intuitionist mathematician. Intuitionists reject the law of excluded middle and the inference of double negation elimination because they accept that a proposition might either lack a truth value or that the truth value can simply be unknown and, therefore, we do not have the justification to assert that it is either true or false. The motivation here is that such assertions, if allowed, license inferences of which one cannot have a clear conception. Griss pushes this commitment further by rejecting logical negation outright. For the intuitionist, not-A is a perfectly acceptable assertion if one has proved that A is false. Griss, on the other hand, is committed to the position that logical negation is always illicit, going so far as to say that ‘Only construction without the use of negation has some sense in intuitionistic mathematics’ (Griss 1948: 1127).