Reduction is one of those things that is interesting to rethink under the light of some process philosophy. It is a good starting point to consider the world in terms of processes - as Latour does in Irréductions. The point is not quite to do with what is reducible, but rather to the very process of reduction which is crucially related to bringing things about - to "instaurer". In fact, things are brought about to play a role, to be treated as someting, as black boxes. Hence, a tick picks on the horse (and the cow, and the human) while reducing it to a mammal, a river brings about its banks reducing the complexity of the mud into something that holds its flow. To bring about is to reduce what is around into something else - and it has to pay the cost of transport. The starting point is gunky, that is, there is no ultimate staring point for composition - and to compose is to reduce. Reduction points at the process of creating something from something else. When we reduce temperature to kinetic mean energy, we are making kinetic mean energy available from temperature: we are bringing about more kinetic mean energy. We open the gates to turn temperature into something that can be treated as energy. Thinking in terms of transport (cost of transport etc), it is a road that is open and even though it needs maintenance (we cannot change, for example, what we take to be energy too much because then we can loose the road), it is available to be travelled.
However, I've got many problems in the area of creation of something out of something else (composing). I'll mention two. First, I have a temptation then to consider Molnar's generalization of intentionality as aimed at explicating not the notion of disposition but rather that of bringing things about. If everything is a composer, everything is bringing something about – in the beautiful and inspired translation of Heidegger's gestiftet by my friend Gerson Brea as sponsored, everything that exists is sponsoring something else. When a is sponsoring b, it is reducing it, it is treating it as something – I would say: b is sponsored as an exemplar (not as a singular item). This is equivalent to the third feature of Brentano's take on intentionality. The fourth feature – what is intended is intended in a specific mode of presentation – can also make sense when we talk about sponsoring. I sponsor my impressions qua impressions – not qua events in my brain (even though they are likely to be events in my brain). The bees sponsor a forest qua forest, not qua ex vitro genetic repositoire. Now, the second feature of the Brentano-Molnar characterisation of intentionality bugs me. I can only make sense of sponsoring the non-existent if we consider the capacity to sponsor – an animal can sponsor a prey who is not around etc. But then the ghost of dispositionalism comes back unless I use possible worlds to dispell it: there is a possible world in which the animal is preying on something that happens not to exist (or to be present in the vicinity) in the actual world. Maybe this is the way forward but I'm not sure.
The second problem has to do with my old obsession with singularities. Duns Scotus thought that if singularity is left to the hands of what implements the forms (i.e. typically matter), it would become contingent on its implementation. Deleuze arranged the ingredients for implementations into a plane, and took it to be a plane of haecceities. It is not matter because Deleuze (and Guattari) takes form and matter to be together both in content and in expression – see, for instance, The Geology of Morals in Mille Plateaux. Those haecceities are singularities on the run, they are not organised (often they are barely ordered) and they are ingredients for composition. But if things are composed as exemplars, how can a singularity come about? I then tend to flirt with bundles. A singular item is a bundle of compositions. Each composition – involving more than one composer – inherits some singularity from its composers who are producing no more than compositions (i.e. exemplars). There are still problems with the identity of the indiscernibles but maybe (only maybe) we can somehow sweep them aside.