Mereology is the study or philosophy of parts and wholes. i.e. In what ways is my toenail a ‘part’ of me and when is it not? What is a ‘me’ and what is a ‘toenail’? How about time? How is some part of time joined to the ‘whole’ of time as it exists? Are the connections straightforward, sliceable into infinitely small sections or does it work some other way? What about space? How small a part of space can we drill down to and find out about how it acts and relates to all the other parts of space?
The Stanford University Encyclopedia of Philosophy has a great entry on mereology, which helps explain some of the terms. Graham Harman’s reading of Latour as a philosopher or metaphysician results in an ‘object oriented philosophy’ that can help with these kinds of questions. It’s also has the best answers for most of them I’ve encountered, despite being often counter-intuitive.
Related to the above questions is the issue of The Infinitesimal. Can we actually get infinitely small in relation to time and space, or are there hard limits to the universe? The desire for a hard-bottom is entirely understandable, as any such discovery would lend an absoluteness and equivalence to any statement or research or analysis. Disciplines would be eradicated overnight as everyone rushed to build the necessary frameworks to start analysing everything from ‘culture’ to ‘love’ to thermodynamics in light of this new ultimate substance. The jury is still out on whether any such ‘substance’ or floor to the universe exists. For Latour (a bit of a post-structuralist in this sense) his unresolved relationism means that there is never a ‘bottom’ to the universe, or indeed anything – it’s networks all the way down, and yet his actor-network theory still ‘works’.
The domain of mathematics has employed the infinitesimal, however, for everything from calculus to some things I’ve never even heard of before. According to Wiki, “In common speech, an infinitesimal object is an object which is smaller than any feasible measurement, hence not zero size, but so small that it cannot be distinguished from zero by any available means.” This is interesting because it means that there is still a difference between the infinitesimal and the nothing. The degree of that difference is on an unimaginably diminished scale, but it remains the same category of difference as the difference between 1 and 0; between chocolate cake and an empty plate; between something and nothing.
Finally, if you are determined to hold onto a mereology based on ‘common sense’, how do you deal with gaps? When does a gap disappear? How close do things need to get before the distance between them is nil (not infinitesimal, mind)? And when that gap disappears, do two become one, and what is that new one? If it takes two things to become completely one for a gap to disappear, how does anything act on anything else except at a distance? Perhaps certain things can act ‘in part’ on other things, but then which object does that part which is acting belong to? One, the other, or both? I hope you’re getting the picture that these distinctions are increasingly untenable. Common sense has deserted us, leaving behind only a confusion of actors and associations.
Radiohead’s Thom Yorke sung about this kind of confusion in the song ‘Where I end and you being’. Ostensibly about relationship difficulty arising from bridging that gap, I think it still addresses the same issue at heart. It’s a strange world out there on the borders between things – it’s a place where:
The dinosaurs roam the earth
The sky turns green
Where I end and you begin