Who are some key modern philosophers who have addressed the paradoxes of parts and wholes (mereology)?

Question

I've read Graham Priest's book One (2014). Where he offers a what he calls "gluon" theory of parts and wholes. (These are metaphysical gluons which are not related to gluons from particle physics, only the term is borrowed.) Priest's theory is an pretty interesting, but it seems to have a high cost. Not only are gluons wildly contradictory entities, but the relation of metaphysical identity must be non-transitive.

Priest's book was my introduction to the metaphysics and logic of parts and wholes (mereology). I am wondering what are other good articles or books to get a sense of the other major positions in this field and how they relate to each other. I'm more interested in metaphysically engaged philosophy as opposed to purely abstract mathematical approaches, but I'm fine if math is deployed in the process of addressing metaphysical issues. I'd like to look at work where philosophers seriously engage with the paradoxes and vicious regresses that arise in considering part-whole relations. For example, Bradley's regress or the ancient paradoxes of the one and the many.

For the more mathematically inclined among you, I'm particularly interested to know if anybody has attempted to give a mereological theory that uses terminal coalgebras (But that is a bonus if anybody knows, it isn't required to answer my question).

Answer 1

Have you looked at the bibliography on both the SEP and Wikipedia articles on mereology? This should clue you in as to some of the current debate on the metaphysics of parts vs wholes.

One of big debates is whether wholes are grounded in parts or whether the whole grounds the parts. Classical Christian & Islamic theology ground parts in the whole, the whole being God/Allah. Something similar is true in Buddhism, the notion of dependent-arising means parts do not, by themselves, have reality. Only the whole does.

This is contrary to the mainstream opinion in science where reductionism rules though there have been attempts to look for a more holistic view. This is more prominent in systems thinking and ecology rather than say physics. For example, Lovelocks notion of Gaia.

Jonathan Schaffer is a prominent advocate of monism, that parts are grounded in wholes. He grounds parts in the entire cosmos. This is in fact an Aristotelian view. Aristotle considered the cosmos as an organism rather than a mechanical being. It has telos (purpose) and evolves. This is not the kind of language favoured in contemporary cosmology but I think its worth noting that Newton used purposeful language in describing his physics. He said in his Principa:

Newton, Law I (pg.83 Motte-Cajori):

Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.

Now "perseveres" is purposeful language as is "compelled" which is a purpose that is perverted. This purposeful language was excised by a number of European mathematicians, many of them French, because of the Cartesian influence - for example, Euler and d'Alembert - and this choice of wording has come to dominate modern physics.

Schaffer draws upon quantum mechanics, and in particular entanglement, to argue for the whole being real. One could also argue that Liebniz and Mach argued for this when they argued for the relational view of space and inertia respectively. These views were taken into account by Einstein when he was forming General Relativity and their views have largely been substantiated by General Relativity. The theory shows that in an empty universe the notions of length and duration, of linear and angular velocity, momentum and inertia lose all meaning.