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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).

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    Somewhat mathematical discussion of mereological paradoxes is in Bigelow, God and the New Math. On mereology of Bradley's regress see Valicella, Three Conceptions of States of Affairs. John Baez's post on behavioral mereology is very mathematical, and even mentions coalgebras.
    – Conifold
    Jun 23, 2022 at 0:00
  • Modern philosophers are squarely interested more in set theory than mereology since the latter is not a foundation of math and perhaps to define the so-called whole independently of the parts is very paradox-prone, and this actually is surprising given combination as core of math seems very related to parts and whole. So this hints the axiom of infinity and related axioms about infinity within set theory is a necessary nature in addition to the mundane "belong to" binary relation of mereology in order to be able to do more math in the Cantorian way... Jun 24, 2022 at 17:46
  • @DoubleKnot I don't quite understand how you are opposing set theory to mereology. It would seem that these are not two competing theories but theories operating in different fields of inquiry. Mereology is a philosophical account of parts and wholes not a mathematical theory (although it could expressed mathematically, e.g, in the language of set theory). On the other hand, it is natural to think of an element of a set as a part of the set, so mereology could be applied in phil of math to set theory itself.
    – Avi C
    Jun 26, 2022 at 20:45
  • People such as Quine/Leśniewski’s tried mereology to be foundation of math, but one problem with attempts to ground math in mereology is relations while abstaining from set-theoretic definitions of the ordered pair, since between parts there's only constraint passing but no order concept (Kuratowski form can't work). Another famous problem is math foundation starts from point set (topology) and it's notoriously difficult to express set of sets unless invoking additional singleton operator to squash set of points as a new point to treat set theory as a definitional extension of mereology. Jun 27, 2022 at 3:38
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    Losing one hair probably won't change my whole body at all but the said hair is clearly a part of the "assumed" whole body. Thus for metaphysical import, the nature of part-whole mereology alone seems has no weight, there must be some other attribute such as constraint passing between neighboring parts and other possible functional relations beyond the assumed tentative whole (if not up to the real substance yet). Spinoza once wrote something like if one treats any natural object as a substance whole, then such person would ridiculously think trees can talk, attribute our passion to God... Jun 27, 2022 at 4:16

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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.

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  • Thanks for your reply. I find it hard to imagine how to make the part-first view work given modern physics. I mean fundamental particles are what they are only relation to space, time, a field of some kind, etc. Perhaps that's what Schaffer is saying. It sounds like the parts-first vs whole-first discussion is about the direction of grounding. I'm more interested in understanding the structure of the part-whole relation itself. It's not obvious to me that the grounding question helps us answer questions about the nature of the part-whole relation.
    – Avi C
    Jun 22, 2022 at 18:11
  • This statement is false: "Classical Christian & Islamic theology ground parts in the whole" In the tradition of Christianity that discusses God in this sort of language (Scholasticism), God is said to be perfectly simple, to have no parts at all. The notion of God as some sort of universal mereological whole is pantheism, not Christianity. Jun 23, 2022 at 8:15
  • @David Gudeman: No, you're wrong. Classical theology in both the Islamic and Christian trafitions state that God/Allah grounds everything. This is why in Islam, Allah is said to be rich and men poor. Al-Ghazali believed even that cause and effect would not be possible without the intervention of Allah everywhere and at every moment. Jun 23, 2022 at 8:25
  • @DavidGudeman: Not just men are poor but the world too. Jun 23, 2022 at 8:37
  • @MoziburUllah, It is clear that you have not read significant Christian philosophy, or you would have recognized immediately what I was talking about. The utter simplicity of God is an essential element of the most well-known branch. Second, it is clear that you don't know what mereology is, since you think "grounds" is a mereological relationship. "Grounds" is very specifically not a mereological relationship. I appreciate the effort you put into your answer, but since you are unfamiliar with the subject matter of this question, I'm going to ask you to delete it. Jun 23, 2022 at 9:08

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