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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).

Avi C
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    Somewhat mathematical discussion of mereological paradoxes is in [Bigelow, God and the New Math](https://www.jstor.org/stable/4320712). On mereology of Bradley's regress see [Valicella, Three Conceptions of States of Affairs](https://www.jstor.org/stable/2671982). John Baez's post on [behavioral mereology](https://golem.ph.utexas.edu/category/2019/06/behavioral_mereology.html) is *very* mathematical, and even mentions coalgebras. – Conifold Jun 23 '22 at 00:00
  • 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... – Double Knot Jun 24 '22 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 '22 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. – Double Knot Jun 27 '22 at 03:38
  • Thus mereology is too *concrete* without subtly different expressive forms (brackets), only plural quantification with fusion. Many people treat mereology as a Boolean lattice thus as a foundation theory it's decidable which is too weak even for PA. On the philosophical import, as Spinoza hinted long ago any modification *is in* its definite cause, and up to a substance (see today's [post](https://philosophy.stackexchange.com/questions/91895/spinoza-what-would-be-a-concrete-example-of-a-thing-that-is-in-another-thing?)), so the import of "is in" relation should be causality not parthood... – Double Knot Jun 27 '22 at 03:56
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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... – Double Knot Jun 27 '22 at 04:16
  • @DoubleKnot Are there some contemporary sources you would recommend that articulate the considerations you mention? The issue you bring up in your last comment about how wholes could change parts over time without losing their identity is interesting to me. – Avi C Jun 27 '22 at 14:32
  • Here's an ancient [source](https://www.rigpawiki.org/index.php?title=Sevenfold_reasoning_of_the_chariot) of the famous *Sevenfold reasoning of the chariot* by renowned Indian scholar Chandrakirti (name means he's of equal weight of the Moon). Chariot is nothing without its surroundings and can only be defined by the ground it moves along, the horses that pull it, the space it moves through... To truly define the chariot the entire universe would need to be taken into consideration and this is where name and form fall apart. At a push one could say the chariot is incomprehensible and empty... – Double Knot Jun 27 '22 at 21:22
  • empty here means it's neutral thus no longer salient from its background as if we only pay attention and focus on one seemingly whole assembly/fusion at this very moment, its conventional function still applies relative to us, but it has no true nature of independent existence any more... – Double Knot Jun 27 '22 at 21:33

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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.

Mozibur Ullah
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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 '22 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. – David Gudeman Jun 23 '22 at 08:15
  • @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. – Mozibur Ullah Jun 23 '22 at 08:25
  • @DavidGudeman: Not just men are poor but the world too. – Mozibur Ullah Jun 23 '22 at 08:37
  • @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. – David Gudeman Jun 23 '22 at 09:08
  • @DavidGudeman: Au contraire, it's clear to me that you haven't even bothered to look at the Wikipedia article on mereology or you would have seen they mention Schaffer's priority monism. And whilst you seem to know the words 'perfect simplicity' and 'to have no parts', it's clear to me that you haven't understood what this means in relation to God/Allah. If God had parts, then he would not be fundamental, his parts would govern him. Likewise with simplicity, if God/Allah had properties, then he would not be wholly self-sufficient. Hemce he is perfectly simple, a being without properties ... – Mozibur Ullah Jun 23 '22 at 09:15
  • @DavidGudeman: Personally, I think the term 'simple' and 'without parts' does not help describe God/Allah very well. It's too easy to confuse with the conventional notions of these terms. Personally, I prefer the term *syad-asti-avak-tavyah* from Jain philosophy and which means that frim a certain perspective, itvis indescribable. This is the route of negative theology which describes by saying what it isn't - God/Allah is not describable - had He parts, we could describe Him through His parts; had He properties, we could describe Him through His properties. It's the same route that the ... – Mozibur Ullah Jun 23 '22 at 09:23
  • @DavidGudeman: ... Daoists took when they described The Dao as indescribable. – Mozibur Ullah Jun 23 '22 at 09:24
  • @DavidGudeman: Since you are asking me to "delete my answer" and I've just shown that I know what I was talking about and you don't. I want an unreserved apology from you. I also consider your attempts to comment here as harassment. You are harassing me to delete my answer by making out that I don't know what I am talkimg about. Is that not correct? That was a rhetorical question. I also want an apology from you for harassing me. – Mozibur Ullah Jun 23 '22 at 09:26
  • @MoziburUllah, I don't learn philosophy from Wikipedia, so, no, I haven't read the article, but I know that you are misunderstanding whatever it said about Shaffer's philosophy. Shaffer claims that the whole grounds the parts; this is not at all the same as saying that whenever A grounds B, then A is the whole and B is the part. As to the rest, if you now admit that in Christian philosophy, God has no parts, then you should see that this sentence is wrong: "Classical Christian & Islamic theology ground parts in the whole, the whole being God/Allah." – David Gudeman Jun 23 '22 at 09:37
  • @DavidGudeman: No, you've misunderstood my point. I'm pointing out a source that ratifies that I wasn't merely throwing out some stream of consciousness but it was grounded in what people have written on mereology. You agree that Schaffer - you mispelt his name twice - says that "the whole grounds the parts", yet you seem unable to follow simple logic that there must be a whole and and parts that statement refers to and some predicate that means 'grounds'. Throwing a few letters around is only confusing the issue. Schaffer claims that the cosmos grounds the parts of the whole in that it, ... – Mozibur Ullah Jun 23 '22 at 09:44
  • Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/137283/discussion-between-david-gudeman-and-mozibur-ullah). – David Gudeman Jun 23 '22 at 09:49
  • @DavidGudeman: ... and only it, gives the parts reality. This is the same story that traditional Islamic and Christian theology says about Allah/God. No, you are wrong about the quoted sentence being wrong. In Christian/Islamic theology it is God/Allah that gives all the things of the world - the parts - their reality. If there were no God/Allah, there would be nothing. Check out al-Ghazali. You're taking a very simple-minded perspective on parts and wholes. And I'm still waiting for my apology for your harassment. Why were you asking me to "delete my answer?" – Mozibur Ullah Jun 23 '22 at 09:50
  • @DavidGudeman: Why do you think I would want to continue a discussion with someone who is harassing me into "delete my answer"? No thank you. And I am only being polite because of SE guidelines, otherwise I would be using much more colourful language. – Mozibur Ullah Jun 23 '22 at 09:53
  • @MoziburUllah, moving a discussion to chat is a courtesy to the readers of the site. If you can't be bothered with courtesy, then that's on you. As to the rest, you have turned this from a discussion into a power struggle. If I'm harassing you, why it it you who went looking for an answer of mine to downvote? That seems more like harassment than anything I've done. As to the rest, I've already explained why your claim is wrong, and why you don't seem to know what a mereological relationship is. Your pride has prevented you from responding rationally to rational criticism, so I give up. – David Gudeman Jun 23 '22 at 10:09
  • @DavidGudeman: I didn't "go looking for an answer of [yours] to downvote", it was simply was on top of the stack when I was looking for questions to answer. That isn't "harassment", I'm merely exercising my right to downvote an answer I didn't like. It's after all why the voting system is there for. On the other hand, insisting that I don't know what I'm talking about - as you appear to be so doing again - and fafter I presented evidence that I do and then insisting that means you have the right to ask me to delete my answer is harassment. It's not a question of "pride" as you put it ... – Mozibur Ullah Jun 23 '22 at 10:21
  • @DavidGudeman: ... but of simple justice. Your criticism isn't rational because you you aren't taking on board any of the evidence that I have presented and nor did you seem to have understood the line of argument I was engaged with in the post. – Mozibur Ullah Jun 23 '22 at 10:23
  • @MoziburUllah, I read all of your answers and none of them convinced me you know what you are talking about. You continue to insist that God can both have no parts and have parts. It's a direct contradiction. As to whether you went looking for a post of mine to downvote, it's curious that there was no action on it for a week, and then within minutes of you accusing me of "harassing" you, you downvoted it. – David Gudeman Jun 23 '22 at 12:54
  • @David Gudeman: You said I "continue to insist that God can both no parts and have parts. It's a direct contradiction." Yes, that would be correct if that is what I was saying. But that is **not** what I said. What I said was "Classical Christian & Islamic theology ground parts in the whole, the whole being God/Allah ... [and] parts do not, by themselves, have reality. Only the whole does." Although I haven't been explicit here, I am not talking about "parts" in God/Allah, but about the all the things that go to make up our cosmos, ... – Mozibur Ullah Jun 25 '22 at 12:00
  • @DavidGudeman: ...atoms, molecules, planets, people etc. These are the parts I'm referring to. There is no direct contradiction to what I said nor with classical theology. That you are still banging on about his just convinces me that you never rea I did sd the post carefully and just leapt to your own conclusions based upon what you think I said, rather than it being tied to what I did say. – Mozibur Ullah Jun 25 '22 at 12:02