Transcript: 217. Andrew Arlig on Parts and Wholes

Andrew Arlig joins Peter to discuss medieval discussions of mereology (the study of parts and wholes).
Podcast series

Note: this transcription was produced by automatic voice recognition software. It has been corrected by hand, but may still contain errors. We are very grateful to Tim Wittenborg for his production of the automated transcripts and for the efforts of a team of volunteer listeners who corrected the texts.

Peter Adamson: Before we get into the issue about what medieval philosophers say about this topic, maybe you could just say something general about why philosophers nowadays are interested in parts and holes. What's so fascinating about this as a philosophical problem?

Andrew Arlig: It's because most of the things we encounter or think exist are complex and therefore they're going to have structure, they're going to have elements and bits that they're made of, components. And as soon as you have this complexity, these bits and elements and so forth, you're going to be invited to think about how they're put together. You're going to be invited to think about the dependence relations that hold between them. So do the bits depend on the hole? Does the hole depend on the bits, the elements? If so, then philosophers can get quite sophisticated about this and come up with fine-grained distinctions and kinds of dependence and all this is again prompted by the mere fact that you have complexity.

Peter Adamson: So the dependence issue would be something like 'do all my parts need to exist in order for me to exist?'

Andrew Arlig: Yeah, that's a very basic way of raising the issue. If I depend on all my parts, then surely that has implications for my identity over time, persistence over time and so forth.

Peter Adamson: Because it seems like if I cut your hand off, I kill you. Because if one of your parts disappears, then you disappear.

Andrew Arlig: And in fact, even medievalists will talk this way, they'll say, when Socrates clips his fingernails, have we committed homicide? That's a question Peter Abelard, the 12th century philosopher, raises. His answer is no. But he raises that question in part because he is thinking about relations of dependence between the parts and the hole.

Peter Adamson: Okay. Well, that brings us on to what we really want to discuss, which is what medieval philosophers have to say about this. Nowadays in analytic philosophy, there's a kind of industry of people who work on what's now called "mereology," the study of this issue of parts and holes, which is from the Greek word for part. But presumably, there isn't a kind of sub-discipline of philosophy done by medieval philosophers, which is about parts and holes. Is there? Or is there a kind of context where they naturally raise this problem?

Andrew Arlig: Well, I think it's anachronistic to say that some of them devoted their energies to mereology, the way a professional metaphysician might do it nowadays. But there are contexts where they do linger over questions about parts and holes. There are places in the commentary tradition in particular where you can predict that they will stop and talk about this. Whereas, for instance, in the logic handbooks throughout the Middle Ages, there's usually a discussion about parts and holes that's prompted by Boethius' On the Vision. Boethius also talks about these things called the 'topics,' and one of the topics has to do with parts and holes. And so they'll rehearse what Boethius says, and they'll comment on that and elaborate on that. There's also, it seems to be standard, stock questions in the physics commentaries where Aristotle says something in Book One of the Physics about the problem of the part and the hole. And a very standard question you find is whether the whole is its parts. And it's raised by this almost incidental remark of Aristotle, but they elaborate it and often elaborate it in quite interesting ways.

Peter Adamson: So the medieval philosophers themselves think of this as a basic issue that arises in both logic and metaphysics.

Andrew Arlig: That's very important to them because most things in their universe have structure, and they've got to figure out the ways in which these things are composed, structured, and so forth. And they're very keen on understanding that there are a variety of different components and things, and there are going to be therefore a variety of different ways in which the parts related to the whole and the whole related to the part for that reason.

Peter Adamson: Yeah, actually, that was the next thing I was thinking I might ask, because on the one hand, it seems like an obvious concept. So you've got a whole that's made of some parts. But on the other hand, once you start thinking about the different kinds of things that there are, for example, there are immaterial objects, which may or may not have parts. There are artifacts, in other words, things that are made by people, which have parts where you can swap out one part from another very easily. There are organic wholes, which have organic parts, so like the hand case or the fingernails. And so in general, it seems like sometimes the parts have a more or less casual relationship to the whole, whereas in other cases, it seems like the whole couldn't exist without exactly having the parts that it has. And so in light of this variety between the different types of part-whole relations, is there anything that the medieval thinkers would say we can say in general to characterize what it means to be a whole and what it means to be a part?

Andrew Arlig: The most general thing you could say is that anything that's a product of a division is a part of some kind or other. But because you have different ways of dividing a thing, you'll have different parts that arrive after the cutting. Or they'll also say, 'look, anything that can be put together is a part.' And as a correlate, you should understand that whole and part are relational notions. So you have a part only if you have a whole, and you have a whole only if you have parts. So a whole is also understood to be anything that embraces a bunch of things as a whole in some way or other. And anything that can be divided up into smaller bits will be a whole for them. The other thing that's quite general that you can say is that for them, a part - and this is something that's interesting, especially if you do contemporary theories of parts and wholes - a part for them is always in some way or other less than the whole. So it's a smaller bit. I mean, I'm speaking quantitatively, and there are ways in which you have to extend that in a metaphorical or analogical sense to get what I'm after. But there's always some way, even in cases like universals, where there's a way in which the part is the whole, but still, even then, the parts, if you had only one of the parts, you still wouldn't be grasping the entire thing.

Peter Adamson: Do they think that just any kind of random assortment of things could be considered as the parts of a whole, so say: me, the Eiffel Tower, and the number four - could those be parts of a whole just by sort of dividing it?

Andrew Arlig: Now, so you've just articulated a position in contemporary mereology that's called universalism. The only person I know of who countenances that is Peter Abelard, this 12th century philosopher. Most others will back off from universalism or the sort of completely unrestricted composition. That said, and one of the reasons why I think this, is that many of them think that God, for instance, can't enter into any kind of whole. So you couldn't have a whole consisting of me and God.

Peter Adamson: So there's at least one restriction.

Andrew Arlig: So there's at least one restriction on universalism. And usually the restriction stops at around 'heaps.' So someone will talk about piles or heaps of stuff. And they'll say that that's a unity of a sort. So often this discussion of holes, by the way, is bound up with the notion of unity being a one. And so someone will say, 'well, a pile of things is one in some weak sense, but it's less of a one than say a chair,' some kind of artifact with structure that's nailed together, glued together, whatever. And then a chair is less of a one than, say, you or I, you know, for substances. So they draw these ontological distinctions that way. And so they have grades of unity.

Peter Adamson: So this goes back to something I was saying before, which is that there are different kinds of parts and holes. And so what you're saying is that it's not just that there's different kinds, it's also that they're kind of rank ordered. So there are the really good examples of holes, like maybe organic bodies or animals, plants. And then there are quite poor examples of holes, which would be like a pile of beans or something.

Andrew Arlig: Well, it's just a hierarchy of being. And this is coming out of the Aristotelian idea that substances are the primary beings. And the traditional distinction between substances and artifacts and then other accidental unities that Aristotle talks about. So a pile again is an accidental unity in a very kind of weak sense. You know, it's just a bunch of stuff that's in the same location at the same time. But for most of them, I think almost to the last one of them, even a table or a chair is strictly speaking an accidental unity and not a substance.

Peter Adamson: Because it's just being held together by nails and not by some physical principle?

Andrew Arlig: The form that's holding them together is still accidental.

Peter Adamson: So is that what led Abelard to adopt the universalist position? Because if you think, well, is it just a kind of continuity that you can have less and less unified holes? So why not just say, well, in the limit case, any old collection of things, even if they're not anywhere near each other?

Andrew Arlig: Yeah, plurality of stuff. Yeah, like I said, Abelard seems to have allowed that there's a weak sense in which any kind of plurality. Now, he doesn't raise the issue of God, but any kind of he says, 'you know, any kind of plurality, even me and a particular instance of paleness could be a whole in some sense of whole,' because you know, they're two bits and you can just sort of draw a ring around them and that's a whole. But you know, it's a rather uninteresting whole. It's not as interesting as say, a chair or Socrates. And he says this as almost kind of a throwaway remark in his treatment of parts and holes.

Peter Adamson: What then should we say about this case? If I cut my hand off, then obviously I don't die. So why doesn't that immediately prove that I don't depend on the existence of my parts in order to exist?

Andrew Arlig: In general, the answer is yes, I don't depend on my hand. There are different ways to divide me up, which means there are different sets of parts you need to consider. And so the hand may be the wrong sort of thing to fixate on when I'm thinking about whether I depend on my parts. It's very common distinction to say that things like hands, flesh, eyes, and so forth, aren't necessary - that some of them can be taken away. Aristotle even discusses this in his book, his Metaphysics book five. He has a whole discussion of being mutilated. And that's linked up, it follows right after his discussion of the word whole in book five. So mutilation can occur when you chop off a hand or something like that. But then there are other kinds of parts that I have, which are often called substantial parts or essential parts. Sometimes the terminology is principal part, and those, I do need all of those.

Peter Adamson: So what would be an example of something like that?

Andrew Arlig: Well, sometimes earlier on, principal parts were identified as things like my head or my heart, or things like that.

Peter Adamson: Or as it just happens that I can't cut your head off without destroying you.

Andrew Arlig: Right. So sometimes the distinction is made that way. Later on, when people talk about the essential or substantial parts, they're talking about the substantial form and the matter.

Peter Adamson: So the soul, you can't lose your soul.

Andrew Arlig: Right. So they'll often reframe the question and say, 'well, we need to think about, the answer is for some kinds of parts, yes, the whole depends on the parts. For other kinds of parts, if we consider those, usually wholes don't depend on those, especially when we're talking about substances like you and I.' That's a traditional answer.

Peter Adamson: One thing that you mentioned before is that they often raise the part-whole topic in the context of thinking about logic. And something that maybe is a little bit surprising for us is that they think about, for example, the genus-species relationship. So for example, animal and human, or animal and giraffe, to use my favorite example. They would think of the species like human and giraffe as parts of the genus "animal." So is that just a metaphor? What sense can we make of this idea that we have these two abstract concepts, one of which is being conceived of as a part of the other?

Andrew Arlig: Yeah, there's this long tradition. And again, I think it goes back to the Greeks of thinking of universals as in some sense a whole. I think intuitively it's this, that hey, when you're talking about human, what you're talking about is all the humans, you're kind of corralling all the humans together and you're making some kind of generalization that holds up all in each of them. And so in some sense, it's a whole. In fact, the Greek word whole is part of the Greek word for universal, "katholou." So this kind of notion that these are related, it goes back quite a ways.

Peter Adamson: And actually we talk about individual instances of a universal as particulars. In Greek, the word that sometimes one of the expressions they use actually has the word for part in it as well.

Andrew Arlig: Right. And actually Boethius remarks on this in On the Vision. He actually notes that etymology. And in fact, in one of the translations, "particular" is the part of particulars italicized for that reason because Boethius seems to be making that point that hey, 'a particular in a way is a part of the universals that embrace it or encompass it.' I mean, actually I noticed that those words embrace and compass contain - those also suggest that we're talking about something that's at least in some interesting sense like a whole, like a crowd, or like a pile of things.

Peter Adamson: So the reason, what I asked about originally though was the relationship between human and giraffe to "animal." So it seems like what you're implying is that the relationship that you and I have to the species human is going to be analogous to the relationship that the species human and the species giraffe have to the genus animal.

Andrew Arlig: Well, animal embraces both species. So it's like a ever widening concentric. If you think of individuals and you draw a circle around them, so you have two groups of things with circles drawn around them, and then "the animal" - you draw a circle around the two groups and you get ever widening wholes, so to speak.

Peter Adamson: Right. And so in theory, the biggest whole would be something like the genus of things, or genus of existence.

Andrew Arlig: Well, no, they won't say that because they all know their Aristotle and being or entity is not a genus. So we'll stop with substance. That's the highest genus for that category.

Peter Adamson: Right. Because then the accidents don't fall under that. So there's actually no whole that embraces everything. Is that right?

Andrew Arlig: Well, it would seem if they're going to follow through on this Aristotelian doctrine that there's no highest genus that... So here's another case where you wouldn't have universalism in this context of abstract entities. You don't have a super genus or a super class that is all the things that exist.

Peter Adamson: Right. Okay. So actually that means that they don't think of wholes as working in quite the way that we think that sets work. Because presumably we would be happy with the notion of the set of 'everything that there is' but there's no whole that's the whole of everything that there is.

Andrew Arlig: That seems right. That seems like a fair characterization.

Peter Adamson: That's interesting. Okay. What you were just saying about the relationship between individuals to species, and species to genus, gets us back, I think, to something we mentioned at the beginning, which is the question of interdependence. And there is a problem here about whether the species depends for its existence on the existence of all the individuals. And in some sense, it seems like it clearly doesn't, right? So when I die, hopefully a long time from now, the species human won't go out of existence. Among the tragic aspects of my death, will not be the perishing of the species human. But on the other hand, it's a little bit harder to tell whether the genus animal somehow depends for its existence on all the species because they seem to kind of come together. So presumably there's a kind of 'domino effect' here. So you might think, well, if the genus will exist, then the species will exist. And if the species exists, then all the individuals exist. Or you could go the other way. If the individuals exist, the species exists. If the species exists, the genus exists. But it's not quite clear whether that's actually true. Right. So what do the medievals think about this?

Andrew Arlig: I mean, the question is raised, certainly. So they're attuned to these kinds of worries. And then what precisely is the dependence between the individuals and the species? Because Aristotle doesn't, at least in the Categories, encourage us to think that. He says that you and I, for instance, are primary substances and the species is a secondary substance. That would suggest that there's a kind of order of dependence - that the species depends on us. And then the genus is even further out. So it depends. It's even got a more tenuous dependence relation. But that can't seem quite right. As you pointed out, when I die, the species shouldn't be compromised. So they are, you know, they're worried about that. And they come up with different stories for how this individual and the universals are related to one another. And it's hard to say there's one party line at that point.

Peter Adamson: But presumably, they're all going to at least say that the continued existence of the species doesn't depend on the existence of every single one of the individuals.

Andrew Arlig: They're going to want to say that. I mean, in fact, this is one of Abelard's criticisms of a view that apparently had some advocates in the 12th century. The view he critiqued was that the species was actually just a crowd - that it was, to use a bit of technical language, the species wasn't a "universal whole," it was an "integral whole," just like a crowd is an integral whole. And one of his criticisms is, 'well, then if you have that, if that's what a species is, that's what a universal is in general, then when I or you die or Socrates dies, the species seems to change. But that can't be right.'

Peter Adamson: So this would be like saying that all of my body parts have to keep existing in order for me to keep existing, which seems false, because you could cut off my hand and I don't die.

Andrew Arlig: Yeah. So it's a very similar kind of reasoning. And so whatever the case is, the species and genus can't be - even if they depend in some way, I mean. Here's one way they're often going to say or speak: They'll say, 'the species human wouldn't exist if there were no humans, ever. But provided you have some humans, even if they change, even if the individuals are born and die, you'll have the species and the species won't depend on any particular individual, any particular set of individuals existing.'

Peter Adamson: But if there were no giraffes at all, there's no species giraffe.

Andrew Arlig: Maybe a way to put it is 'if there had never been and never will be giraffes, there would be no species giraffe.'

Peter Adamson: Do they get into the question about what if there's only one?

Andrew Arlig: Yes. Because they worry about the Phoenix. Do you have a distinction between the individual Phoenix and the species Phoenix?

Peter Adamson: Because there's only ever one.

Andrew Arlig: There's only one, because by definition there's only ever one. And they're not just mythological examples. They raise the example of a sun. There's only one sun, as far as their worldview goes. So do you have a species sun in addition to the individual sun? And usually the answer is, well, 'even though there is in fact only one sun, or only one Phoenix, you could always - there's no reason why you couldn't have two and therefore you have a species that covers both the actual and possible individuals.'

Peter Adamson: So staying with this issue about universals, one of the things that I've been talking about in the podcast is this famous problem of universals. And maybe one way of describing the problem is whether universals are some real thing out in the world. That's kind of an oversimplistic way of putting the problem. And it seems to me that if someone says, 'well, look, universals are just wholes of parts and the parts in this case are the individual instances, since the individuals are real, clearly the universal is real.' So I was wondering whether thinking about universal-particular as a whole-part relation immediately gives you a realist position on the problem with universals.

Andrew Arlig: That's an interesting question. In part, my answer is that the way we now draw the line between realism and nominalism may not be the best way to think about the medieval problem. So here's an example. Abelard again has a very famous discussion - which is in translation if your readers wanted to follow up on it. And in it, Abelard talks about, he describes a number of positions that we would now call nominalisms - or using, say, David Armstrong's categories, would now call a nominalist position, which he identifies as a realist position precisely because his opponents have picked out some thing, some, to use the Latin term "res," out there that the universal term corresponds to. Now, here's an example. David Armstrong would classify that position I referred to earlier, which this 12th century view - which is sometimes called the collection theory of universals, the view that says what the species human is, is just the collection of individual humans. And David Armstrong would call that a class or a mereological nominalism. Whereas Abelard, because of the way he construes things, describes it as a realism.

Peter Adamson: Because the whole is really out there.

Andrew Arlig: Because the whole is really out there. But there were problems with it. And his own recommended view is that you identify, that you associate the property of universality only with terms. So he takes a very classical anti-realist position in part.

Peter Adamson: One last thing I wanted to ask you is that we've been talking about this, as it were, as a purely abstract philosophical issue. But one thing that's, of course, always notable about medieval philosophers is that they have theological worries. And this seems like a case where that would happen. If you are a Christian theologian, which they are, then if you start thinking about parts and holes, you might think, 'oh, well, I've got to explain the Trinity.' So you might be tempted to think that the persons of the Trinity are parts of the unified Godhead. Or you might worry about Christ, because Christ is both God and man. So you might think of divinity and humanity as two parts of the whole that is Christ. Do they explicitly apply these part-whole worries to these theological cases or other theological cases?

Andrew Arlig: They bring in premises. Well, first, I should maybe back up and say that almost any Christian theologian who talks about these issues will say, 'by the way, we're having a speculative discussion of this, but these are mysteries at the end of the day. And so there's going to be a point at which maybe reason is going to give out, or at least unaided human reason is going to give out.' They then will, you know, then often go on and have very sophisticated, philosophically interesting discussions of how this is supposed to work. Now the Trinity case where you have three persons in the Godhead, there's going to be a problem because of absolute simplicity. Many of the discussions of absolute simplicity, they're very - in many of those discussions, they're very, very adamant that there are no parts. Really no parts! I mean it, no parts in the divine! So any way in which you might want to try to divide up the Godhead, they're not having it. Now here's where the mereology comes in in the Trinity. The reasons that they give for why you can't have absolute simplicity include, 'well look, if you had parts, then you'd have to have some cause that unified them, but God's not caused, certainly by not anything outside of his own essence. So that can't be.' Or another interesting thing, and this picks up on, you know, this has applications for mundane objects that will say, look, 'if you have parts, then the Godhead would depend on those parts, but God doesn't depend on anything.' Now here's why this might apply to mundane things. There is an interesting question about whether I depend on my parts, or at least some parts. They use this thesis to defend absolute simplicity. Now for the incarnation, there maybe mereology gets a bit more traction because you do have just two distinct natures. You're trying to cram them into one person. And so they'll think about, 'okay, well how can I do this?' Interestingly someone like Aquinas - I looked at this just recently, he said, 'no, actually you do have composition, but you don't have parts. So you have a composition but not with respect to parts.' You have a composition merely, as he says, "with respect to number." Now how you cache that out, I'm not quite sure, but then again, maybe this is one of those places where we have run out of things to say as philosophers.

Peter Adamson: Yeah, I think that's actually a very distinctive feature of the whole medieval approach to these theological issues. When they talk about it philosophically, on the one hand they want to get as far as they can using reason, but on the other hand, they really have to make sure that they don't get the whole way to explaining it because then they've compromised the mystery aspect of it.


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