| 13259 | It seems that the One must be composed of parts, which contradicts its being one [Plato] |
| Full Idea: The One must be composed of parts, both being a whole and having parts. So on both grounds the One would thus be many and not one. But it must be not many, but one. So if the One will be one, it will neither be a whole, nor have parts. | |
| From: Plato (Parmenides [c.364 BCE], 137c09), quoted by Kathrin Koslicki - The Structure of Objects 5.2 | |
| A reaction: This is the starting point for Plato's metaphysical discussion of objects. It seems to begin a line of thought which is completed by Aristotle, surmising that only an essential structure can bestow identity on a bunch of parts. |
| 15843 | The whole can't be the parts, because it would be all of the parts, which is the whole [Plato] |
| Full Idea: The whole does not consist of parts; for it did, it would be all the parts and so would be the sum. | |
| From: Plato (Theaetetus [c.368 BCE], 204e) | |
| A reaction: That is, 'the whole is the sum of its parts' is a tautology! The claim that 'the whole is more than the sum of its parts' gets into similar trouble. See Verity Harte on this. |
| 15844 | A sum is that from which nothing is lacking, which is a whole [Plato] |
| Full Idea: But this sum now - isn't it just when there is nothing lacking that it is a sum? Yes, necessarily. And won't this very same thing - that from which nothing is lacking - be a whole? | |
| From: Plato (Theaetetus [c.368 BCE], 205a) | |
| A reaction: This seems to be right, be rather too vague and potentially circular to be of much use. What is the criterion for deciding that nothing is lacking? |
| 13260 | Plato says wholes are either containers, or they're atomic, or they don't exist [Plato, by Koslicki] |
| Full Idea: Plato considers a 'container' model for wholes (which are disjoint from their parts) [Parm 144e3-], and a 'nihilist' model, in which only wholes are mereological atoms, and a 'bare pluralities' view, in which wholes are not really one at all. | |
| From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.2 | |
| A reaction: [She cites Verity Harte for this analysis of Plato] The fourth, and best, seems to be that wholes are parts which fall under some unifying force or structure or principle. |
| 12878 | Wholes are continuous, rigid, uniform, similar, same kind, similar matter [Aristotle, by Simons] |
| Full Idea: Aristotle gives certain samples of 'hanging together', notably continuity, rigidity, uniformity, qualitative similarity, being of a like kind, being of like matter. | |
| From: report of Aristotle (Metaphysics [c.324 BCE], 1015b05-) by Peter Simons - Parts 8.1 | |
| A reaction: Families are scattered, lakes aren't rigid, cakes aren't uniform, complex gadgets have dissimilar parts, two kinds can be united, and only boring things are made of one sort of matter. Nice try, though. Simons rightly adds causation. |
| 16136 | A syllable is something different from its component vowels and consonants [Aristotle] |
| Full Idea: The syllable is something in its own right, not just a heap of vowel and consonant but something different. | |
| From: Aristotle (Metaphysics [c.324 BCE], 1041b16) | |
| A reaction: This is the classic Greek example of a whole, and a slogan for claims that wholes are not merely collections of parts. |
| 9071 | We first sense whole entities, and then move to particular parts of it [Aristotle] |
| Full Idea: We have to progress from the general to the particular, because whole entities are more intelligible to the senses, and anything general is a kind of whole, in the sense that it includes a number of things which we could call its parts. | |
| From: Aristotle (Physics [c.337 BCE], 184a22) | |
| A reaction: This is the first step in the process of abstraction, which Aristotle describes further in Posterior Analytics. It is common sense that a child will be aware of a horse before it is aware of its hoof, or its colour, or its strength. |
| 16791 | There is no whole except for the parts [Aristotle] |
| Full Idea: There is no whole over and above the parts. | |
| From: Aristotle (Physics [c.337 BCE], 210a16) | |
| A reaction: Pasnau says Aristotle contradicts this at Met. 1041b12, where the syllable is more than its elements. |
| 22525 | The whole is prior to its parts, because parts are defined by their role [Aristotle] |
| Full Idea: It is necessary for the whole to be prior to the part. For if the whole body is put to death, there will no longer be a foot or a hand. For everything is defined by its function and by its capacity (so the hands and feet would no longer be the same). | |
| From: Aristotle (Politics [c.332 BCE], 1253a20) | |
| A reaction: It may be a mistake to ask which of these is 'prior'. If bricks make a wall, the whole depends on the parts, but the parts can exist without the whole. They continue to be possible parts of a wall (unlike severed feet). |
| 13269 | In the case of a house the parts can exist without the whole, so parts are not the whole [Aristotle] |
| Full Idea: In the case of a house, where the process of compounding the parts is obvious, though the parts exist, there is no reason why the whole should not be non-existent, and so the parts are not the same as the whole. | |
| From: Aristotle (Topics [c.331 BCE], 150a19) | |
| A reaction: Compare buying a piece of furniture, and being surprised to discover, when it is delivered, that it is self-assembly. This idea is a simple refutation of the claims of classical mereology, that wholes are just some parts. Aristotle uses modal claims. |
| 20825 | How is divisibility possible, if stoics say things remain united when they are divided? [Alexander on Stoic school] |
| Full Idea: How could the divisibility of bodies be preserved if division is the separation of what is united, and according to them all things stay united with each other, all the same even when they are divided? | |
| From: comment on Stoic school (fragments/reports [c.200 BCE]) by Alexander - On Mixture 2.2 | |
| A reaction: Evidently the stoics were committed to unrestricted mereological composition (that any parts make a whole, no matter how scattered). Alexander points out that this makes the concept of 'division' of an entity meaningless. |
| 20826 | How is separateness possible, if separated things are always said to be united? [Alexander on Stoic school] |
| Full Idea: How could one avoid the inconsistency of saying that adjacent objects that can easily be separated are all the same united with each other, being coherent and never able o be separated from each other without division? | |
| From: comment on Stoic school (fragments/reports [c.200 BCE]) by Alexander - On Mixture 2.2 | |
| A reaction: In general my sympathies are with Alexander on this. If you abandon all principles of unity apart from unrestricted mereological composition, you save yourself a lot of bother, but you abandon the most useful concepts in ontology. |
| 20872 | Stoics say wholes are more than parts, but entirely consist of parts [Stoic school, by Sext.Empiricus] |
| Full Idea: Stoics say the wholes are not the same as their parts, for a human being is not his hand, nor are they other than their parts, for they do not exist without the parts. | |
| From: report of Stoic school (fragments/reports [c.200 BCE]) by Sextus Empiricus - Outlines of Pyrrhonism 3.170 | |
| A reaction: 'A human being is not his hand' is not much of a reason. Surely some holistic claim is needed here? The conflict of these two ideas was spotted by Plato. |
| 22744 | Parts are not parts if their whole is nothing more than the parts [Sext.Empiricus] |
| Full Idea: If the whole is nothing more than the sum of the parts, the parts will not be parts. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.343) | |
| A reaction: Nice. Bricks lying on the ground are not parts of a wall. For them to be parts of a wall there has to be a wall which is not just the bricks. Nihilists like Van Inwagen can deny the wall in ontology, but in thought we need walls. Conceptual dependence. |
| 10919 | What prevents a stone from being divided into parts which are still the stone? [Duns Scotus] |
| Full Idea: What is it in this stone, by which ...it is absolutely incompatible with the stone for it to be divided into several parts each of which is this stone, the kind of division that is proper to a universal whole as divided into its subjective parts? | |
| From: John Duns Scotus (Ordinatio [1302], II d3 p1 q2 n48) | |
| A reaction: This is the origin of the concept of haecceity, when Scotus wants to know what exactly individuates each separate entity. He may have been mistaken in thinking that such a question has an answer. |
| 17244 | To make a whole, parts needn't be put together, but can be united in the mind [Hobbes] |
| Full Idea: In composition, it is to be understood that for the making up of a whole there is no need of putting the parts together, so as to make them touch one another, but only of collecting them into one sum in the mind. | |
| From: Thomas Hobbes (De Corpore (Elements, First Section) [1655], 2.07.08) | |
| A reaction: This seems to the 'unrestricted composition' of classical mereology, since it appears that Hobbes offers no restriction on which parts can be united by a mind, no matter how bizarre. |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| Full Idea: A whole must possess an attribute peculiar to and characteristic of it as a whole; there must be a characteristic relation of dependence between the parts; and the whole must have some structure which gives it characteristics. | |
| From: Rescher,N/Oppenheim,P (Logical Analysis of Gestalt Concepts [1955], p.90), quoted by Peter Simons - Parts 9.2 | |
| A reaction: Simons says these are basically sensible conditions, and tries to fill them out. They seem a pretty good start, and I must resist the temptation to rush to borderline cases. |
| 15474 | Properly understood, wholes do no more causal work than their parts [Martin,CB] |
| Full Idea: There is no causal work for the whole that is not done by the parts, provided the complex role of the parts is fully appreciated. | |
| From: C.B. Martin (The Mind in Nature [2008], 04.1) | |
| A reaction: It seems like a truth that because some parts are doing particular causal work (e.g. glue), the whole can acquire causal powers that the mereological sum of parts lacks. |
| 11844 | If I destroy an item, I do not destroy each part of it [Wiggins] |
| Full Idea: If I repair or destroy an item, I do not repair or destroy each part of it (and since each part of a part is a part this would be difficult). | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.6) | |
| A reaction: This seems like a nice refutation of any attempt to claim that a thing is no more than the sum of its parts, but one could analyse the notion of 'destroy', and find it just meant introducing gaps between parts. |
| 10810 | I say that absolutely any things can have a mereological fusion [Lewis] |
| Full Idea: I accept the principle of Unrestricted Composition: whenever there are some things, no matter how many or how unrelated or how disparate in character they may be, they have a mereological fusion. ...The trout-turkey is part fish and part fowl. | |
| From: David Lewis (Mathematics is Megethology [1993], p.07) | |
| A reaction: This nicely ducks the question of when things form natural wholes and when they don't, but I would have thought that that might be one of the central issues of metaphysicals, so I think I'll give Lewis's principle a miss. |
| 9667 | Mereological composition is unrestricted: any class of things has a mereological sum [Lewis] |
| Full Idea: I claim that mereological composition is unrestricted: any old class of things has a mereological sum. Whenever there are some things, even out of different possible worlds, there is something composed of just those things. | |
| From: David Lewis (On the Plurality of Worlds [1986], 4.3) | |
| A reaction: To say the least, a rather unusual usage for the English word 'thing'. I presume that Lewis is in the grip of a slippery slope problem - that there is no way to define the borderline between things and non-things. Presumably 'class' is unrestricted too. |
| 13268 | There are no restrictions on composition, because they would be vague, and composition can't be vague [Lewis, by Sider] |
| Full Idea: Lewis says that if not every class has a fusion then there must be a restriction on composition. The only plausible restrictions would be vague ones, which is impossible, because then whether composition occurs would be vague. So every class has a fusion. | |
| From: report of David Lewis (On the Plurality of Worlds [1986], p.212-3) by Theodore Sider - Four Dimensionalism 9.1 | |
| A reaction: This is Lewis's key argument in favour of unrestricted composition, his Vagueness Argument. Why can't composition be vague? If you gradually reassemble a broken mirror, at what point does the mirror acquire its unity? |
| 10566 | Lewis prefers giving up singletons to giving up sums [Lewis, by Fine,K] |
| Full Idea: In the face of the conflict between mereology and set theory, Lewis has advocated giving up the existence of singletons rather than sums. | |
| From: report of David Lewis (Parts of Classes [1991]) by Kit Fine - Replies on 'Limits of Abstraction' 1 |
| 14244 | Lewis only uses fusions to create unities, but fusions notoriously flatten our distinctions [Oliver/Smiley on Lewis] |
| Full Idea: Lewis employs mereological fusion as his sole method of making one thing out of many, and fusion is notorious for the way it flattens out and thereby obliterates distinctions. | |
| From: comment on David Lewis (Parts of Classes [1991]) by Oliver,A/Smiley,T - What are Sets and What are they For? 3.1 | |
| A reaction: I take this to be a key point in the discussion of mereology in ontological contexts. As a defender of intrinsic structural essences, I have no use for mereological fusions, and look for a quite different identity for 'wholes'. |
| 10660 | A commitment to cat-fusions is not a further commitment; it is them and they are it [Lewis] |
| Full Idea: Given a prior commitment to cats, a commitment to cat-fusions is not a further commitment. The fusion is nothing over and above the cats that compose it. It just is them. They just are it. | |
| From: David Lewis (Parts of Classes [1991], p.81), quoted by Achille Varzi - Mereology 4.3 | |
| A reaction: I take this to make Lewis a nominalist, saying the same thing that Goodman said about Utah in Idea 10657. Any commitment to cat-fusions being more than the cats, or Utah being more than its counties, strikes me as crazy. |
| 15440 | A whole is distinct from its parts, but is not a further addition in ontology [Lewis] |
| Full Idea: A whole is an extra item in our ontology only in the minimal sense that it is not identical to any of its proper parts; but it is not distinct from them either, so when we believe in the parts it is no extra burden to believe in the whole. | |
| From: David Lewis (Against Structural Universals [1986], 'The pictorial') | |
| A reaction: A little confusing, to be 'not identical' and yet 'not different'. As Lewis says elsewhere, the whole is one, and the parts are not. A crux. Essentialism implies a sort of holism, that parts with a structure constitute a new thing. |
| 15444 | Different things (a toy house and toy car) can be made of the same parts at different times [Lewis] |
| Full Idea: Different things can be made of the same parts at different times, as when the tinkertoy house is taken apart and put back together as a tinkertoy car. | |
| From: David Lewis (Against Structural Universals [1986], 'Variants') | |
| A reaction: More important than it looks! This is Lewis's evasion of the question of the structure of the parts. Times will individuate different structures, but if I take type-identical parts and make a house and a car simultaneously, are they type-identical? |
| 17557 | Special Composition Question: when is a thing part of something? [Inwagen] |
| Full Idea: The Special Composition Question asks, In what circumstances is a thing a (proper) part of something? | |
| From: Peter van Inwagen (Material Beings [1990], 02) | |
| A reaction: [He qualifies this formulation as 'misleading'] It's a really nice basic question for the metaphysics of objects. |
| 13328 | Two sorts of whole have 'rigid embodiment' (timeless parts) or 'variable embodiment' (temporary parts) [Fine,K] |
| Full Idea: I develop a version of hylomorphism, in which the theory of 'rigid embodiment' provides an account of the timeless relation of part, and the theory of 'variable embodiment' is an account of the temporary relation. We must accept two new kinds of whole. | |
| From: Kit Fine (Things and Their Parts [1999], Intro) | |
| A reaction: [see Idea 13326 and Idea 13327 for the two concepts of 'part'] This is easier to take than the two meanings for 'part'. Since Aristotle, everyone has worried about true wholes (atoms, persons?) and looser wholes (houses). |
| 18514 | Many wholes can survive replacement of their parts [Heil] |
| Full Idea: A whole - or some wholes - might be thought to survive gradual replacement of its parts, perhaps, but not their elimination. | |
| From: John Heil (The Universe as We Find It [2012], 03.1) | |
| A reaction: You can't casually replace the precious golden parts of a statue with cheap lead ones. It depends on whether the parts matter. Nevertheless this is a really important idea in metaphysics. It enables the s=Ship of Theseus to survive some change. |
| 18517 | Dunes depend on sand grains, but line segments depend on the whole line [Heil] |
| Full Idea: A sand dune depends on the individual grains of sand that make it up. In an important sense, however, a line's segments depend on the line rather than it on them. | |
| From: John Heil (The Universe as We Find It [2012], 03.4) | |
| A reaction: The illustrations are not clear cut. As you cut off segments of the line, you reduce its length. Heil is hoping for something neat here, but I don't think he has quite got. The difficulty of trying to do pure metaphysics! |
| 6154 | It is argued that wholes possess modal and counterfactual properties that parts lack [Rowlands] |
| Full Idea: Some have argued that a mereological whole should not be identified with the sum of its parts on the grounds that the former possess certain properties - specifically modal and (perhaps) counterfactual properties - that the latter lacks. | |
| From: Mark Rowlands (Externalism [2003], Ch.2) | |
| A reaction: I am not convinced that modal and counterfactual claims should count as properties. If my pen is heated it melts (a property), but if my pen were intelligent it could do philosophy. Intelligence is a property, but the situation isn't. |
| 10658 | Sameness of parts won't guarantee identity if their arrangement matters [Varzi] |
| Full Idea: We might say that sameness of parts is not sufficient for identity, as some entities may differ exclusively with respect to the arrangement of the parts, as when we compare 'John loves Mary' with 'Mary loves John'. | |
| From: Achille Varzi (Mereology [2003], 3.2) | |
| A reaction: Presumably wide dispersal should also prevent parts from fixing wholes, but there is so much vagueness here that it is tempting to go for unrestricted composition, and then work back to the common sense position. |
| 12888 | The wholeness of a melody seems conventional, but of an explosion it seems natural [Simons] |
| Full Idea: The example of a melody shows that what counts as a temporal individual is partly a matter of human stipulation. But with a natural event like an explosion there is little or no room for decision about what is a part, and whether it is a single event. | |
| From: Peter Simons (Parts [1987], 9.6) | |
| A reaction: You could have a go at giving a natural account of the wholeness of a melody, in terms of the little aesthetic explosion that occurs in the brain of a listener. |
| 13742 | There exist heaps with no integral unity, so we should accept arbitrary composites in the same way [Schaffer,J] |
| Full Idea: I am happy to accept universal composition, on the grounds that there are heaps, piles etc with no integral unity, and that arbitrary composites are no less unified than heaps. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1 n11) | |
| A reaction: The metaphysical focus is then placed on what constitutes 'integral unity', which is precisely the question which most interested Aristotle. Clearly if there is nothing more to an entity than its components, scattering them isn't destruction. |
| 13752 | The notion of 'grounding' can explain integrated wholes in a way that mere aggregates can't [Schaffer,J] |
| Full Idea: The notion of grounding my capture a crucial mereological distinction (missing from classical mereology) between an integrated whole with genuine unity, and a mere aggregate. x is an integrated whole if it grounds its proper parts. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 3.1) | |
| A reaction: That gives a nice theoretical notion, but if you remove each of the proper parts, does x remain? Is it a bare particular? I take it that it will have to be an abstract principle, the one Aristotle was aiming at with his notion of 'form'. Schaffer agrees. |
| 6956 | At what point does an object become 'whole'? [Westaway] |
| Full Idea: At what point does an object become 'whole'? | |
| From: Luke Westaway (talk [2005]), quoted by PG - Db (ideas) | |
| A reaction: This nice question strikes me as the central one in mereology. It is tempting to reply that the matter is entirely conventional, but there seems an obvious fact about something missing if one piece is absent from a jigsaw, or a cube is chipped. |
| 14949 | A sum of things is not a whole if the whole does not support some new generalisation [Ladyman/Ross] |
| Full Idea: A nostril, a city and a trumpet solo is not a real pattern, because identification of it supports no generalisations not supported by identification of the three conjuncts considered separately. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.4) | |
| A reaction: This is a nice try at offering a criterion for unity, but I doubt whether it will work, because an ingenious person could come up with wild generalisations. These three combined make possible a charming new line of poetry. |
| 10665 | Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack] |
| Full Idea: We can employ Leibniz's Law against mereological atomism. Water is wet, but no water molecule is wet. The set of infinite numbers is infinite, but no finite number is infinite. ..But with plural reference the atomist can resist this argument. | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: The idea of plural reference is to state plural facts without referring to complex things, which is interesting. The general idea is that we have atomism, and then all the relations, unities, identities etc. are in the facts, not in the things. I like it. |
| 10682 | The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack] |
| Full Idea: The fusion of five rectangles may have a decomposition into more than five parts that are rectangles. | |
| From: Keith Hossack (Plurals and Complexes [2000], 8) |
| 15392 | If an object survives the loss of a part, complex objects can have autonomy over their parts [Robb] |
| Full Idea: Sometimes a whole can survive a loss of parts: the chair would still exist if it lost one of its legs. This seems to give complex objects a sort of autonomy over their parts. | |
| From: David Robb (Substance [2009], 'Ident') | |
| A reaction: There is then a puzzle as to how much loss of parts the whole can survive, and why. The loss of a major part could be devastating, so why do all wholes not exhibit this relation to all their parts? I demand rules, now! |
| 13266 | Wholes in modern mereology are intended to replace sets, so they closely resemble them [Koslicki] |
| Full Idea: The modern theory of parts and wholes was intended primarily to replace set theory; in this way, wholes came out looking as much like sets as they possibly could, without set theory's commitment to an infinite hierarchy of abstract objects. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], Intro) | |
| A reaction: A very nice clarificatory remark, which explains well this rather baffling phenomenon of people who think there is nothing more to a whole than a pile of parts, as if a scrap heap were the same as a fleet of motor cars. |
| 14500 | Wholes are entities distinct from their parts, and have different properties [Koslicki] |
| Full Idea: A commitment to wholes is a commitment to entities that are numerically distinct from their parts (by Leibniz's Law, they don't share all of their properties - the parts typically exist, but the whole doesn't, prior to its creation). | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 3.1) | |
| A reaction: Presumably in classical mereology no act of 'creation' is needed, since all the parts in the universe already form all the possible wholes into which they might combine, however bizarrely. |
| 13281 | Wholes are not just their parts; a whole is an entity distinct from the proper parts [Koslicki] |
| Full Idea: In my approach (as in that of Plato and Aristotle), wholes are in no way identified with parts; rather, a commitment to wholes is a commitment to entities numerically distinct from their proper parts. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 7.2.11) | |
| A reaction: Calling the whole an 'entity' doesn't seem to capture it. She seems to think there are some extra parts, in addition to the material parts, that make something a whole. I think this might be a category mistake. A structure is an abstraction. |
| 18434 | That a whole is prior to its parts ('priority monism') is a view gaining in support [Edwards] |
| Full Idea: The view of 'priority monism' - that the whole is prior to its parts - is controversial, but has been growing in support | |
| From: Douglas Edwards (Properties [2014], 5.4.4) | |
| A reaction: The simple and plausible thought is, I take it, that parts only count as parts when a whole comes into existence, so a whole is needed to generate parts. Thus the whole must be prior to the parts. Fine by me. |