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Axioms and primitive notions[edit]






Overlap and Underlap are reflexive, symmetric, and intransitive.



The axioms are:

M1, Reflexive: An object is a part of itself.
M3, Transitive: If Pxy and Pyz, then Pxz.
Top is a theorem if M8 holds.

Various systems[edit]



Label Name System Included Axioms
M1-M3 Parthood is a partial order M M1–M3
M4 Weak Supplementation MM M, M4
M5 Strong Supplementation EM M, M5
M5' Atomistic Supplementation
M6 General Sum Principle (Sum)
M7 Product CEM EM, M6–M7
M8 Unrestricted Fusion GM M, M8
M8' Unique Fusion GEM EM, M8'
M9 Atomicity AGEM M2, M8, M9
AGEM M, M5', M8










Set theory[edit]




  • They deny that sets are in any way ontologically suspect












Mereology and natural language[edit]


Mereology and Metaphysics[edit]

In Metaphysics there are many troubling questions pertaining to parts and wholes. One question addresses constituion and persistence, another asks about composition.

Mereological Constitution[edit]

In Metaphysics, there are several puzzles concerning cases of mereological constitution. That is, what makes up a whole. We are still concerned with parts and wholes, but instead of looking at what parts make up a whole, we are wondering what a thing is made of, such as its materials: e.g. the bronze in a bronze statue. Below are two of the main puzzles that philosophers use to discuss constitution.

Ship of Theseus: Briefly, the puzzle goes something like this. You have a ship called the Ship of Theseus. Overtime the boards start to rot so you replace the boards and place the old boards in a pile. First question, is the ship made of the new boards the same as the ship that had all the old boards? Second, if we reconstruct a ship using all of the old planks, etc. from the Ship of Theseus, and we also have a ship that was build out of new boards (each added one-by-one over time to replace old decaying boards), which ship is the real Ship of Theseus.

Statue and Lump of Clay: Roughly, a sculptor decides to mold a statue out of a lump of clay. At time t1 the sculptor has a lump of clay. After many manipulations at time t2 there is a statue. The question asked is, is the lump of clay and the statue (numerically) identical? If so, how and why?[2]

Constitution typically has implications for views on persistence: how does an object persist over time if any of its parts (materials) change or are removed, as is the case with humans who lose cells, change height, hair color, memories, and yet we are said to be the same person today as we were when we were first born. For example, Ted Sider is the same today as he was when he was born—he just changed. But how can this be if many parts of Ted today did not exist when Ted was just born? Is it possible for things, such as organisms to persist? And if so, how? There are several views that attempt to answer this question. Some of the views are as follows (note, there are several other views):[3][4]

(a) Constitution View. This view accepts cohabitation. That is, two objects share the exact same matter. Here, it follows, that there are no temporal parts.

(b) Mereological Essentialism, which states that the only objects that exist are quantities of matter, which are things defined by their parts. The object persists if matter is removed (or the form changes); but the object ceases to exist if any matter is destroyed.

(c) Dominant Sorts. This is the view that tracing is determined by which sort is dominant; they reject cohabitation. For example, lump does not equal statue because they're different "sorts".

(d) Nihilism—which makes the claim that no objects exist, except simples, so there is no persistence problem.

(e) 4 Dimensionalism, or Temporal Parts (may also go by the names Perdurantism or Exdurantism), which roughly states that aggregates of temporal parts are intimately related. For example, two roads merging, momentarily and spatially, are still one road, because they share a part.

(f) 3 Dimensionalism (may also go by the name Endurantism), where the object is wholly present. That is, the persisting object retains numerical identity.

Mereological Composition[edit]

One question that is addressed by philosophers is which is more fundamental: parts, wholes, or neither?[5][6][7][8][9][10][11][12][13][14] Another pressing question is called the Special Composition Question (SCQ): For any Xs, when is it the case that there is a Y such that the Xs compose Y?[3][15][16][17][18][19][20] This question has caused philosophers to run in three different directions: nihilism, universal composition (UC), or a moderate view (restricted composition). The first two views are considered extreme since the first denies composition, and the second allows any and all non-spatially overlapping objects to compose another object. The moderate view encompasses several theories that try to make sense of SCQ without saying 'no' to composition or 'yes' to unrestricted composition.


There are philosophers who are concerned with the question of fundamentality. That is, which is more ontologically fundamental the parts or their wholes. There are several responses to this question, though one of the default assumptions is that the parts are more fundamental. That is, the whole is grounded in its parts. This is the mainstream view. Another view, explored by Shaffer (2010) is monism, where the parts are grounded in the whole. Shaffer does not just mean that, say, the parts that make up my body are grounded in my body. Rather, Shaffer argues that the whole cosmos is more fundamental and everything else is a part of the cosmos. Then, there is the identity theory which claims that there is no hierarchy or fundamentality to parts and wholes. Instead wholes are just (or equivalent to) their parts. You can also have a two-object view which says that the wholes are not equal to the parts—they are numerically distinct from one another. Each of these theories has benefits and costs associated with them.[5][6][7][8]

Special Composition Question (SCQ)[edit]

Philosophers want to know when some, Xs, composes something Y. One response to this question is called Nihilism. Nihilism states that there are no mereological complex objects (read: composite objects); there are only simples. Nihilists' do not entirely reject composition because they do think that simples compose themselves, but this is a different point. More formally Nihilists would say: Necessarily, for any non-overlapping Xs, there is an object composed of the Xs if and only if there is only one of the Xs.[16][20][21] This theory, though well explored, has its own set of problems. Some of which include, but are not limited to: experiences and common sense, incompatible with atomless gunk, and it is unsupported by space-time physics.[16][20]

Another prominent response is called Universal Composition (UC). UC says that so long as the Xs do not spatially overlap, the Xs can compose a complex object. Universal Compositionalists are also considered those who support unrestricted composition. More formally: Necessarily, for any non-overlapping Xs, there is a Y such that Y is composed of the Xs. For example, your left thumb, the top half of my right shoe, and a quark in the center of our galaxy can compose a complex object according to Universal Composition. Likewise, this theory also has some issues, most of them dealing with our experiences that these randomly chosen parts make up a complex whole and there are far too many objects posited in our ontology.

A third way to answer this question is less favored and left mainly unexplored—at least with respect to the other two responses. These are the restricted composition views. A potential problem with restricted composition as an answer to the Special Composition Question is that there is not just one theory to examine. Many thinkers have posited several possible restricted composition views. Though there are several views, they all share a common idea: that there is a restriction on what counts as a complex object: that is at least some of the time Xs come together to compose a complex Y. Some of these theories include:

(a) Contact View—where the Xs compose a complex Y if and only if the Xs are in contact;

(b) Fastenation—the Xs compose a complex Y if and only if the Xs are fastened;

(c) Cohesion—the Xs compose a complex Y if and only if the Xs cohere (cannot be pulled apart or moved in relation to each other without breaking);

(d) Fusion—the Xs compose a complex Y if and only if the Xs are fused (fusion is when the Xs are joined together such that there is no boundary);

(e) VIPA: van Inwagen Proposed Answer—Xs compose a complex Y if and only if either the activities of the Xs constitute a life or there is only one of the Xs;[21] and

(f) Brutal Composition—"It's just the way things are." There is no true, nontrivial, and finitely long answer.[22]

This is not an exhaustive list as many more hypothesis continue to be explored. However, a common problem with these theories is that they are vague. It remains unclear what "fastened" or "life" mean, for example. But there are many other issues within the restricted composition responses—though many of them are subject to which theory you are discussing.[16]

Important surveys[edit]



See also[edit]


  2. ^ Rea, Michael (1995). "The Problem of Material Constitution". The Philosophical Review. 104.4: 525–552. 
  3. ^ a b Ney, Alyssa (2014). Metaphysics: An Introduction. Routledge. 
  4. ^ In Theodore Sider, John Hawthorne & Dean W. Zimmerman (eds.), Contemporary Debates in Metaphysics. Blackwell Pub. 241--262 (2007).
  5. ^ a b Healey, Richard; Uffink, Jos (2013). "Part and Whole in Physics: An Introduction". Studies in History and Philosophy of Science Part B. 44.1: 20–21. 
  6. ^ a b Healey, Richard (2013). "Physical Composition". Studies in History and Philosophy of Science Part B. 44.1: 48–62. 
  7. ^ a b Kadanoff, Leo (2013). "Relating Theories Via Renormalization". Studies in History and Philosophy of Science Part B. 44.1: 22–39. 
  8. ^ a b Ghirardi, GianCarlo (2013). "The Parts and the Whole: Collapse Theories and Systems with Identical Constituents". Studies in History and Philosophy of Science Part B. 44.1: 40–47. 
  9. ^ Shaffer, Jonathan (2010). "Monism: The Priority of the Whole". Philosophical Review. 119.1: 31–76. 
  10. ^ Cameron, Ross (2014). "Parts Generate the Whole but they are not Identical to it". Oxford University Press. 
  11. ^ Loss, Roberto (2016). "Parts Ground the Whole and are Identical to it". Australasian Journal of Philosophy. 94.3. 
  12. ^ Cotnoir, Aaron (2014). "Composition as Identity: Framing the Debate". Oxford University Press. 
  13. ^ Sider, Ted (2015). "Nothing Over and Above". Grazer Philosophische Studien. 91: 191–216. 
  14. ^ Wallace, Megan (2011). "Composition as Identity: Pt. I & II". Philosophy Compass. 6.11: 804–827. 
  15. ^ Sider, Ted (2008). "The Moon and Sixpence: A Defense of Mereological Universalism". Contemporary Debates in Metaphysics. Blackwell Publishing.  Unknown parameter |chapter author= ignored (help)
  16. ^ a b c d Sider, Ted (2008). "Restricted Composition". Contemporary Debates in Metaphysics. Blackwell Publishing. pp. 341–363.  Unknown parameter |chapter author= ignored (help)
  17. ^ McDaniel, Kris (2010). "Parts and Wholes". Philosophy Compass. 5.5: 412–425. 
  18. ^ Korman, Daniel; Carmichael, Chad (2016). "Composition (Draft: 9/29/15)". Oxford Handbooks Online. 
  19. ^ Varzi, Achille. "Mereology". 
  20. ^ a b c Sider, Ted (2013). "Against Parthood". Oxford Studies in Metaphysics. 8: 237–293. 
  21. ^ a b van Inwagen, Peter (1990). Material Beings. Cornell University Press. 
  22. ^ Markosian, Ned (1998). "Brutal Composition". Philosophical Studies. 92: 211–249. 
  • Eberle, Rolf, 1970. Nominalistic Systems. Kluwer.

External links[edit]