Glossary of mereology

This is a glossary of mereology. Mereology is the philosophical study of part-whole relationships, also called parthood relationships.

A
anti-symmetry of parthood: In mereology, a principle stating that if A is part of B and B is part of A, then A and B are identical, reinforcing the notion of precise part-whole relationships.

atomic mereology: A branch of mereology that deals with wholes that are ultimately composed of indivisible parts, or atoms, focusing on how such atomic parts combine to form larger wholes.

atomless gunk: See.

C
calculus of individuals: Because mereology applies to individuals, it is called the calculus of individuals, in contrast to set theory, which is called the calculus of classes.

classical mereology: Classical mereology is the mereological theory obtained by assuming that the relation is a, and that the unrestricted fusion principle holds.

composition: The relation that connects many things to a single thing that includes whatever is in the many things, and nothing extraneous to them.

compositional universalism: A position in mereology that holds any collection of entities, regardless of how disparate, can constitute a whole, leading to the possibility of any entities forming a composite object. Also called "".

E
extensional mereology: A branch of mereology that focuses on the relations of parts to wholes based on the extensions of the parts, without regard to the nature or properties of the parts.

extensionality: The principle in mereology stating that two objects are identical if they have the same.

F
fusion: Synonym for "".

G
general extensional mereology: General extensional mereology is the mereological theory obtained by assuming that the parthood relation is a and that the strong supplementation principle, and the unrestricted fusion principle, hold.

ground mereology: Ground mereology is the mereological theory obtained by assuming that the parthood relation is a.

gunk: An object or substance whose parts all have, which means the object is divisible into indefinitely, with no simplest parts or atoms. (Short for "atomless gunk".)

gunky: Adjective describing entities, or worlds, made out of atomless gunk – that is, objects all of whose parts have.

H
harmony: The principle that an object x is part of an object y if, and only if, the region in space occupied by x is part of the region in space occupied by y.

hunky: Adjective describing a possible world that is both and.

I
identity of indiscernibles: A principle often discussed in the context of mereology, stating that no two distinct objects have exactly the same properties, thus differentiating even similar wholes by their specific parts.

J
junk: A state of affairs where all objects are of something else, which means objects are composable into further objects indefinitely, never forming a complete "world". (Short for "worldless junk"; coined as the converse of "atomless ".)

junky: Adjective describing a possible world with in it, i.e., a world where every object is a of something else.

K
knug: Term coined by John Parsons for what is more commonly called ""; coined to be "" written backwards.

knunk: A proposed term for structures that are and all their members are ; coinage by Giberman, inspired by Parsons's "knug", to reflect what must have been meant by the coiners of "hunky", since, if worlds are taken to be concrete objects, no gunky-and-junky worlds are possible.

M
mereological continuity: The principle in mereology that suggests wholes are continuously divisible into smaller and smaller parts, with no abrupt discontinuities in the structure of the objects.

mereological essentialism: The view in mereology that parts are essential to the wholes they constitute; that is, a whole cannot exist without having precisely those parts.

mereological extensionality: The principle in mereology stating that two objects are identical if they have the same.

mereological fusion: Synonym for "".

mereological harmony: See.

mereological monism: The view that, in a large and significant domain of things, is the only correct theory of  and. Not to be confused with.

mereological nihilism: The philosophical position that denies the existence of composite objects, asserting that only basic, partless entities exist.

mereological sum: An object that is composed of all and only the entities in a given collection, according to the principles of mereology.

mereological universalism: The view that two objects always compose a third, which is to say, that mereological composition is unrestricted. Also called "".

mereology: The study of the relationships between parts and wholes, and the principles governing the composition of objects.

minimal mereology: Minimal mereology is the mereological theory obtained by assuming that the parthood relation is a, and that the weak supplementation principle holds.

monism: The view that there is only one fundamental object, which is the cosmos, and that all other objects (its parts) derive their reality from it. Formally, $(\exists ! x) Bx ~ \& ~ Bu$, where $u$ represents the cosmos, and $B$ represents the status of being a basic actual concrete object, i.e., an object that is concrete and does not depend on anything concrete. Not to be confused with senses of "monism" outside of mereology, or with.

N
non-well-founded mereology: An approach to mereology where parts and wholes can form circular or self-referential structures, challenging traditional, well-founded notions of parthood.

O
overlap: In mereology, the relation between objects or sets that share at least one in common.

P
parthood: The relation between an entity and a composite object of which it is a part, central to mereology, the study of parts and wholes.

proper parthood: A relation between two entities where one is a part of the other but not equivalent to it, indicating a strict subset relationship in the context of mereology.

pluralism: The view there are more than one fundamental object; opposed to. Not to be confused with senses of "pluralism" outside of mereology.

priority pluralism: Another term for, emphasizing that pluralities are metaphysically prior to wholes, although wholes exist.

R
reflexivity of parthood: The property according to which everything is part of itself.

S
simple: In mereology, a simple is an object that has no parts other than itself, often considered in discussions of mereological nihilism and the debate over the existence of composite objects.

strong supplementation principle: A principle in mereology stating that if an object is not part of another, then there must be a part of the latter that does not overlap with the object, emphasizing the distinctness and separability of parts within wholes.

T
transitivity of parthood: The property where if A is part of B, and B is part of C, then A is part of C, emphasizing the chain-like nature of.

U
underlap: A concept in mereology where two objects do not share any parts in common, opposite of, emphasizing the disjointness of the objects.

unrestricted fusion: A principle in mereology allowing for the existence of a composite object consisting of any collection of parts, regardless of how dispersed or unrelated those parts may be.

W
worldless junk: See.