Glossary of mereology

Last updated

This is a glossary of mereology. Mereology is the philosophical study of part-whole relationships, also called parthood relationships. [1]

Contents

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. [2]
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. [3]
atomless gunk
See gunk.

B

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. [4]
classical mereology
Classical mereology is the mereological theory obtained by assuming that the parthood relation is a partial ordering , and that the unrestricted fusion principle holds. [5]
composition
The relation that connects many things to a single thing that includes whatever is in the many things, and nothing extraneous to them. [2]
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. [6] Also called "mereological universalism". [7]

D

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. [2]
extensionality
The principle in mereology stating that two objects are identical if they have the same proper parts. [8]

F

fusion
Synonym for "mereological sum". [9]

G

general extensional mereology
General extensional mereology is the mereological theory obtained by assuming that the parthood relation is a partial ordering and that the strong supplementation principle, and the unrestricted fusion principle, hold. [5]
ground mereology
Ground mereology is the mereological theory obtained by assuming that the parthood relation is a partial ordering . [5]
gunk
An object or substance whose parts all have proper parts, which means the object is divisible into parts 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 proper parts. [10]

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. [2] [11]
hunky
Adjective describing a possible world that is both gunky and junky. [12] [10]

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 proper parts 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 gunk".) [13]
junky
Adjective describing a possible world with junk in it, i.e., a world where every object is a proper part of something else. [12]

K

knug
Term coined by John Parsons [14] for what is more commonly called "junk"; coined to be "gunk" written backwards. [10]
knunk
A proposed term for structures that are junky and all their members are gunky; 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. [10]

L

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 proper parts. [8]
mereological fusion
Synonym for "mereological sum". [15]
mereological harmony
See harmony. [2] [11]
mereological monism
The view that, in a large and significant domain of things, classical extensional mereology is the only correct theory of parthood and composition. [16] [2] Not to be confused with monism.
mereological nihilism
The philosophical position that denies the existence of composite objects, asserting that only basic, partless entities exist. [17]
mereological sum
An object that is composed of all and only the entities in a given collection, according to the principles of mereology. [9]
mereological universalism
The view that two objects always compose a third, which is to say, that mereological composition is unrestricted. [7] Also called "compositional universalism". [6]
mereology
The study of the relationships between parts and wholes, and the principles governing the composition of objects. [9]
minimal mereology
Minimal mereology is the mereological theory obtained by assuming that the parthood relation is a partial ordering , and that the weak supplementation principle holds. [5]
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. [18] Formally, , where represents the cosmos, and represents the status of being a basic actual concrete object, i.e., an object that is concrete and does not depend on anything concrete. [13] Not to be confused with senses of "monism" outside of mereology, or with mereological monism.

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. [19]

O

overlap
In mereology, the relation between objects or sets that share at least one part in common. [9]

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. [1]
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. [9]
pluralism
The view there are more than one fundamental object; opposed to monism. [18] Not to be confused with senses of "pluralism" outside of mereology.
priority pluralism
Another term for pluralism, emphasizing that pluralities are metaphysically prior to wholes, although wholes exist. [10]

Q

R

reflexivity of parthood
The property according to which everything is part of itself. [9]

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. [20]

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 part-whole relationships. [21]

U

underlap
A concept in mereology where two objects do not share any parts in common, opposite of overlap, emphasizing the disjointness of the objects. [9]
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. [22]

V

W

worldless junk
See junk.

X

Y

Z

See also

Related Research Articles

<span class="mw-page-title-main">Metaphysics</span> Study of fundamental reality

Metaphysics is the branch of philosophy that examines the basic structure of reality. It is often characterized as first philosophy, implying that it is more fundamental than other forms of philosophical inquiry. Metaphysics is traditionally seen as the study of mind-independent features of the world, but some modern theorists understand it as an inquiry into the conceptual schemes that underlie human thought and experience.

<span class="mw-page-title-main">Ontology</span> Philosophical study of being and existence

In metaphysics, ontology is the philosophical study of being. It investigates what types of entities exist, how they are grouped into categories, and how they are related to one another on the most fundamental level. Ontologists often try to determine what the categories or highest kinds are and how they form a system of categories that encompasses the classification of all entities. Commonly proposed categories include substances, properties, relations, states of affairs, and events. These categories are characterized by fundamental ontological concepts, including particularity and universality, abstractness and concreteness, or possibility and necessity. Of special interest is the concept of ontological dependence, which determines whether the entities of a category exist on the most fundamental level. Disagreements within ontology are often about whether entities belonging to a certain category exist and, if so, how they are related to other entities.

<span class="mw-page-title-main">World</span> The totality of existing entities

The world is the totality of entities, the whole of reality, or everything that exists. The nature of the world has been conceptualized differently in different fields. Some conceptions see the world as unique while others talk of a "plurality of worlds". Some treat the world as one simple object while others analyze the world as a complex made up of parts.

Mereology is the philosophical study of part-whole relationships, also called parthood relationships. As a branch of metaphysics, mereology examines the connections between parts and their wholes, exploring how components interact within a system. This theory has roots in ancient philosophy, with significant contributions from Plato, Aristotle, and later, medieval and Renaissance thinkers like Thomas Aquinas and John Duns Scotus. Mereology gained formal recognition in the 20th century through the pioneering works of Polish logician Stanisław Leśniewski, who introduced it as part of a comprehensive framework for logic and mathematics, and coined the word "mereology". The field has since evolved to encompass a variety of applications in ontology, natural language semantics, and the cognitive sciences, influencing our understanding of structures ranging from linguistic constructs to biological systems.

Roderick Milton Chisholm was an American philosopher known for his work on epistemology, metaphysics, free will, value theory, and the philosophy of perception.

Truthmaker theory is "the branch of metaphysics that explores the relationships between what is true and what exists". The basic intuition behind truthmaker theory is that truth depends on being. For example, a perceptual experience of a green tree may be said to be true because there actually is a green tree. But if there were no tree there, it would be false. So the experience by itself does not ensure its truth or falsehood, it depends on something else. Expressed more generally, truthmaker theory is the thesis that "the truth of truthbearers depends on the existence of truthmakers". A perceptual experience is the truthbearer in the example above. Various representational entities, like beliefs, thoughts or assertions can act as truthbearers. Truthmaker theorists are divided about what type of entity plays the role of truthmaker; popular candidates include states of affairs and tropes.

In formal ontology, a branch of metaphysics, and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts.

Perdurantism or perdurance theory is a philosophical theory of persistence and identity. The debate over persistence currently involves three competing theories—one three-dimensionalist theory called "endurantism" and two four-dimensionalist theories called "perdurantism" and "exdurantism". For a perdurantist, all objects are considered to be four-dimensional worms and they make up the different regions of spacetime. It is a fusion of all the perdurant's instantaneous time slices compiled and blended into a complete mereological whole. Perdurantism posits that temporal parts alone are what ultimately change. Katherine Hawley in How Things Persist states that change is "the possession of different properties by different temporal parts of an object".

In philosophy, mereological nihilism is the metaphysical thesis that there are no objects with proper parts. Equivalently, mereological nihilism says that mereological simples, or objects without any proper parts, are the only material objects that exist. Mereological nihilism is distinct from ordinary nihilism insofar as ordinary nihilism typically focuses on the nonexistence of common metaphysical assumptions such as ethical truths and objective meaning, rather than the nonexistence of composite objects.

In mathematics, point-free geometry is a geometry whose primitive ontological notion is region rather than point. Two axiomatic systems are set out below, one grounded in mereology, the other in mereotopology and known as connection theory.

In contemporary mereology, a simple or indivisible monomere is any thing that has no proper parts. Sometimes the term "atom" is used, although in recent years the term "simple" has become the standard.

In philosophy, mereological essentialism is a mereological thesis about the relationship between wholes, their parts, and the conditions of their persistence. According to mereological essentialism, objects have their parts necessarily. If an object were to lose or gain a part, it would no longer be the original object.

<span class="mw-page-title-main">Reism</span>

Reism, reificationism, concretism or concretionism is a view that only concrete material things exist. It is a philosophical theory associated with Tadeusz Kotarbiński who proposed that it involves both the proper view about the kinds of objects that exist and the literal way of speaking about things. It is based on the ontology of Stanislaw Lesniewski, specifically, his "calculus of names". This theory, which is also referred to as somatism and pansomatism, has been interpreted as an analogue of defended classic physicalism.

Jonathan Schaffer is an American philosopher specializing in metaphysics and also working in epistemology, mind, and language. He is best known for his work on grounding and his development of monism, and is also a notable proponent of contrastivism.

In philosophy, specifically in the area of metaphysics, counterpart theory is an alternative to standard (Kripkean) possible-worlds semantics for interpreting quantified modal logic. Counterpart theory still presupposes possible worlds, but differs in certain important respects from the Kripkean view. The form of the theory most commonly cited was developed by David Lewis, first in a paper and later in his book On the Plurality of Worlds.

Metaphysics is the branch of philosophy that investigates principles of reality transcending those of any particular science. Cosmology and ontology are traditional branches of metaphysics. It is concerned with explaining the fundamental nature of being and the world. Someone who studies metaphysics can be called either a "metaphysician" or a "metaphysicist".

The following outline is provided as an overview of and topical guide to metaphysics:

In mereology, an area of metaphysics, the term gunk applies to any whole whose parts all have further proper parts. That is, a gunky object is not made of indivisible atoms or simples. Because parthood is transitive, any part of gunk is itself gunk. The term was first used by David Lewis in his work Parts of Classes (1991), in which he conceived of the possibility of "atomless gunk", which was shortened to "gunk" by later writers. Dean W. Zimmerman defends the possibility of atomless gunk.

<span class="mw-page-title-main">Jessica Wilson</span> Canadian metaphysician

Jessica M. Wilson is an American professor of philosophy at the University of Toronto Scarborough. Her research focuses on metaphysics, especially on the metaphysics of science and mind, the epistemologies of skepticism, a priori deliberation, and necessity. Wilson was awarded the Lebowitz Prize for excellence in philosophical thought by Phi Beta Kappa in conjunction with the American Philosophical Association.

Compositional objects are wholes instantiated by collections of parts. If an ontology wishes to permit the inclusion of compositional objects it must define which collections of objects are to be considered parts composing a whole. Mereology, the study of relationships between parts and their wholes, provides specifications on how parts must relate to one another in order to compose a whole.

References

  1. 1 2 Champollion, Lucas; Krifka, Manfred (2016), Aloni, Maria; Dekker, Paul (eds.), "Mereology", The Cambridge Handbook of Formal Semantics, Cambridge Handbooks in Language and Linguistics, Cambridge: Cambridge University Press, pp. 369–388, doi:10.1017/cbo9781139236157.014, ISBN   978-1-139-23615-7 , retrieved 2024-04-21
  2. 1 2 3 4 5 6 Lando, Giorgio (2017). Mereology: a philosophical introduction. London Oxford New York: Bloomsbury Academic. ISBN   978-1-4725-8367-3.
  3. ↑ Koslicki, Kathrin (2008). The structure of objects. Oxford: Oxford University press. p. 15. ISBN   978-0-19-953989-5.
  4. ↑ Bunnin, Nicholas; Yu, Jiyuan (2004). The Blackwell dictionary of Western philosophy. Malden, MA: Blackwell Pub. p. 424. ISBN   978-1-4051-0679-5.
  5. 1 2 3 4 Cook, Roy T. (2009-03-20). A Dictionary of Philosophical Logic. doi:10.1515/9780748631971. ISBN   978-0-7486-3197-1.
  6. 1 2 McDaniel, Kris (2020). This is metaphysics: an introduction. This is philosophy. Hoboken, New Jersey: Wiley-Blackwell. p. 103. ISBN   978-1-118-40078-4.
  7. 1 2 Contessa, Gabriele (2012). "The junk argument: safe disposal guidelines for mereological universalists". Analysis. 72 (3): 455–457. doi:10.1093/analys/ans071. ISSN   0003-2638. JSTOR   23250552.
  8. 1 2 Cotnoir, A. J.; Varzi, Achille C. (2021). "What is Mereology?". Mereology. New York: Oxford University Press. ISBN   9780191811647.
  9. 1 2 3 4 5 6 7 Varzi, Achille (2019), "Mereology", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Spring 2019 ed.), Metaphysics Research Lab, Stanford University, retrieved 2024-04-21
  10. 1 2 3 4 5 Giberman, Daniel; Philosophy Documentation Center (2020). "What it takes to be hunky". Thought: A Journal of Philosophy. 9 (1): 51–57. doi:10.1002/tht3.442. ISSN   2161-2234.
  11. 1 2 Bennett, Karen; Zimmerman, Dean W. (2011-02-10). Oxford Studies in Metaphysics: volume 6. Oxford University Press. pp. 199–224. doi:10.1093/acprof:oso/9780199603039.001.0001. ISBN   978-0-19-172541-8.
  12. 1 2 Bohn, Einar Duenger (April 2009). "Must There be a Top Level?". The Philosophical Quarterly. 59 (235): 193–201. doi:10.1111/j.1467-9213.2008.573.x.
  13. 1 2 Schaffer, Jonathan (2010-01-01). "Monism: The Priority of the Whole". The Philosophical Review. 119 (1): 31–76. doi:10.1215/00318108-2009-025. ISSN   0031-8108.
  14. ↑ Parsons, Josh (2007-05-31), "Theories of Location", Oxford Studies In Metaphysics, Oxford University PressOxford, pp. 201–232, doi:10.1093/oso/9780199218394.003.0007, ISBN   978-0-19-921839-4 , retrieved 2024-04-22
  15. ↑ Gruszczyński, R. (2013). "Mereological Fusion as an Upper Bound". Bulletin of the Section of Logic. 42: 135–150.
  16. ↑ Fine, Kit (1994). "Compounds and Aggregates". Noûs. 28 (2): 137–158. doi:10.2307/2216046. ISSN   0029-4624. JSTOR   2216046.
  17. ↑ Ney, Alyssa (2023). Metaphysics: an introduction (2nd ed.). London ; New York, NY: Routledge, Taylor & Francis Group. ISBN   978-1-351-14120-8.
  18. 1 2 Bohn, Einar Duenger (2012-03-01). "Monism, Emergence, and Plural Logic". Erkenntnis. 76 (2): 211–223. doi: 10.1007/s10670-011-9280-4 . ISSN   1572-8420.
  19. ↑ COTNOIR, AARON J.; BACON, ANDREW (2011-12-09). "Non-Wellfounded Mereology". The Review of Symbolic Logic. 5 (2): 187–204. doi:10.1017/s1755020311000293. hdl: 10023/3157 . ISSN   1755-0203.
  20. ↑ Canavotto, Ilaria; Giordani, Alessandro (2022-10-01). "An Extensional Mereology for Structured Entities". Erkenntnis. 87 (5): 2343–2373. doi:10.1007/s10670-020-00305-5. ISSN   1572-8420.
  21. ↑ Johansson, Ingvar (2013-05-02), "On the Transitivity of the Parthood Relations", Relations and Predicates, De Gruyter, pp. 161–182, doi:10.1515/9783110326857.161, ISBN   978-3-11-032685-7 , retrieved 2024-04-21
  22. ↑ Kleinschmidt, Shieva, ed. (2014-01-09). "Mereology and Modality". Mereology and Location. Oxford University Press. pp. 33–56. doi:10.1093/acprof:oso/9780199593828.003.0003. ISBN   978-0-19-959382-8.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.