School
Mereology
Overview
Mereology (; from Greek μέρος 'part' (root: μερε-, mere-) and the suffix -logy, 'study, discussion, science') is the philosophical study of part-whole relationships, also called parthood relationships. As a branch of ontology, 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 was formally axiomatized in the 20th century by Polish logician Stanisław Leśniewski, who introduced it as part of a comprehensive framework for logic and mathematics, and coined the word "mereology".
Mereological ideas were influential in early § Set theory, and formal mereology continues to be used by some working on the § Foundations of mathematics. Different axiomatizations of mereology have been applied in § Ontology, used in § Linguistic semantics to analyze "mass terms", used in the cognitive sciences, and developed in § General systems theory. Mereology has been combined with topology, for more on which see the article on mereotopology. Mereology is also used in the foundation of Whitehead's point-free geometry, on which see Tarski 1956 and Gerla 1995. Mereology is used in discussions of entities as varied as musical groups, geographical regions, and abstract concepts, demonstrating its applicability to a wide range of philosophical and scientific discourses.
In ontology, mereology is used to formulate the thesis of "composition as identity", the theory that individuals or objects are identical to mereological sums (also called fusions) of their parts. A metaphysical thesis called "mereological monism" suggests that the version of mereology developed by Stanisław Leśniewski and Nelson Goodman (commonly called General Extensional Mereology, or GEM) serves as the general and exhaustive theory of parthood and composition, at least for a large and significant domain of things. This thesis is controversial, since parthood may not seem to be a transitive relation (as claimed by GEM) in some cases, such as the parthood between organisms and their organs. Nevertheless, GEM's assumptions are very common in mereological frameworks, due largely to Leśniewski influence as the one to first coin the word and formalize the theory: mereological theories commonly assume that everything is a part of itself (reflexivity), that a part of a part of a whole is itself a part of that whole (transitivity), and that two distinct entities cannot each be a part of the other (antisymmetry), so that the parthood relation is a partial order. An alternative is to assume instead that parthood is irreflexive (nothing is ever a part of itself) but still transitive, in which case antisymmetry follows automatically.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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In modern expositions of the axioms of geometry certain conditions are laid down which the relation of congruence between segments is to satisfy. It is supposed that we have a complete theory of points, straight lines, planes, and the order of points on planes--in fact, a complete theory of non-metrical geometry. We then enquire about congruence and lay down the set of conditions--or axioms as they are called--which…
Alfred North Whitehead, The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919
States what Mereology is; the author is tied to Mereology in the knowledge graph.
=132.= The next step, in defining a form of externality, is obtained from the idea of _dimensions_. Positions, we have seen, are defined solely by their relations to other positions. But in order that such definition may be possible, a finite number of relations must suffice, since infinite numbers are philosophically inadmissible. A position must be definable, therefore, if knowledge of our form is to be possible…
Bertrand Russell, An essay on the foundations of geometry
States what Mereology is; the author is tied to Mereology in the knowledge graph.
This is nothing else than the necessity of abstract logic, which is the presupposition involved in the very fact of interrelated existence as disclosed in each immediate occasion of experience. The key to the pattern means this fact:—that from a select set of those general conditions, exemplified in any one and the same occasion, a pattern involving an infinite variety of other such conditions, also exemplified in…
Alfred North Whitehead, Science and the modern world
States what Mereology is; the author is tied to Mereology in the knowledge graph.
Philosophers who discussed Mereology
- Nelson Goodman
- Nagarjuna
- David Lewis (philosopher)
- Roderick Chisholm
- Stanisław Leśniewski
- Alfred Tarski
- Edmund Husserl
- Jonathan Schaffer
- Richard Milton Martin
- Achille Varzi (philosopher)
Related ideas
- First-order logic
- Nelson Goodman
- Georg Cantor
- Ancient Greek
- Plural
- Zermelo–Fraenkel set theory
- Foundations of mathematics
- Ernst Zermelo
- Axiomatic system
- Metaphysics
- Geometry
- Theoretical physics
- Model theory
- Reflexive relation
- Ivor Grattan-Guinness
- Real number
- Perdurantism
- Nominalism
- Thomas Aquinas
- Nihilism
- Ontology
- Ordered pair
- Plato
- Richard Dedekind
Place in the tradition
Part of Analytic philosophy.