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In philosophy and mathematical logic, mereology (from the Greek μέρος, root: μερε(σ)-, "part" and the suffix -logy "study, discussion, science") is the study of parts and the wholes they form. Whereas set theory is founded on the membership relation between a set and its elements, mereology emphasizes the meronomic relation between entities, which—from a set-theoretic perspective—is closer to the concept of inclusion between sets. Mereology has been explored in various ways as applications of predicate logic to formal ontology, in each of which mereology is an important part. Each of these fields provides their own axiomatic definition of mereology. A common element of such axiomatizations is the assumption, shared with inclusion, that the part-whole relation orders its universe, meaning 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), thus forming a poset. A variant of this axiomatization denies that anything is ever part of itself (irreflexive) while accepting transitivity, from which antisymmetry follows automatically. Although mereology is an application of mathematical logic, what could be argued to be a sort of "proto-geometry", it has been wholly developed by logicians, ontologists, linguists, engineers, and computer scientists, especially those working in artificial intelligence. "Mereology" can also refer to formal work in General Systems Theory on system decomposition and parts, wholes and boundaries (by, e.g., Mihajlo D. Mesarovic (1970), Gabriel Kron (1963), or Maurice Jessel (see Bowden (1989, 1998)). A hierarchical version of Gabriel Kron's Network Tearing was published by Keith Bowden (1991), reflecting David Lewis's ideas on Gunk. Such ideas appear in theoretical computer science and physics, often in combination with Sheaf, Topos, or Category Theory. See also the work of Steve Vickers on (parts of) specifications in Computer Science, Joseph Goguen on physical systems, and Tom Etter (1996, 1998) on Link Theory and Quantum mechanics. In computer science, the ''class'' concept of object-oriented programming lends a mereological aspect to programming not found in either imperative programs or declarative programs. Method inheritance enriches this application of mereology by providing for passing procedural information down the part-whole relation, thereby making method inheritance a naturally arising aspect of mereology. ==History== Informal part-whole reasoning was consciously invoked in metaphysics and ontology from Plato (in particular, in the second half of the ''Parmenides'') and Aristotle onwards, and more or less unwittingly in 19th-century mathematics until the triumph of set theory around 1910. Ivor Grattan-Guinness (2001) sheds much light on part-whole reasoning during the 19th and early 20th centuries, and reviews how Cantor and Peano devised set theory. In seventh century India, parts and wholes were studied extensively by Dharmakirti (see 〔Dunne, John D., 2004. ''Foundations of Dharmakirti's Philosophy''. Wisdom Publications.〕). In Europe, however, it appears that the first to reason consciously and at length about parts and wholes was Edmund Husserl, in 1901, in the second volume of ''Logical Investigations'' - Third Investigation: «On the Theory of Wholes and Parts» (Husserl 1970 is the English translation). However, the word "mereology" is absent from his writings, and he employed no symbolism even though his doctorate was in mathematics. Stanisław Leśniewski coined "mereology" in 1927, from the Greek word μέρος (''méros'', "part"), to refer to a formal theory of part-whole he devised in a series of highly technical papers published between 1916 and 1931, and translated in Leśniewski (1992). Leśniewski's student Alfred Tarski, in his Appendix E to Woodger (1937) and the paper translated as Tarski (1984), greatly simplified Leśniewski's formalism. Other students (and students of students) of Lesniewski elaborated this "Polish mereology" over the course of the 20th century. For a good selection of the literature on Polish mereology, see Srzednicki and Rickey (1984). For a survey of Polish mereology, see Simons (1987). Since 1980 or so, however, research on Polish mereology has been almost entirely historical in nature. A.N. Whitehead planned a fourth volume of ''Principia Mathematica'', on geometry, but never wrote it. His 1914 correspondence with Bertrand Russell reveals that his intended approach to geometry can be seen, with the benefit of hindsight, as mereological in essence. This work culminated in Whitehead (1916) and the mereological systems of Whitehead (1919, 1920). In 1930, Henry Leonard completed a Harvard Ph.D. dissertation in philosophy, setting out a formal theory of the part-whole relation. This evolved into the "calculus of individuals" of Goodman and Leonard (1940). Goodman revised and elaborated this calculus in the three editions of Goodman (1951). The calculus of individuals is the starting point for the post-1970 revival of mereology among logicians, ontologists, and computer scientists, a revival well-surveyed in Simons (1987) and Casati and Varzi (1999). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Mereology」の詳細全文を読む スポンサード リンク
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