Literally, indivisible is that which cannot be divided. One may distinguish mathematical from physical indivisibles and their uses in philosophy and mathematics. Since division follows upon distinction, in turn dependent upon opposition, the term is understood with reference to material (quantitative) or to formal opposition. Material indivisibles are either absolute—points and numerical units; or relative—that which de facto is not divided or would be destroyed by division, e.g., an electron. Formally, indivisibles have, or are considered to have, simple intelligibility, e.g., a genus or a specific nature. Because a definition, being complex, cannot be formed of them, absolute formal indivisibles are often known only negatively or in relation to composites.
In the physical universe, perhaps exclusively, there are relative quantitative indivisibles. The discrete particles that, as a result of experimental and theoretical physics, are thought to constitute physical reality—e.g., atoms, subatomic particles, and photons—are destroyed when divided, although the matter-energy balance is thought to be preserved. Such indivisibles are not always individuals, though true individuals are always indivisibles.
Linear extension, along with motion and time, are considered instances of continua within which indivisibles are distinguished. The instant of time and the moment of motion are compared analogously to the geometric point, and the question has been debated concerning their actual continuing and/or terminating function. Granted that they terminate, there is still question of their precise nature. The general view is that terminating indivisibles, e.g., points at the ends of lines, are positive and really but only modally distinct from that which they terminate. Concerning indivisibles in mathematics, see boyer.
See Also: continuum.
Bibliography: j. gredt, Elementa philosophiae Aristotelico–Thomisticae, ed. e. zenzen, 2 v. (13th ed. Freiburg 1961). r. p. phillips, Modern Thomistic Philosophy, 2 v. (Westminster, Md. 1934; repr. 1945). c. b. boyer, The History of the Calculus and Its Conceptual Development (pa. New York 1959).
[c. f. weiher]
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