The principle of continuity is therefore open to proof, as are Leibniz's other principles (principle of identity of the indiscernibles, principle of sufficient reason). The principle of continuity is not an Aristotelian first principle strictly speaking, what constitutes a principle is that something follows it, but nothing precedes it. The principle of continuity, or "lex continuitatis", is one of Leibniz's most interesting contributions to western science and philosophy. In this philosophical issue is heightened by the debate raging between continuismĪnd discontinuism in contemporary scientific theories. Reality understood with all the breadth of Aristotle's definition. The continuity of the sciences, which is a consequence of the continuity of Is to contiguity as the genus is to the species. To trace the notion of continuity in all its philosophical extension. Simply mean that things are contiguous in space, or even successive in time,īut that there may be continuity in all that is real. Things can be together without even being one, and can be one without necessarilyīeing together" ( Phys V, 3, 227a 22-24). Should be thought of as an aggregate of points and atoms which are related toĮach other in some accidental way. Problem lies in whether the existence of continuity should be admitted, or reality The complexity and interest of continuity is obvious. Frank compares Anaxagoras' view with that of Leibniz, who also "associated infinitesimal calculus with monadology and, while being fully aware of the scarcely discernible differences between individual beings, asserted the principle of universal continuity with the greatest rigour" 4. Anaxagoras found that the infinite is in both the large and the small, and reached the conclusion that everything is in everything "in such a way that even though nothing is the same as anything else, there are infinite degrees of variation between one thing and another" 3. Anaxagoras drew on Zeno's paradoxes, especially the so-called dichotomy, and on the reflections of Leucippus and Democritus concerning matter as being made up of atoms. Magnitudes considered from a quantitative point of view.Īnaxagoras conceived of matter as being composed of particles, each of which is irreducible (quality) but not indivisible (quantity). Indivisible in magnitude, and that plurality does not arise out of unity, norĭoes unity out of plurality, but that all things are generated by the joining As Aristotle says ( De Caelo,Ĥ, 303a 5), they "state that the first magnitudes are infinite in number and Small particles: atoms, which are indivisible. Leucippus and Democritus hold that reality is made up of infinitely Zeno of Elea, influenced by Parmenides, considered that unity and divisibility,Īnd therefore continuity, must go together. Zeno of Elea, Leucippus, Democritus,Īnaxagoras and Aristotle devote special attention to analyzing this problem. Just like that of the one and the many, which "becomes evident at the very heart The subject of the continuous arose out of the subject of infinity and divisibility, Either space and time are infinitelyĭivisible, in which case motion is continuous and smooth-flowing or else theyĪre made up of indivisible minima, in which case motion is what Lee aptly calls Of space and time were held in antiquity. Inevitably on theories of the nature of space and time and two opposed views As Raven wrote "theories of motion depend The origin of the subject of continuity can be traced back to the problem of In Leibniz 3) Continuity in Peirce and 4) Continuity in Quine *. According to this framework, ourĭiscussion is divided into four sections: 1) The history of continuity 2) Continuity Though maintaining that a continuity exists between science and philosophy,Įnds up by reducing the latter to the former. Perspective contrasts with Quine's contemporary scientist naturalism which, Not only in its original mathematical formulation, but in its broad metaphysicalĪnd epistemological scope as a central component of Leibniz's thought. We aim to trace some of the landmarks in the history of the principle of continuity, The shortcomings of the specializing scientism of our century. Metaphysical ideas and his Leibnizian heritage, and affords an insight into The notion of continuity is of vital importance for an understanding of Peirce's Gottfried-Wilhelm-Leibniz-Gesellschaft e. Jaime Nubiola: "The Continuity of Continuity: A Theme in Leibniz, Peirce and Quine"
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