Topological Representation of Material Implication and the Rule of Inference Modus Ponens

##plugins.themes.bootstrap3.article.main##

A. B. Banovac

Abstract

In the present paper we introduce and elaborate some basic elements of the methodological approach characterized by the application of topological means in the analysis and representation of entities through the actualization of some explicit differentiation scheme (scheme of discernment). The latter is understood as a set of rules — termed differentiation criteria — that individuate particular invariants (symmetries) of the entity under examination. We introduce the notion of differentiation invariants as symbolic representatives of the latter, and show that, in all instances of differentiation, topological structure can be induced on the set of such invariants. Given that, we proceed in describing the theoretical framework within which objects of logical theories and systems, as well as properties and interrelations between them, can be represented and treated by formal means of topology and characterized in terms of topological properties. Exposition of the proposed method is given through its application, resulting in topological representation of material implication and the rule of inference modus ponens.

##plugins.generic.usageStats.downloads##

##plugins.generic.usageStats.noStats##

##plugins.themes.bootstrap3.article.details##

Section
Статьи

References

Бескова И.А. Рифы логико-методологического анализа истинности // Многомерность истины / Под ред. А.А. Горелова, М.М. Новосёлова. М.: ИФ РАН, 2008. С. 162–181.
Генисаретский О.И. Пространственность в иконологии и эстетике священника Павла Флоренского // Свящ. Павел Флоренский. Статьи и исследования по истории и философии искусства и археологии / Под ред. иг. Андроника (А.С. Трубачева). М.: Мысль, 2000. С. 9–46.
Флоренский П.А. Анализ пространственности (и времени) в художественно-изобразительных произведениях // Свящ. Павел Флоренский. Статьи и исследования по истории и философии искусства и археологии / Под ред. иг. Андроника (А.С. Трубачева). М.: Мысль, 2000. С. 81–259.
Флоренский П.А. Значение пространственности // Свящ. Павел Флоренский. Статьи и исследования по истории и философии искусства и археологии / Под ред. иг. Андроника (А.С. Трубачева). М.: Мысль, 2000. С. 272–274.
Шалак В.И. Протологика: новый взгляд на природу логического: Автореф. дис. . . д-ра филос. наук. М.: ИФ РАН, 2010. 42 c.
Johansen J.D., Larsen S.E. Uvod u semiotiku. Zagreb: Croatialiber, 2000. 360 pp.
Munkres J.R. Topology. Upper Saddle River: Prentice Hall, 2000. 537 pp.
Rodin A. Axiomatic Method and Category Theory. Springer, 2014. 285 pp.
Rosen J. Symmetry in science. N.Y.: Springer-Verlag, 1995. 213 pp.