Logical Thinking In The Pyramidal Schema Of Concepts The Logical And Mathematical Elements

Logical Thinking in the Pyramidal Schema of Concepts: The Logical and Mathematical Elements

This new volume on logic follows a recognizable format that deals in turn with the topics of mathematical logic, moving from concepts, via definitions and inferences, to theories and axioms. However, this fresh work offers a key innovation in its ‘pyramidal’ graph system for the logical formalization of all these items. The author has developed this new methodology on the basis of original research, traditional logical instruments such as Porphyrian trees, and modern concepts of classification, in which pyramids are the central organizing concept. The pyramidal schema enables both the content of concepts and the relations between the concept positions in the pyramid to be read off from the graph. Logical connectors are analyzed in terms of the direction in which they connect within the pyramid. Additionally, the author shows that logical connectors are of fundamentally different types: only one sort generates propositions with truth values, while the other yields conceptual expressions or complex concepts. On this basis, strong arguments are developed against adopting the non-discriminating connector definitions implicit in Wittgensteinian truth-value tables. Special consideration is given to mathematical connectors so as to illuminate the formation of concepts in the natural sciences. To show what the pyramidal method can contribute to science, a pyramid of the number concepts prevalent in mathematics is constructed. The book also counters the logical dogma of ‘false’ contradictory propositions and sheds new light on the logical characteristics of probable propositions, as well as on syllogistic and other inferences.

Das Nichts und das Sein

Dreißig Jahre kollegialer Beziehung zwischen der Japanischen und der Internationalen Fichte Gesellschaft haben im Band 46 der Fichte Studien ihren Ausdruck gefunden, einer Sammlung von Aufsätzen auf der Grundlage transzendentaler Philosophie (Kants, Fichtes und Husserls) und klassischer Texte des Mahayana Buddhismus (und der japanischen Kyoto Schule). Ohne unvereinbare Unterschiede zwischen westlichem und östlichem Denken zu leugnen, finden sie ihre Grundlage in prä-reflexiver Erkenntnis. Beitragende sind Kogaku Arifuko, Martin Bunte, Luis Fellipe Garcia, Lutz Geldsetzer, Helmut Girndt, Katsuki Hayashi, Saša Josifović, Michael Lewin, Hitoshi Minobe, Kunihiko Nagasawa, Akira Omine, Valentin Pluder, Raji C. Steineck, Johannes Stoffers und Fabian Völker. Thirty years of friendly connections between the Japanese Fichte Association and the International Fichte Society have found expression in volume 46 of Fichte Studien. It contains a collection of comparative studies between European and Japanese philosophy centered on transcendental philosophy (of Kant, Fichte and Husserl) and classical Mahayana Buddhism (plus Japan ́s Kyoto school). Without denying irreconcilable differences between western and eastern thinking these essays demonstrate that western as well as eastern thinking is based on the universal ground of pre-reflexive cognition.

IRE Transactions on Electronic Computers