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E-grāmata: Towards Scientific Metaphysics, Volume 2: Benedykt Bornstein's Geometrical Logic and Modern Philosophy

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In the first half of the 20th century, many Polish philosophers focused on defining scientific concepts that could lead to the development of a philosophical synthesis of reality. Benedykt Bornstein elaborated an algebraic logic and developed novum organum philosophiae in the form of geometrical logic, a mathematical system of universal science. It can also be stated that Bornstein was unquestionably the forerunner of philosophers who started research into spatial logic in the second half of the 20th century.

The aim of this study on Bornstein’s Geometrical Logic is to draw readers’ attention not only to the algebraic and geometrical tools used in philosophical research, but also to demonstrate its importance for contemporary philosophical discussions which use mathematical tools in topology and category theory.



The book presents Bornstein’s work on development of algebraic logic as well as the most important areas and findings of research on the theory of knowledge, logic, ontology and metaphysics. Bornstein notices new possibilities in the use of spatial logic in philosophical studies.

Introduction 7(8)
Part One Philosophical Logic and Selected Issues in Benedykt Bornstein's Philosophy
15(1)
1 From Epistemology to the Ontology of Mathematics and Category Theory
15(1)
1.1 Overcoming the Antithesis between Sensibility and Reason
15(4)
1.2 Epistemological Decisions in the Philosophy of Mathematics
19(5)
1.3 Selected Issues in the Theory of Scientific Knowledge
24(3)
2 From the Algebra of Logic and Projective Geometry to Categorial and Dialectical Geometrical Logic
27(2)
2.1 Categorial Logic of Geometry
29(3)
2.2 Generalisations of Categorial Logic of Geometry
32(2)
3 Structural and Ontological Model of whole-being
34(2)
3.1 Universalism of the Structures of Geometrical Logic
36(2)
3.2 Geometrical Ontology as a Generalization of Geometrical Logic
38(5)
3.3 Logical and Ontological Reality
43(4)
Part Two Geometrical Logic. The Structures of Thought and Space
47(92)
Preface
47(1)
Introduction: The Idea of Geometrical Logic
47(4)
Chapter I Geometrization of the Axioms of Algebraic Logic
51(10)
Chapter II Geometrization of the Theorems of Algebraic Logic
61(12)
Chapter III The Logical Plane and Space, and their Elements
73(16)
Chapter IV The Elements of the Categorial Plane and Complete Dual Squares
89(3)
Chapter V Sets of Four and Six Elements of the Categorial Plane
92(5)
Chapter VI Harmonic Elements in Geometrical Logic
97(10)
Chapter VII The Dichotomical and Tetrachotomical Harmonic Division of Concepts in Geometrical Logic
107(7)
Chapter VIII Specification of Mathematical Pan-Logic
114(6)
Chapter IX Spatial Forms of Specifications of Pan-Logic
120(9)
Appendix: The Logic of Dichotomy and the Three Pythagorean Means
129(10)
Part Three Comments and Remarks on Geometrical Logic
139(38)
1 Algebraic Symbolism
139(3)
2 Categorial, Geometrical Logic and Whitehead's Universal Algebra
142(5)
3 Selection of Axioms for Categorial-Algebraic Logic
147(4)
4 Interpretation of Algebraic Logic
151(4)
5 Algebraism of the Categorial and Projective Plane
155(5)
6 Topological Space of Topologic
160(3)
7 Idea of Mathematical Categorial Theory in Categorial and Algebraic Logic
163(14)
7.1 Definition of a Category
163(1)
7.2 Finite Categories in Bornstein's Geometrical Logic
164(1)
7.2.1 The First Possible Application of the Category Theory into the Geometrical Logic
164(8)
7.2.2 The Second Possible Application of the Category Theory into the Geometrical Logic
172(5)
Conclusion 177(4)
Summary 181(14)
Bibliography 195(20)
Index 215
Krzysztof leziski is a professor of philosophy at the University of Silesia in Katowice, Poland. His research and teaching interests focus on philosophy of nature, philosophy of science, ontology, philosophy of education and the history of philosophy in Poland.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
Permanent link: https://www.kriso.lv/db/97836317775416e.html