Covering the evolution of mathematics since the ancient times, this work observes the changes that have taken place in the conception of rational theory. It places emphasis on the philosophic and logical systems, from Aristotle onward, that provide the basis for the fusion of mathematics and logic in contemporary thought.
Covering the evolution of mathematics since the ancient times, this work observes the changes that have taken place in the conception of rational theory. It places emphasis on the philosophic and logical systems, from Aristotle onward, that provide the basis for the fusion of mathematics and logic in contemporary thought.
I. The Meaning, Purpose and Methods History of Mathematics and of Logic II. Pre-Hellenic Mathematics III. Greek Mathematics before Euclid IV. The Logic of Aristotle V. Euclid's Elements in Hellenistic culture VI. Infinitesimal Methods in Classical Archimedes of the page Times: VII. Introduction to Higher Geometry: Apollonius and His Followers VIII. Mathematics in the Roman World IX. The Decline of Ancient Science X. Mathematics and Logic in the Middle Ages XI. The Mathematical Renaissance and the Algebraists XII. Origins of Analytical Geometry and Cartesian Rationalism: Vico's Gnoseology XIII. Modern Infinitesimal Analysis and the Philosophical Thought of its Constructors XIV. From the Origins of Projective Geometry to the Development of the Erlanger Programme XV. Criticism of Euclid's Postulate V: Non-Euclidean Geometries XVI. Combinatorial Analysis and Calculus of Probability XVII. Sets, Functions, Curves, Non-Archimedeau Geometries XVIII. Symbolic Logic and the Fundamentals of Arithmetic XIX. Hypothetical-Deductive Systems, Non-Contradictoriness, Antinomies XX. Problems of Contemporary Logic
I. The Meaning, Purpose and Methods History of Mathematics and of Logic II. Pre-Hellenic Mathematics III. Greek Mathematics before Euclid IV. The Logic of Aristotle V. Euclid's Elements in Hellenistic culture VI. Infinitesimal Methods in Classical Archimedes of the page Times: VII. Introduction to Higher Geometry: Apollonius and His Followers VIII. Mathematics in the Roman World IX. The Decline of Ancient Science X. Mathematics and Logic in the Middle Ages XI. The Mathematical Renaissance and the Algebraists XII. Origins of Analytical Geometry and Cartesian Rationalism: Vico's Gnoseology XIII. Modern Infinitesimal Analysis and the Philosophical Thought of its Constructors XIV. From the Origins of Projective Geometry to the Development of the Erlanger Programme XV. Criticism of Euclid's Postulate V: Non-Euclidean Geometries XVI. Combinatorial Analysis and Calculus of Probability XVII. Sets, Functions, Curves, Non-Archimedeau Geometries XVIII. Symbolic Logic and the Fundamentals of Arithmetic XIX. Hypothetical-Deductive Systems, Non-Contradictoriness, Antinomies XX. Problems of Contemporary Logic
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