Bernard Bolzano: Theory of Science

VOLUME I: Theory of Fundamentals and Theory of Elements (Part I); INTRODUCTION; BOOK ONE: THEORY OF FUNDAMENTALS; PART I: Of the Existence of Truths in Themselves; PART II: Of the Recognizability of Truth; BOOK TWO: THEORY OF ELEMENTS; PART I: Of Ideas in Themselves; VOLUME TWO: Theory of Elements (Part II); BOOK TWO: THEORY OF ELEMENTS (continued); PART II: Of Propositions in Themselves; PART III: Of True Propositions; PART IV: Of Inferences; VOLUME THREE: Theory of Knowledge and The Art of Discovery; BOOK THREE: THEORY OF KNOWLEDGE; PART I: Of Ideas; PART II: Of Judgements; PART III: Of the Relation between our Judgements and Truth; PART IV: Of Certainty, Probability, and Confidence in Judgements; BOOK FOUR: THE ART OF DISCOVERY; PART I: General Rules; PART II: Particular Rules; VOLUME FOUR: Theory of Science Proper; BOOK FIVE: THEORY OF SCIENCE PROPER; PART I: General Rules; PART II: On the Determination of the Extensions of the Sciences; PART III: On the Choice of a Class of Readers for a Treatise; PART IV: On the Propositions which Should Appear in a Treatise; PART V: On the Divisions of a Treatise; PART VI: On the Order in which the Propositions Belonging to a Treatise Should Appear; PART VII: Theory of Signs or, On the Signs Used in or Recommended by a Treatise; PART VIII: How the Author of a Treatise Should Behave; PART IX: On Scientific Books that are not Genuine Treatises

Bernard Bolzano (1781-1848) made outstanding contributions to many areas of philosophy as well as to mathematics and theology. In mathematics, he is best known for his work in analysis and the foundations of mathematics, which included rigorous definitions of continuity and convergence as well as the construction of a continuous, nowhere-differentiable function and anticipations of Cantor's set theory. His work in logic, presented in the Theory of Science, marks a new beginning in the history of the discipline. Among his discoveries, the most noted are his definition of deducibility, which anticipates Tarski's definition of logical consequence, and his notion of logical analyticity, which closely resembles later concepts of logical truth. On account of these and many other accomplishments, Bolzano is now widely recognised as one of the great philosophers of the nineteenth century.; Rolf George is Professor emeritus of Philosophy at the University of Waterloo, Canada.; Paul Rusnock