Introduction To Logic And Theory Of Knowledge

Claire Ortiz Hill The publication of all but a small, unfound, part of the complete text of the lecture course on logic and theory of knowledge that Edmund Husserl gave at Göttingen during the winter semester of 1906/07 became a reality in 1984 with the publication of Einleitung in die Logik und Erkenntnistheorie, Vorlesungen 1906/07 edited by 1 Ullrich Melle. Published in that volume were also 27 appendices containing material selected to complement the content of the main text in significant ways. They provide valuable insight into the evolution of Husserl’s thought between the Logical Investigations and Ideas I and, therefore, into the origins of phenomenology. That text and all those appendices but one are translated and published in the present volume. Omitted are only the “Personal Notes” dated September 25, 1906, November 4, 1907, and March 6, 1908, which were translated by Dallas Willard and published in his translation of Husserl’s Early 2 Writings in the Philosophy of Logic and Mathematics. Introduction to Logic and Theory of Knowledge, Lectures 1906/07 provides valuable insight into the development of the ideas fun- mental to phenomenology. Besides shedding considerable light on the genesis of phenomenology, it sheds needed light on many other dimensions of Husserl’s thought that have puzzled and challenged scholars.

An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.

This book reclaims logic as a branch of philosophy, offering a self-contained and complete introduction to the three traditional systems of classical logic (term, sentence, and predicate logic) and the philosophical issues that surround those systems. The exposition is lucid, clear, and engaging. Practical methods are favored over the traditional, and creative approaches over the merely mechanical. The author’s guiding principle is to introduce classical logic in an intellectually honest way, and not to shy away from difficulties and controversies where they arise. Relevant philosophical issues, such as the relation between the meaning and the referent of a proper name, logical versus metaphysical possibility, and the conceptual content of an expression, are discussed throughout. In this way, the book is not only an introduction to the three main systems of classical logic, but also an introduction to the philosophy of classical logic.

Part of a trilogy exploring the theory of knowledge by one of the world's foremost philosophers.

An enlightening introduction to the study of logic: its history, philosophical foundations, and formal structures Logic: Inquiry, Argument, and Order is the first book of its kind to frame the study of introductory logic in terms of problems connected to wider issues of knowledge and judgment that arise in the context of racial, cultural, and religious diversity. With its accessible style and integration of philosophical inquiry and real-life concerns, this book offers a novel approach to the theory of logic and its relevance to questions of meaning and value that arise in the world around us. The book poses four problems for logic: Is logic separate from experience? Does logic require dualisms? Can logic reconcile opposed ways of understanding the world? And when things are divided, does the boundary have a logic? The author begins the exploration of these questions with a discussion of the process of analyzing and constructing arguments. Using the logical theories of C. S. Peirce, John Dewey, and Josiah Royce to frame the investigation, subsequent chapters outline the process of inquiry, the concept of communicative action, the nature of validity, categorical reasoning through the theory of the syllogism, and inductive reasoning and probability. The book concludes with a presentation of modal logic, propositional logic, and quantification. Logic is presented as emerging from the activities of inquiry and communication, allowing readers to understand even the most difficult aspects of formal logic as straightforward developments of the process of anticipating and taking action. Numerous practice problems use arguments related to issues of diversity and social theory, and the book introduces methods of proving validity that include Venn diagrams, natural deduction, and the method of tableaux. Logic: Inquiry, Argument, and Order is an ideal book for courses on philosophical methods and critical reasoning at the upper-undergraduate and graduate levels. It is also an insightful reference for anyone who would like to explore a cross-cultural approach to the topic of logic.

Phenomenology and existentialism transformed understanding and experience of the Twentieth Century to their core. They had strikingly different inspirations and yet the two waves of thought became merged as both movements flourished. The present collection of research devoted to these movements and their unfolding interaction is now especially revealing. The studies in this first volume to be followed by two succeeding ones, range from the predecessors of existentialism – Kierkegaard/Jean Wahl, Nietzsche, to the work of its adherents – Shestov, Berdyaev, Unamuno, Blondel, Blumenberg, Heidegger and Mamardashvili, Dufrenne and Merleau-Ponty to existentialism’s congruence with Christianity or with atheism. Among the leading Husserlian insights are treated essence and experience, the place of questioning, ethics and intentionality, temporality and passivity and the life world. The following book will uncover the perennial concerns guiding the wondrous interplay of these two inspirational sources.