The volume contains twenty essays devoted to the philosophy of mathematics and the history of logic. They have been divided into four parts: general philosophical problems of mathematics, Hilbert's program vs. the incompleteness phenomenon, philosophy of mathematics in Poland, mathematical logic in Poland. Among considered problems are: epistemology of mathematics, the meaning of the axiomatic method, existence of mathematical objects, distinction between proof and truth, undefinability of truth, Goedel's theorems and computer science, philosophy of mathematics in Polish mathematical and logical (...) schools, beginnings of mathematical logic in Poland, contribution of Polish logicians to recursion theory. (shrink)

The paper is devoted to the presentation of Chwistek’s philosophical ideas concerning logic and mathematics. The main feature of his philosophy was nominalism, which found full expression in his philosophy of mathematics. He claimed that the object of the deductive sciences, hence in particular of mathematics, is the expression being constructed in them according to accepted rules of construction. He treated geometry, arithmetic, mathematical analysis and other mathematical theories as experimental disciplines, and obtained in this way a nominalistic interpretation of (...) them. The fate of Chwistek’s philosophical conceptions was similar to the fate of his logical conceptions. The system of rational meta-mathematics was not developed by him in detail. He worked on his own ideas without any collaboration with other logicians, mathematicians or philosophers. His investigations were not in the mainstream of the development of logic and philosophy of mathematics. (shrink)

Never one to back away from controversy, Friedrich Nietzsche assails the Christian church in Twilight of the Idols. In this classic work, he sets out to substitute the morality of the Catholic and Protestant churches with that of Dionysian morality. Twilight of the Idols furthermore lays the foundation for key arguments that Nietzsche more fully develops in later writings.

The paper is devoted to the discussion of some philosophical and historical problems connected with the theorem on the undefinability of the notion of truth. In particular the problem of the priority of proving this theorem will be considered. It is claimed that Tarski obtained this theorem independently though he made clear his indebtedness to Gödel’s methods. On the other hand, Gödel was aware of the formal undefinability of truth in 1931, but he did not publish this result. Reasons for (...) that are also considered. (shrink)

The book is a collection of the author’s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the (...) history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered.This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields. (shrink)

In the paper some applications of Gödel's incompleteness theorems to discussions of problems of computer science are presented. In particular the problem of relations between the mind and machine (arguments by J.J.C. Smart and J.R. Lucas) is discussed. Next Gödel's opinion on this issue is studied. Finally some interpretations of Gödel's incompleteness theorems from the point of view of the information theory are presented.

Nietzsche called The Gay Science "the most personal of all my books." It was here that he first proclaimed the death of God -- to which a large part of the book is devoted -- and his doctrine of the eternal recurrence. Walter Kaufmann's commentary, with its many quotations from previously untranslated letters, brings to life Nietzsche as a human being and illuminates his philosophy. The book contains some of Nietzsche's most sustained discussions of art and morality, knowledge and truth, (...) the intellectual conscience and the origin of logic. Most of the book was written just before Thus Spoke Zarathustra, the last part five years later, after Beyond Good and Evil. We encounter Zarathustra in these pages as well as many of Nietzsche's most interesting philosophical ideas and the largest collection of his own poetry that he himself ever published. Walter Kaufmann's English versions of Nietzsche represent one of the major translation enterprises of our time. He is the first philosopher to have translated Nietzsche's major works, and never before has a single translator given us so much of Nietzsche. (shrink)

A work of Nietzsche's later years, The Antichrist was written after Thus Spoke Zarathustra and shortly before the mental collapse that incapacitated him for the rest of his life. The work is both an unrestrained attack on Christianity and a further exposition of Nietzsche's will-to-power philosophy so dramatically presented in Zarathustra. Christianity, says Nietzsche, represents "everything weak, low, and botched; it has made an ideal out of antagonism towards all the self-preservative instincts of strong life." By contrast, Nietzsche defines good (...) as: "All that enhances the feeling of power, the Will to Power, and power itself in man. What is bad?-All that proceeds from weakness. What is happiness?-The feeling that power is increasing,-that resistance has been overcome." In attempting to redefine the basis of Western values by demolishing the formative influence of the Judeo-Christian tradition, The Antichrist has proved to be highly controversial and continuously stimulating to later generations of philosophers. (shrink)

The aim of this paper is to describe the history of logical investigations at the University of Poznań. The organisational structures within the discipline as well as the outstanding logicians and their achievements are presented. Connections with the Lviv–Warsaw School are indicated.

Zygmunt Ratajczyk was a deep and subtle mathematician who, with mastery, used sophisticated and technically complex methods, in particular combinatorial and proof-theoretic ones. Walking always along his own paths and being immune from actual trends and fashions he hesitated to publish his results, looking endlessly for their improvement.

Friedrich Nietzsche is one of the most influential thinkers of the past 150 years and On the Genealogy of Morality (1887) is his most important work on ethics and politics. A polemical contribution to moral and political theory, it offers a critique of moral values and traces the historical evolution of concepts such as guilt, conscience, responsibility, law and justice. This is a revised and updated edition of one of the most successful volumes to appear in Cambridge Texts in (...) the History of Political Thought. Keith Ansell-Pearson has modified his introduction to Nietzsche's classic text, and Carol Diethe has incorporated a number of changes to the translation itself, reflecting the considerable advances in our understanding of Nietzsche in the twelve years since this edition first appeared. In this new guise the Cambridge Texts edition of Nietzsche's Genealogy should continue to enjoy widespread adoption, at both undergraduate and graduate level. (shrink)

This volume is written jointly by Witold Marciszewski, who contributed the introductory and the three subsequent chapters, and Roman Murawski who is the author of the next ones - those concerned with the 19th century and the modern inquiries into formalization, algebraization and mechanization of reasonings. Besides the authors there are other persons, as well as institutions, to whom the book owes its coming into being. The study which resulted in this volume was carried out in the Historical Section (...) of the research project _Logical Systems and Algorithms for Automatic Testing of Reasoning,_ 1986-1990, in which participated nine Polish universities; the project was coordinated by the Department of Logic, Methodology and Philosophy of Science of the Bia??l??ystok Branch of the University of Warsaw, and supported by the Ministry of Education 1987). The major part of the project was focussed on the software for computer-aided theorem proving called Mizar MSE ) due to Dr. Andrzej Trybulec. He and other colleagues deserve a grateful mention for a hands-on experience and theoretical stimulants owed to their collaboration. (shrink)

On the future of our educational institutions -- Lecture I (January 16, 1872) -- Lecture II (February 6, 1872) -- Lecture III (February 27, 1872) -- Lecture IV (March 5, 1872) -- Lecture V (March 23, 1872).

Claims that agents must accept or reject certain propositions “on pain of self-contradiction” play a key role in Alan Gewirth’s dialectically necessary method. The aim of this paper is to investigate Gewirth’s method with respect to the relation between such claims, entailment and self-contradiction. I will identify certain bridge principles connecting obligatory acceptance, rejection and entailment that seem to be presupposed by Gewirth. Contrary to what seems to be Gewirth’s view, these principles, e. g., that one must accept simple and (...) direct consequences of propositions that one must accept, do not follow from minimal rationality demands with respect to the avoidance of self-contradiction. Moreover, the bridge principles themselves appear to be rather problematic. Still, plausible dialogical versions of them can be developed. This dialogical treatment is not confined to the transfer of obligatory acceptance and rejection via entailment, but can be extended to primary acceptance with respect to the starting premises. It might seem questionable whether such a dialogical strategy is acceptable to a strict Gewirthian, since agents would have to accept certain propositions not “on pain of self-contradiction,” but on pain of violating dialogical principles which would have to be justified independently. However, even Gewirth’s demands with respect to the avoidance of self-contradiction go beyond what the rules of logic require. It seems that the dialectically necessary method cannot proceed without acknowledging a normative sphere of discursive practices. (shrink)

Divided into three essays, this title offers an investigation into the origins of our moral values, or as the author calls them 'moral prejudices'. It addresses the concept of guilt and its role in the development of civilization and religion. It also considers suffering and its role in human existence.

"God is dead. God remains dead. And we have killed him." This is the book in which Nietzsche put forth his boldest declaration. It is also his most personal. Essential reading for students of philosophy, history, and literature, it features some of Nietzsche's most important discussions of art, morality, knowledge, and, ultimately, truth.

This abridged and revised edition of the original book (Springer-Verlag Vienna, 2001) offers the only comprehensive history and documentation of the Vienna Circle based on new sources with an innovative historiographical approach to the study of science. With reference to previously unpublished archival material and more recent literature, it refutes a number of widespread clichés about "neo-positivism" or "logical positivism". Following some insights on the relation between the history of science and the philosophy of science, the book offers an accessible (...) introduction to the complex subject of "the rise of scientific philosophy" in its socio-cultural background and European philosophical networks till the forced migration in the Anglo-Saxon world. The first part of the book focuses on the origins of Logical Empiricism before World War I and the development of the Vienna Circle in "Red Vienna" (with the "Verein Ernst Mach"), its fate during Austro-Fascism (Schlick's murder 1936) and its final expulsion by National-Socialism beginning with the "Anschluss" in 1938. It analyses the dynamics of the Schlick-Circle in the intellectual context of "late enlightenment" including the minutes of the meetings from 1930 on for the first time published and presents an extensive description of the meetings and international Unity of Science conferences between 1929 and 1941. The chapters introduce the leading philosophers of the Schlick Circle (e.g., Hans Hahn, Otto Neurath, Rudolf Carnap, Philipp Frank, Felix Kaufmann, Edgar Zilsel) and describe the conflicting interaction between Moritz Schlick and Otto Neurath, the long term communication between Moritz Schlick, Friedrich Waismann and Ludwig Wittgenstein, as well as between the Vienna Circle with Heinrich Gomperz and Karl Popper. In addition, Karl Menger's "Mathematical Colloquium" with Kurt Gödel is presented as a parallel movement. The final chapter of this section describes the demise of the Vienna Circle and the forced exodus of scientists and intellectuals from Austria.The second part of the book includes a bio-bibliographical documentation of the Vienna Circle members and for the first time of the assassination of Moritz Schlick in 1936, followed by an appendix comprising an extensive list of sources and literature. (shrink)

In The Birth of Tragedy Nietzsche expounds on the origins of Greek tragedy and its relevance to the German culture of its time. He declares it to be the expression of a culture which has achieved a delicate but powerful balance between Dionysian insight into the chaos and suffering which underlies all existence and the discipline and clarity of rational Apollonian form. In order to promote a return to these values, Nietzsche critiques the complacent rationalism of late nineteenth-century German culture (...) and makes an impassioned plea for the regenerative potential of the music of Wagner. A wide ranging discussion of the nature of art, science, and religion, The Birth of Tragedy's argument raises important questions about the problematic nature of cultural origins which are still valid today. (shrink)

One hundred years after his death, Friedrich Nietzsche remains the most influential philosopher of the modern era. Basic Writings of Nietzsche gathers the complete texts of five of Nietzsche's most important works, from his first book to his last: The Birth of Tragedy; Beyond Good and Evil; On the Genealogy of Morals; The Case of Wagner; and Ecce Homo. Edited and translated by the great Nietzsche scholar Walter Kaufmann, this volume provides a definitive guide to the full range of (...) Nietzsche's thought. Included also are seventy-five aphorisms, selections from Nietzsche's correspondence, and variants from drafts for Ecce Homo. (shrink)

1. Stück. David Strauss, der Bekenner und der Schriftsteller -- 2. Stück. Vom Nutzen und Nachteil der Historie für das Leben -- 3. Stück. Schopenhauer als Erzieher -- 4. Stück. Richard Wagner in Bayreuth.

Beyond Good and Evil is one of the most scathing and powerful critiques of philosophy, religion, science, politics and ethics ever written. In it, Nietzsche presents a set of problems, criticisms and philosophical challenges that continue both to inspire and to trouble contemporary thought. In addition, he offers his most subtle, detailed and sophisticated account of the virtues, ideas, and practices which will characterize philosophy and philosophers of the future. With his relentlessly energetic style and tirelessly probing manner, Nietzsche embodies (...) the type of thought he wants to foster, while defining its historical role and determining its agenda. This edition offers a new and readable translation, by Judith Norman, of one of the most influential texts in the history of philosophy, together with an introduction by Rolf-Peter Horstmann that sets it in its historical and philosophical context. (shrink)

Throughout his career, Friedrich Wilhelm Nietzsche explored the concept of the will to power, interpreting it variously as a psychological, biological, and metaphysical principle. This posthumously produced volume, drawn from his unpublished notebooks, collects the nineteenth-century philosopher's thoughts on the force that drives humans toward achievement, dominance, and creative activity. Misunderstandings of Nietzsche's previous works compelled the author to attempt to express his doctrines in a more unequivocal form. These writings elucidate the principle that he held to be the (...) essential factor of all existence — the drive and energy to develop independently according to one's nature, rather than being dominated by outside forces. A work that both illuminates and extends our understanding of Nietzsche's earlier books, this volume offers reflections on art, morality, Christianity, nihilism, and other topics that provide absorbing glimpses into the mind of one of philosophy's great thinkers. (shrink)

“Supposing that truth is a women-what then?” This is the very first sentence in Nietzsche’s Beyond Good and Evil . Not very often are philosophers so disarmingly explicit in their intention to discomfort the reader. In fact, one might say that the natural state of Nietzsche’s reader is one of perplexity. Yet it is in the process of overcoming the perplexity that one realizes how rewarding to have one’s ideas challenged. In Beyond Good and Evil, Nietzsche critiques the mediocre in (...) modernity and challenges the reader to accept their state of becoming and accept improvisation and creativity of the process. Nietzsche’s book is carefully designed to disorient the reader, to systematically provoke and tease her to the point of stealing away her certainties. It is challenging yet rewarding to overcome the perplexities of Nietzsche’s teachings. (shrink)

Sich in diesem Irrgarten zu orientieren, ist das Ziel dieses Buches. Dabei geht es vornehmlich um vier Fragestellungen, zwei philosophische und zwei theologische: 1.

Published posthumously in 1908, Ecce Homo was written in 1888 and completed just a few weeks before Nietzsche's complete mental collapse.

Nietzsche regarded 'Thus Spoke Zarathustra' as his most important work, and his story of the wandering Zarathustra has had enormous influence on subsequent culture. Nietzsche uses a mixture of homilies, parables, epigrams and dreams to introduce some of his most striking doctrines, including the Overman, nihilism, and the eternal return of the same. This edition offers a new translation by Adrian Del Caro which restores the original versification of Nietzsche's text and captures its poetic brilliance. Robert Pippin's introduction discusses many (...) of the most important interpretative issues raised by the work, including who is Zarathustra and what kind of 'hero' is he and what is the philosophical significance of the work's literary form? The volume will appeal to all readers interested in one of the most original and inventive works of modern philosophy. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

”It is often assumed that knowledge claims must be justified. But what kind of justification is required for knowledge ? . . . ” (*) -/- presupposition: the kind of epistemic justification depends on the type of the knowledge claim and its respective knowledge claim tradeoff ’vague vs. precise’. -/- procedere: in two - almost purely logical - case studies I account for this tradeoff and question in each case what (if any) were its general outcome wrt justification -/- first (...) for basic measurement statements of the form ′′ϕ(x) = r ∈ IR ± δ′′ (wrt ”measurement accuracy realism” debate) -/- and secondly predication statements of the form ′′x is ( a case of )P′′ (wrt ”epistemic vagueness” debate). (shrink)

The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophical reflection. We try to answer those questions by analyzing (...) both works of Polish logicians and mathematicians who have a philosophical temperament as well as their research practice. Works and philosophical views of the following Polish scientists will be analyzed: Wacław Sierpiński, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stefan Banach Hugo Steinhaus, Eustachy Żylińsk and Leon Chwistek, Jan Łukasiewicz, Zygmunt Zawirski, Stanisław Leśniewski, Tadeusz Kotarbiński, Kazimierz Ajdukiewicz, Alfred Tarski, Andrzej Mostowski and Henryk Mehlberg, Jan Sleszyński, Stanisław Zaremba and Witold Wilkosz. To indicate the background of scientists being active in the 1920s and 1930s we consider in Chapter 1 some predecessors, in particular: Jan Śniadecki, Józef Maria Hoene-Wroński, Samuel Dickstein and Edward Stamm. (shrink)

The stark theological polarities of damnation and salvation have haunted representations of guilt in Western culture for thousands of years. Friedrich Ohly's classic study The Damned and the Elect, first published in English in 1992, offers a comparative cultural history of figures such as Oedipus, Judas and Faust, from antiquity, through the Middle Ages, into modern times. Looking at the works of writers such as Sophocles, Dante, Marlowe, Bunyan, Goethe, and Thomas Mann (and illustrating his ideas with reference to (...) representation in the visual arts), Ohly's wide-ranging arguments weave deftly across different cultures and periods to illuminate one of the most salient themes in Western literature. (shrink)

A central aim of cognitive science is to understand the fundamental mechanisms that enable humans to navigate and make sense of complex environments. In this letter, we argue that computational complexity theory, a foundational framework for evaluating computational resource requirements, holds significant potential in addressing this challenge. As humans possess limited cognitive resources for processing vast amounts of information, understanding how humans perform complex cognitive tasks requires comprehending the underlying factors that drive information processing demands. Computational complexity theory provides a (...) comprehensive theoretical framework to achieve this goal. By adopting this framework, we can gain new insights into how cognitive systems work and develop a more nuanced understanding of the relation between task complexity and human behavior. We provide empirical evidence supporting our argument and identify several open research questions and challenges in applying computational complexity theory to human decision‐making and cognitive science at large. (shrink)

This collection of more than two hundred of Nietzsche's letters offers a representative body of correspondence on subjects of main concern to him--philosophy, history, morals, music and literature. Also included are letters of biographical interest which, in Middleton's words, mark the stresses and turnings of his life. Among the addressees are Richard Wagner, Erwin Rohde, Jacob Burkhardt, Lou Salome, his mother, and his sister Elisabeth. The annihilating split in Nietzsche's personality that has been associated with his collapse on a street (...) in Turin in 1889 is described in a moving letter from Franz Overbeck which forms the Epilogue. Index. (shrink)