This new translation of the first volume of Hegel's Lectures on the History of Philosophy includes material not available to Haldane and Simson when they made their translation nearly 100 years ago. Indispensable for the student of Hegel, it can also serve as an introduction to Hegel's conception of philosophy for the general reader.

This new translation of the first volume of Hegel's Lectures on the History of Philosophy is a welcome and valuable addition to the new translations of Hegel's works, and now appears in paperback for the first time. Hegel's History of Philosophy has been described as perhaps one of his greatest achievements, and also as the first systematic history of philosophy since Aristotle. The translation included material from lecture notes taken by Hegel's pupils in 1923-4, (...) 1925-6, and 1927-8. This material was not available to Haldane and Simson when they made their translation nearly 100 years ago. The present volume, which supersedes that earlier one, besides being indispensable for the professional student, will also introduce those unfamiliar with Hegel to his conception of philosophy. (shrink)

This new translation of the first volume of Hegel's Lectures on the History of Philosophy is a welcome and valuable addition to the new translations of Hegel's works, and now appears in paperback for the first time. Hegel's History of Philosophy has been described as perhaps one of his greatest achievements, and also as the first systematic history of philosophy since Aristotle. The translation included material from lecture notes taken by Hegel's pupils in 1923-4, (...) 1925-6, and 1927-8. This material was not available to Haldane and Simson when they made their translation nearly 100 years ago. The present volume, which supersedes that earlier one, besides being indispensable for the professional student, will also introduce those unfamiliar with Hegel to his conception of philosophy. (shrink)

The chapter draws a very rough (and rather idiosyncratic) map of the terrain of the contemporary scene in the philosophy of language, as it was set out in the work of Frege, Russell and the early Wittgenstein – the presupposed common background, taught to beginners in the discipline, for the themes to be further explored from a present-day perspective in the rest of the book. The chapter outlines some core issues as they are presented in the insightful systematic articulation (...) of Frege’s and Russell’s themes in Wittgenstein’s Tractatus Logico-Philosophicus. Then it sums up the main issues, describes some contributions to them in Frege, Russell, Wittgenstein and other historical landmarks, and indicates how they are approached today, as presented in the book's chapters. The introduction concludes with a brief discussion of research methods and problems in the field. (shrink)

This edition offers for the first time an English translation of what Hegel actually said in his landmark Lectures on the History of Philosophy. Volume I contains Hegel's discussion of the history of Chinese and Indian philosophy, and it also sets out the significant changes that Hegel made to his stage-setting introduction to the lectures.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Cambridge History of Philosophy in Late AntiquityJohn RistLloyd P. Gerson, editor. The Cambridge History of Philosophy in Late Antiquity. 2 vols. Cambridge-New York: Cambridge University Press, 2010. Pp. 1313. Cloth, $240.00.1313 pages, including 915 pages of text and 200 of bibliography; 51 authors—in about 800 words! The editor of the present Cambridge History makes plain that his new two-volume monument is the (...) successor to Armstrong’s Cambridge History of Late Greek and Early Medieval Philosophy—8 contributors—and is intended to build on its strengths and correct its deficiencies in the light of some 40 years of highly successful investigation of the thought of late antiquity. The result is a professional structure in which the “giants” (Plotinus and Augustine) are awarded comparatively modest coverage, while figures often neglected, such as Damascius, of whom our understanding has greatly increased of late, are given much more space. Damascius secures 30 pages: the only individual to get more is Porphyry (33), while Augustine has 29 and Plotinus 24 (four more than Hierocles). There are those (as Tacitus might have put it) who will fear that the wood has been lost for the trees, and at least it must be said that one overall impression of these volumes is that some of their authors are recounting what will be of interest to a worldwide group of aficionados whose number can be counted on the fingers of a mutilated hand—and the importance of which lies less in philosophical achievement than in the handing on of a great tradition.Gilbert Ryle is supposed to have asserted that in France everyone can talk about philosophy but that there are no philosophers; some of Gerson’s more philosophically minded readers may find their prejudices confirmed that in late antiquity there were many who talked about Plato and Aristotle but few who understood what they were trying to do. For it is clear that a general theme of the present volumes is that in late antiquity philosophers were largely concerned to “interpret” Plato and (especially after Porphyry) Aristotle while occasionally seizing the opportunity not merely to rubbish their similarly-engaged predecessors but to add (if shamefacedly) something of their own. Except, that is, for the Christians, whose enterprise was very different and who, quite properly, are more visible in Gerson’s account of late antique thought than in that of Armstrong (though there remain strange omissions in a work on this scale: Methodius, Ambrose, Evagrius).Gerson has tried to contextualize his story by including short (and helpful) historical introductions by Elizabeth DePalma Digeser to the various epochs with which his volumes are concerned, and which can perhaps be divided into four sections: pre-Plotinian Platonism [End Page 136] (plus extras) from Cicero to Numenius; later pagan Platonism, including extensive treatment of the Neoplatonic commentators on Aristotle; Christian thought before Constantine; and later Christian philosophy-cum-theology. Rounding off the volume are introductions to the transition from “ancient” to “medieval” thought in the Latin West (Gersh), in Byzantium—a remarkably honest presentation of a largely stagnant philosophical world by Ierodiakonou and Zografidis—and (in a magisterial improvement on what is to be found in Armstrong) in Islam (Cristina d’Ancona) where (inter multa alia) the roots of the virtually inevitable later destruction of a flourishing philosophical tradition founded by al-Kindi and al-Farabi are identified in the more “orthodox” and theocratic approach—here there are Byzantine parallels—of the followers of al-Ash’ari (885).Gerson’s readers can inspect philosophical wisdom and conceptual muddle among late antique intellectuals—Christians, a few Muslims, pagans—down to Scotus Eriugena and al-Farabi. But some of them may suspect that an opportunity has been lost to reflect on the origins and nature of early Christian thought, and to ask why Christians soon jumped for Platonism rather than Stoicism (Aristotle, let alone Epicurus, was not—yet—considered a serious option)—and that is not intended as criticism of the excellent, if brief, treatment of important Christian thinkers such as Origen. But it was an adventure for Christians to begin to philosophize, and when they embarked on this adventure—here the significance... (shrink)

This new edition of Hegel's Lectures on the History of Philosophy sets forth clearly, for the first time for the English reader, what Hegel actually said. These lectures challenged the antiquarianism of Hegel's contemporaries by boldly contending that the history of philosophy is itself philosophy, not just history. It portrays the journey of reason or spirit through time, as reason or spirit comes in stages to its full development and self-conscious existence, through the successive (...) products of human intellect and activity. These lectures proved to be extremely influential on the intellectual history of the past two centuries. They are crucial to understanding Hegel's own systematic philosophy in its constructive aspect, as well as his views on the centrality of reason in human history and culture. Volume I holds additional importance because, as well as setting out Hegel's discussion of the history of Chinese and Indian philosophy, it presents the interesting and significant changes that Hegel made to the stage-setting introduction to these lectures across the years from 1819 to 1831. This edition adapts the considerable editorial resources of the German edition that it translates, to the needs of the general reader as well as the serious scholar, so as to constitute an unparalleled resource on this topic in the English language. (shrink)

INTRODUCTION. 1. THE THEATRE. 1. In olden time the Arabian desert was, as it is at this da)7, the roaming-ground of independent Bedouin tribes. ...

The ancient problem of the relationship of the continuous to the discrete, since its discovery by the Greeks, has posed a range of immensely fruitful challenges to both philosophical and mathematical thought, leading to a variety of mathematical and conceptual innovations whose positive development actively continues today. In this brief section introduction, I selectively outline some significant moments at which this problem has provided important historical occasions for concrete mathematical innovation as well as closely linked philosophical insights, before introducing the (...) particular contributions of the section authors to historical and contemporary research and practice into the nature and structure of the continuum, the construction of real numbers, the foundations of analysis, and the logical, set-theoretical, and computational underpinnings of the structure of continuously valued numbers in the most general sense, in both constructive and nonconstructivist contexts. (shrink)

This new edition of Hegel's Lectures on the History of Philosophy sets forth clearly, for the first time for the English reader, what Hegel actually said. These lectures challenged the antiquarianism of Hegel's contemporaries by boldly contending that the history of philosophy is itself philosophy, not just history. It portrays the journey of reason or spirit through time, as reason or spirit comes in stages to its full development and self-conscious existence, through the successive (...) products of human intellect and activity. These lectures proved to be extremely influential on the intellectual history of the past two centuries. They are crucial to understanding Hegel's own systematic philosophy in its constructive aspect, as well as his views on the centrality of reason in human history and culture. Volume I holds additional importance because, as well as setting out Hegel's discussion of the history of Chinese and Indian philosophy, it presents the interesting and significant changes that Hegel made to the stage-setting introduction to these lectures across the years from 1819 to 1831. This edition adapts the considerable editorial resources of the German edition that it translates, to the needs of the general reader as well as the serious scholar, so as to constitute an unparalleled resource on this topic in the English language. (shrink)

HEGEL EXPLICATES HIS THEORY of the history of philosophic thinking in several introductions to the various cycles of Lectures on the History of Philosophy held in Jena, Heidelberg, and Berlin. Only the introductions to the first cycle of Heidelberg lectures and to the second cycle of Berlin lectures survive in Hegel's own hand. Since the earlier of these is an integral part of the latter, an analysis of the 1820 Introduction provides a reliable account of Hegel's theory.

A. Kenny, Frege, an introduction to the founder of modern analytic philosophy. London:Penguin, 1995. viii-h223pp. £7.99 T. Willamson, Vagueness. London:Routledge, 1994. xiii-f-325 pp. £35.00 TOM BU...

European philosophy from the late seventeenth century through most of the eighteenth is broadly conceived as `the Enlightenment', the period of empirical reaction to the great seventeenth century Rationalists. This volume begins with Herbert of Cherbury and the Cambridge Platonists and with Newton and the early English Enlightenment. Locke is a key figure in late chapters, as a result of his importance both in the development of British and Irish philosophy and because of his seminal influence in the (...) Enlightenment as a whole. British Philosophy and the Age of Enlightenment includes discussion of Scottish Enlightenment and its influence on the German Aufklarung , and consequently on Kant. French thought, which in turn affected the late radical Enlightenment, especially Bentham, is also considered here. This survey brings together clear, authoritative chapters from leading experts and provides a scholarly introduction to this period in the history of philosophy. It includes a glossary of technical terms and a chronological table of important political, philosophical, scientific and other cultural events. (shrink)

Father Copleston’s now established series of textbooks on the history of philosophy divides progressively like a live cell. Vol. I expounded Greek philosophy, Vols. II and III examined Mediaeval and Renaissance philosophy and Vol. IV, which was originally intended to cover modern philosophy from the 17th to the 19th century, expands now into three monographs dealing respectively with classic Rationalism, British Empiricism and the continental Enlightenment of the 18th century up to Kant. Thus the present (...) volume, after a general Introduction which states the broad currents of thinking and makes the qualifications appropriate to offset their artificial discussion in three separate books, concentrates upon the personal and capital philosophies of Descartes, Spinoza and Leibniz. (shrink)

This impeccable publication, the second of a four-volume History of Philosophy under the editorship of M Gilson, impressively inaugurates a series which should liberally endow undergraduate studies and the educated English-speaking public. More succinct and in some respects more decisive than Fr Copleston’s two-volume treatment, more developed than Hirschberger’s genial outline, more systematically philosophical than Dom Knowles’ biographico-historical survey, Dr Maurer’s exposition can stand comparison with Gilson’s own specialist History of Christian Philosophy in the Middle Ages (...) to which he modestly claims to offer an introduction, ‘and beyond all histories to the works of the medieval philosophers themselves’. He concentrates a masterful attention upon the key Christian thinkers from Augustine to Suarez, presenting a rich sweep of some twelve centuries from the patristic thought of the fourth century through the Scholastic era to the late Renaissance scholastics of the sixteenth century. This mature survey, emphasising sympathetic presentation rather than critical evaluation of each philosopher, is fitted succinctly and lucidly into less than 400 pages, reinforced by some 40 pages of select notes and followed by a scholarly bibliography and systematic index. The text is limpedly written, based squarely upon the original sources in the light of the best contemporary scholarship with a bias towards the well-known Gilson thesis, and pleasantly illuminated by the personal research judgment of the author. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:History of Philosophy and the Reflective Society by Riccardo PozzoRobert R. ClewisPOZZO, Riccardo. History of Philosophy and the Reflective Society. Berlin: Walter de Gruyter, 2021. vi + 231 pp. Cloth, $94.99In a forward-looking proposal, Pozzo lays out his vision for a multidisciplinary history of philosophy "from a global perspective." This book is "a long position paper, an extended essay dedicated to twenty-first (...) century policies of philosophical research from a global perspective." The chosen format is a Denkschrift, that is, a memorandum in the sense of a document that experts lay out for their government to ponder. Perhaps, Pozzo suggests, the history of philosophy could even have an impact on economic authorities and policymakers. Indeed, the work seems driven by the laudable aim of promoting access and equality around the world. The author reveals a just concern for migrants in particular, since they bring [End Page 156] with them their intellectual traditions and philosophical texts, which can be translated and thereby foster intercultural dialogue.The book consists of an introduction (chapter 1) followed by nine chapters. It has a thirty-page references list as well as subject and name indexes. In part one, Pozzo argues for the need for new narratives in the history of philosophy (chapter 2), in order to establish its role in addressing migration (chapter 3). The second part concerns reflective society (chapter 4). It considers societal readiness (chapter 5) and cultural innovation (chapter 6). Part three explores the paradigm shift from a close reading of texts to a "distant" reading of corpora (chapter 7), a shift Pozzo endorses. It examines implications for the translation of languages (chapter 8) and the translation of studies (knowledge) and competencies (chapter 9). Chapter 10 concludes by briefly reflecting on the notions of the "fluidity" of peoples and their ideas, biodiversity (and food), and spiritual humanism based on dignity.Scholars in the history of philosophy "should be open to the idea of a pluriversum of a history of facts and places, whereby history of philosophy finds its grounding in spatial heterogeneity." Nowadays, when people migrate and transfer competencies at increasing velocity, the "history of philosophy can be usefully reinvented on the basis of its consideration of intercultural dialogue." Pozzo considers the World Digital Library to be "one of the most exciting examples of corpora that talk to each other"—an idea he uses not merely metaphorically. By "corpora" is meant not just the sum of separate books, but XML-accessible complete collections of traditions of texts, with corresponding dictionaries, thesauri, and reference works, which make it possible to analyze a number of original texts as well as transliterations into other alphabets or hanzi characters. The result would be a "data-driven" history of philosophy.Given that history of philosophy is a product of culture, it is influenced by migrating peoples, who bring philosophical ideas and religious traditions with them. Research on migration thus ought to also consider translations of texts and competencies from one to another context, be it linguistic, economic, political, or cultural. The humanities, and a reflective society more generally, might provide a partial basis for intercultural dialogue. The history of philosophy might even thereby improve the quality of life of citizens.Pozzo rightly emphasizes that we need multilingual philosophers and historians of philosophy. History of philosophy ought to also be based on robust lexical and historical considerations, and historians of philosophy should be trained in a number of the world's languages as well as face the challenge of dealing with multilingualism and with validating translations. Pozzo's proposed methodology, informed by computational techniques, relies on tools such as vocabularies, ontologies, concordances, frequencies, or the analysis of texts and corpora, which integrates quantitative and formal methods into the portfolio of the methods of history of philosophy and intellectual history. Since Pozzo has published [End Page 157] widely on Kant, it is fitting that he explores Kant on migration as well as the editorial contexts and translation projects concerning the philosopher's writings.As for aesthetics, Pozzo notes that the history of philosophy can reflect on migrants' cultural and artistic creations. Historians of philosophy should thus start observing and interpreting phenomena created by... (shrink)

Father Copleston is nearing the end of what has become a monumental History of European Philosophy, whose single-handed composition and urbane scholarship rival any grand history of the nineteenth century. After Volumes III and IV, which dealt respectively with modern rationalism from Descartes to Leibniz and British empiricism from Hobbes to Hume, Volume VI expounded the French and German philosophies of the Enlightenment before analysing Kant in some 200 pages - possibly the most masterful and succinct introduction (...) to Kant in English. Volume VII now enters the author’s speciality, the study of post-Kantian German philosophy in the nineteenth century, including a chapter on the Socratic Dane, Kierkegaard and looking forward to contemporary Heidegger. The series, daunting enough to any one man’s industry, will be completed in two further volumes as the author modestly announces. (shrink)

From ancient conceptions of becoming a philosopher to modern discussions of psychedelic drugs, the concept of transformation plays a fascinating part in the history of philosophy. However, until now there has been no sustained exploration of the full extent of its role. Transformation and the History of Philosophy is an outstanding survey of the history, nature, and development of the idea of transformation, from the ancient period to the twentieth century. Comprising twenty-two specially commissioned chapters (...) by an international team of contributors, the volume is divided into four clear parts: -/- - Philosophy as Transformative: Ancient China, Greece, India, and Rome - Transformation Between the Human and the Divine: Medieval and Early Modern Philosophy - Transformation After the Copernican Revolution: Post-Kantian Philosophy - Treatises, Pregnancies, Psychedelics, and Epiphanies: Twentieth-Century Philosophy. -/- Each of these sections begins with an introduction by the editors. Transformation and the History of Philosophy is essential reading for students and researchers in the history of western and non-western philosophy, ethics, metaphysics, and aesthetics. It will also be extremely useful for those in related disciplines such as religion, sociology, and the history of ideas. (shrink)

This very short introduction will first outline how ontological investigations and questions of practice go together. The second section will bring in the next pole of this entire book, history of mathematics. How do ontology, practice, and history go together? Is this a forced marriage or one born in true love? That is, do these three belong together in some very basic way? One chapter in the section argues that the philosophy of mathematical practice intersects with the (...) history of mathematics essentially. If the first section of this introduction is persuasive that will also show that the history of mathematics intersects with ontological questions as well, specifically, that historical questions are very much about the ontological commitments of past mathematicians. The last section will take up what might seem a very different theme, namely, how these things matter to mathematics education. This section is connected closely to the second section since mathematics education has taken an interest in the role of history of mathematics in mathematics education, and much insight can be gained by seeing the issues in relation to the ontology-practice-history triad. The question of education is also important since teachers must consider what it is exactly that they are teaching, or, to adapt the title of Reuben Hersh’s well-known book, “What is mathematics really about?” And the “aboutness” of mathematics is really the ontological question. (shrink)

This is the editorial introduction to the special edition of Cosmos & History on the future of philosophy.

The thirteenth-century logician Lambert of Auxerre was well known for his Summa Lamberti, or simply Logica, written in the mid-1250s, which became an authoritative textbook on logic in the Western tradition. Our knowledge of medieval logic comes in great part from Lambert's Logica and three other texts: William of Sherwood's Introductiones in logicam, Peter of Spain's Tractatus, and Roger Bacon's Summulae dialectics. Of the four, Lambert's work is the best example of question-summas that proceed principally by asking and answering questions (...) on the subject matter. Thomas S. Maloney's translation of Logica, the only complete translation of this work in any language, is a milestone in the study of medieval logic. More than simply a translation, Maloney's project is a critical, comprehensive study of Lambert's logic situated in the context of his contemporaries and predecessors. As such, it offers a wealth of annotation and commentary. The lengthy introduction and extensive notes to the text explain the origin, theoretical context, and intricacies of the text and its doctrines. Maloney also addresses the disputed issues of authorship, date, and place of publication of the Summa Lamberti and makes available to the English-only audience the French, German, and Italian secondary sources--all translated--that are needed to enter the discussion. "Thomas S. Maloney fully commands the primary and secondary sources necessary to elucidate Lambert's Logica. An expert on Roger Bacon's philosophy, he demonstrates a rare proficiency in medieval Latin and scholastic logic. His references to sources from the ancient (Aristotle and Boethius) and medieval worlds are apposite, perspicuous, and useful. The volume's presentation with an appropriate introduction and commentary in the endnotes will no doubt establish it as an indispensable resource for scholars in the twenty-first century." --Alan Perreiah, University of Kentucky. (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)

Father Copleston’s now established series of textbooks on the history of philosophy divides progressively like a live cell. Vol. I expounded Greek philosophy, Vols. II and III examined Mediaeval and Renaissance philosophy and Vol. IV, which was originally intended to cover modern philosophy from the 17th to the 19th century, expands now into three monographs dealing respectively with classic Rationalism, British Empiricism and the continental Enlightenment of the 18th century up to Kant. Thus the present (...) volume, after a general Introduction which states the broad currents of thinking and makes the qualifications appropriate to offset their artificial discussion in three separate books, concentrates upon the personal and capital philosophies of Descartes, Spinoza and Leibniz. (shrink)

The latest volume in the Cambridge Histories of Philosophy series, The Cambridge History of Philosophy in the Nineteenth Century brings together twenty-nine leading experts in the field and covers the years 1790-1870. Their twenty-seven chapters provide a comprehensive survey of the period, organizing the material topically. After a brief editor's introduction, it begins with three chapters surveying the background of nineteenth century philosophy: followed by two on logic and mathematics, two on nature and natural science, five (...) on mind and language, including psychology, the human sciences and aesthetics, four on ethics, three on religion, seven on society, including chapters on the French Revolution, the decline of natural right, political economy, and social discontent, and three on history, dealing with historical method, speculative theories of history and the history of philosophy. The essays are framed by an editor's introduction and a bibliography. (shrink)

This bibliographical guide gives a comprehensive overview of the historiography of philosophy and thought in the Japanese language through an extensive and thematically organized collection of relevant literature. Comprising over one thousand entries, the bibliography shows not only how extensive and complex the Japanese tradition of philosophical and intellectual historiography is, but also how it might be structured and analyzed to make it accessible to a comparative and intercultural approach to the historiography of philosophy worldwide. The literature is (...) categorized and organized according to thematic focus areas such as geographical regions and continents, nations or peoples, religious traditions and philosophical teachings such as Buddhism, Islam, Shintō, and Confucianism, as well as disciplines such as ethics, aesthetics, and political thought. The bibliography is accompanied by an introduction outlining the research method as well as quantitative and qualitative approaches to analyzing the material, followed by a chronological overview of the historiography of philosophy and thought in the Japanese language and of the Japanese tradition of writing “world histories of philosophy.” As a first step towards a “history of the historiography of philosophy” in non-European languages, we hope that this guide will provide a useful tool for interculturally oriented scholarship aimed at a non-Eurocentric and diversified historiography of philosophy in a global perspective. (Open access, see link below.). (shrink)

This introductory chapter reviews the history of the reception of philosophy from Asia and the Islamic World in Western philosophy and argues in favor of conceptualizing philosophy from a more globally informed point of view.

As the author mentions in the preface to the English edition, this History of Philosophy is the fruit of ideas and research efforts shared in common by the Madrid School of Ortega y Gasset, 1931-1936. Most of these men were educated in Germany, and, besides being original authors in their own right, carried out remarkable efforts of historical research in philosophy, practicing the best techniques of German historical investigation. Marias benefited from these efforts and complemented them with (...) meritorious personal studies. Given the circumstances of its composition, the book is an introduction to, and a dictionary of, philosophy. Because of this, the properly historical side of it is strongly interpretative and somewhat unbalanced. Although Anglo-American philosophy is given some attention, it is not, sufficiently or intimately appreciated. It gives certain authors-the Stoics, Leibniz, Kant, Brentano, the philosophers of life of recent time—a special emphasis that is necessary for a good understanding of our philosophical present. The translation is adequate in preserving the author's elegant and suggestive style.—A. M. (shrink)

"Continental philosophy" is now a well-established term in the English-speaking world: it has a point and is taken to refer to a fairly well-defined entity. It is, for example, regularly used in job descriptions. But any explanation that goes beyond something like the following, "Continental philosophy is the sort of philosophy produced by or in the wake of philosophers such as Heidegger and Adorno, Habermas and Apel, Sartre and Lévinas, Foucault, Lacan, Althusser and Derrida" is likely to (...) be controversial. The term excludes analytical and other types of exact philosophy done on the continent.1 Nor is the contrast between Analytic and Continental Philosophy supposed to encourage the assumption that Wittgenstein and Carnap are honorary Anglo-Saxons. (shrink)

We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. (...) We conclude that Frege, and even more so Peirce, developed new notations not to make drawing logical conclusions easier but in order to answer the needs of logical analysis. (shrink)

This introductory chapter sets the stage for an engaging exploration of the multifaceted concept of proof in the philosophy of mathematical practice. As a fundamental pillar of mathematics, proof has long been a subject of intense scrutiny for mathematicians and philosophers alike. Traditionally, proofs have been perceived as rigorous and deductive arguments, and this analysis was directed towards the notion of formal proof. However, recent developments have challenged this traditional view, highlighting the dynamic and evolving nature of mathematical proofs. (...) In this section, we bring together diverse perspectives from leading scholars to delve into the philosophical significance and complexity of mathematical proof. (shrink)