History of Logic from Aristotle to Gödel (www.historyoflogic.com)

by Raul Corazzon | e-mail: rc@ontology.co

General Works on the History of Logic in Western Thought


This part of the section History of logic: Introduction includes the following pages:

General Works on the History of Logic: English studies A-C

General Works on the History of Logic: D - Z (Current page)

Bibliography of General Studies in French, Italian, German and Spanish

Studies in English

D - Z

  1. Drucker, Thomas, ed. 2008. Perspectives on the History of Mathematical Logic. Boston: Birkhäuser.

    Contents: Acknowledgments VII; Contributors XIII; Irving H. Anellis: Jean van Heijenoort (1912-1986) XIII; Thomas Drucker: Introduction XV; Judy Green: The Problem of Elimination in the Algebra of Logic 1; Nathan Houser: Peirce and the Law of Distribution 10; Irving H. Anellis: The First Russell Paradox 33; Daniel J. O'Leary: Principia Mathematica and the Development of Automated Theorem Proving 47; William Aspray: Oswald Veblen and the Origins of Mathematical Logic at Princeton 54; Irving H. Anellis: The L6wenheim-Skolem Theorem, Theories of Quantification, and Proof Theory 71; John W. Dawson Jr.: The Reception of G6del's Incompleteness Theorems 84; Hao Wang: G6del's and Some Other Examples of Problem Transmutation 101; C. Smorynski: The Development of Self-Reference: Löb's Theorem 110; Wim Ruitenburg: The Unintended Interpretations of Intuitionistic Logic 134; Stephen C. Kleene: The Writing of Introduction to Metamathematics 161; Jomathan P. Seldin: In Memoriam: Haskell Brooks Curry 169; Drtag Siefkes: The Work of J. Richard Büchi 176; Index Nominum 191-195.

    "The chapters included in this volume range broadly in time and subject, but they are all dedicated to unraveling the thoughts and the circumstances that have contributed to the evolution of mathematical logic. They involve technical details and philosophical underpinnings, support of colleagues and establishment of chairs. Some of the chapters give an insider's view of a particular development in the field, while others are detailed critical analyses of influential pieces of work. Their common feature is making sense rather than magic out of advances, binding together a community of contributors rather than leaving the impression of isolated wonder-workers. As the motto of the international chess federation has it, Gens una sumus. (We are one people.)" (p. XVI)


    "These chapters put together do not give a history of mathematical logic over the last century. Even on individual logicians they do not claim to be exhaustive. The collection does, however, indicate some of the richness of ideas that are involved in studying the history of logic and the variety of materials which can be pressed into service. National and chronological boundaries are not respected by the development of the field." (p. XXII)

  2. Dumitriu, Anton. 1977. History of Logic. Volume I. Tunbridge Wells: Abacus Press.

    Revised, updated, and enlarged translation from the Roumanian of the second edition of "Istoria logicii".

    Contents: Foreword IX; Historical note on works on the history of logic XIII-XVI;

    Part I: Logic in Non-European Cultures

    Chapter I. The logical structure of primitive mentality 3; Chapter II. Logic in ancient China 12; Chapter III. Indian logic 39;

    Part II: Logic in ancient Greece

    Chapter IV: The beginning of Greek logic 69; Chapter V: The sophists 95; Chapter VI: Socrates' reaction. Plato 103; Chapter VII: The lesser Socratics 128; Chapter VIII: Aristotle's logic 141; Chapter IX: The Peripatetic School 207; Chapter X: The logic of the Stoics 216; Chapter XI: The Epicurean School. Scepticism and the New Academy 284;

    Part III: Rhetors and commentators

    Chapter XII: Logic and rhetoric in rome 273; Chapter XIII: Commentaries and commentators 261;

    Index of names 323; Index of subjects 335-342.

    "The potential author of a history of logic should not depend on any preconceived point of view. The formalistic option, for example, requires logic to be treated in a purely symbolic way, as a logical syntax of meaningless signs; obviously the historian who adopts such a view, hoping to achieve an absolute objectivity by eliminating any philosophical hypothesis, will be bound by it.

    Such a logic is a logic without any philosophical content, and surely its history will have to adopt the same line. But is it possible to deal with logic without having any philosophical point of view? It is evident that such an intention is not realistic, and even in the formalistic point of view a certain philosophy is understood. Aristotle's statement "he who philosophizes, philosophizes, and he who does not philosophize, philosophizes too, so everybody philosophizes" is very significant.

    A history of logic based on such a view would have to leave out of the list of logicians names like Thomas Aquinas, Kant, Hegel, Husserl, and many others. Is it possible to explain the development of logic without commenting on thinkers of great influence, who actually moulded the whole frame of human thought in their time? Obviously such a point of view is inadmissible.

    A history of logic without philosophical references leads to very important consequences, to wide mutations and alterations of the very concept of logic and philosophy. After two and a half millennia, logic is taken from philosophy, and belongs henceforth to another domain, that of mathematics. In this way, logic has escaped from the jurisdiction of philosophy, but philosophy has remained independent of logic. In the past logic was, on the contrary, closely connected to philosophy, whether it was conceived as a part of philosophy, or an introduction to it, or as an organon, or even as the philosophy itself." (Foreword, pp. IX-X)

  3. ———. 1977. History of Logic. Volume II. Tunbridge Wells: Abacus Press.

    Contents: Foreword V;

    Part IV: Scholastic logic

    Chapter XIV: Scholasticism 3; Chapter XV: The formation of the Scholastic logic 11; Chapter XVI: The place of logic among the other sciences 50; Chapter XVII: The problem of universals 62; Chapter XVIII: Scholastic terminology 100; Chapter XIX: Parva logicalia 124; Chapter XX: The properties of terms 130; Chapter XXI: Syncategoremata 142; Chapter XXII: The theory of consequences 151; Chapter XXIII: Insolubilia 162; Chapter XXIV: General conclusion on Scholastic logic 173;

    Part V: Renaissance logic

    Chapter XXV: The Renaissance 183; Chapter XXVI: Renaissance Aristotelianism 189; Chapter XXVII: The logic of Humanism 220;

    Index of names 251; index of subjects 263-265.


    The first volume of this book showed the development of the two great logical systems of Aristotle and Chrysippus. In this volume we look at the third great system of logic, that of the Scholastics. They studied the teachings of the Greeks, of the Arab and Jewish commentators, and from them evolved a logica perennis based on a single, well-founded philosophical doctrine. We shall see the crystallization of Scholastic logic into a well defined system, the contributions of the Scholastic logicians and the subsequent decline of the philosophical and logical doctrines to mere didactics.

    At the dawn of the Renaissance the opponents of Scholastic logic were searching for new logical systems. But the Renaissance failed to achieve a unitary doctrine which could provide an adequate critique of the old logic as well as an independent, valid, logical system. The Renaissance produced new ideas and trends which though interesting failed to make any major contribution to logic comparable to other great conceptions such as Scholasticism.

    Both periods have been studied in the past, but not with special reference to the logic of the period. The historian has very great problems in his attempt to sort and classify the enormous amount of material available. In order to deal with this material synthetically and avoid repetition we have adopted a synchronous and diachronous approach.

  4. ———. 1977. History of Logic. Volume III. Tunbridge Wells: Abacus Press.

    Part VI: Methodological logic

    Chapter XXVIII: The beginnings of experimental science 3; Chapter XXIX: Francis Bacon 11; Chapter XXX: Descartes 32; Chapter XXXI: Post-Cartesian methodological researches 46; Chapter XXXII: Contemporary sciences and their problems 62; Chapter XXXIII: New dialectics 68; Chapter XXXIV: Science as language 77; Chapter XXXV: Induction and probability 99; Chapter XXXVI: Logic of research 112;

    Part VII: Development of modern logic

    Chapter XXXVII: Logic from Leibniz to Kant 135; Chapter XXXVIII: Transcedendental logic 163; Chapter XXXIX: Hegel's logic 205; Chapter XL: Reactions to the philosophy of Romanticism. Late trends 235; Chapter XLI: Materialist dialectic 260; Chapter XLII: Psychologism in logic and related trends 311; Chapter XLIII: Phenomenology and pure logic 353;

    Index of names 373; index of subjects 387-393.


    The third volume of the “History of Logic deals with the evolution of logic since Renaissance.

    Two great issues faced the modern epoch, the meaning of the most important scientific attainments being contingent upon the solutions found. These were:

    (a) how to make scientific discoveries and

    (b) what is the logico-theoretical basis of the truths discovered by science?

    The first query gave rise to much methodologic research the principal aim of which was to establish an ars inveniendi, establishing rules which would enable anyone to discover scientific truths. With the development of contemporary science, however, the classical concept of method underwent a fundamental change and the solutions found are to be taken as the hypotheses of possible methods.

    The second query provoked a widespread critical reevaluation of all those principles and concepts of logic, improperly designated “philosophy of logic".

    Recent critical analysis is explained by the need to establish the logical foundations of science.

    These are the problems that the present volume will attempt to pursue."

  5. ———. 1977. History of Logic. Volume IV. Tunbridge Wells: Abacus Press.

    Contents: Foreword IX,

    Part VIII: Mathematical logic

    Chapter XLIV: Logic and mathematics 3; Chapter XLV: Raymundus Lullus' system 8; Chapter XLVI: Leibniz's logic 15; Chapter XLVII: The algebra of logic 39; Chapter XLVIII: Gottlob Frege 51; Chapter XLIX: Peano and the Italian School 64; Chapter L: Principia Mathematica 87; Chapter LI: The logico-mathematical paradoxes 113; Chapter LII: The development of mathematical logic 118; Chapter LIII: Many-valued logics 145; Chapter LIV: The decision problem 182; Chapter LV: Formal technique (systems and metasystems) 196; Chapter LVI: General considerations on mathematical logic 224; Chapter LVII: Reactions to mathematical logic 239;

    Part IX: Conclusion

    Chapter LVIII: General conclusions 259;

    Index of names 267; index of subjects 273-275.


    This volume (the last) of the “History of Logic" is devoted to mathematical logic. It will show that mathematical logic did not appear suddenly but as a natural consequence of the advancement of the sciences and of the crisis they went through at the turn of the century.

    We will focus on the following points:

    (a) philosophical theories from Boole to Husserl provide a theoretical basis to the concept of a formal symbolic-mathematical logic;

    (b) such is the prestige of the mathematical methods which have now pervaded every area that logic could not call itself a science, had it not also clad itself in a mathematical garb;

    (c) finally, many fundamental problems of mathematics and the logical elucidation of its basic concepts (such as number, set etc.) have made it necessary to develop a mathematical tool which could be rigorously applied to such problems.

    We shall follow the historical development of symbolic logic systems. It is apparent that mathematical logic has been developed in response to logical, philosophical and purely mathematical problems.

    A history of logic cannot cover all three areas, pure mathematics, in particular, being of little relevance here. They will be dealt with only when explaining certain developments in symbolic logic, though making it clear that they are separate sciences. Certain critical remarks have been made in an attempt to delimit the nature of issues which may appear paradoxical."

  6. Filkorn, Vojtech. 1963. Pre-Dialectical Logic. Bratislava: Publishing House of the Slovak Academy of Sciences.

    "This work is the first part of Pre-Dialectical Logic in two volumes. We deal in it with some periods of the history of this logic. Pre-dialectical logic has also its own systematic-methodologic aspect which we investigate in the second volume.(1) Both volumes are conceived as a preparation for further studies in which we want to investigate dialectical logic from its historical and systematic aspects. This is also the reason why the definition of logic and the description of its properties which the first part deals with are only preliminary; such is also the investigation of the relation between formal and dialectical logic. We shall have to return to this problem once more when we shall investigate dialectical logic." (Preface, p. 5)

    (1) 1 In the O vod do melodologie vied (Introduction to !he Methodology of Sciences), Bratislava 1960.

  7. Gensler, Harry. 2006. Historical Dictionary of Logic. Lanham: Scarecrow Press.

    Also titled The A to Z Logic.

    Contents: Editor's Foreword by Jon Woronoff IX; Preface XI; Notation XIII; Chronology XV; Introduction XXIX-XLIV; The Dictionary 1; Bibliography 255; About the Author 307.

    This book is an encyclopedia of logic. It introduces the central concepts of the field in a series of brief, nontechnical "dictionary entry" articles. These deal with topics like logic's history, its various branches, its specialized vocabulary, its controversies, and its relationships to other disciplines. While the book emphasizes deductive logic, it also has entries on areas like inductive logic, fallacies, and definitions -- and on key concepts from epistemology, mathematics, and set theory that are apt to arise in discussions about logic. Following the series guidelines, Historical Dictionary of Logic tries to be useful for specialists (especially logicians in areas outside their subspecialties) but understandable to students and other beginners; so I avoid topics or explanations that are so technical that only math majors would understand.

    The major part of this book is the dictionary section, with 352 entries. While these are arranged alphabetically, there is also an organization based on content. Four very general entries start with "logic:" and serve mainly to point to more specific entries (like "propositional logic"); these in turn often point to related topics (like "negation," "conditionals," "truth tables," and "proofs"). So we have here a hierarchy of topics. Here are the four "logic:" entries:

    * logic: deductive systems points to entries like propositional logic, modal logic, deontic logic, temporal logic, set theory, many-valued logic, mereology, and paraconsistent logic.

    * logic: history of is about historical periods and figures and includes entries like medieval logic, Buddhist logic, twentieth-century logic, Aristotle, Ockham, Boole, Frege, and Quine.

    * logic: and other areas relates logic in an interdisciplinary way to other areas and includes entries like biology, computers, ethics, gender, God, and psychology.

    * logic: miscellaneous is about everything else (including technical terms) and includes entries like abstract entities, algorithm, ad hominem, inductive logic, informal/formal logic, liar paradox, metalogic, philosophy of logic, and software for learning logic.

    The entries vary in length from a sentence or two to several pages. The front of the book has three important parts:

    A short notation section gives the main logical symbols that I use in the book, along with alternative symbols that others sometimes use.

    A chronology lists some of the main events in the history of logic.

    An introduction tries to give an overall view of logic, the big picture, in order to give a broader context for the dictionary entries.

    The back of the book has a substantial bibliography on related readings." (from the Preface).

  8. Haaparanta, Leila, ed. 2009. The Development of Modern Logic. New York: Oxford University Press.

    Contents: Preface V-VI; 1. Leila Haaparanta: Introduction 3; 2. Tuomo Aho and Mikko Yrjönsuuri: Late medieval logic 11; 3. Mirella Capozzi, Gino Roncaglia: Logic and philosophy of logic from Humanism to Kant 78; 4. Volker Peckhaus: The mathematical origins of Nineteenth century algebra of logic 159; 5. Christian Thiel: Gottlob Frege and the interplay between logic and mathematics 196; 6. Risto Vilkko: The logic question during the first half of the Nineteenth century 203; 7. Leila Haaparanta: The relations between logic and philosophy, 1874-1931 222; 8. Göran Sundholm: A century of judgement and inference, 1837-1936: Some strands in the development of logic; 9. Paolo Mancosu, Richard Zach, Calixto Badesa: The development of mathematical logic from Russell to Tarski 1900-1935 318; 10. Wilfrid Hodges: Set theory, model theory, and computability theory 471; 11. Jan von Plato: Proof theory of Classical and Intuitionistic logic 499; 12. Tapio Korte, Ari Maunu, Tuomo Aho: Modal logic from Kant to possible worlds semantics 516; Appendix to Chapter 12: Risto Hilpinen: Conditionals and possible worlds: On C. S. Peirce's conception of conditionals and modalities 551; 13. Gabriel Sandu, Tuomo Aho: Logic and semantics in the Twentieth century 562; 14. Andrew Aberdein and Stephen Read: The philosophy of alternative logics 613; 15. Sandy Zabell: Philosophy of inductive logic: the Bayesian perspective 724; 16. Alessandro Lenci, Gabriel Sandu: Logic and linguistics in the Twentieth century 775; 17. Richmond Thomason: Logic and artificial intelligence 848; 18. J. N. Mohanty, S. R. Saha, Amita Chatterjee, Tushar Kanti Sarkar, Sibajiban Bhattacharyya: Indian logic 903; Index 963-994.

    "This volume is the result of a long project. My work started sometime in the 1990s, when Professor Simo Knuuttila urged me to edit, together with a few colleagues, a volume on the history of logic from ancient times to the end of the twentieth century. Even if the project was not realized in that form, I continued with the plan and started to gather together scholars for a book project titled The Development of Modern Logic, thus making a reference to the famous book by William and Martha Kneale. Unlike that work, the new volume was meant to be written by a number of scholars almost as if it had been written by one scholar only. I decided to start with thirteenth-century logic and come up with quite recent themes up to 2000, hence, to continue the history written in The Development of Logic. My intention was to find a balance between the chronological exposition and thematic considerations. The philosophy of modern logic was also planned to be included; indeed, at the beginning the book had the subtitle "A Philosophical Perspective," which was deleted at the end, as the volume reached far beyond that perspective. The collection of articles is directed to philosophers, even if some chapters include a number of technical details. Therefore, when it is used as a textbook in advanced courses, for which it is also planned, those details are recommended reading to students who wish to develop their skills in mathematical logic." (From the Preface by Leila Haaparanta)

  9. Kneale, William Calvert, and Kneale, Martha. 1962. The Development of Logic. Oxford: Clarendon Press.

    Reprinted 1975 with corrections.

    "As its name indicates, this book is an account of the growth of logic, rather than an attempt to chronicle all that past scholars, good and bad, have said about the science. For the sake of continuity, and in order to give historical perspective to our story, my wife and I have included some references to work which does not deserve to be remembered for its own sake; and occasionally we have allowed ourselves to indulge an antiquarian curiosity, when we thought that the result might be of some interest to others. But our primary purpose has been to record the first appearances of those ideas which seem to us most important in

    the logic of our own day. Such a programme is based on judgements of value, and we realize that our selection of material and still more our comments, especially in the later chapters, may seem eccentric to some readers. In defence of our undertaking we can only say that we have followed the plan which our interests suggested, and that we could not have written in any other way." (Preface, p. V)


    "For the fifth impression we have corrected some surviving mistakes and misprints, re-worded some passages in the hope of achieving greater clarity, and added some references. But the chief novelty is an appendix in which we translate the Latin quotations of Chapter IV. Many of these improvements, like those in earlier impressions, are due to the suggestions of readers, whom we thank for their kindness in writing to us." (Preface, p. VI, May 1971)

  10. Knuuttila, Simo, ed. 1988. Modern Modalities: Studies of the History of Modal Theories from Medieval Nominalism to Logical Positivism. Dordrecht: Kluwer.

    Contents: Simo Knuuttila: Introduction VII-XIV; Lilli Alanen and Simo Knuuttila: The foundations of modality and conceivability in Descartes and his predecessors 1; Ilkka Patoluoto: Hobbes's system of modalities 71; Jaakko Hintikka: Was Leibniz Deity an Akrates? 85; Martin Kusch and Juha Manninen: Hegel on modalities and monadology 109; Pascal Engel: Plenitude and contingency: modal concepts in Nineteenth century French philosophy 179; Leila Haaparanta: Frege and his German contemporaries on alethic modalities 239; Ilkka Niiniluoto: From possibility to probability: British discussions on modality in the Nineteenth century 275; Hans Poser: The failure of Logical Positivism to cope with problems of modal theory 311; Index of names 329; Index of subjects 341.

    "The word "modern" in the title of this book refers primarily to post-medieval discussions, but it also hints at those medieval modal theories which were considered modern in contradistinction to ancient conceptions and which in different ways influenced philosophical discussions during the early modern period. The medieval developments are investigated in the opening paper, 'The Foundations of Modality and Conceivability in Descartes and His Predecessors', by Lilli Alanen and Simo Knuuttila.

    Boethius's works from the early sixth century belonged to the sources from which early medieval thinkers obtained their knowledge of ancient thought. They offered extensive discussions of traditional modal conceptions the basic forms of which were: (1) the paradigm of possibility as a potency striving to realize itself; (2) the "statistical" interpretation of modal notions where necessity means actuality in all relevant cases or omnitemporal actuality, possibility means actuality in some relevant cases or sometimes, and impossibility means omnitemporal non-actuality; and (3) the "logical" definition of possibility as something which, being assumed, results in nothing contradictory. Boethius accepted the Aristotelian view according to which total possibilities in the first sense must prove their mettle through actualization and possibilities in the third sense are assumed to be realized in our actual history. On these presumptions, all of the above-mentioned ancient paradigms imply the Principle of Plenitude according to which no genuine possibility remains unrealized. (For the many-faceted role of the Principle of Western thought, see A.O. Lovejoy, The Great Chain of Being. A Study of the History of an Idea, Harvard University Press, Cambridge, Mass. 1936, and S. Knuuttila (ed.), Reforging the Great Chain of Being. Studies of the History of Modal Theories (Synthese Historical Library 20), Dordrecht, Reidel 1981.)

    Boethius sometimes says that there can be opposite diachronic possibilities vis-à-vis future moments of time, but even in these cases unrealized alternatives cease to be possibilities when one of them is actualized. The idea of spelling out the meaning of modal notions with the help of synchronic alternative states of affairs hardly played any role in ancient thought; after having been suggested by some Patristic thinkers, it became a systematic part of modal thinking only in the twelfth century. It was realized that even if the traditional philosophical conceptions might be applicable to the phenomenal reality, possibilities of God, acting by choice, refer to alternative providential plans or histories. Although there were not many twelfth or thirteenth century figures who, like Gilbert of Poitiers or Robert Grosseteste, would have understood the theoretical significance of the idea of modality as referential multiplicity, the doctrine of special theological modalities motivated new kinds of discussions of the nature of natural necessities and the relations between the notions of possibility, conceivability, and knowability.

    In ancient metaphysics, modality and intelligibility were considered real moments of being. A Christian variant of this doctrine can be found in such thirteenth century Parisian scholars as Thomas Aquinas, Bonaventura, and Henry of Ghent. They thought that God's infinite act of understanding contains the ideas of all conceivable kinds of beings. Ideas as possibilities have an ontological foundation, however, because God's act of thinking consists of understanding the infinite ways in which his essence could be imitated by finite beings. Because the ontological foundation of possibilities remains as such unknown to men, it is claimed that we usually cannot decide whether an alleged unrealized possibility really is a possibility or not.

    In Duns Scotus's modal theory, the ontological foundation of thinkability is given up. The area of logical possibility is characterized as an infinite domain of thinkability which, without having any kind of existence, is objective in the sense that it would be identical in any omniscient intellect thinking about all thinkable things. This theory of the domain of possibility as an absolute precondition of all being and thinking was accepted by Ockham and many other medievals, and through Suárez's works it was commonly known in the seventeenth century, too. Another historically important feature of Scotus's modal theory is that it systematically developed the conception of modality as referential multiplicity. The domain of possibility as an a priori area of conceptual consistency is partitioned into equivalence classes on the basis of relations of compossibility. One of them is the actual world." (pp. VII-IX)

  11. Lejewski, Czeslaw. 1981. "Logic and Ontology." In Modern Logic. A Survey. Historical, Philosophical, and Mathematical Aspects of Modern Logic and its Applications, edited by Agazzi, Evandro, 379-398. Dordrecht: Reidel.

    "My discussion of the topic prescribed by the title of the paper will consist of two parts. In Part I, I propose to discuss, in very general and informal terms, the nature of logic and ontology, and the relationship that seems to connect these two disciplines. In Part II, I intend to examine, in some detail, a certain specific problem, which concerns logicians as well as ontologists, a problem which has been with us for about forty years, and which lacks a generally acceptable solution." (p. 379)

  12. Lewis, Clarence Irving. 1918. A Survey of Symbolic Logic. Berkeley: University of California Press.

    Reprinted New York: Dover Publishing 1960.

    Chapter I: The development of symbolic logic.

    Section I. The Scope of Symbolic Logic. Symbolic Logic and Logistic. Summary Account of their Development 1; Section II. Leibniz 5; Section III. From Leibniz to De Morgan and Boole 18; Section IV. De Morgan 37;

    Section V. Boole 51; Section VI. Jevons 72; Section VII. Peirce 79; Section VIII. Developments since Peirce 107-117.

    "The historical summary in Chapter I attempts to follow the main thread of development, and no reference, or only passing mention, is given to those studies which seem not to have affected materially the methods of later researches. In the remainder of the book, the selection has been governed by the same purpose. Those topics comprehension of which seems most essential, have been treated at some length, while matters less fundamental have been set forth in outline only, or omitted altogether." (Preface, p. VI)

    "The presentation of the subject matter of logic in this mathematical form constitutes what we mean by symbolic logic. Hence the essential characteristics of our subject are the following: (1) Its subject matter is

    the subject matter of logic in any form that is, the principles of rational or reflective procedure in general, as contrasted with principles which belong exclusively to some particular branch of such procedure. (2) Its

    medium is an ideographic symbolism, in which each separate character represents a relatively simple and entirely explicit concept. And, ideally, all non-ideographic symbolism or language is excluded. (3) Amongst the ideograms, some will represent variables (the "terms" of the system) having a definite range of significance. Although it is non-essential, in any system so far developed the variables will represent "individuals",

    or classes, or relations, or propositions, or "propositional functions", or they will represent ambiguously some two or more of these. (4) Any system of symbolic logic will be developed deductively that is, the whole

    body of its theorems will be derived from a relatively few principles, stated in symbols, by operations which are, or at least can be, precisely formulated." (pp. 3-4)

  13. Malpass, Alex, and Antonutti Marfori, Marianna, eds. 2017. The History of Philosophical and Formal Logic: From Aristotle to Tarski. London: Bloomsbury.

    Contents: Marianna Antonutti Marfori: Preface VII-VIII; Introduction 1;

    Part I The Origins of Formal Logic

    1 Adriane Rini: Aristotle’s Logic 29; 2 Katerina Ierodiakonou: Stoic Logic 51; 3 Sara L. Uckelman: Medieval Logic 71;

    Part II The Early Modern Period

    4 Jaap Maat: Leibniz 101; 5 Jönne Kriener: Bolzano 121; 6 Giulia Terzian: Boole 143;

    Part III Mathematical Logic

    7 Peter Øhrstrøm: C.S. Peirce 165; 8 Walter B. Pedriali: Frege 183; 9 Alexander Bird: Peano and Russell 229; 10 Curtis Franks: Hilbert 243;

    Part IV Twentieth- Century Logic

    11 P.D. Welch: Gödel 269; 12Benedict Eastaugh: Tarski 293;

    Index 315-322.

    "The History of Philosophical and Formal Logic was conceived as a way for undergraduate students with little training in formal logic to discover the roots of logical concepts. However, we also hope that it provides a starting point for anyone with an interest in this wonderful discipline to become acquainted with its history. By producing an introductory book whose chapters span the entire history of the discipline, we aim to show how the elements of the standard undergraduate logic curriculum took their current form only relatively recently, emerging from a long development by many hands whose interests and motivations varied widely. Moreover, by shedding light on a few topics that have not been given as much attention in standard histories of logic, such as the contributions of Leibniz and Bolzano, as well as the diagrammatic logics of C.S. Peirce, we hope to play a part in encouraging a broader view of the history of logic, which as a discipline surely has much to gain in being more inclusive of other fi gures and traditions. We only regret not having been able to contribute more in this regard ourselves." (p. VIII)

  14. Marciszewski, Witold, and Murawski, Roman. 1995. Mechanization of Reasoning in a Historical Perspective. Amsterdam: Rodopi.

    "Table of Contents: Acknowledgement 7; 1, From the Mechanization of Reasoning to a Study of Human Intelligence 12; 2. The Formalization of Arguments in the Middle Age 45; 3. Leibniz's Idea of Mechanical Reasoning at the Historical Background 77; 4. Between Leibniz and Boole: Towards the Algebraizatlon of Logic 113; 5. The English Algebra of Logic in the 19th Century 129; 6. The 20th Century Way to Formalization and Mechanization 161; 7. Mechanized Deduction Systems 209; References 231; Index of Subjects 253; Index of Names. 257; Extended Table of Contents 261-267.

    "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." (p. 7)

    "There are no bare facts in history, be it political history, be it a story of ideas. Historical narration tells about past facts, but there a.re as many stories as are persputives into which we put data found in sources. The choice of a perspective may depend on axiological assumptions, as well as the position in time assumed by a historian. The latter obviously divides into (i) the standpoint of the past under study (e.g., an attempt to read Aristotle in the light of Aristotle), (ii) the standpoint of the present state of affairs (as, e.g., in Lukasiewicz 1951), and (iii) the standpoint of an envisaged future development.

    It was Jan Lukasiewicz who was the pioneer of approach (ii), as expressed in the title of his Aristotle's Syllogistic from the Standpoint of Modem Formal Logic, 1951. Among his seminal achievements in this field there was an interpretation of Stoic logical writings in the light of modern propositional logic.

    Approach (iii) highlights those facts which one deems relevant to a forecasted course of events. The forecast to be substantiated in this chapter, and to shed light at the content of this volume, is as follows. There starts a process of merging logic with cognitive science, the latter being the theory of perception and intelligence advanced in terms of information-processing; this is not to mean any loss of autonomy on either side, rather the emergence of a new research area to which both sides essentially contribute. When seen in this perspective, the development of logic leads in the direction which was hardly expected by the founding fathers. In their intention, logic should have been an indispensable tool of research. In fact, though, discoveries do not happen to result from a conscious use of logical inference rules. Instead, logic made it possible to create artificial reasoners, and these prove apt models to help us in a better understanding of natural reasoning ( even if they function as negative models to yield a contrastive background); and once we see reasoning as a method of problem-solving, we enter on a study of intelligence.

    This volume is to show how the main stream of development of logic has led to that result.


    Within that formalization trend there was the result of the utmost importance for the mechanization of reasoning, namely the algebraization of logic in the form of binary algebra (claimed by Leibniz and effected by Boole and others), the latter having been combined with binary arithmetical notation and with the two-states functioning of electrical circuits; to that came methods of arithmetizing syntax and, moreover, methods of reducing the whole of logic to the binary algebra (the elimination of quantifiers). That development resulted in the present state of logic and essentially contributed to the rise of computers. Those, in turn, made it possible to mechanize deductive reasoning which proves a suitable base to start with an inquiry into the nature of intelligence.

    In such a historical perspective the development of logic is viewed from the position taken in this volume. This is the standpoint of the present relations between logic and cognitive science, the present being seen as pregnant with an expected future development - according to Leibniz's dictum praesens gravidum est futuro." (pp. 11-12)

  15. Mates, Benson. 1965. "A Brief Outline of the History of Logic." In Elementary Logic, 205-230. New York: Oxford University Press.

    Second revised edition 1972.

    Chapter 12: A brief outline of the history of logic, pp. 205-230.

    "In approaching the history of logic one must keep in mind that the term 'logic' and its cognates have been applied to many subjects other than the one presently under consideration, and, conversely, that the latter has been denoted by many terms other than 'logic'. Even if our competence permitted it, there would seem to be little point in undertaking a simultaneous history of all those topics in epistemology, metaphysics, psychology, sociology, and philology that at one time or another have been discussed under the heading 'logic'. The goal here is only to set forth the history of what we call 'logic' -roughly characterizable, perhaps, as the general theory of the consequence relation-by whatever names this subject may be known to other authors, past or present.

    For the sake of clarity it should also be borne in mind that the proper business of a logician is the investigation and formulation of general principles concerning what follows from what; whether particular examples of his own reasoning are valid or not is essentially irrelevant. By the same token, correct reasoning, however praiseworthy it may be, does not of itself constitute a contribution to logic; men were giving valid arguments long before there was any such thing as the science of logic, just as stones were no doubt efficiently pried up long before anyone formulated the principle of the lever." (p. 205)

  16. Nidditch, Peter H. 1962. The Development of Mathematical Logic. London: Routledge & Kegan Paul.

    Contents: 1. Purpose and language of the Book 1; 2. Aristotle's syllogistic 3; 3. The idea of a complete, automatic language for reasoning 14; 4. Changes in algebra and geometry, 1825-1900 23; 5. Consistency and metamathematics 30; 6. Boole's algebra of logic 33; 7. The algebra of logic after Boole: Jevons, Peirce and Schroeder 44; 8. Frege's logic 59; 9. Cantor's arithmetic of classes 66; 10. Peano's logic 73; 11. Whitehead and Russell's 'Principia Mathematica' 77; 12. Mathematical logic after 'Principia Mathematica': Hilbert's metamathematics 79; Further reading 86; Index 87.

    "1.1. Purpose of book. The purpose of the present book is to give such an account of Mathematical Logic as will make clear in the framework of its history some of the chief directions of its ideas and teachings. It is these directions, not the mass of detail forming the theory and its history, which are important for the rest of philosophy and are important, in addition, from the point of view of a general education. In the limits of our space we are able to give attention only to what has been, or seems as if it may be, fertile or of special value in some other way. More than this, Mathematical Logic having no small number of important developments, a selection of material is necessary, the selection being guided by the rule to take up the simpler questions, other things being roughly equal. Facts have to be looked at in the light of one’s purpose. Though they may all have the same value simply as facts, they are not at all equal as judged by the profit and the pleasure that thought, and not least the thought of the learner, is able to get from them." (p. 1)

  17. Nuchelmans, Gabriel. 1973. Theories of Proposition. Ancient and Medieval Conceptions of the Bearers of Truth and Falsity. Amsterdam: North-Holland.

    Contents: Preface V; 1. Introduction 1; 2. Plato 13; 3. Aristotle 23; 4. The Stoic lekton 45; 5. The Stoic axioma 75; 6. Later developments in Greek antiquity 89; 7. The transition to the Latin West 105; 8. Boethius and the beginning of the Middle Ages 123; 9. Abelard 139; 10. The doctrine of the dictum in the century after Abelard 165; 11. Preliminaries to the fourteenth century debate 177; 12. The complexum theory of Ockham and Holkot 195; 13. Some reist opponents of Ockham and Holkot 209; 14. The theory of the complexe significabile 227; 15. The oppositions against the theory of the complexe significabile 243; 16. The significate of a true propositio 273; Selective bibliography 281; Indices 289-309.

    "This book is intended as the first part of a history of those problems and theories in the domain of philosophical semantics which nowadays are commonly referred to as problems and theories about the nature and the status of propositions. Although the conceptual apparatus and the terminology by means of which questions concerning propositions were asked and answered have considerably varied from period to period, the main types of disputes and solutions have remained remarkably constant. One of the aims of this study is precisely to trace the vicissitudes of the vocabulary in which this refractory topic was treated in the remote past. As is evident from the Bibliography, many parts of the field have been explored by predecessors. Guided by their results, I have tried to fill in more details and to design a provisional map of the area as a whole." (From the Preface).

  18. ———. 1980. Late-Scholastic and Humanist Theories of Proposition. Amsterdam: North-Holland.

    Contents: Part One: Late-Scholastic theories of the proposition. 1. Introduction 3; 2. Different kinds of propositions and their ways of signifying 9; 3. The tie between the principal parts of a proposition 27; 4. The adequate signification and the adequate significate of a proposition 45; 5. Disguised propositions 74; 6. Judgment 90; 7. The object of judgment 103; 8. Propositions as bearer of truth-values 114; Part Two: Humanist theories of proposition. 9. Introduction 143; 10. The first attempt at reorientation 146; 11. The Melanchtonian treatment of a theme 159; 12. Peter Ramus 168; 13. The diffusion of Ramist terminology 180; 14. Eclectics 189; Epilogue 204; Bibliography 209; Indices 224-237.

    "After publishing, more than six years ago, my Theories of the Proposition. Ancient and Medieval Conceptions of the Bearers of Truth and Falsity, I initially intended to cover the remaining phases of the history of the semantics of declarative sentences in one volume. As the material proved more abundant and unwieldy than I had anticipated, I decided to limit the next instalment to the period between 1450 and 1650. Accordingly, the present book treats the theories of the proposition put forward by late-scholastic and humanist philosophers. It will be followed, in the not too distant future, I hope, by a third volume which will continue the account until the first decades of the nineteenth century.

    In making my way through the intricate mass of sources, which are often works that are completely forgotten and extremely hard to obtain, I was greatly assisted by Professor Ashworth's pioneering book on Language and Logic in the Post-Medieval Period. Moreover, when I had practically finished my manuscript, she was kind enough to send me the draft of an article entitled 'Theories of the Proposition: Some Early Sixteenth Century Discussions'. As this article is based on a corpus of texts which is slightly different from mine, it enabled me to check some of my results against the findings of a very competent collaborator in this lonely field of research. I can only advise the reader to do the same when the article will have been published (in Franciscan Studies [38, 1978 pp. 81-121])."

  19. ———. 1983. Judgment and Proposition. From Descartes to Kant. Amsterdam: North-Holland.

    Contents: 1. The legacy of scholasticism and humanism 9; 2. Idea and judgment in Descartes 36; 3. Repercussions of Descartes' theory of judgment 55; 4. Arnauld and the Port-Royal Logic 70; 5. Some eighteenth-century critics of the Port-Royal view 88; 6. Geulincx's contribution to Cartesian philosophy of logic 99; 7. Ideas and Images. Gassendi and Hobbes 121; 8. The heyday of British empiricism 139; 9. Sensationalism and its critics in France 174; 10. Common sense philosophy and nominalism in Great Britain 194; 11. Leibniz's logical realism 214; 12. The German enlightenment 233; 13. Some problems in Kant and his contemporaries 246; Epilogue 257; Bibliography 262; Indices 280-295.

    "This volume completes -- for the time being -- a series of investigations that were undertaken with the purpose of tracing in some detail the development of that field of logico-semantic research for which the foundations were laid in the first chapters of Aristotle's De interpretatione and which, in honour of that pioneer, might perhaps be called apophantics. The first part -- Theories of the Proposition. Ancient and Medieval Conceptions of the Bearers of Truth and Falsity -was published in 1973, followed by a second part -- Late-Scholastic and Humanist Theories of the Proposition -- in 1980. The last instalment takes the account from the beginning of the modern period to roughly that point in the nineteenth century from which on discussions of the subject in the recent past and contemporary systematic treatment tend to coalesce. " (From the Preface).

  20. Nye, Andrea. 1990. Words of Power: A Feminist Reading of the History of Logic. New York: Routledge.

    Contents: "Prologue IX; Acknowledgments XIII; Introduction: Reading Logic 1;

    Part I: Classical Logic 7

    1. The Desire of Logic: Parmenides's Passion 9; 2. Weaving the Seine of Logos: Plato and the Sophist 23; 3. Aristotle's Syllogisms 41; 4. Logos Spermatikos: The Logic of Empire 65;

    Part II: Medieval Logic 83

    5. An Arsenal of Reasons: Abelard's Dialectic 85; 6. The Antinomies of Power: Ockham's Razor 103;

    Part III: Reading Frege 125

    7. Breaking the Power of the Word 129; 8. The Marriage of Mathematics and Language 139; 9. Frege's Thoughts 154; 10. A Thought like a Hammer: The Logic of Totalitarianism 163;

    Conclusion: Words of Power and the Power of Words 173;

    Index 187-190.

    "I attempt here a different kind of validation of the feminist indictment of logic, one not based on any theory of language or logic, whether transactional, structuralist, poststructuralist, or psychoanalytic. In my view, there is no one Logic for which such a theory can account, but only men and logics, and the substance of these logics, as of any written or spoken language, are material and historically specific relations between men, between men and women, and between them and objects of human concern.

    Unlike either the logician or theorist I make no pretense at anonymity. I am a woman reading logic. I am also a philosopher who, like many other women philosophers, has often felt uneasy claiming that title. Perhaps only a woman would undertake such a project, would do such a thing as try to read logic, a woman uncomfortable in the world of men, involved in the physical details of family life, births, marriages, the keeping of houses, a woman too intent on emotional commitments to be capable of purely abstract thought. Perhaps only a woman would not make even the pretense of disinterested scholarship, but would admit to believing that involvement and commitment can lead to an understanding that logical analysis bound to consistency and univocality cannot.

    You cannot ask of such readings that they reveal any absolute or complete truth about logic. There is never only one reading. You can ask that they be sensitive, accurate, attentive, revealing, and informed by an aspiration to a better life for women and for men. These are the standards by which I ask my reader to judge what follows."

  21. Prior, Arthur Norman. 1962. Formal Logic. Oxford: Clarendon Press.

    Second edition (First edition 1955).

    "This book is designed primarily as a textbook; though like most writers of textbooks I hope it will prove to be of interest to others beside Logic students. Part I covers what I would regard as the 'fundamentals' of the subject-the propositional calculus and the theory of quantification. Part II deals with the traditional formal logic, and with developments which have taken that as their starting-point. I do not regard this as covering different ground from that covered in Part I under quantification theory, but rather as covering the same ground in a different way. Both ways seem to me to have their merits, and to throw light on one another and the subject. I would say the same of the logic of classes and relations in extension, discussed in Part III, Ch. III ; but the other chapters of this last Part deal with what I take to be genuine extensions of the subject-matter opened up in Part I, in two different directions -modal logic, and `non-classical' systems of propositional calculus. Negatively, I have attempted to keep within the range indicated by my title: I have touched hardly at all upon `scientific method', and have indulged in a minimum of metaphysical reflection (avoiding, for example, such topics as the relations between 'propositions' and sentences).In the greater part of the book the symbolic notation used is that of Lukasiewicz, with minor modifications. This seems to me unquestionably the best logical symbolism for most purposes, and I should like to have helped to show that it is. In Part III, Ch. III, however, I have used the notation of Principia Mathematic a (referred to throughout this work as PM) ; in the particular field there covered, there is no other as fully developed or as deservedly well known. It does students no harm to learn to use two different notations, and to employ the one that is best for whatever they may have in hand at the time.Other innovations beside the symbolism are these: (i) throughout the book, a fairly frequent setting out of formal proofs (something to which the Polish notation particularly lends itself) ; (ii), in Part I, the devotion of particular attention to completeness proofs, and to forms of the propositional calculus not yet widely studied, especially to varieties of it which use the 'standard false proposition' o, and variable operators as well as propositional variables; (iii), in Part II, considerable use of scholastic material and of material from the writings of de Morgan. I have included these items from a sense of their importance rather than of their novelty, and have placed them where their appearance seems to me most rational and economical; but if any teacher wishes to use this book for a more orthodox type of logic course, there are various ways in which he may do so. If, for example, he wishes to introduce the traditional logic at an early stage, he could pass to Part II immediately from Part I, Ch. I, Ch. II, § 1, and Ch. IV, §§ and 2. (This procedure would have in any case the advantage of giving the student an interval of rest from pure symbolism before passing to the more interesting but more difficult aspects of the propositional calculus.) If he wishes to give the more usual sort of 'modern' course, he could pass immediately on from the same portions of Part I to Part III, Ch. I, § 2 and Ch. III." (from the Preface to the first edition).

    "Apart from one or two very small corrections, I have in this edition left the body of the work just as it was, but have completely revised the two original appendixes and placed a wholly new appendix (the present Appendix II) between them. These alterations and additions will, I hope, make the appendixes much more valuable both for general reference and for pedagogical use. In the latter connexion I would particularly recommend that what I have said in the body of the book on quantification theory - which has met with some just criticisms - be read in conjunction with § 4 of Appendix I. There is also abundant material for exercises in simply verifying some of the relations asserted to hold between postulate-sets in this Appendix, using to this end the techniques sketched in the one that follows it." (from the Preface to the Second edition).

  22. ———. 2006. "Logic, History of." In Encyclopedia of Philosophy. Second Edition, edited by Borchert, Donald M., 397-484. New York: Thomson Gale.

    The first edition of the Encyclopedia of Philosophy, edited by Paul Edwards, was published in 1967.

    The editor of the article Logic, history of in the first edition was Arthur Norman Prior.

    "The mainstream of the history of logic begins in ancient Greece and comes down through the Arabian and European logic of the Middle Ages and through a number of post-Renaissance thinkers to the more or less mathematical developments in logic in the nineteenth and twentieth centuries. In the period after the fall of Rome many of the ancient achievements were forgotten and had to be relearned; the same thing happened at the end of the Middle Ages. Otherwise this Western tradition has been fairly continuous. Indian and Chinese logic developed separately. Today logic, like other sciences, is studied internationally, and the same problems are treated in the Americas, western and eastern Europe, and Asia and Australasia. The story of the development of logic will be told here under the following headings:

    Susanne Bobzien: Ancient logic; Brendan S. Gillon: Logic and inference in Indian philosophy; A. C. Graham (1967): Chinese logic (Bibliography updated by Huichieh Loy); Nicholas Rescher (1967): Logic in the Islamic world (with an Addendum by Tony Street); Christopher J. Martin: Medieval (European) logic; Ivo Thomas (1967): The Interregnum (between medieval and modern logic); Precursors of modern logic: Ivo Thomas (1967): Leibniz; Ivo Thomas (1967): Euler; Ivo Thomas (1967): Lambert and Ploucquet; Yehoshua Bar-Hillel (1967): Bolzano; Modern logic: the Boolean period; P. L. Heath (1967): Hamilton; P. L. Heath (1967): De Morgan; John Corcoran: Boole; P. L. Heath (1967): Jevons; P. L. Heath (1967): Venn; Francine F. Abeles: Carroll; A. N. Prior (1967): Peirce; A. N. Prior (1967): A. N. Prior (1967): Keynes; A. N. Prior (1967): Johnson; The heritage of Kant and Mill; A. N. Prior (1967): From Frege to Gödel; Ivo Thomas (1967): Nineteenth century mathematics; Bede Rundle (1967): Frege; Bede Rundle (1967): Whitehead and Russell; Bede Rundle (1967): Ramsey; Bede Rundle (1967): Brouwer and Intuitionism; Bede Rundle (1967): Hilbert and Formalism; Bede Rundle (1967): Löwenheim; Bede Rundle (1967): Skolem; Bede Rundle (1967): Herbrand; Bede Rundle (1967):Gödel; John P. Burgess: Since Gödel: Bede Rundle (1967): Gentzen; Bede Rundle (1967): Church; Herbert B. Enderton: Turing and computability theory; Wilfrid Hodges: Decidable and undecidable theories; Wilfrid Hodges: Model theory; Grahan Priest: The proliferation of nonclassical logics; Peter Cholak and Red Solomon: Friedman and revers mathematics." (from the Second Edition)

  23. Rastogi, Maharaj Narain. 1983. The Theories of Implication in Indian and Western Philosophy. A Critical Study. Delhi: Bharatiya Vidya Prakashan.

    Contents: Irving Copi: Foreword VII; Preface IX-X; I Introduction: Inference and implication 1; II Liner Implication: Aristotle 8; III Linear Implication: Nyāyā 24; IV Absolute Systematic Implication 43; V Material and Formal Implication 57; VI Strict implication 68; VII Implication and Meaning 85; VIII Implication and Facts100; IX Implication and Necessity 115; X Conclusion: Systematic Intensional Implication 136; Appendix: Implication and Arthāpatti 153; List of Symbols 159; Bibliography 160; Corrigenda 164.

    "This work presents an original conception and analysis of implication in the sense of entailment. It proceeds in both historical and critical fashion. After distinguishing the relation of implication from the process of inference, the author examines the relevant ideas of Aristotle and those involved in the Nyāyā Syllogism. The logical doctrines of Absolute Idealism are next considered with special reference to the writings of Bosanquet. They are criticized primarily for their connection with the unsatisfactory coherence theory of truth. The notion of material implication is examined carefully and found not to be a satisfactory model of what we mean by implication as the relation between premises and conclusion in a valid argument. C.I. Lewis's strict implication is considered with some sympathy, but is also ultimately rejected for good cause. The analyses of a number of other contemporary writers on logic are examined, including E.J. Nelson, J. Bennet, Strawson, Geach, Hampshire, and Körner. From the shortcomings of earlier treatments we are led to the new definition of implication in terms of systems of thought and their constituents. The new conception of implication does indeed seem to be free from the difficulties connected with earlier treatments of it. The work represents a considerable amount of research and hard, careful thinking." (Foreword by Irving Copi)

  24. Scholz, Heinrich. 1961. Concise History of Logic. New York: Philosophical Library.

    Translated from the German edition "Abriss der Geschichte der Logik" (1931) by Kurt F. Leidecker.

    Translated in Italian as: "Breve storia della logica" Milano, Silva Editore 1967.

    Contents: Preface to the first edition (1931) V; Introduction by Kurt F. Leidecker IX; Abbreviations XIII-XIV; Types of logic 1; The Classical type fof formal logic 24; The Modern type of formal logic 50; Bibliographic appendix 76; Supplementary observation 86; Notes 89; Index of names 137-140.

    "The reader of this Concise History of Logic is entitled to know what the objections to this book are and why it was nevertheless published.

    Carl Prantl (1820-1888) produced between 1855 and 1870 a standard work and source book for the history of logic from Aristotle to the end of the 15th century in which it is possible even now to appreciate an admirable mastery of the material, an exemplary punctiliousness in presenting the sources, and a nearly equally perfect intuitive certainty with which the material has been selected. For the history of modern logic there simply does not exist any work which could remotely be compared with Prantl's. Indeed, such a work will be written only when more shelf footage of monographs is available and each monograph can be considered on a par with the one Louis Couturat (1868-1914) wrote on the logic of Leibniz. (1)

    It is, therefore, incumbent on us to state boldly that the present concise history is a hazardous enterprise. For, it is impossible to summarize knowledge which does not even exist as yet, and which cannot since his time. However, in our endeavor we must never lose sight of the fact that the logic of antiquity, and to a considerable degree the logic of the middle ages, have come down to us in heaps of fragments.

    A third and very great flaw is the multiplicity of forms in which logic manifested itself, particularly in three stages; when it was raised to the first power in the days after the Logic of Port Royal (1662); when it was raised to the second power after Kant; and finally when it was raised to the third power after Hegel, a stage in which we have witnessed a plethora of forms right down to the present where we are no longer able to survey them.

    I have risked writing this brief history nevertheless, supported by my belief in the new logic, a belief that has aided me in conquering my inhibitions. This belief has encouraged me again and again in the difficult task of condensing the vast material into the limited space available. I owe thanks to my publisher for the understanding which prompted him to acknowledge the necessity of my going beyond the limits which. I had agreed to at the outset. This made it possible to produce a little volume in which not merely beliefs could be stated, but knowledge could be spread out; knowledge, I might add, which I can back up completely by my own researches. Nothing has been referred to or touched upon in this concise history which has not passed through my fingers or which has not been thoroughly studied by me. All dates, likewise, were checked so that I have been able to correct, and that without much ado, not a few of the errors in Eisler's indispensable Philosophen Lexikon as well as other, older, reference works." (From the Preface).

  25. Shenefelt, Michael, and White, Heidi. 2013. If A then B: How the World Discovered Logic. New York: Columbia University Press.

    "There are excellent histories of logic already in circulation (including the magisterial Development of Logic by William and Martha Kneale, Oxford University Press, 1962). And thanks to online sources, there are also

    many able accounts of the latest work in the field, including nonclassical symbolic logic. Nevertheless, we believe our book to be fundamentally different from previously published works. Earlier histories of logic have focused on the specific stories of individual logicians, relating their discoveries, their intellectual influences, and their personal predicaments. But logic is the work of more than logicians alone; logicians, like other writers, need readers, and the forming of a readership is just as vital to the survival of a logician’s insights as the logician’s individual circumstances.

    In logic, as in other departments of intellectual history, a readership is a consequence of social forces—forces that affect large numbers of people, quite apart from individual will. As a result, if one then leaves out of consideration the forces shaping such a readership (or the forces shaping a logician’s audience), one is in danger of missing much of the explanation of why logical discoveries show up when and where they do.


    "More broadly, to treat logic’s history as if it were only a matter of individuals, without considering the larger forces shaping the audience and the logician alike, would be like treating political history as if it were only a matter of individuals—as a tale of specific rulers or rebels but with no account of why large numbers of contemporaries reacted to their actions in any particular way. It would be like treating political history as only a story of the insights, villainies, and sacrifices of particular persons, with no social analysis.

    In making these claims for the importance of social forces in the development of logic, we in no way deny the significance of the individual in history; rather, we contend that historical changes can have many different causes. The social process can be an important force—just as important as the individual. And in stressing this point, we see ourselves not as contradicting earlier work in the history of logic but as offering a further level of explanation." (Preface, pp. XI-XIII)

  26. Styazkhin, N. I. 1969. History of Mathematical Logic from Leibniz to Peano. Cambridge: The M.I.T. Press.

    Contents: Preface V-VI; Chapter One. The Development of Mathematical Logic During the Middle Ages in Europe 1; Chapter Two. Leibniz, The Founder of Symbolic Logic 56; Chapter Three. The Development of Symbolic Logic After Leibniz; the Seventeenth and Eighteenth Centuries 93; Chapter Four. Forerunners of the Algebra of Logic of George Boole 137; Chapter Five. George Boole’s Calculus of Classes 170; Chapter Six. The Development of the Algebra of Logic After Boole at the End of the Nineteenth Century 203; Conclusions 283; References 285; Index 315-333.

    "Two basic approaches have been used by researchers in studying the history of logic: the philological and the “retrospective- logical.” The first approach entails careful terminological examination of source materials, comparison of different variants of the same documents, and clarification of the relationships between the logical facts and the data from the science of language. The second approach reduces to analysis of older logical concepts in order to find elements of contemporary viewpoints, using contemporary logical apparatus as a thread of Ariadne for guidance through the labyrinth of past logical investigations.

    While both these approaches have undeniable advantages, they also have disadvantages. Historians who use the philological approach risk reducing their study to a history of terminological innovation, while researchers using the retrospective-logical method run the risk of modernizing the material under investigation. This book attempts to combine both approaches to avoid undesirable excesses. In considering older logical theories, the author has tried to explain how they have affected the corresponding modern viewpoints and simultaneously to devote the requisite attention to philological aspects.

    This book deals with the development of a number of ideas and attitudes in mathematical logic, covering the period from the Middle Ages to the beginning of the twentieth century.

    Throughout its entire history, mathematical logic has been closely related to development of other sciences, and its own development has been affected by the state of scientific methodology (primarily mathematics)." (Preface, p. V)