This chapter contains sections titled: Introduction How to Read Maimonides' Guide of the Perplexed Belief and Articles of Faith The Art of Biblical Exegesis: Harvesting “Apples of Gold” Language and Logic Philosophy and the Art of Demonstration Conclusion: Implications of Maimonides' Views further reading.

This Handbook documents the main trends in current research between logic and language, including its broader influence in computer science, linguistic theory and cognitive science. The history of the combined study of Logic and Linguistics goes back a long way, at least to the work of the scholastic philosophers in the Middle Ages. At the beginning of this century, the subject was revitalized through the pioneering efforts of Gottlob Frege, Bertrand Russell, and Polish philosophical logicians such as Kazimierz Ajdukiewicz. Around (...) 1970, the landmark achievements of Richard Montague established a junction between state-of-the-art mathematical logic and generative linguistic theory. Over the subsequent decades, this enterprise of Montague Grammar has flourished and diversified into a number of research programs with empirical and theoretical substance. This appears to be the first Handbook to bring logic-language interface to the fore. Both aspects of the interaction between logic and language are demonstrated in the book i.e. firstly, how logical systems are designed and modified in response to linguistic needs and secondly, how mathematical theory arises in this process and how it affects subsequent linguistic theory. The Handbook presents concise, impartial accounts of the topics covered. Where possible, an author and a commentator have cooperated to ensure the proper breadth and technical content of the papers. The Handbook is self-contained, and individual articles are of the highest quality. (shrink)

The mnemonic arts and the idea of a universal language that would capture the essence of all things were originally associated with cryptology, mysticism, and other occult practices. And it is commonly held that these enigmatic efforts were abandoned with the development of formal logic in the seventeenth century and the beginning of the modern era. In his distinguished book, Logic and the Art of Memory Italian philosopher and historian Paolo Rossi argues that this view is belied by an examination (...) of the history of the idea of a universal language. Based on comprehensive analyses of original texts, Rossi traces the development of this idea from late medieval thinkers such as Ramon Lull through Bruno, Bacon, Descartes, and finally Leibniz in the seventeenth century. The search for a symbolic mode of communication that would be intelligible to everyone was not a mere vestige of magical thinking and occult sciences, but a fundamental component of Renaissance and Enlightenment thought. Seen from this perspective, modern science and combinatorial logic represent not a break from the past but rather its full maturity. Available for the first time in English, this book (originally titled Clavis Universalis ) remains one of the most important contributions to the history of ideas ever written. In addition to his eagerly anticipated translation, Steven Clucas offers a substantial introduction that places this book in the context of other recent works on this fascinating subject. A rich history and valuable sourcebook, Logic and the Art of Memory documents an essential chapter in the development of human reason. (shrink)

The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on logic. (...) -/- Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed. The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept. -/- Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study. (shrink)

The mnemonic arts and the idea of a universal language that would capture the essence of all things were originally associated with cryptology, mysticism, and other occult practices. And it is commonly held that these enigmatic efforts were abandoned with the development of formal logic in the seventeenth century and the beginning of the modern era. In his distinguished book, _Logic and the Art of Memory_ Italian philosopher and historian Paolo Rossi argues that this view is belied by an examination (...) of the history of the idea of a universal language. Based on comprehensive analyses of original texts, Rossi traces the development of this idea from late medieval thinkers such as Ramon Lull through Bruno, Bacon, Descartes, and finally Leibniz in the seventeenth century. The search for a symbolic mode of communication that would be intelligible to everyone was not a mere vestige of magical thinking and occult sciences, but a fundamental component of Renaissance and Enlightenment thought. Seen from this perspective, modern science and combinatorial logic represent not a break from the past but rather its full maturity. Available for the first time in English, this book remains one of the most important contributions to the history of ideas ever written. In addition to his eagerly anticipated translation, Steven Clucas offers a substantial introduction that places this book in the context of other recent works on this fascinating subject. A rich history and valuable sourcebook, _Logic and the Art of Memory_ documents an essential chapter in the development of human reason. (shrink)

The mnemonic arts and the idea of a universal language that would capture the essence of all things were originally associated with cryptology, mysticism, and other occult practices. And it is commonly held that these enigmatic efforts were abandoned with the development of formal logic in the seventeenth century and the beginning of the modern era. In his distinguished book, Logic and the Art of Memory Italian philosopher and historian Paolo Rossi argues that this view is belied by an examination (...) of the history of the idea of a universal language. Based on comprehensive analyses of original texts, Rossi traces the development of this idea from late medieval thinkers such as Ramon Lull through Bruno, Bacon, Descartes, and finally Leibniz in the seventeenth century. The search for a symbolic mode of communication that would be intelligible to everyone was not a mere vestige of magical thinking and occult sciences, but a fundamental component of Renaissance and Enlightenment thought. Seen from this perspective, modern science and combinatorial logic represent not a break from the past but rather its full maturity. Available for the first time in English, this book (originally titled Clavis Universalis) remains one of the most important contributions to the history of ideas ever written. In addition to his eagerly anticipated translation, Steven Clucas offers a substantial introduction that places this book in the context of other recent works on this fascinating subject. A rich history and valuable sourcebook, Logic and the Art of Memory documents an essential chapter in the development of human reason. (shrink)

This long-awaited translation of Das literarische Kunstwerk makes available for the first time in English Roman Ingarden's influential study. Though it is inter-disciplinary in scope, situated as it is on the borderlines of ontology and logic, philosophy of literature and theory of language, Ingarden's work has a deliberately narrow focus: the literary work, its structure and mode of existence. The Literary Word of Art establishes the groundwork for a philosophy of literature, i.e., an ontology in terms of which the basic (...) general structure of all lliterary works can be determined. This "essential anatomy" makes basic tools and concepts available for rigorous and subtle aesthetic analysis. (shrink)

This long-awaited translation of _Das literarische Kunstwerk_ makes available for the first time in English Roman Ingarden's influential study. Though it is inter-disciplinary in scope, situated as it is on the borderlines of ontology and logic, philosophy of literature and theory of language, Ingarden's work has a deliberately narrow focus: the literary work, its structure and mode of existence. _The Literary Word of Art _establishes the groundwork for a philosophy of literature, i.e., an ontology in terms of which the basic (...) general structure of all lliterary works can be determined. This "essential anatomy" makes basic tools and concepts available for rigorous and subtle aesthetic analysis. (shrink)

This volume contains twelve previously published essays, dealing with non-formal modes of inference, with some specifically logical issues, with language and symbolic representation, with Goodman, Chomsky, and Skinner. In the first, "Reasonableness," we are told that "it would be heroic folly to aspire to be reasonable in all situations," and that reasonableness turns out to be "a somewhat humdrum, pedestrian virtue, involving... a problematic calculation of probabilities and expected values in situations of inescapable fallibility." Still, we are happily told that (...) "in a situation in which it is uncertain which action to take, an action is reasonable if there is some sufficient reason to take it, and no better reason to choose one of the alternatives.". (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 36.2 (2003) 168-172 [Access article in PDF] Logic and the Art of Memory: The Quest for a Universal Language. Paolo Rossi. Trans. Stephen Clucas. Chicago: University of Chicago Press, 2000. Pp. xxviii + 333. $32.00 cloth. Of the traditional five canons of rhetoric—inventio, dispositio, elocutio, memoria, and actio—the most circuitous and fascinating history belongs to memoria. From its propulsion of Homeric lore to its grounding of (...) rhetorical invention to its exile under print culture to its recent revival in public memory studies, the promiscuous and perplexing history of memory in the West may be one of the least appreciated, and perhaps least understood, elements of rhetorical and intellectual history. The publication in 1966 of Frances Yates's highly praised The Art of Memory drew the attention of contemporary scholars to the importance of mnemotechnics to the culture of late medieval and early modern Europe. 1 Yates persuasively argued that the art of memory is an integral element of European intellectual history, one that can enrich our understanding of everything from Dominican theology to Shakespearian theater. However, six years earlier, in 1960, the Italian intellectual historian Paolo Rossi published in Italian an important precursor to Yates's work entitled Clavis Universalis: Arti Della Memoria e Logica Combinatoria da Lullo a Leibniz. The book traces the encyclopaedic and mnemotechnical traditions from Aristotle through Cicero and Raymond Lull and into the early-modern period, arguing that the art of memory provides an important antecedent to the advent of method in seventeenth-century philosophy, especially in the works of Bacon, Descartes, and Leibniz. Yates, in her preface to The Art of Memory, acknowledges her debt to Rossi's work, and now this work has been made available in English translation. Stephen Clucas's translation, under the title Logic and the Art of Memory, will no doubt stimulate and supplement research into the mnemotechnical tradition in the English-speaking world, and perhaps lead us to reconsider the relationship between philosophy and rhetoric.Rossi argues that the neglect of the mnemotechnical tradition in its Ciceronian and Lullian strands has distorted our understanding of the "new" science and philosophy of the seventeenth-century, which is often interpreted as constituting, in a Kuhnian sense, a drastic paradigm shift from a [End Page 168] Renaissance worldview that still retained occult elements. Rossi places the work of Bacon, Descartes, and Leibniz within the historical strand of the logico-encyclopaedic and mnemotechnical traditions, suggesting that these figures culminate late medieval and early modern intellectual and cultural ambitions as much as they give rise to new ones. Rossi makes his argument by providing a history of mnemotechnics from Aristotle into the fifteenth century in chapter one; by examining the fascination with encyclopaedism, combinatoria, and memory in the sixteenth century in chapters two and three; by investigating the role of artificial memory in the works of key intellectual figures in the late sixteenth and seventeenth centuries in chapters four through six; and by tracing the impulse toward universal knowledge and its connection to mnemotechnics among seventeenth-century Cartesians, Baconians, and in the work of Leibniz, in chapters seven and eight.Chapter one, after showing the pervasiveness of Renaissance mnemotechnical literature, surveys its classical and medieval antecedents in philosophy and rhetoric. Rossi argues that Aristotle's De memoria et reminiscentia, Cicero's De oratore, Quintilian's De institutione oratoria, the Rhetorica ad Herennium, and the works of Albertus Magnus and Thomas Aquinas were each important to the mnemotechnical tradition into the seventeenth century. Fourteenth- and fifteenth-century treatises on the ars memorativa and the ars predicandi, drawing on these classical and medieval theories, emphasize the importance of memory places (loci), images (imagines), and order or arrangement (dispositio) in mnemotechnics. Additionally, they intimately link the memory to the imagination, stressing the importance of exciting and stimulating the imagination in memorization. The Italian Pietro da Ravenna, for example, attributed the might of his memory to, in his own words, turning "the images of the most beautiful virgins into memory places" (22). Such imaginative mnemonic techniques were considered to... (shrink)

This book explores the reaction of tenth-century Arab philosopher Abu Nasr Alfarabi to the logical works of Aristotle. From numerous short treatises the author develops a systematic and comprehensive topical survey of Alfara bi's logical writings. The book is divided into two major parts: language as a tool of logic and logic as a tool with which to analyze language. The first five chapters deal with Alfarabi's analysis of the meanings of various terms as they are used in logic and (...) philosophy. Alfarabi refutes the Arab grammarians who claimed that Arab logicians were building a language within a language and shows that the philosophical meanings of terms are in fact their most original and essential meanings. The final chapter deals with Alfarabi's analysis of certain aspects of the Arabic language and demonstrates that Arabic, like any natural language, conforms to universal logical structures of which natural languages are only a concrete expression. (shrink)

The papers collected in this volume exemplify some of the trends in current approaches to logic, language and computation. Written by authors with varied academic backgrounds, the contributions are intended for an interdisciplinary audience. The first part of this volume addresses issues relevant for multi-agent systems: reasoning with incomplete information, reasoning about knowledge and beliefs, and reasoning about games. Proofs as formal objects form the subject of Part II. Topics covered include: contributions on logical frameworks, linear logic, and different approaches (...) to formalized reasoning. Part III focuses on representations and formal methods in linguistic theory, addressing the areas of comparative and temporal expressions, modal subordination, and compositionality. (shrink)

This volume presents a collection of refereed papers reflecting the state of the art in the area of over-constrained systems. Besides 11 revised full papers, selected from the 24 submissions to the OCS workshop held in conjunction with the First International Conference on Principles and Practice of Constraint Programming, CP '95, held in Marseilles in September 1995, the book includes three comprehensive background papers of central importance for the workshop papers and the whole field. Also included is an introduction by (...) one of the volume editors together with a bibliography listing 243 entries. All in all this is a very useful reference book relevant for all researchers and practitioners interested in hierarchical, partial, and over-constrained systems. (shrink)

Monique Roelofs offers a pathbreaking systematic model of the field of address and puts it to work in the arts, critical theory, and social life. She shows how address props up finely hewn modalities of relationality, agency, and normativity. Address exceeds a one-on-one pairing of cultural productions with their audiences. As ardently energizing tiny slippages and snippets as fueling larger impulses in the society, it activates and reaestheticizes registers of race, gender, class, coloniality, and cosmopolitanism. In readings of writers and (...) artists ranging from Julio Cortázar to Jamaica Kincaid and from Martha Rosler to Pope.L, Roelofs demonstrates the centrality of address to freedom and a critical political aesthetics. Under the banner of a unified concept of address, Hume, Kant, and Foucault strike up conversations with Benjamin, Barthes, Althusser, Fanon, Anzaldúa, and Butler. Drawing on a wide array of artistic and theoretical sources and challenging disciplinary boundaries, the book illuminates address's significance to cultural existence and to our reflexive aesthetic engagement in it. (shrink)

During the early 19th century, a peculiarly systematic way of organizing books emerged in Germany. This systematization, which purported to be a rational organization of subject matter, was an outgrowth of the philosophy of Hegel. This article attempts to outline Hegel's organizational practice. It argues that Hegel's encyclopedia was a reaction against the Enlightenment encyclopedia, and that it attempted to restore the systematic mindset of pre-modern reference books. Yet it did this, not in a straightforward fashion, but by developing a (...) method for organizing material that both stresses the interconnectedness of knowledge and promises to be highly scalable. In its attempt to trace the Hegelian organizational method, this article revisits and calls attention to a forgotten work in Hegel scholarship by Michael John Petry, who was the first writer to seriously stress the importance of classification in Hegel's work. This article is an attempt to demonstrate that Hegelianism and information organization can be brought into fruitful and mutually beneficial dialogue. (shrink)

Antoine Arnauld and Pierre Nicole were philosophers and theologians associated with Port-Royal Abbey, a centre of the Catholic Jansenist movement in seventeenth-century France. Their enormously influential Logic or the Art of Thinking, which went through five editions in their lifetimes, treats topics in logic, language, theory of knowledge and metaphysics, and also articulates the response of 'heretical' Jansenist Catholicism to orthodox Catholic and Protestant views on grace, free will and the sacraments. In attempting to combine the categorical theory of the (...) proposition with a Cartesian account of knowledge, their Logic represents the classical view of judgment which inspired the modern transformation in logic and semantic theory by Frege, Russell, Wittgenstein and recent philosophers. This edition presents a new translation of the text, together with a historical introduction and suggestions for further reading. (shrink)

In ancient philosophy, Logic was seen as the instrument and method of philosophy. However, sometimes detailed and profound discussions have been made about the demonstrativeness of philosophical sciences. Most philosophers have accepted that the mathematical sciences were especially demonstrative and likewise, most of the natural sciences are demonstrative for them. But can metaphysics be demonstrative or not? This is one of the fundamental issues around which the great debates were made in Islamic philosophy. While these issues are known to specialists (...) in this field, we can hardly find studies and research that deal with this issue to a sufficient degree and precise discussions in our day, I mean the issue of demonstrativeness of art of demonstration, art of dialectic, art of sophistry, art of rhetoric and art of poetry. It is clear that the peripatetic philosophers did not write a separate book or treatise on the issue of the demonstrativeness of the logical arts, but we can claim that they believed that all these arts were demonstrative and that they were extracted/abstracted using the art of demonstration. We can come across important phrases and statements that prove this claim between the lines of the books that these philosophers wrote in the science of logic. And while Aristotle is the founder of the science of logic, then how is it to be understood that there are practical particular examples and some easy rules of these arts? According to their texts, we can say that they believed that the actual performance of these arts by their actors in materials by particular and practical actions differs from extracting their universal rules by abstracting them from their materials through theoretical and analytical research. For example, the poems of the great poets; Homer and al-Mutanabbi, are particular works in the matter of the art of poetry performed by poets. The books written by Aristotle and Ibn Rushd in the art of poetry contain universal rules extracted abstractly from the materials of their particular poems. As for understanding the demonstrativeness of the remaining four arts, it is easier, but how should we understand the demonstrativeness of the art of demonstration itself? It seems that the peripatetic logicians also distinguished between applying demonstrative inferences to significant materials and extracting the universal rules of the art of demonstration from these materials. These five logical arts are not particular and practical things, but they are philosophical, demonstrative, and analytical studies for the peripatetic logicians in Islam. In this paper, we will try to draw attention to the issue of the demonstrativeness of the five arts and to open a new discussion about it based on some important sentences and phrases expressed by al-Fārābī, Ibn Zur‘a, Ibn Sīnā, Ibn Bājja and Ibn Rushd between the lines in their books, which they wrote in the field of logic and within different and multiple contexts. (shrink)

This introduction to logic, which aims to reflect recent advances in the field, focuses on natural language, analyzing the structure of arguments conducted in English. The text includes problems with which students can test their skills.

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 translation of a classic and original work of intellectual history is beautifully done. Rossi’s book Clavis Universalis was first published in Italian in 1960, but Clucas translates the second, revised edition of 1983. The book is about Renaissance and 17th-century encyclopedism, hieroglyphics and cryptography, the techniques of artificial memory, the history of rhetoric, changes in views about logic and method in the scientific revolution, and new ideas about how language and images might reflect or capture reality. Frances Yates’s brilliant (...) The Art of Memory, published in 1966, has so far had much more influence in the English-speaking world. Despite warm citations and many points of contact with Yates’s work, Rossi is less interested in uncovering hidden occult traditions, and more focussed on the way major 17th-century thinkers’ work must be understood against the rich background of schemes for universal grammar and local memory. He shows that scholars working on Bacon, Descartes, and Leibniz miss key references to this intellectual heritage. Half of the book [152] introduces relevant mnemonic, rhetorical, linguistic, medical, and occult writings. Rossi includes illuminating discussions not only of Ramon Lull, Petrus Ramus, Cornelius Agrippa, Giordano Bruno, and all, but also of fascinating minor writers like Guglielmo Gratorolo who systematized advice on medical aids to memory in the mid-16th century, and the wonderful Johannes Spangerbergius, who classified various forms of amnesia in 1570. He then argues that polemic against the arts of memory in both Bacon and Descartes coexisted with intense interest on their part in the supplementing of weak powers of natural memory by various artificial aids and objects outside the boundaries of skull and skin. Rossi tells the strange stories of the great 17th-century encyclopedists and universal language schemers—Alsted, Comenius, Wilkins, Dalgarno—making important connections between Wilkins’s scheme and worries about methods for botanical classification in the early Royal Society. The final chapter is a tour de force on ‘the sources of Leibniz’s universal character’, placing him (as Clucas neatly puts it) ‘at the “end” of a Renaissance intellectual tradition rather than reading him “forwards” as an innovative precursor of modern formal logic’. Historians of science, linguistics, and philosophy have built on many aspects of Rossi’s work since 1983, and Clucas contributes an outstanding introduction which summarizes key strands of recent scholarship. (shrink)

Early in the 1240s the University of Paris hired a recent graduate from Oxford, Roger Bacon by name, to teach the arts and introduce Aristotle to its curriculum. Along with eight sets of questions on Aristotle's natural works and the Metaphysics he claims to have authored another eight books before he returned to Oxford around 1247. Within the prodigious output of this period we find a treatise on logic titled Summulae dialectices, and it is this that is here annotated and (...) presented in translation. The book is unique in several respects. First, there is the breadth of its sources. Not only do we find explicit reference to the usual authors such as Aristotle, Plato, Boethius, Porphyry, Cicero, and Priscian, we also find unexpected reference to Augustine, Bernardus Silvestris, Donatus, Terence, and Themistius, along with mention of the Muslim philosophers Algazel and Ibn Rushd. Second, it is clear that Bacon is drawing on or reacting to an extraordinarily wide variety of medieval sources: Garland the Computist, Hugh of St. Victor, Master Hugo, Hugutius of Pisa, Isidore of Seville, Nicholas of Damas, Nicholas of Paris, Richard of Cornwall, Robert Kilwardby, Robert of Lincoln, and Robert the Englishman. Third, it unexpectedly presents a full-blown treatment of Aristotle's theory of demonstration. And finally, Bacon reveals a highly unorthodox view of the signification of common terms. Bacon, here, takes his students and us deeper into medieval sources and controversy than any of his rivals do. (shrink)

Natural languages are riddled with context-sensitivity. One and the same string of words can express many different meanings on occasion of use, and yet we understand one another effortlessly, on the fly. How do we do so? What fixes the meaning of context-sensitive expressions, and how are we able to recover the meaning so effortlessly? -/- This book offers a novel response: we can do so because we draw on a broad array of subtle linguistic conventions that determine the interpretation (...) of context-sensitive items. Contrary to the dominant tradition, which maintains that the meaning of context-sensitive language is underspecified by grammar and that interpretation relies on non-linguistic cues and speakers' intentions, this book argues that meaning is determined entirely by discourse conventions, rules of language that have largely been missed and the effects of which have been mistaken for extra-linguistic effects of an utterance situation on meaning. The linguistic account of context developed here sheds new light on the nature of linguistic content and the interaction between content and context. At the same time, it provides a novel model of context that should constrain and help evaluate debates across many subfields of philosophy where appeal to context has been common, often leading to surprising conclusions such as epistemology, ethics, value theory, metaphysics, metaethics, and logic. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Logic Pamphlets of Charles Lutwidge Dodgson and Related PiecesIrving H. AnellisFrancine F. Abeles, editor. The Logic Pamphlets of Charles Lutwidge Dodgson and Related Pieces. The Pamphlets of Lewis Carroll, 4. New York-Charlottesville-London: Lewis Carroll Society of North America-University Press of Virginia, 2010. Pp. xx + 271. Cloth, $75.00.Until William Bartley’s rediscovery and reconstruction of Dodgson’s lost Part II of Symbolic Logic, Lewis Carroll’s reputation in logic, when (...) taken seriously, rested upon his few published articles on logical paradoxes and puzzles, while his published books, The Game of Logic and Symbolic Logic, were regarded as suitable perhaps as pedagogical tools, but dismissed otherwise as amusements, on a par with the Alice works. Richard Braithwaite asserted (“Lewis Carroll as Logician”) that “Carroll regarded formal and symbolic logic not as a corpus of systematic knowledge about valid thought nor yet as an art for teaching a person to think correctly.” He suggested that Dodgson used his pseudonym for his popular and whimsical writings, reserving his legal name only for his serious mathematical products. Philosophers practicing linguistic analysis in their assault on nonsense deriving from misuse of language meanwhile developed an interest in Carroll (e.g. George Pitcher, “Wittgenstein, Nonsense, and Lewis Carroll”). Abeles, on the contrary, stresses the seriousness of Dodgson’s pedagogical and popularizing mission (195–99).Bartley’s discovery opened the door for reevaluating Dodgson as a serious logician, and Abeles has been in the forefront of that reevaluation. Her general introduction and introductions to the main divisions of this collection of Carroll’s publications (and additional material from his Nachlass and a handful of publications of others, composed in response to Carroll’s published articles) place his serious logical work and its significance in historical perspective, providing a deeper, more sophisticated view than found in Bartley’s “Editor’s Introduction” to Lewis Carroll’s Symbolic Logic. Abeles also offers brief introductions to the individual entries, which describe their physical characteristics and circumstances of composition.Dodgson aligned with the majority of those British logicians of his day, starting with George Boole, who understood formal logic to be Aristotelian syllogistic, and symbolic logic to be syllogistic logic expressed algebraically. His notational innovation was employing indices to terms so that, independently of the arrangement of terms, propositions could easily be read; thus, “xy0” can be read as “no x are y” or “no y are x” and “x1y0” as “all x are not y” or “no x are y”. In dealing with the classical elimination problem in the class calculus—to determine the maximum information, without duplications, obtainable from a given set of premises—Dodgson in his later work and unpublished letters anticipated several concepts of automated theorem proving.Central to both geometry and to formal logic are the rules of logical inference that establish the validity of arguments and guarantee that conclusions inferred from true [End Page 506] premises are true. The modern analytic tableaux, or tree method, is a fundamental tool in this regard, both for deriving theorems and for determining the validity or invalidity of the proofs for propositional calculus and first-order predicate calculus.Introducing his reconstruction of Part II of Symbolic Logic, Bartley noted that, along with the logic diagrams that Carroll devised, he also devised a tableau method that strongly resembled Beth’s semantic tableaux. Abeles went more deeply and convincingly into that resemblance in her earlier research. Beth’s tableaux, together with Hintikka’s model sets, were the direct ancestors of Smullyan’s analytic tableaux, which in turn are the theoretical basis for the Robinson resolution method that continues to be central to much work in programming logic.Abeles has also shown that the work in Studies in Logic by Charles Peirce and his logic students at Johns Hopkins University served as a source of inspiration for Dodgson. More critically, she demonstrated that Dodgson devised and employed the tree method for carrying out proofs of syllogisms and chains of syllogisms, or soriteses, in Part II of Symbolic Logic (see her “Lewis Carroll’s Method of Trees: Its Origins in Studies in Logic,” Modern Logic 1 [1990]: 25–34). The tree... (shrink)

George Wilhelm Friedrich Hegel has seldom been considered a major figure in the history of logic. His two texts on logic, both called The Science of Logic, both written in Hegel's characteristically dense and obscure language, are often considered more as works of metaphysics than logic. But in this highly readable book, John Burbidge sets out to reclaim Hegel's Science of Logic as logic and to get right at the heart of Hegel's thought. Burbidge examines the way Hegel moves from (...) concept to concept through every chapter of his work, and traces the origins of Hegel's effort to "think through the way thought thinks" to Plato, Kant, and Fichte. Having established the framework of Hegel's logical thought, Burbidge demonstrates how Hegel organized the rest of his system, including the Philosophy of Nature, Philosophy of Spirit and his Lectures on World History, Art, Religion and Philosophy. A final section discusses English-language interpretations of Hegel's logic from the nineteenth through twentieth centuries. Burbidge's The Logic of Hegel's 'Logic' is written with an eye to the reader of general interests, avoiding as much as possible the use of Hegel's technical vocabulary. It is an excellent introduction to an otherwise very difficult text, and has recently appeared in an Iranian translation. (shrink)

Though it is inter-disciplinary in scope, situated as it is on the borderlines of ontology and logic, philosophy of literature and theory of language, Ingarden's work has a deliberately narrow focus: the literary work, its structure and ...

Kaplan (1989a) insists that natural languages do not contain displacing devices that operate on character—such displacing devices are called monsters. This thesis has recently faced various empirical challenges (e.g., Schlenker 2003; Anand and Nevins 2004). In this note, the thesis is challenged on grounds of a more theoretical nature. It is argued that the standard compositional semantics of variable binding employs monstrous operations. As a dramatic first example, Kaplan’s formal language, the Logic of Demonstratives, is shown to contain monsters. For (...) similar reasons, the orthodox lambda-calculus-based semantics for variable binding is argued to be monstrous. This technical point promises to provide some far-reaching implications for our understanding of semantic theory and content. The theoretical upshot of the discussion is at least threefold: (i) the Kaplanian thesis that “directly referential” terms are not shiftable/bindable is unmotivated, (ii) since monsters operate on something distinct from the assertoric content of their operands, we must distinguish ingredient sense from assertoric content (cf. Dummett 1973; Evans 1979; Stanley 1997), and (iii) since the case of variable binding provides a paradigm of semantic shift that differs from the other types, it is plausible to think that indexicals—which are standardly treated by means of the assignment function—might undergo the same kind of shift. (shrink)

This paper determines the state of mind, logic and language in medieval philosophy. It also exhibits the journey from medieval to early modern philosophy. In medieval philosophy, concept of mind was intimately connected soul or spirit with its harmony with religious tradition. Logic and language as well were corresponding with religion and faith. However in early modern philosophy the schema of mind, logic and language were different. These concepts were bailed from the clutches of religious dogmatism and faith towards the (...) mechanical correspondence. Mind was treated as non-modular. Logical truth which includes mostly inductive and deductive in medieval and modern period has been explained clearly. This paper shows the evolution of these concepts in the tradition of Rationalists, Empiricists and Critical Philosophers. In this paper I would as well show the interrelation between mind along with language and logic. This write up further shows the development of language in medieval period to early modern philosophy. it also demonstrates the footprints for the analytical study and international study in contemporary philosophy. (shrink)

Goldin thus begins the book by asking the basic question "What are we reading?" while also considering why it has been so rarely asked. Yet far from denigrating Chinese philosophy, he argues that liberating these texts from the mythic idea that they are the product of a single great mind only improves our understanding and appreciation. By no means does a text require single and undisputed authorship to be meaningful; nor is historicism the only legitimate interpretive stance. The first chapter (...) takes up a hallmark of Chinese philosophy that demands a Western reader's cognizance: its preference for non-deductive argumentation. Chinese philosophy is an art he demonstrates, more than it is a rigorous logical method. Then comes the core of the book, eight chapters devoted to the eight philosophical texts divided into three parts: Philosophy of Heaven, Philosophy of the Way, and Two Titans at the End of an Age.. (shrink)

Antoine Arnauld and Pierre Nicole were philosophers and theologians associated with Port-Royal Abbey, a centre of the Catholic Jansenist movement in seventeenth-century France. Their enormously influential Logic or the Art of Thinking, which went through five editions in their lifetimes, treats topics in logic, language, theory of knowledge and metaphysics, and also articulates the response of 'heretical' Jansenist Catholicism to orthodox Catholic and Protestant views on grace, free will and the sacraments. In attempting to combine the categorical theory of the (...) proposition with a Cartesian account of knowledge, their Logic represents the classical view of judgment which inspired the modern transformation in logic and semantic theory by Frege, Russell, Wittgenstein and recent philosophers. This edition presents a new translation of the text, together with a historical introduction and suggestions for further reading. (shrink)

This is the first of two volumes comprising the papers submitted for publication by the invited participants to the Tenth International Congress of Logic, Methodology and Philosophy of Science, held in Florence, August 1995. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science. The invited lectures published in the two volumes demonstrate much of what goes on in the fields of the Congress and give (...) the state of the art of current research. The two volumes cover the traditional subdisciplines of mathematical logic and philosophical logic, as well as their interfaces with computer science, linguistics and philosophy. Philosophy of science is broadly represented, too, including general issues of natural sciences, social sciences and humanities. The papers in Volume One are concerned with logic, mathematical logic, the philosophy of logic and mathematics, and computer science. (shrink)

How do you tell what’s right from what’s wrong? Can you always? What’s the difference between deduction, induction, and abduction? What are the best techniques for making an argument logically sound? In this fascinating little book, the smallest on its subject ever produced, philosopher Earl Fontainelle explores the ancient art of discursive Logic and demonstrates some of the techniques that have long been used to triumph over the debates and deceptions that assail us every day. Filled with helpful examples of (...) good and bad reasoning, Logic is an invaluable introduction to a defining human characteristic. (shrink)

Sport occupies a significant role in modern society and has a wide following. In his Leftist Theories of Sport, Morgan examines what he considers to be a degradation of modern sport and the lack of proper critical theory to address this challenge. In the latter part of LTS, Morgan presents a reconstructed critical theory with ‘a liberal twist’ in terms of an analysis of what he sees as the internal ‘gratuitous’ logic of sport, and a call for critical deliberation in (...) sporting practice communities. I depart from Morgan’s ideas of the ‘gratuitous’ logic of sport which, I believe, has significant potential and operative force. I interpret the logic of sport as forms of self-imposed constraints at three levels: in the logic of the rules, in norms for fair play, and in a particular interpretation of sporting excellence as a form of human excellence. Using the practical case of performance-enhancing drugs, I demonstrate how this interpretation can exert operative power. I conclude by pointing to th... (shrink)

Wittgenstein’s language games can be put into a wider service by virtue of elements they share with some contemporary opinions concerning logic and the semantics of computation. I will give two examples: manifestations of language games and their possible variations in logical studies, and their role in some of the recent developments in computer science. It turns out that the current paradigm of computation that Girard termed Ludics bears a striking resemblance to members of language games. Moreover, the kind of (...) interrelations that are emerging could be scrutinised from the viewpoint of logic that virtually necessitates game-theoretic conceptualisations, demonstrating the fact that the meaning of utterances may, in many situations, be understood as Wittgenstein’s language games of ‘showing or telling what one sees’. This provides motivation for the use of games in relation to logic and formal semantics that some commentators have called for. Many of the ideas can be traced to C.S. Peirce, for whom signs were vehicles of strategic communication. The conclusion about Wittgenstein is that the notions of saying and showing converge in his late philosophy. (shrink)

"The role of logic in the Middle Ages. Regarding the role of logic within the framework of arts and sciences during the Middle Ages, we have to distinguish two related aspects, one institutional and the other scientific. As to the first aspect, we have to remember that the medieval educational system was based on the seven liberal arts, which were divided into the trivium, i.e., three arts of language, and the quadrivium, i.e., four mathematical arts. The so-called trivial arts were (...) grammar, rhetoric, and logic, and during a period of several centuries virtually every educated person, at least every university graduate, received a training in these matters, especially in logic. Students in the medieval faculty of arts probably spent more time studying logic than any other discipline. This first -- institutional -- aspect concerning the role of logic is explained by the second -- scientific -- aspect. The trivial disciplines provided techniques of analysis and a technical vocabulary that permeate philosophical, scientific and theological writings. Logic, as mentioned before, was referred to and was generally regarded as the art of arts and the science of sciences. The increasing cultural dominance of the universities with their obligatory disputationes and their hierarchy of examinations on the one hand and the outstanding status of logic on the other were corresponding features of the educational world of the 13th century. The core of the logic curriculum from the 12th century onwards was provided by the logical works of Aristotle. These represented the material for the study of types of predication, the analysis of simple propositions or statements (2) and their relations of inference and equivalence, the analysis of modal propositions, of the structure and the types of the syllogism, dialectical topics, fallacies and scientific reasoning as based on the demonstrative syllogism. Medieval logicians, however, realized that there were other, non-Aristotelian, approaches to logical subjects, questions and methods that could be investigated.. (shrink)

This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by Yli-Vakkuri and Hawthorne, who seek to establish that mathematics is committed to its own necessity. I demonstrate that their assumptions collapse the counterfactual conditional into the material conditional. This collapse entails the success of counterfactual strengthening, which is controversial within counterfactual logic, and which has counterexamples within pure and applied mathematics. I close (...) by discussing the dispensability of counterfactual conditionals within the language of mathematics. (shrink)

In the twelfth and thirteenth centuries, new ways of storytelling and inventing fictions appeared in the French-speaking areas of Europe. This new art still influences our global culture of fiction. Virginie Greene explores the relationship between fiction and the development of neo-Aristotelian logic during this period through a close examination of seminal literary and philosophical texts by major medieval authors, such as Anselm of Canterbury, Abélard, and Chrétien de Troyes. This study of Old French logical fictions encourages a broader theoretical (...) reflection about fiction as a universal human trait and a defining element of the history of Western philosophy and literature. Additional close readings of classical Greek philosophers Plato and Aristotle, and modern analytic philosophy including the work of Bertrand Russell and Rudolf Carnap, demonstrate peculiar traits of Western rationalism and expose its ambivalent relationship to fiction. (shrink)

Duality in Logic and Language [draft--do not cite this article] Duality phenomena occur in nearly all mathematically formalized disciplines, such as algebra, geometry, logic and natural language semantics. However, many of these disciplines use the term ‘duality’ in vastly different senses, and while some of these senses are intimately connected to each other, others seem to be entirely … Continue reading Duality in Logic and Language →.

The Joint International Conference on Logic Programming, sponsored by the Association for Logic Programming, is a major forum for presentations of research, applications, and implementations in this important area of computer science. Logic programming is one of the most promising steps toward declarative programming and forms the theoretical basis of the programming language Prolog and its various extensions. Logic programming is also fundamental to work in artificial intelligence, where it has been used for nonmonotonic and commonsense reasoning, expert systems implementation, (...) deductive databases, and applications such as computer-aided manufacturing. Krzysztof R. Apt is project leader at the Centre for Mathematics and Computer Science in Amsterdam and part-time Professor in Computer Science at the University of Amsterdam. Topics covered: Theory Foundations. Programming Languages. Implementation. Programming Methodologies and Tools. Applications. Deductive Databases. Artificial Intelligence. Parallelism. (shrink)

Speaking of truth inescapably confronts us with paradoxes, i.e., correct deductive propositions like a Cretan claiming that all Cretans lie which (due to negative systemic self-reference) end up as circular contradictions, indeterminable questions, or dilemmas. Faced with the numerous paradoxical statements (apparently 82) found in the Bible, the German Protestant reformer Sebastian Franck (14991542), for example, conceded that any truth of God cannot be found in language but only in the immediate silent experience of God. Likewise, believers in an uncompromising (...) search for true facts about this world would certainly agree with (though arguably misappropriate) Wittgenstein in claiming that Whereof one cannot speak, thereof one must be silent. Paradoxes this article claims must neither be feared, nor avoided, nor become subject to hopeless attempts in searching for logic solutions. Paradoxes lead the way to truth in demonstrating that questions of truth, or truth claims, cannot be adequately addressed within the same system of communication (ortho-system) in which they are raised. The encounter with paradoxes (e.g., a God who creates but is uncreated) elevates language and communication onto a meta-level (or system) of communication in which new means (like for instance Gdel's numbering) are needed to speak of what is real but apparently cannot be true. These means, however, will turn out to be likewise paradoxes that furthermore call for new and creative ways of speaking of such truths that previously could not be communicated. The creative admission of paradoxes into communication philosophy will not solve age-old problems or dilemmas; however, it will playfully open up the conversation of science with religion to the creative means of the arts were truth is not argued but performed in paradoxes. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Ethics and Economies of Inquiry: Certeau, Theory, and the Art of PracticeTony Schirato (bio) and Jen Webb (bio)In this paper we will look at what Certeau, in The Practice of Everyday Life, calls “Theories of the Art of Practice.” Certeau is perhaps best known as a theorist of the ways in which everyday practices inhabit the institutions and sites of power and official culture, while not being in (...) any sense recuperable or explicable to these “proper places.” In “Theories of the Art of Practice” he concerns himself not with cultural practices themselves but, rather, with the specific relationship between theoretical discourse and the object of that discourse. In order to do this he takes as examples certain cultural theorists—most obviously Foucault and Bourdieu—whose work is strongly underpinned by an emphasis on the relation between discourse and practice. He offers a detailed consideration and critique of their theories of practice and the tactics those theorists use to escape the theory/practice dichotomy.In the first two paragraphs of “Theories of the Art of Practice,” Certeau identifies the two points which, taken together, constitute the broad narrative of this section of Practice. The first relates to the theoretical basis from which we can approach practice. “Everyday practices,” he writes:depend on a vast ensemble which is difficult to delimit but which we may provisionally designate as an ensemble of procedures. The latter are schemas of operations and of technical manipulations. On the basis of some recent and fundamental analyses (those of Foucault, Bourdieu, Vernant and Détienne, and others) it is possible, if not to define them, at least to clarify their functioning relative to discourse (or to “ideology,” as Foucault puts it), to the acquired (Bourdieu’s habitus), and to the form of time we call an occasion (the kairos discussed by Vernant and Détienne). These are different ways of locating a technicity of a certain type and at the same time situating the study of this technicity with respect to current trends in research.[43]An important issue here is Certeau’s critique of the extent to which each theorist applies a specific technicity (Foucault’s disciplinary procedures, Bourdieu’s habitus) in an attempt to delimit the field, to reduce the multiplicity of practice—or the theorizing of practice—to a singularity. As he points out in his essay on Nicholas of Cusa [“The Gaze” 6], such “ways of proceeding are subject to a common problematics,” because they inscribe a particular way of thinking and seeing and, in that process, risk excluding other ways of understanding. However, Cusa’s praxis: [End Page 86]does not presuppose a language proper to theory, an autonomous metalanguage that would provide a distinct linguistic space for speculation.... A task related to each singularity liberates, as it were, and develops... the “impulsion” which is integral to each and which is revealed to be infinite by the very impossibility of finding a hierarchical unity among singularities.[“The Gaze” 7]What Certeau looks for in the work of Bourdieu and Foucault is the moment, or the “impulsion,” which allows a theoretical engagement with practice. If practice can’t be called up, defined, or finally explicated, what can be done is to plot the relationships between power and its structures, logics, places, and discourse and the objects of power (practices) it seeks to identify and regulate. This allows us to identify both how power seeks to exclude the heterogeneity that is practice and the ways in which practice, despite these acts of exclusion and regulation, leaves its mark on official places (discourses, institutions, the objective structures of cultural fields). What Certeau does is to explore how others (Foucault and Bourdieu in particular, Vernant and Détienne) have explored this terrain.The second move Certeau makes is to contextualize those theories of practice, not so much as metadiscourses or generalized maps but as practices themselves, specific to a time and place and informed both by their theoretical antecedents and by the politics, logics, and discourses of the field(s) within which they operate. This allows Certeau to exemplify both how bodies of theory (as well as intellectual fields) come about and develop and... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Bodily Arts: Rhetoric and Athletics in Ancient GreeceMindy FenskeBodily Arts: Rhetoric and Athletics in Ancient Greece by Debra Hawhee. Austin: University of Texas Press, 2004. Pp. xiv + 226. $40.00, hardcover.In Bodily Arts, Debra Hawhee constructs an often compelling, always interesting case for the conceptual and material linkages between the ancient arts of rhetoric and athletics. In so doing, Hawhee also highlights the integral role of the musical (...) arts to rhetorical and athletic training. Throughout the book, Hawhee weaves together close readings of multiple texts (poetry, oratory, sculpture, painting, architecture) in order to illuminate the intricate “network of overlapping practices” that connect the bodies of rhetoric, athletes, and musicians in Ancient Greece. To this reader, the central strengths of the study are methodological as well as conceptual. In terms of method, Hawhee carefully and with studied finesse integrates close readings of visual, spatial, and verbal texts and practices. In the wrong hands, this type of endeavor can easily appear as the worst kind of pastiche. Not so in this case where Hawhee manages the textual interpretation with deft expertise. Conceptually, the central premise that rhetoric was a practice that was fully embodied and, most importantly, that embodiment was not in a hierarchical relation to reason, rationality, and the mind is provocative. Hawhee argues that the relations of mind-body in Ancient Greek culture were understood as a complex interlocking system that, when trained through physical practices emphasizing rhythm, repetition, and response (to/with an encounter), resulted in the possible transformation of the very nature of the self. [End Page 197]In the process of constructing the argument for the connections between rhetorical and athletic training and performance, Bodily Arts moves through three phases. The Introduction and first three chapters lay the theoretical groundwork for the second phase: the introduction of the concept of phusiopoieses in Chapter 4. Chapters 5–7 then discuss the actual rhetorical and athletic spaces, practices, and bodies of and in phusiopoiesis.The introduction opens with description of a first-century BC bronze statue of an “Antikythera Youth” (3). Hawhee uses the mystery surrounding the identity of the figure (deciphered largely through interpretations of the actions implied by the stature of the statue) to articulate the connections between the body of the rhetor and the body of the athlete as well as to introduce the importance of the body to Greek values of hexis (comportment) and aretē (virtuosity). The Introduction also presents three critical relations that serve both as conceptual departure points as well as hail the multiple audiences of the book: relations of body and mind, learning and performing, and classical studies and rhetorical studies. Hawhee’s perspective is quite straightforwardly that rhetoric is an art that required physical training and physical performance.Chapter 1, “Contesting Virtuosity: Agonism and the Production of Aretē,” connects the values of agon and aretē and argues that the “very logic for linking rhetoric and athletics” lies at the heart of this relation (22). Hawhee argues that agon and aretē are less about ends (victory and virtue) and more centrally concerned with embodied processes. Agon, through Hawhee’s reading of Hesiod’s Work and Days, is articulated as a mode of encounter that produces a particular, and possibly transformative, response. Aretē is the bodily performance of virtuosity. Central to this performance, according to Hawhee’s interpretation of the Olympic ethos through Pindar’s poetry, is the activity of questing. Aretē is demonstrated rather than simply won or attained. Following these definitions of agon and aretē, the chapter moves to illustrating the shared language of rhetoric and athletics in terms of these values. Hawhee argues that this shared vocabulary confirms that sophistic rhetoric was understood and practiced as an embodied and agonistic art “fused and infused” with athletics (43).In Chapter 2, “Sophistic Mētis : An Intelligence of the Body,” Hawhee describes mētis as cunning and somatic becoming that “infuses the arts of rhetoric and athletics with a kind of bodily intelligence... not an explicit set of precepts but rather a tacit style of movement running through most kinds of actions, including thought” (47). Moreover, the movement of mētis [End Page 198] is corporeal. It... (shrink)

A common reaction to Hegel’s suggestion that we collapse Kant’s distinction between form and content is that, since such a move would also deprive us of any way of distinguishing the merely logical from the real possibility of our concepts, it is incoherent and ought to be rejected. It is true that these two distinctions are intimately related in Kant, such that if one goes, the other does as well. But it is less obvious that giving them up as Kant (...) conceives them is as incoherent a proposal as many of Hegel’s critics think. It has been the point of a recent account of Hegel’s idealism to demonstrate that his critique of Kant’s dichotomy between form and content or concept and intuition does not commit him to the view that human cognition is materially creative of its content in the manner of a God-like or intuitive intellect—does not, in other words, signify a return to a pre-Critical metaphysics. This is the interpretative stance I adopt here as well, in hope of giving defenders of Kant reasons for taking Hegel more seriously. (shrink)

We humans are a curious species. Of all the life forms that inhabit the earth, we alone strive to make sense of the world in which we find ourselves. For thousands of years we understood the world through stories. Our ancestors told stories of how the world began, how our people originated and came to be at this place, and how those people across the river or beyond the mountains came to be where they are. Some stories were of animals (...) and plants in our neighborhood, and their powers to help us, feed us, or cure our ailments. But in the last few centuries, starting in Europe and spreading throughout the world, a new way of understanding began competing with storytelling as a means of comprehending our world. Science supplanted storytelling largely because it empowered us to transform the world in ways that were unimaginable to our ancestors. We understand the world scientifically by describing the world instead of by telling stories about it. The stories our ancestors told no longer explain the world, but are data within the world, part of the world that science describes. Our stories have become myths, cultural artifacts that may be interesting and a subject of study, but cannot possibly be true. Yet even in societies that have thoroughly embraced science as a means of understanding the world, myths remain a powerful force. Myth and science exist side by side, often creating confusion and conflict. (shrink)