Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th–16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

The book from which these sections are excerpted is concerned with the prospects for assimilating the study of human intelligence and its products to the natural sciences through the investigation of cognitive structures, understood as systems of rules and representations that can be regarded as “mental organs.” These mental structui′es serve as the vehicles for the exercise of various capacities. They develop in the mind on the basis of an innate endowment that permits the growth of rich and highly articulated (...) structures along an intrinsically determined course under the triggering and partially shaping effect of experience, which fixes parameters in an intricate system of predetermined form. It is argued that the mind is modular in character, with a diversity of cognitive structures, each with its specific properties arid principles. Knowledge of language, of the behavior of objects, and much else crucially involves these mental structures, and is thus not characterizable in terms of capacities, dispositions, or practical abilities, nor is it necessarily grounded in experience in the standard sense of this term.Various types of knowledge and modes of knowledge acquisition are discussed in these terms. Some of the properties of the language faculty are investigated. The basic cognitive relation is “knowing a grammar”; knowledge of language is derivative and, correspondingly, raises further problems. Language as commonly understood is not a unitary phenomenon but involves a number of interacting systems: the “computational” system of grammar, which provides the representations of sound and meaning that permit a rich range of expressive potential, is distinct from a conceptual system with its own properties; knowledge of language must be distinguished from knowledge of how to use a language; and the various systems that enter into the knowledge and use of language must be further analyzed into their specific subcomponents. (shrink)

The idea that the language we speak influences the way we think has evoked perennial fascination and intense controversy. According to the strong version of this hypothesis, called the Sapir-Whorf hypothesis after the American linguists who propounded it, languages vary in their semantic partitioning of the world, and the structure of one’s language influences how one understands the world. Thus speakers of different languages perceive the world differently. Although the last two decades have been marked by extreme skepticism concerning the (...) possible effects of language on thought, recent theoretical and methodological advances in cognitive science have given the question new life. Research in linguistics and linguistic anthropology has revealed striking differences in cross-linguistic semantic patterns, and cognitive psychology has developed subtle techniques for studying how people represent and remember experience. It is now possible to test predictions about how a given language influences the thinking of its speakers. Language in Mind includes contributions from both skeptics and believers and from a range of fields. It contains work in cognitive psychology, cognitive development, linguistics, anthropology, and animal cognition. The topics discussed include space, number, motion, gender, theory of mind, thematic roles, and the ontological distinction between objects and substances. I Introduction 1 Whither Whorf 3 Dedre Gentner and Susan Goldin-Meadow II Position Statements 15 1 Languages and Representations 17 Eve V. Clark 2 Language and Mind: Let’s Get the Issues Straight! 25 Stephen C. Levinson 3 The Key Is Social Cognition 47 Michael Tomasello III Language as Lens: Does the Language We Acquire Influence How We See the World? 59 4 Sex, Syntax, and Semantics 61 Lera Boroditsky, Lauren A. Schmidt, and Webb Phillips 5 Speaking versus Thinking about Objects and Actions 81 Barbara C. Malt, Steven A. Sloman, and Silvia P. Gennari 6 The Effects of Spatial Language on Spatial Representation: Setting Some Boundaries 113 Edward Munnich and Barbara Landau 7 Language and Thought Online: Cognitive Consequences of Linguistic Relativity 157 Dan I. Slobin IV Language as Tool Kit: Does the Language We Acquire Augment Our Capacity for Higher-Order Representation and Reasoning? 193 8 Why We’re So Smart 195 Dedre Gentner 9 Does Language Help Animals Think? 237 Stan A. Kuczaj, II, and Jennifer L. Hendry 10 What Makes Us Smart? Core Knowledge and Natural Language 277 Elizabeth S. Spelke 11 Conceptual and Linguistic Factors in Inductive Projection: How Do Young Children Recognize Commonalities between Animals and Plants? 313 Kayoko Inagaki and Giyoo Hatano 12 Language for Thought: Coming to Understand False Beliefs 335 Jill G. de Villiers and Peter A. de Villiers V Language as Category Maker: Does the Language We Acquire Influence Where We Make Our Category Distinctions? 385 13 Space under Construction: Language-Specific Spatial Categorization in First Language Acquisition 387 Melissa Bowerman and Soonja Choi 14 Reevaluating Linguistic Relativity: Language-Specific Categories and the Role of Universal Ontological Knowledge in the Construal of Individuation 429 Mutsumi Imai and Reiko Mazuka 15 Interaction of Language Type and Referent Type in the Development of Nonverbal Classification Preferences 465 John A. Lucy and Suzanne Gaskins 16 Thought before Language: Do We Think Ergative? 493 Susan Goldin-Meadow. (shrink)

A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional (...) coverage of introductory material such as sets. Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses. Reduced mathematical rigour to fit the needs of undergraduate students. (shrink)

"A valuable collection both for original source material as well as historical formulations of current problems."-- The Review of Metaphysics "Much more than a mere collection of papers . . . a valuable addition to the literature."-- Mathematics of Computation An anthology of fundamental papers on undecidability and unsolvability by major figures in the field, this classic reference opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by (...) Godel, Church, Turing, and Post single out the class of recursive functions as computable by finite algorithms. Additional papers by Church, Turing, and Post cover unsolvable problems from the theory of abstract computing machines, mathematical logic, and algebra, and material by Kleene and Post includes initiation of the classification theory of unsolvable problems. Suitable for graduate and undergraduate courses. 1965 ed. (shrink)

The first full-scale history of cognitive science, this work addresses a central issue: What is the nature of knowledge?

The book from which these sections are excerpted is concerned with the prospects for assimilating the study of human intelligence and its products to the natural sciences through the investigation of cognitive structures, understood as systems of rules and representations that can be regarded as These mental structui′es serve as the vehicles for the exercise of various capacities. They develop in the mind on the basis of an innate endowment that permits the growth of rich and highly articulated structures along (...) an intrinsically determined course under the triggering and partially shaping effect of experience, which fixes parameters in an intricate system of predetermined form. It is argued that the mind is modular in character, with a diversity of cognitive structures, each with its specific properties arid principles. Knowledge of language, of the behavior of objects, and much else crucially involves these mental structures, and is thus not characterizable in terms of capacities, dispositions, or practical abilities, nor is it necessarily grounded in experience in the standard sense of this term. (shrink)

Drawing on recent groundbreaking discoveries in modern linguistics, the author exposes the elusive forces of creation at work in human communication, giving fresh insight into how language emerges, evolves, and decays.

In Mindblindness, Simon Baron-Cohen presents a model of the evolution and development of "mindreading." He argues that we mindread all the time, effortlessly, automatically, and mostly unconsciously. It is the natural way in which we interpret, predict, and participate in social behavior and communication. We ascribe mental states to people: states such as thoughts, desires, knowledge, and intentions. Building on many years of research, Baron-Cohen concludes that children with autism, suffer from "mindblindness" as a result of a selective impairment in (...) mindreading. For these children, the world is essentially devoid of mental things. Baron-Cohen develops a theory that draws on data from comparative psychology, from developmental, and from neuropsychology. He argues that specific neurocognitive mechanisms have evolved that allow us to mindread, to make sense of actions, to interpret gazes as meaningful, and to decode "the language of the eyes." A Bradford Book. (shrink)

The Unprovability of Consistency is concerned with connections between two branches of logic: proof theory and modal logic. Modal logic is the study of the principles that govern the concepts of necessity and possibility; proof theory is, in part, the study of those that govern provability and consistency. In this book, George Boolos looks at the principles of provability from the standpoint of modal logic. In doing so, he provides two perspectives on a debate in modal logic that has persisted (...) for at least thirty years between the followers of C. I. Lewis and W. V. O. Quine. The author employs semantic methods developed by Saul Kripke in his analysis of modal logical systems. The book will be of interest to advanced undergraduate and graduate students in logic, mathematics and philosophy, as well as to specialists in those fields. (shrink)

This collection of articles and review essays, including many hard to find pieces, comprises the most important and fundamental studies of Indian logic and linguistics ever undertaken. Frits Staal is concerned with four basic questions: Are there universals of logic that transcend culture and time? Are there universals of language and linguistics? What is the nature of Indian logic? And what is the nature of Indian linguistics? By addressing these questions, Staal demonstrates that, contrary to the general assumption among Western (...) philosophers, the classical philosophers of India were rationalists, attentive to arguments. They were in this respect unlike contemporary Western thinkers inspired by existentialism or hermeneutics, and like the ancient Chinese, Greeks, and many medieval European schoolmen, only--as Staal says--more so. Universals establishes that Asia's contributions are not only compatible with what has been produced in the West, but a necessary ingredient and an essential component of any future human science. (shrink)