This new volume on logic follows a recognizable format that deals in turn with the topics of mathematical logic, moving from concepts, via definitions and inferences, to theories and axioms. However, this fresh work offers a key innovation in its ‘pyramidal’ graph system for the logical formalization of all these items. The author has developed this new methodology on the basis of original research, traditional logical instruments such as Porphyrian trees, and modern concepts of classification, in which pyramids are the central organizing concept. The pyramidal schema enables both the content of concepts and the relations between the concept positions in the pyramid to be read off from the graph. Logical connectors are analyzed in terms of the direction in which they connect within the pyramid. Additionally, the author shows that logical connectors are of fundamentally different types: only one sort generates propositions with truth values, while the other yields conceptual expressions or complex concepts. On this basis, strong arguments are developed against adopting the non-discriminating connector definitions implicit in Wittgensteinian truth-value tables. Special consideration is given to mathematical connectors so as to illuminate the formation of concepts in the natural sciences. To show what the pyramidal method can contribute to science, a pyramid of the number concepts prevalent in mathematics is constructed. The book also counters the logical dogma of ‘false’ contradictory propositions and sheds new light on the logical characteristics of probable propositions, as well as on syllogistic and other inferences.

Originally published: Boston: Houghton Mifflin, 1987.

This book explains the role of language in causing and in resolving the ecocrisis, showing that ecologically adaptive behavior can be facilitated through language. The authors explore the discourses of deep ecology, ecofeminism, Judeo-Christianity, quantum theory, and Native American world views, all to the end of empowering ecosocial change.

The Bulletin of the Atomic Scientists is the premier public resource on scientific and technological developments that impact global security. Founded by Manhattan Project Scientists, the Bulletin's iconic "Doomsday Clock" stimulates solutions for a safer world.

Kant claims to have established his table of categories or "pure concepts of the understanding" according to the "guiding thread" provided by logical forms of judgment. By drawing extensively on Kant's logical writings, Béatrice Longuenesse analyzes this controversial claim, and then follows the thread through its continuation in the transcendental deduction of the categories, the transcendental schemata, and the principles of pure understanding. The result is a systematic, persuasive new interpretation of the Critique of Pure Reason. Longuenesse shows that although Kant adopts his inventory of the forms of judgment from logic textbooks of his time, he is nevertheless original in selecting just those forms he holds to be indispensable to our ability to relate representations to objects. Kant gives formal representation to this relation between conceptual thought and its objects by introducing the term "x" into his analysis of logical forms to stand for the object that is "thought under" the concepts that are combined in judgment. This "x" plays no role in Kant's forms of logical inference, but instead plays a role in clarifying the relation between logical forms (forms of concept subordination) and combinations ("syntheses") of perceptual data, necessary for empirical cognition. Considering Kant's logical forms of judgment thus helps illuminate crucial aspects of the Transcendental Analytic as a whole, while revealing the systematic unity between Kant's theory of judgment in the first Critique and his analysis of "merely reflective" (aesthetic and teleological) judgments in the third Critique.

In this book the author's theoretical framework builds on linguistic and psychological research, arguing that similar image-schematic notions should be grouped together into interconnected family hierarchies, with complexity increasing with regard to the addition of spatial and conceptual primitives. She introduces an image schema logic as a language to model image schemas, and she shows how the semantic content of image schemas can be used to improve computational concept invention. The book will be of value to researchers in artificial intelligence, cognitive science, psychology, and creativity.

This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy" so-called. Careful exposition and critique is given to every serious alternative account of number and number relations available at the time.