When ordinary people--mathematicians among them--take something to follow (deductively) from something else, they are exposing the backbone of our self-ascribed ability to reason.
If we must take mathematical statements to be true, must we also believe in the existence of abstracta eternal invisible mathematical objects accessible only by the power of pure thought?
The work of Thomas Aquinas has always enjoyed a privileged position as a pillar of Catholic theology, but for centuries his standing among western philosophers was less sure.
Simple Heuristics That Make Us Smart invites readers to embark on a new journey into a land of rationality that differs from the familiar territory of cognitive science and economics.
This clear, accessible account of Hegelian logic makes a case for its enormous seductiveness, its surprising presence in the collective consciousness, and the dangers associated therewith.
Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "e;undecidable.
Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science.
The term "e;fuzzy logic,"e; as it is understood in this book, stands for all aspects of representing and manipulating knowledge based on the rejection of the most fundamental principle of classical logic---the principle of bivalence.
'Don't hope that events will turn out the way you want, welcome events in whichever way they happen'How can we cope when life's events seem beyond our control?
'This is a blast of fresh air' Jonathan Clark, TLS'Thank goodness for Gottlieb' Daily Telegraph'A joy to read' EconomistThe author of the celebrated The Dream of Reason vividly explains the rise of modern thought from Descartes to RousseauIn a short period - from the early 1640s to the eve of the French Revolution - Descartes, Hobbes, Spinoza, Locke, Leibniz, and Hume all made their mark on Western thought.
The book contains a collection of chapters written by experts from the fields of philosophy, law, logic, computer science and artificial intelligence who pay tribute to Professor Risto Hilpinen's impressive work on the logic of induction, on deontic logic and epistemology, and on philosophy of science.
This monograph proposes a new (dialogical) way of studying the different forms of correlational inference, known in the Islamic jurisprudence as qiyas.
This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions.
This edited book focuses on concepts and their applications using the theory of conceptual spaces, one of today's most central tracks of cognitive science discourse.
This monograph addresses the question of the increasing irrelevance of philosophy, which has seen scientists as well as philosophers concluding that philosophy is dead and has dissolved into the sciences.
This monograph offers a new foundation for information theory that is based on the notion of information-as-distinctions, being directly measured by logical entropy, and on the re-quantification as Shannon entropy, which is the fundamental concept for the theory of coding and communications.
This volume sheds a new light on Philosophical Investigations, Ludwig Wittgenstein's master opus, by taking a new approach to its first stretch (sections 1-88), with special emphasis on its atypical opening.
This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic.
This book offers insights relevant to modern history and epistemology of physics,mathematics and, indeed, to all the sciences and engineering disciplines emergingof 19th century.