Roy T Cook examines the Yablo paradox--a paradoxical, infinite sequence of sentences, each of which entails the falsity of all others later than it in the sequence--with special attention paid to the idea that this paradox provides us with a semantic paradox that involves no circularity.
Descartes and the First Cartesians adopts the perspective that we should not approach Rene Descartes as a solitary thinker, but as a philosopher who constructs a dialogue with his contemporaries, so as to engage them and elements of his society into his philosophical enterprise.
While we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means.
While we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means.
Individual objects have potentials: paper has the potential to burn, an acorn has the potential to turn into a tree, some people have the potential to run a mile in less than four minutes.
Unity and Plurality presents novel ways of thinking about plurality while casting new light on the interconnections among the logical, philosophical, and linguistic aspects of plurals.
Paolo Mancosu presents a series of innovative studies in the history and the philosophy of logic and mathematics in the first half of the twentieth century.
The volume is the first collection of essays that focuses on Gottlob Frege's Basic Laws of Arithmetic (1893/1903), highlighting both the technical and the philosophical richness of Frege's magnum opus.
Vagueness is the study of concepts that admit borderline cases: the property of being bald is vague because there are people who are neither definitely bald, nor definitely not bald.
In recent years there have been a number of books-both anthologies and monographs-that have focused on the Liar Paradox and, more generally, on the semantic paradoxes, either offering proposed treatments to those paradoxes or critically evaluating ones that occupy logical space.
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.
In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision and philosophical insight.
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.
