Antoine Arnauld (1612—1694) Antoine Arnauld was considered by his peers as one of the preeminent 17th century European intellectuals. Arnauld had been remembered primarily as a correspondent of René Descartes, Gottfried Leibniz and Nicolas Malebranche, and as a dogmatic and uncritical Cartesian who made few if any philosophical contributions. In fact, as much newer research suggests, Arnauld was not a dogmatic and uncritical Cartesian, and

Paraconsistent Logic A paraconsistent logic is a way to reason about inconsistent information without lapsing into absurdity. In a non-paraconsistent logic, inconsistency explodes in the sense that if a contradiction obtains, then everything (everything!) else obtains, too. Someone reasoning with a paraconsistent logic can begin with inconsistent premises—say, a moral dilemma, a Kantian antinomy, or a semantic paradox—and still reach sensible conclusions, without completely exploding

Rudolf Carnap (1891—1970) Rudolf Carnap, a German-born philosopher and naturalized U.S. citizen, was a leading exponent of logical positivism and was one of the major philosophers of the twentieth century. He made significant contributions to philosophy of science, philosophy of language, the theory of probability, inductive logic and modal logic. He rejected metaphysics as meaningless because metaphysical statements cannot be proved or disproved by experience.

René Descartes (1596—1650) René Descartes is often credited with being the “Father of Modern Philosophy.” This title is justified due both to his break with the traditional Scholastic-Aristotelian philosophy prevalent at his time and to his development and promotion of the new, mechanistic sciences. His fundamental break with Scholastic philosophy was twofold. First, Descartes thought that the Scholastics’ method was prone to doubt given their

Modal Logic: A Contemporary View Modal notions go beyond the merely true or false by embedding what we say or think in a larger conceptual space referring to what might be or might have been, should be, or should have been, or can still come to be. Modal expressions occur in a remarkably wide range across natural languages, from necessity, possibility, and contingency to expressions