Predicative and Impredicative Definitions The distinction between predicative and impredicative definitions is today widely regarded as an important watershed in logic and the philosophy of mathematics. A definition is said to be impredicative if it generalizes over a totality to which the entity being defined belongs. Otherwise the definition is said to be predicative. In the examples below, (2) and (4) are impredicative. Let π be

Ernst Cassirer (1874-1945) Ernst Cassirer was the most prominent, and the last, Neo-Kantian philosopher of the twentieth century. His major philosophical contribution was the transformation of his teacher Hermann Cohen’s mathematical-logical adaptation of Kant’s transcendental idealism into a comprehensive philosophy of symbolic forms intended to address all aspects of human cultural life and creativity. In doing so, Cassirer paid equal attention to both sides of

Knowledge-First Theories of Justification Knowledge-first theories of justification are theories of justification that give knowledge priority when it comes to explaining when and why someone has justification for an attitude or an action. The emphasis of this article is on knowledge-first theories of justification for belief. As it turns out, there are a number of ways of giving knowledge priority when theorizing about justification, and

Arthur Schopenhauer: Logic and Dialectic For Arthur Schopenhauer (1788-1860), logic as a discipline belongs to the human faculty of reason, more precisely to the faculty of language. This discipline of logic breaks down into two areas. Logic or analytics is one side of the coin; dialectic or the art of persuasion is the other. The former investigates rule-oriented and monological language. The latter investigates result-oriented language

Dynamic Epistemic Logic This article tells the story of the rise of dynamic epistemic logic. The rise began in the 1960s with the creation and development of epistemic logic, the logic of knowledge, Then in the late 1980s came dynamic epistemic logic, the logic of change of knowledge. Much of it was motivated by puzzles and paradoxes. The number of active researchers in these logics