The Compactness Theorem The compactness theorem is a fundamental theorem for the model theory of classical propositional and first-order logic. As well as having importance in several areas of mathematics, such as algebra and combinatorics, it also helps to pinpoint the strength of these logics, which are the standard ones used in mathematics and arguably the most important ones in philosophy. The main focus of

Wittgenstein: Epistemology Although Ludwig Wittgenstein is generally more known for his works on logic and on the nature of language, but throughout his philosophical journey he reflected extensively also on epistemic notions such as knowledge, belief, doubt, and certainty. This interest is more evident in his final notebook, published posthumously as On Certainty (1969, henceforth OC), where he offers a sustained and, at least apparently,

The Aesthetics of Popular Music Popular music is widely assumed to be different in kind from the serious music or art music that, until very recently, monopolized attention in philosophical discussions of music. In recent years, however, popular music has become an important topic for philosophers pursuing either of two projects. First, popular music receives attention from philosophers who see it as a test case

Art and Interpretation Interpretation in art refers to the attribution of meaning to a work. A point on which people often disagree is whether the artist’s or author’s intention is relevant to the interpretation of the work. In the Anglo-American analytic philosophy of art, views about interpretation branch into two major camps: intentionalism and anti-intentionalism, with an initial focus on one art, namely literature. The

Morality and Cognitive Science What do we know about how people make moral judgments? And what should moral philosophers do with this knowledge? This article addresses the cognitive science of moral judgment. It reviews important empirical findings and discusses how philosophers have reacted to them. Several trends have dominated the cognitive science of morality in the early 21st century. One is a move away from

Knowledge by Acquaintance and Knowledge by Description Our own experiences of pain are better known to us than the bio-chemical structure of our brains. Some philosophers hold that this difference is due to different kinds of knowledge: knowledge by acquaintance and knowledge by description. I have first-hand or direct knowledge of my own experiences; whereas I have only second-hand or indirect knowledge of my brain’s