[Revised entry by Christoph Helmig and Carlos Steel on May 14, 2012. Changes to: Bibliography, Internet resources] Proclus of Athens (*412 - 485 C.E.) was the most authoritative philosopher of late antiquity and played a crucial role in the transmission of Platonic philosophy from antiquity to the Middle Ages. For almost fifty years, he was head or 'successor' (diadochos, sc. of Plato) of the Platonic 'Academy' in Athens. Being an exceptionally productive...

[Revised entry by John Tucker on May 12, 2012. Changes to: Bibliography] "Confucianism" is a term used largely by westerners to refer to an often diverse set of philosophical movements that have been variously known in Japanese history as Jugaku (the learning of the scholars), Jukyo (the teachings of the scholars), seigaku (the learning of the sages), senno gaku (the learning of the early kings),...

[Revised entry by Duncan Pritchard and John Turri on May 11, 2012. Changes to: Bibliography] Value of knowledge has always been a central topic within epistemology. An important question to address, which can be traced right back to Plato's Meno, is: what is it about knowledge (if anything) that makes it more valuable than mere true belief? Interest in this topic has re-emerged in recent years, in response to a rediscovery of the Meno problem regarding the value of...

[Revised entry by Piergiorgio Odifreddi and S. Barry Cooper on May 11, 2012. Changes to: Main text, Bibliography] The recursive functions, which form a class of computable functions, take their name from the process of "recurrence" or "recursion". In its most general numerical form the process of recursion consists in defining the value of a function by using other values of the same function. In this entry, we provide an account of the class of recursive functions, with particular emphasis...

[Revised entry by John Corcoran on May 10, 2012. Changes to: Bibliography] A schema (plural: schemata, or schemas), also known as a scheme (plural: schemes), is a linguistic template or pattern together with a rule for using it to specify a potentially infinite multitude of phrases, sentences, or arguments, which are called instances of the schema. Schemas are used in logic to specify rules of inference, in mathematics to...

[New Entry by Sandra Shapshay on May 9, 2012.] The focus of this entry is on Schopenhauer's aesthetic theory, which forms part of his organic philosophical system, but which can be appreciated and assessed to some extent on its own terms (for ways in which his aesthetic insights may be detached from his metaphysics see Shapshay, 2012b). The theory is found predominantly in Book 3 of the World as Will and Representation (WWR I) and in the...

[Revised entry by Alfred Tauber on May 9, 2012. Changes to: Main text, Bibliography, Internet resources] Fundamental to biology are (1) defining the characteristics of identity, which distinguish individual organisms from those of similar kind, and (2) describing the mechanisms that defend organisms from their predators. Immunology is the science devoted to these problems. A progeny of late 19th-century pathology and microbiology, and the clinical discipline of infectious diseases, immunology did not...

[Revised entry by Wayne Cristaudo on May 4, 2012. Changes to: Bibliography] Eugen Rosenstock-Huessy (1888 - 1973) was a sociologist and social philosopher who, along with his close friend Franz Rosenzweig, and Ferdinand Ebner and Martin Buber, was a major exponent of speech thinking or dialogicism. The central insight of speech thinking is that speech or language is not merely, or even primarily, a descriptive act, but a responsive and creative act which is the basis...

[Revised entry by Oliver Schulte on May 4, 2012. Changes to: Main text, Bibliography] Formal learning theory is the mathematical embodiment of a normative epistemology. It deals with the question of how an agent should use observations about her environment to arrive at correct and informative conclusions. Philosophers such as Putnam, Glymour and Kelly have developed learning theory as a normative framework for scientific reasoning and inductive inference....

[Revised entry by Rainer Forst on May 4, 2012. Changes to: Main text, Bibliography] The term "toleration" - from the Latin tolerare: to put up with, countenance or suffer - generally refers to the conditional acceptance of or non-interference with beliefs, actions or practices that one considers to be wrong but still "tolerable," such that they should not be prohibited or constrained. There are many contexts in which we...

[Revised entry by Carmela Baffioni on May 3, 2012. Changes to: Main text, Bibliography] The Ikhwan al-Safa' or "Brethren of Purity", as their name is commonly translated, are the authors of one of the most complete Medieval encyclopedias of sciences, antecedent at least two centuries to the best known in the Latin world (by Alexander Neckham, Thomas de Cantimpre, Vincent de Beauvais, Bartholomaeus Anglicus, all dating back to the 13th...

[Revised entry by Stewart Candlish and George Wrisley on May 2, 2012. Changes to: Bibliography] The idea of a private language was made famous in philosophy by Ludwig Wittgenstein, who in s243 of his book Philosophical Investigations explained it thus: "The words of this language are to refer to what can be known only to the speaker; to his immediate, private, sensations. So another cannot understand the language."[1]...

[Revised entry by Leon Horsten on May 2, 2012. Changes to: Main text, Bibliography] If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are...

[Revised entry by Andrea Cantini on April 30, 2012. Changes to: Main text] By "paradox" one usually means a statement claiming something which goes beyond (or even against) 'common opinion' (what is usually believed or held). Paradoxes form a natural object of philosophical investigation ever since the origins of rational thought; they have been invented as part of complex arguments and as tools for refuting philosophical theses (think of the...

[Revised entry by Ingo Brigandt and Alan Love on April 30, 2012. Changes to: Main text, Bibliography, notes.html] Reductionism encompasses a set of ontological, epistemological, and methodological claims about the relations between different scientific domains. The basic question of reduction is whether the properties, concepts, explanations, or methods from one scientific domain (typically at higher levels of organization) can be deduced from or explained by the properties, concepts, explanations, or methods from...

[Revised entry by Ann Garry on April 24, 2012. Changes to: Main text, Bibliography, Internet resources, notes.html] Analytic feminists are philosophers who believe that both philosophy and feminism are well served by using some of the concepts, theories, and methods of analytic philosophy modified by feminist values and insights. By using 'analytic feminist' to characterize their style of feminist philosophizing, these philosophers acknowledge their dual feminist and analytic roots and their intention to...

[Revised entry by Barton Schultz on April 23, 2012. Changes to: Main text, Bibliography, Internet resources] Henry Sidgwick was one of the most influential ethical philosophers of the Victorian era, and his work continues to exert a powerful influence on Anglo-American ethical and political theory. His masterpiece, The Methods of Ethics (1907), was first published in 1874 and in many ways marked the culmination of the classical utilitarian tradition - the tradition of Jeremy Bentham and James and John Stuart...

[Revised entry by Markus Führer on April 20, 2012. Changes to: Bibliography] Albertus Magnus, also known as Albert the Great, was one of the most universal thinkers to appear during the Middle Ages. Even more so than his most famous student, St. Thomas of Aquinas, Albert's interests ranged from natural science all the way to theology. He made contributions to logic, psychology, metaphysics, meteorology, mineralogy, and zoology. He was an avid commentator on nearly all the...

[Revised entry by Markus Führer on April 20, 2012. Changes to: Bibliography] The extraordinary long life and active teaching career of Albert the Great (c.1193 - 1280) produced many benefits for the inception of philosophy in medieval Germany. Besides the vast corpus of his writings that fostered a generation of Dominican scholars in the German-speaking province, Albert lived long enough to impart continuity to this generation, which included Ulrich of...

[Revised entry by Frederick Rauscher on April 19, 2012. Changes to: Main text, Bibliography] Kant wrote his social and political philosophy in order to champion the Enlightenment in general and the idea of freedom in particular. His work came within both the natural law and the social contract traditions. Kant held that every rational being had both an innate right to freedom and a duty to enter into a civil condition governed by a social contract in order to realize and preserve that freedom....