Lambda Calculi Lambda calculi (λ-calculi) are formal systems describing functions and function application. One of them, the untyped version, is often referred to as the λ-calculus. This exposition will adopt this convention. At its core, the λ-calculus is a formal language with certain reduction rules intended to capture the notion of function application [Church, 1932, p. 352]. Through the primitive notion of function application, the

Metaphilosophy What is philosophy? What is philosophy for? How should philosophy be done? These are metaphilosophical questions, metaphilosophy being the study of the nature of philosophy. Contemporary metaphilosophies within the Western philosophical tradition can be divided, rather roughly, according to whether they are associated with (1) Analytic philosophy, (2) Pragmatist philosophy, or (3) Continental philosophy. The pioneers of the Analytic movement held that philosophy should begin with

Cheng Yi (1033—1107) Cheng Yi was one of the leading philosophers of Neo-Confucianism in the Song (Sung dynasty (960-1279). Together with his elder brother Cheng Hao (1032-1085), he strove to restore the tradition of Confucius and Mencius in the name of “the study of dao” (dao xue), which eventually became the main thread of Neo-Confucianism. Despite diverse disagreements between them, the two brothers are usually

Pudgalavada Buddhist Philosophy The Pudgalavāda was a group of five of the Early Schools of Buddhism. The name arises from their adherents’ distinctive doctrine (vāda) concerning the self or person (pudgala). The doctrine holds that the person, in a certain sense, is real. To other Buddhists, their view seemed to contradict a fundamental tenet of Buddhism, the doctrine of non-self. However, the Pudgalavādins were convinced

The Lucas-Penrose Argument about Gödel’s Theorem In 1961, J.R. Lucas published “Minds, Machines and Gödel,” in which he formulated a controversial anti-mechanism argument. The argument claims that Gödel’s first incompleteness theorem shows that the human mind is not a Turing machine, that is, a computer. The argument has generated a great deal of discussion since then. The influential Computational Theory of Mind, which claims that the