Formalism (philosophy of mathematics)In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings (alphanumeric sequences of symbols, usually as equations) using established manipulation rules. A central idea of formalism "is that mathematics is not a body of propositions representing an abstract sector of reality, but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess.
Linguistic turnThe linguistic turn was a major development in Western philosophy during the early 20th century, the most important characteristic of which is the focusing of philosophy primarily on the relations between language, language users, and the world. Very different intellectual movements were associated with the "linguistic turn", although the term itself is commonly thought to have been popularised by Richard Rorty's 1967 anthology The Linguistic Turn, in which he discusses the turn towards linguistic philosophy.
PsychologismPsychologism is a family of philosophical positions, according to which certain psychological facts, laws, or entities play a central role in grounding or explaining certain non-psychological facts, laws, or entities. The word was coined by Johann Eduard Erdmann as Psychologismus, being translated into English as psychologism. The Oxford English Dictionary defines psychologism as: "The view or doctrine that a theory of psychology or ideas forms the basis of an account of metaphysics, epistemology, or meaning; (sometimes) spec.
Naming and NecessityNaming and Necessity is a 1980 book with the transcript of three lectures, given by the philosopher Saul Kripke, at Princeton University in 1970, in which he dealt with the debates of proper names in the philosophy of language. The transcript was brought out originally in 1972 in Semantics of Natural Language, edited by Donald Davidson and Gilbert Harman. Among analytic philosophers, Naming and Necessity is widely considered one of the most important philosophical works of the twentieth century.
ImpredicativityIn mathematics, logic and philosophy of mathematics, something that is impredicative is a self-referencing definition. Roughly speaking, a definition is impredicative if it invokes (mentions or quantifies over) the set being defined, or (more commonly) another set that contains the thing being defined. There is no generally accepted precise definition of what it means to be predicative or impredicative. Authors have given different but related definitions.
ReferenceA reference is a relationship between objects in which one object designates, or acts as a means by which to connect to or link to, another object. The first object in this relation is said to refer to the second object. It is called a name for the second object. The next object, the one to which the first object refers, is called the referent of the first object. A name is usually a phrase or expression, or some other symbolic representation. Its referent may be anything – a material object, a person, an event, an activity, or an abstract concept.
Philosophy of logicPhilosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application. This involves questions about how logic is to be defined and how different logical systems are connected to each other. It includes the study of the nature of the fundamental concepts used by logic and the relation of logic to other disciplines.
Theory of descriptionsThe theory of descriptions is the philosopher Bertrand Russell's most significant contribution to the philosophy of language. It is also known as Russell's theory of descriptions (commonly abbreviated as RTD). In short, Russell argued that the syntactic form of descriptions (phrases that took the form of "The aardvark" and "An aardvark") is misleading, as it does not correlate their logical and/or semantic architecture.
Mediated reference theoryA mediated reference theory (also indirect reference theory) is any semantic theory that posits that words refer to something in the external world, but insists that there is more to the meaning of a name than simply the object to which it refers. It thus stands opposed to direct reference theory. Gottlob Frege is a well-known advocate of mediated reference theories. Similar theories were widely held in the middle of the twentieth century by philosophers such as Peter Strawson and John Searle.
Hume's principleHume's principle or HP says that the number of Fs is equal to the number of Gs if and only if there is a one-to-one correspondence (a bijection) between the Fs and the Gs. HP can be stated formally in systems of second-order logic. Hume's principle is named for the Scottish philosopher David Hume and was coined by George Boolos. HP plays a central role in Gottlob Frege's philosophy of mathematics. Frege shows that HP and suitable definitions of arithmetical notions entail all axioms of what we now call second-order arithmetic.
