IntuitionismIn the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and mathematics are not considered analytic activities wherein deep properties of objective reality are revealed and applied, but are instead considered the application of internally consistent methods used to realize more complex mental constructs, regardless of their possible independent existence in an objective reality.
Naive set theoryNaive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language. It describes the aspects of mathematical sets familiar in discrete mathematics (for example Venn diagrams and symbolic reasoning about their Boolean algebra), and suffices for the everyday use of set theory concepts in contemporary mathematics.
SemanticsSemantics () is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and computer science. In English, the study of meaning in language has been known by many names that involve the Ancient Greek word σῆμα (sema, "sign, mark, token"). In 1690, a Greek rendering of the term semiotics, the interpretation of signs and symbols, finds an early allusion in John Locke's An Essay Concerning Human Understanding: The third Branch may be called σημειωτική [simeiotikí, "semiotics"], or the Doctrine of Signs, the most usual whereof being words, it is aptly enough termed also λογικὴ, Logick.
Proper name (philosophy)In the philosophy of language, a proper name - examples include a name of a specific person or place - is a name which ordinarily is taken to uniquely identify its referent in the world. As such it presents particular challenges for theories of meaning, and it has become a central problem in analytic philosophy. The common-sense view was originally formulated by John Stuart Mill in A System of Logic (1843), where he defines it as "a word that answers the purpose of showing what thing it is that we are talking about but not of telling anything about it".
Sense and referenceIn the philosophy of language, the distinction between sense and reference was an idea of the German philosopher and mathematician Gottlob Frege in 1892 (in his paper "On Sense and Reference"; German: "Über Sinn und Bedeutung"), reflecting the two ways he believed a singular term may have meaning. The reference (or "referent"; Bedeutung) of a proper name is the object it means or indicates (bedeuten), whereas its sense (Sinn) is what the name expresses. The reference of a sentence is its truth value, whereas its sense is the thought that it expresses.
Abstract and concreteIn metaphysics, the distinction between abstract and concrete refers to a divide between two types of entities. Many philosophers hold that this difference has fundamental metaphysical significance. Examples of concrete objects include plants, human beings and planets while things like numbers, sets and propositions are abstract objects. There is no general consensus as to what the characteristic marks of concreteness and abstractness are.
Ordinary language philosophyOrdinary language philosophy (OLP) is a philosophical methodology that sees traditional philosophical problems as rooted in misunderstandings philosophers develop by distorting or forgetting how words are ordinarily used to convey meaning in non-philosophical contexts. "Such 'philosophical' uses of language, on this view, create the very philosophical problems they are employed to solve." This approach typically involves eschewing philosophical "theories" in favor of close attention to the details of the use of everyday "ordinary" language.
Term logicIn logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, the Peripatetics. It was revived after the third century CE by Porphyry's Isagoge. Term logic revived in medieval times, first in Islamic logic by Alpharabius in the tenth century, and later in Christian Europe in the twelfth century with the advent of new logic, remaining dominant until the advent of predicate logic in the late nineteenth century.
Domain of discourseIn the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range. The domain of discourse is usually identified in the preliminaries, so that there is no need in the further treatment to specify each time the range of the relevant variables. Many logicians distinguish, sometimes only tacitly, between the domain of a science and the universe of discourse of a formalization of the science.
Descriptivist theory of namesIn the philosophy of language, the descriptivist theory of proper names (also descriptivist theory of reference) is the view that the meaning or semantic content of a proper name is identical to the descriptions associated with it by speakers, while their referents are determined to be the objects that satisfy these descriptions. Bertrand Russell and Gottlob Frege have both been associated with the descriptivist theory, which is sometimes called the mediated reference theory or Frege–Russell view.
