Burali-Forti paradoxIn set theory, a field of mathematics, the Burali-Forti paradox demonstrates that constructing "the set of all ordinal numbers" leads to a contradiction and therefore shows an antinomy in a system that allows its construction. It is named after Cesare Burali-Forti, who, in 1897, published a paper proving a theorem which, unknown to him, contradicted a previously proved result by Cantor.
Principle of compositionalityIn semantics, mathematical logic and related disciplines, the principle of compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. The principle is also called Frege's principle, because Gottlob Frege is widely credited for the first modern formulation of it. However, the principle has never been explicitly stated by Frege, and arguably it was already assumed by George Boole decades before Frege's work.
Anti-psychologismIn logic, anti-psychologism (also logical objectivism or logical realism) is a theory about the nature of logical truth, that it does not depend upon the contents of human ideas but exists independent of human ideas. The anti-psychologistic treatment of logic originated in the works of Immanuel Kant and Bernard Bolzano. The concept of logical objectivism or anti-psychologism was further developed by Johannes Rehmke (founder of Greifswald objectivism) and Gottlob Frege (founder of logicism the most famous anti-psychologist in the philosophy of mathematics), and has been the centre of an important debate in early phenomenology and analytical philosophy.
Singular termA singular term is a paradigmatic referring device in a language. Singular terms are of philosophical importance for philosophers of language, because they refer to things in the world, and the ability of words to refer calls for scrutiny. Singular terms are defined as expressions that purport to denote or designate particular individual people, places, or other objects. They contrast with general terms (such as "car" or "chair") which can apply to more than one thing. There are various kinds of singular terms: proper names (e.
Actual infinityIn the philosophy of mathematics, the abstraction of actual infinity involves the acceptance (if the axiom of infinity is included) of infinite entities as given, actual and completed objects. These might include the set of natural numbers, extended real numbers, transfinite numbers, or even an infinite sequence of rational numbers. Actual infinity is to be contrasted with potential infinity, in which a non-terminating process (such as "add 1 to the previous number") produces a sequence with no last element, and where each individual result is finite and is achieved in a finite number of steps.
Truth-bearerA truth-bearer is an entity that is said to be either true or false and nothing else. The thesis that some things are true while others are false has led to different theories about the nature of these entities. Since there is divergence of opinion on the matter, the term truth-bearer is used to be neutral among the various theories.
Definite descriptionIn formal semantics and philosophy of language, a definite description is a denoting phrase in the form of "the X" where X is a noun-phrase or a singular common noun. The definite description is proper if X applies to a unique individual or object. For example: "the first person in space" and "the 42nd President of the United States of America", are proper. The definite descriptions "the person in space" and "the Senator from Ohio" are improper because the noun phrase X applies to more than one thing, and the definite descriptions "the first man on Mars" and "the Senator from some Country" are improper because X applies to nothing.
Phosphorus (morning star)Phosphorus (Phōsphoros) is one of the Astra Planeta, specifically the god of the planet Venus in its appearance as the Morning Star. Another Greek name for the Morning Star is "Eosphorus" (Heōsphoros), which means "dawn-bringer". The term "eosphorus" is sometimes met in English. As an adjective, the word "phosphorus" is applied in the sense of "light-bringing" (for instance, the dawn, the god Dionysus, pine torches and the day) and "torch-bearing" as an epithet of several gods and goddesses, especially of Hecate but also of Artemis/Diana and Hephaestus.
HesperusIn Greek mythology, Hesperus (ˈhɛspərəs; Hésperos) is the Evening Star, the planet Venus in the evening. He is one of the Astra Planeta. A son of the dawn goddess Eos (Roman Aurora), he is the half-brother of her other son, Phosphorus (also called Eosphorus; the "Morning Star"). Hesperus' Roman equivalent is Vesper (cf. "evening", "supper", "evening star", "west"). By one account, Hesperus' father was Cephalus, a mortal, while Phosphorus was the star god Astraios.
