Nonexistent objectsIn metaphysics and ontology, Austrian philosopher Alexius Meinong advanced nonexistent objects in the 19th and 20th centuries within a "theory of objects". He was interested in intentional states which are directed at nonexistent objects. Starting with the "principle of intentionality", mental phenomena are intentionally directed towards an object. People may imagine, desire or fear something that does not exist.
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.
AbstractionAbstraction is a conceptual process wherein general rules and concepts are derived from the usage and classification of specific examples, literal (real or concrete) signifiers, first principles, or other methods. "An abstraction" is the outcome of this process—a concept that acts as a common noun for all subordinate concepts and connects any related concepts as a group, field, or category. Conceptual abstractions may be formed by filtering the information content of a concept or an observable phenomenon, selecting only those aspects which are relevant for a particular purpose.
Philosophy of mathematicsThe philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics makes this branch of philosophy broad and unique. The philosophy of mathematics has two major themes: mathematical realism and mathematical anti-realism. The origin of mathematics is of arguments and disagreements.
PlatonismPlatonism is the philosophy of Plato and philosophical systems closely derived from it, though contemporary Platonists do not necessarily accept all doctrines of Plato. Platonism had a profound effect on Western thought. In its most basic fundamentals, Platonism affirms the existence of abstract objects, which are asserted to exist in a third realm distinct from both the sensible external world and from the internal world of consciousness, and is the opposite of nominalism.
Bertrand RussellBertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, artificial intelligence, cognitive science, computer science and various areas of analytic philosophy, especially philosophy of mathematics, philosophy of language, epistemology, and metaphysics.
