In philosophy of mathematics, a foundation ontology is an ontology in the formal philosophical sense that is deemed to play a role in the foundations of mathematics. Most notably, the role played by Plato's ontology in some theories of realism in mathematics. Hilary Putnam made the distinction in 1975, arguing that one could believe in a realist philosophy of mathematical foundations without also accepting Plato's ontology or his sacred geometry, thus the labels "Platonist" and "realist" were not to be held equivalent. Philosophy of mathematics is that branch of philosophy which attempts to answer questions such as: why is mathematics useful in describing nature?, in which sense(s), if any, do mathematical entities such as numbers exist? and why and how are mathematical statements true?. Various approaches to answering these questions will... In philosophy, ontology (from the Greek όντος = part. ... The term foundations of mathematics is sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. ... Platonic idealism is the theory that the substantive reality around us is only a reflection of a higher truth. ... Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... Hilary Whitehall Putnam (born July 31, 1926) is a key figure in the philosophy of mind during the 20th century. ... 1975 was a common year starting on Wednesday (the link is to a full 1975 calendar). ... Sacred geometry is geometry that is sacred to the observer or discoverer of the geometry. ...

This is discussed further in the article on foundations of mathematics. The term foundations of mathematics is sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. ...

In computer science, a foundation ontology or upper ontology is a hierarchy of entities and associated rules (both theorems and regulations) that attempts to describe those general entities that do not belong to a specific problem domain. See ontology (computer science) for a more detailed description and examples. Wikibooks Wikiversity has more about this subject: School of Computer Science Open Directory Project: Computer Science Collection of Computer Science Bibliographies Belief that title science in computer science is inappropriate Categories: Computer science ... A hierarchy (in Greek hieros, sacred, and arkho, rule) is a system of ranking and organizing things or people. ... A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. ... This article needs to be cleaned up to conform to a higher standard of quality. ...