**Peano's postulates** — The postulates isolated by R. Dedekind (1831–1916) and formulated by the Italian mathematician G. Peano (1858–1932), that define the number series as the series of successors to the number zero. Informally they are: (i) zero is a number; (ii)… … Philosophy dictionary

**Peano's postulates** — Math. a collection of axioms concerning the properties of the set of all positive integers, including the principle of mathematical induction. Also called Peano s axioms. Cf. principle of mathematical induction. [named after G. PEANO] … Useful english dictionary

**Peano axioms** — In mathematical logic, the Peano axioms, also known as the Dedekind Peano axioms or the Peano postulates, are a set of axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used… … Wikipedia

**Peano, Giuseppe** — ▪ Italian mathematician born Aug. 27, 1858, Cuneo, Kingdom of Sardinia [now in Italy] died April 20, 1932, Turin, Italy Italian mathematician and a founder of symbolic logic (logic) whose interests centred on the foundations of mathematics… … Universalium

**implicit definition** — An implicit definition of a term is given when a number of principles or axioms involving it are laid down, none of which give an equation identifying it with another term. Thus number may be said to be implicitly defined by Peano s postulates ;… … Philosophy dictionary

**ancestral relation** — Intuitively, a relation that stands to another as ‘ancestor of’ stands to ‘parent of’: an ancestor is a parent, or parent of a parent, and so on. The formal definition of the ancestral is due to Frege . Suppose, to simplify, we allow that y is… … Philosophy dictionary

**logic, history of** — Introduction the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic There was a medieval tradition according to which the Greek philosopher … Universalium

**Axiom** — This article is about logical propositions. For other uses, see Axiom (disambiguation). In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self evident or to define and… … Wikipedia

**Principia Mathematica** — For Isaac Newton s book containing basic laws of physics, see Philosophiæ Naturalis Principia Mathematica. The title page of the shortened version of the Principia Mathematica to *56. The Principia Mathematica is a three volume work on the… … Wikipedia

**mathematics, foundations of** — Scientific inquiry into the nature of mathematical theories and the scope of mathematical methods. It began with Euclid s Elements as an inquiry into the logical and philosophical basis of mathematics in essence, whether the axioms of any system… … Universalium