Postulate

Postulate is a fundamental principle or assumption that is not proven but considered to be either self-evident or necessary. In different fields of knowledge, postulates are taken as given and serve as starting points for deducing and inferring other (complex) truths.

Definition

In mathematics, a postulate is a statement that is assumed to be true without proof. These postulates are then used to prove theorems. The most famous set of postulates are the Euclidean postulates, which are the basis for Euclidean geometry.

In philosophy, a postulate is a proposition that is not proven or demonstrated but considered to be either self-evident or necessary. In the latter case, a postulate is a logical foundation upon which to build the rest of a theory or argument.

In Mathematics

In mathematics, postulates form the foundation of logical systems. They are the basic assumptions, or axioms, upon which the system is built. For example, in Euclidean geometry, there are five postulates that Euclid assumed to be self-evident truths. These postulates are used to prove all other theorems within Euclidean geometry.

In Philosophy

In philosophy, postulates are often used in a similar way to mathematics. They are basic assumptions that are not proven but are used as the starting point for further reasoning. For example, René Descartes famously postulated "Cogito, ergo sum" ("I think, therefore I am") as a fundamental element of his philosophy.

See Also

• Axiom
• Theorem
• Hypothesis
• Euclidean postulates
• René Descartes

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