postulate

Postulate is a proposition assumed to be true without proof and used as a basis for deriving other statements within a formal system. It is not proven within the system, but it constrains reasoning and shapes its consequences. The term derives from Latin postulatus, "that which is placed before."

In mathematics and geometry, postulates (often called axioms) provide the foundations of a theory. Euclid's Elements begins with five postulates about points, lines, and angles; these are statements accepted as true without proof to deduce theorems. One famous example is the parallel postulate, whose different forms lead to Euclidean vs non-Euclidean geometries.

In logic and formal systems, a postulate can be a basic assumption or a premise accepted for the sake of argument, separate from the rules of inference. Many modern texts distinguish postulates from theorems and even from axioms, though usage varies: some writers use "postulate" for self-evident propositions and reserve "axiom" for more general assumptions.

In science, postulates are foundational assumptions underlying theories. They are not proven within the theory and may be revised in light of evidence. Examples include postulates of special relativity (such as the constancy of the speed of light) and general principles that guide quantum mechanics and thermodynamics.