Axiom vs. Idiom

Main Difference

The main difference between Axiom and Idiom is that the Axiom is a statement that is taken to be true and Idiom is a combination of words that has a figurative meaning

• Axiom

  An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek axíōma (ἀξίωμα) ‘that which is thought worthy or fit’ or ‘that which commends itself as evident.’The term has subtle differences in definition when used in the context of different fields of study. As defined in classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. As used in modern logic, an axiom is a premise or starting point for reasoning.As used in mathematics, the term axiom is used in two related but distinguishable senses: “logical axioms” and “non-logical axioms”. Logical axioms are usually statements that are taken to be true within the system of logic they define (e.g., (A and B) implies A), often shown in symbolic form, while non-logical axioms (e.g., a + b = b + a) are actually substantive assertions about the elements of the domain of a specific mathematical theory (such as arithmetic). When used in the latter sense, “axiom”, “postulate”, and “assumption” may be used interchangeably. In general, a non-logical axiom is not a self-evident truth, but rather a formal logical expression used in deduction to build a mathematical theory. To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms). There are typically multiple ways to axiomatize a given mathematical domain.

  Any axiom is a statement that serves as a starting point from which other statements are logically derived. Whether it is meaningful (and, if so, what it means) for an axiom to be “true” is a subject of debate in the philosophy of mathematics.

• Idiom

  An idiom (Latin: idiomī, “special property”, from Ancient Greek: ἰδίωμα, translit. idíōma, “special feature, special phrasing, a peculiarity”, f. Ancient Greek: ἴδιος, translit. ídios, “one’s own”) is a phrase or an expression that has a figurative, or sometimes literal, meaning. Categorized as formulaic language, an idiom’s figurative meaning is different from the literal meaning. There are thousands of idioms, occurring frequently in all languages. It is estimated that there are at least twenty-five thousand idiomatic expressions in the English language.