The difference between Axiom and Formal system

When used as nouns, axiom means a seemingly self-evident or necessary truth which is based on assumption, whereas formal system means the grouping of a formal language and a set of inference rules and/or axioms.

check bellow for the other definitions of Axiom and Formal system

  1. Axiom as a noun (philosophy):

    A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.

  2. Axiom as a noun (logic, mathematics, proof theory):

    A fundamental assumption that serves as a basis for deduction of theorems; a postulate (sometimes distinguished from postulates as being universally applicable, whereas postulates are particular to a certain science or context).

  3. Axiom as a noun:

    An established principle in some artistic practice or science that is universally received.

    Examples:

    "The axioms of political economy cannot be considered absolute truths."

  1. Formal system as a noun (logic):

    The grouping of a formal language and a set of inference rules and/or axioms.

Compare words:

Compare with synonyms and related words: