a statement of self-evident truth

An aphorism is a short, pithy statement containing a truth of general import; an axiom is a statement of self-evident truth; a theorem is a demonstrable proposition in science or mathematics; an epigram is like an aphorism, but lacking in general import.

a string of symbols

At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system.

a mathematical statement that is assumed to be true

An Axiom is a mathematical statement that is assumed to be true.

something assumed to be true without proof

An axiom is something assumed to be true without proof.

a statement that identifies the base of knowledge

An axiom is a statement that identifies the base of knowledge and of any further statement pertaining to that knowledge, a statement necessarily contained in all others, whether any particular speaker chooses to identify a statement or not.

a proposition that defeats a proposition's opponents by the fact that Segers have to accept a proposition and use a proposition in the process of any attempt to deny a proposition

An axiom is a proposition that defeats a proposition's opponents by the fact that Segers have to accept a proposition and use a proposition in the process of any attempt to deny a proposition .

a foundation or a starting point of reasoning

In reference to mathematics, the difference between an axiom, postulate and theorem is that axiom is a foundation or a starting point of reasoning, and a postulate is the act of demanding, where any two points can be joined by a straight line.

at a formal level

At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system.

that serves as a starting point from which other statements are logically derived

Any axiom is a statement that serves as a starting point from which other statements are logically derived.

a statement that is so evident or well-established

As defined in classic philosophy, an axiom is a statement that is so evident or well-established, that a statement is accepted without controversy or question.

a self-evident truth, but rather a formal logical expression used in a deduction to yield further results

In logic and mathematics, an axiom is not necessarily a self-evident truth, but rather a formal logical expression used in a deduction to yield further results.

a statement taken to be self-evidently true

An axiom is a statement taken to be self-evidently true.

a mixture of tokens that is included in a given formal system without needing to be derived using the principles of the system

In formal programs, an axiom is a mixture of tokens that is included in a given formal system without needing to be derived using the principles of the system.

a statement that is established, accepted or self-evidently true

An axiom is a statement that is established, accepted or self-evidently true, and that's how the company talks about An axiom's future.

propositions that are not susceptible of proof or disproof

Axioms are propositions that are not susceptible of proof or disproof, derived from logic.

something believed to be true, but cannot be proven in any practical way

An axiom is something believed to be true, but cannot be proven in any practical way.

a premise or starting

As used in modern logic, an axiom is a premise or starting point for reasoning.

a self-evident truth ' that requires no proof

An Axiom is 'a self-evident truth that requires no proof'.

In logic/mathematics

In logic and mathematics, an axiom is not necessarily a self-evident truth, but rather a formal logical expression used in a deduction to yield further results.

which cannot be proven true or false and from which one is able to construct a system of rules

An axiom is a proposition which cannot be proven true or false and from which one is able to construct a system of rules.