So the answer is a trivial yes. Unless by “preexisting axioms” you mean some preexisting conceptual background in some vague sense, in which case the answer is trivially no. Is that really what you are asking? In logic and mathematics anyway, no formal theory can exist without axioms or rules of syntax and inference.

Are axioms necessary?

Axioms are important to get right, because all of mathematics rests on them. If there are too few axioms, you can prove very little and mathematics would not be very interesting. If there are too many axioms, you can prove almost anything, and mathematics would also not be interesting.

Can math exist without axioms?

To do mathematics, one obviously needs definitions; but, do we always need axioms? For all prime numbers, there exists a strictly greater prime number. cannot be demonstrated computationally, because we’d need to check infinitely many cases. Thus, it can only be proven by starting with some axioms.

What happens without axiom of choice?

Without the Axiom of Choice, a lot of things fall apart, and rather quickly. We require the Axiom of Choice to determine cardinalities. If you remove the Axiom of Choice, then it is consistent that the real numbers can be written as a countable union of countable sets.

Are axioms necessary truths?

An established principle in some art or science, which, though not a necessary truth, is universally received; as, the axioms of political economy. These definitions are the root of much Evil in the worlds of philosophy, religion, and political discourse.

What are axioms used for?

An axiom, postulate, or assumption 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 Ancient Greek word ἀξίωμα (axíōma), meaning ‘that which is thought worthy or fit’ or ‘that which commends itself as evident’.

Are all axioms self-evident?

In any case, the axioms and postulates of the resulting deductive system may indeed end up as evident, but they are not self-evident. The evidence for them comes from some of their consequences, and from the power and coherence of the system as a whole.

Are theories axioms?

In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems.

Can axioms be wrong?

Since pretty much every proof falls back on axioms that one has to assume are true, wrong axioms can shake the theoretical construct that has been build upon them.

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