what do we call statements that we assume to be true without proofs
Mathematical proof In mathematics, a proof is an inferential argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms,[2][3][4] along with accepted rules of inference. Axioms may be treated as conditions that must be met before the statement applies. Proofs are examples of exhaustive deductive reasoning or inductive reasoning and are distinguished from empirical arguments or non-exhaustive inductive reasoning (or "reasonable expectation"). A proof must demonstrate that a statement is always true (occasionally by listing all possible cases and showing that it holds in each), rather than enumerate many confirmatory cases. An unproved proposition that is believed to be true is known as a conjecture.
Reasonable doubt Reasonable doubt is a term used in jurisdiction of common law countries. Evidence that is beyond reasonable doubt is the standard of evidence required to validate a criminal conviction in most adversarial legal systems.[1]