Auxiliary hypotheses are the assumptions that are laid out before a scientist proceeds with a plan to achieve falsifiability. These assumptions represent statements of truth the scientist seeks to falsify.

In the fields of logic and mathematics, an axiomatized, or axiomatic, system is a set of statements that can be taken as true and work together to form a complete system. Popper suggests that this system of statements must exclude any superfluous assumptions and that the axioms should only be selected based on their relation to the subject.

When Popper refers to the methodology of the scientific process, he refers to the rules of this process as “conventions.” Popper outlines two conventions he feels should be an inherent part of the scientific process: (1) science should be unending and never reach a conclusion, and (2) new ideas should be based on established ones that have proven their worth through extreme testing.