A certain premise is a proposition whose truth is established rather than merely asserted with confidence. In the classical framework, certainty concerns warranted assent corresponding to reality, not intensity of personal conviction.
“Every proper whole is greater than its proper part” is intelligible as a necessary relationship. By contrast, “It will rain next week” may be strongly probable without being a first principle.
Demonstration requires both valid logical form and warranted certain premises. Certainty cannot repair an invalid inference, and valid form cannot upgrade weak premises into certainty.