Is Knowledge of Axioms Contextual and Provisional?

Near the end of yesterday’s class we discussed that, as all knowledge is contextual, certainty is also contextual (and provisional since more relevant facts could be discovered leading to a different conclusion). Thus we could once say that no causal link exists between smoking and lung cancer and be correct in the context of what was known at the time. But we also came to realize such a link exists based on newly discovered facts. The key for my understanding of the contextual nature of certainty is that the standard by which to judge it is not omniscience (which is impossible). A question I had was whether axioms (eg “existence exists”) are also contextual and provisional.I believe the answer is that with axioms (and other knowledge such as 2+2=4) the context is as wide as possible ie there can be no additional facts which could lead to a different conclusion.