Axioms
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Induction doesn't provide certainty, though. Axioms do.
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Axioms do not provide certainty either.
Axioms are the arbitrary (i.e. without proof) foundations upon which a system of thought is built, through the laws of logical inference (themselves axiomatic) that we elect to employ.
The systems of thought that are thusly constructed do not necessarily provide certainty, in and by themselves. But they assist us to further understand, to promote our knowledge.
We arrive at certainty (perhaps, more precisely, conviction above a certain arbitrarily defined threshold) when empirical evidence is combined with systems of thought which have been constructed as above. Intuition is not necessarily correct, at all times, nor necessarily useful, e.g. Euclidian geometry, constructed upon its specific axioms, appeared to be intuitively, certainly correct for millenia but was proven last century to be insufficient for the description of our cosmos.
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