There are two kinds of proof, direct and indirect and they relate exactly to our ability to prove incommensurable and commensurable numbers and so relates induction to deduction. Starting in experience we relate our ability to wiggle a certain finger with the finger's wiggle. There is a sense that we caused the finger to wiggle. We can also think of this finger as an example of what we mean when we think of a unit. It is one of five on each hand. We are comfortable in equating 'the finger' with the unit 'one'. There is a sense where they are the same. But, change is universal, nothing in reality escapes it. The only variable is time, some things change faster, some slower. Some things change so slowly that we treat them, most of the time, as if they didn't change, (the sixty minute hour). My finger is changing all the time. My fingernail is a tad longer now than when I started the argument. Does it make a difference? Yes and no. It depends on the context. If you choose the non-change context the answer will differ from choosing the changing context. If you want to know the length of a cardinal hour it is sixty minutes. An ordinal hour is some small plus or minus different. Its the same as how we measure the length of a year or any irrational number, if we didn't use a calculus to stop the change we would never be able to predict how a number would affect the future. If at any time someone asked me to hold up the finger I wiggled and I replied that I couldn't because it is no longer the same finger I would be mixing contexts. Similar things can be unified directly, dissimilar things, indirectly. Everything must be verifiable.
Where does Pythagoras stand on the idea of certainty? Since the Pythagoreans never explained the meaning of irrational numbers they end up unable to prove a number's cardinality. There is gibberish about trancendental certainty, but there is neither direct or indirect proof.
What indicates that we have no understanding of the value of Thales and his discovery of deductive reasoning? In today's world deductive reasoning is held either to be about an abstract certainty devoid of existential import or only one of many deductive systems we could make up to prove things with certainty. If either were the case we would still be thinking in the old Egyptian mode and in fact most of the world has reverted to, or never left the subjective mode. Objectivity is implicit in most of our daily activities but the world gives credit for objectivity to things it can't prove, making the defense of objectivity absurd.
To demonstrate how inverted today's world of philosophy is I direct your attention to todays stand on induction and deduction. The Encyclopedia of Philosophy has a long complex article on induction which cites philosophy's inability to explain, (this in the context of an explanation). On the other hand, deduction, which depends on induction for its being, has no defining article, but is only a short sub-topic for something deemed more important. It is clear the modern world has no idea of how to relate the two. An absolute, justified by reason (proof), is neither mystical or whimsical. Modern philosophy has no sense of the absolute