But you don't need to prove them to use them. Many people go around believing unproven theories. In the sciences the preference is for verified theories(and theorems in math) and we prove them by deduction.
But it seems that you know that. I don't understand why you don't like induction in a general algorithm. We don't have to restrict ourselves to a single type of reasoning. Induction, deduction, abduction are all valid and used by humans for generating new knowledge.
I might be misunderstanding something in which case please correct me.
The article says that current research focuses on achieving intelligence by means of induction alone, but induction cannot explain all of intelligence, because we reason in ways that contradict induction (although maybe they're a result of higher-order induction).
But, as the author explains, epistemology doesn't work this way, and is certainly not inductive (maybe high-order inductive -- whatever that means). We don't treat physics as simply "something that works", but as knowledge based on assumptions (codified in symmetry laws) which are not inductive by any means. The laws of symmetry (assumptions, really) are a justification for induction, but can't be a result of induction alone. In fact, all of mathematics is a set of justifications for inductions that humans have developed.