I had not the time to write something shorter.
Stanley Jevons, 1874, Principles of Science, 2, wrote: Bacon's method is strictly impossible, and if were possible, is the least productive method one could imagine: observe everything, write it all down, and wait for it to digest itself by eliminating disagreements into theories.
The problem with scholastics was not that they did not base their universals on experience. They did not believe in laws of nature, or even principles, universals. The Nominalists based all on the concrete, much like Hutton (1794) and Joachim (1948) and Wheeler (1990), but significantly unlike them in that Hutton and Joachim and Wheeler based their universals ontologically on the concrete. The Nominalists rejected universals.
They believed all was special intervention of God and God could always change his mind (even Jevons superstitiously inserted that clause in his book at late as 1874). They never bothered to make sense of their experience and Bacon recommends against it; he suggests it must be accumulated to digest itself. If it fails to give a theory, you just need more experience. But this method always fails. No amount of instances can prove a universal. At best we can assume an experiment is well controlled, so the sequence falsifies all other theories, because it is the same everywhere and everywhen, since all is measurable and nothing measurable can be inconsistent (Hutton) or simply that it at least falsified a competing conjecture because its predictions failed, regardless of how controlled the experiment was, at most leaving fewer explanations than before (Popper).
The problem with the Nominalists's methods is that they did not take theories or conjectures seriously. They did not believe in universals. For example: Buridan writes: an ass is a horse is true. Huh? What did you say? Buridan explains: it is written on a piece of paper, the words are objective now (in a sense Popper (1972) reintroduced), therefore an instance of this exists, and truth is correspondence with experience.
The scholastics and nominalists did not take any predictions seriously, did not believe in universals, in laws of nature, all was special arbitrary choice of god, so they alleged, and they collected experience and tested theories, but never admitted that the theory applies to any other instances. No wonder science made no progress prior the seventeenth and eighteenth centuries.
That had to wait for others to champion the idea of simple laws of nature explicitly. James Hutton (1794, 1795) and Ralph Gerard (1940) and then Stephen Wolfram (2002) write that all the universe complexity and complication is by repeated operation of extremely simple constant laws which have enormous scope in time to work out. Wheeler (1994) suggests the laws may self modify over time as part of their operation but that is it. Uniformitarianism. Conjectured universals. That was the big idea. First tacitly then in public, finally, by Leibniz and Hume and Hutton.
Newton writes that explanations should be as simple as possible to explain appearances. (Menger later added: Yes, but not simpler.) Newton also postulated rules that Euler revised into the Newtonian classical mechanics. The explicit fact that however even simpler rules over a long time can create complexity and all natural forms, instead of merely describing interaction of complex or complicated natural forms, had to wait.
Jevons agrees with Hume and Popper that induction, in sense of learning universals from experience, does not exist at all, and there is no problem of induction, except strict inverse deduction, enumerating all combinations and solving a very complex combinatorics to find out all combinations of objects that could combine to construct those instances according to their know behavior. Enumerating all finite instances and eliminating the contradictions is not a method but proves nothing about universals.
Joachim, Eddington, Hayek, Wheeler, Popper, Harris write that there are no foundations and no justifications only falsifications and elimination of free conjectures. The precedence of the conjectures allows us to know and use the truth without having to prove it and let us survive for often had we to prove it be some inductive procedure we would know what exists in our environment to late to survive (Hayek 1952, Popper 1962).
I think some misunderstand Popper. He does not say anything about how conjectures are formed. True; but that is only because the conjectures are purely unfounded, free constructions. They can be aesthetic as Dirac, Eccles, Popper, Atiyah, Penrose, Poincare, Wheeler, etc, think. Based on nothing more than this would be pretty if it were true.
There is no justification stage. Only falsification. We cannot justify a conjecture, only falsify competing ones. Popper's (and Hayek's), Wheeler's, and Errol Harris's are basically the first completely without foundations methods of science. Because foundations, justification of justification, leads to infinite regress, foundations that have foundations and yet in the end no foundations, no towers of turtles ...
Joachim, Blanshard, Wheeler, Eddington, Hayek (but not Popper), Harris, etc, also point out that all is without foundations but circular and consistent in epistemology as in ontology. The conjecture not only defines what falsifies it (and this is what it means) but also what and how to measure. Fodor (1968) writes: different conjectures not only predict different results but perform different experiments and measure different things in different ways. Deutsch (2011) writes: most conjectures are not even falsified but cease to be entertain or become unentertainable.
This is all consistent with some empiricists (Hume, Condillac, Hutton, Bailey, modern physicists) and inconsistent with others (Bacon, Mill, Russell, Wittgenstein, logical positivists).
Some further thoughts.
Boden, 2006, Mind As Machine, 1, 2, is an empiricist who correctly emphasizes the framing problem for empiricism. You need a conjecture ready to decide what is relevant to then use to build bottom-up associations for further empirical theory generation. Chomsky basically alleges this frame is genetically inherited. That is because he tacitly assumes conjectures can be falsified only a finite number at a time so only a finite number must be posited for an experience sieve to leave a finite filter. I disagree with him; genes do not code for reasoning nor how to reason. Rather they are developmental resources. They only code for proteins, which have enormous degrees of freedom; the framing problem is still unsolved after five decades.
There are hundreds of different algorithms, all possible for generating conjectures from experience, that is why Popper and all but Harris avoided talking about how conjectures are made. That is the field of artificial cognition and not methodology. Dozens of journals with new algorithms each year.