104. But the intellect mustn’t be allowed •to jump—to fly—from particulars a long way up to axioms that are of almost the highest generality (such as the so-called ‘first principles’ of arts and of things) and then on the basis of them (taken as unshakable truths) •to ‘prove’ and thus secure middle axioms. That has been the practice up to now, because the intellect has a natural impetus to do that
...
Our only hope for good results in the sciences is for us to proceed thus: using a valid ladder, we move up gradually—not in leaps and bounds—from particulars to lower axioms, then to middle axioms, then up and up until at last we reach the most general axioms. ·The two ends of this ladder are relatively unimportant· because the lowest axioms are not much different from ·reports on· bare experience, while the highest and most general ones—or anyway the ones that we have now—are notional and abstract and without solid content. It’s the middle axioms that are true and solid and alive; they are the ones on which the affairs and fortunes of men depend.
...
the human intellect should be •supplied not with wings but rather •weighed down with lead, to keep it from leaping and flying. This hasn’t ever been done; when it is done we’ll be entitled to better hopes of the sciences.
105. For establishing axioms we have to devise a different form of induction from any that has been use up to now, and it should be used for proving and discovering not only so-called ‘first principles’ but also the lesser middle axioms— indeed all axioms.
The treatment of this subject in Novum Organum might be illuminating.
From The Baconian Method: