The boot-strapping process generates a hierarchy of theories starting from an accepted base theory T_0 via an extension procedure T -> T' that leads from a correct theory to a more encompassing correct theory
A theory that accurately describes or explains the way things actually are in reality, without errors or gaps.
Encompassing(as used in comparing theories)
Broader or more comprehensive; able to include and explain everything that a smaller theory could, plus additional cases or phenomena.
Extension procedure (T → T')(as used in logic and theory development)
A systematic method of taking an existing theory and expanding it to cover more cases or explain more things while keeping it correct.
Hierarchy of theories(as used in philosophy of science)
A ranked ordering of scientific or philosophical explanations where some theories are more basic and others build on top of them, arranged from simplest to most complex.
In the foregoing progressions the ordinals remained external to the theory. Autonomous progressions of theories are the proper internalization of the general concept of progressions. In the autonomous case one is allowed to ascend to a theory \(\bT_a\) only if one already has shown in a previously accepted theory \(\bT_b\) that \(a\in{\cO}\). This idea of generating a hierarchy of theories via a boot-strapping process appeared for the first time in Kreisel 1960, where it was proposed as a way of