The phrase "a background theory" is correct and usable in written English.
It can be used when referring to a theoretical framework or context that supports or explains a particular subject or phenomenon.
Example: "In order to understand the results of the experiment, we must first establish a background theory that explains the underlying principles."
Alternatives: "a foundational theory" or "a theoretical background".
Here one must assume a background theory, a law about laws, which predicts for this area that these two laws hold.
Both Andreasen and Guze assume that to find the specific causes of disease we need a background theory of normal function.
There is a difficulty in articulating this view, which may be brought out as follows: To begin with, one must pick a background theory in which to discuss the various models and this leads to a difficult.
A variety of computational approaches and reasoning problems are considered, the use of translation-based and tableau-based algorithms for deciding the satisfiability of a formula is focused, both with and without reference to a background theory.
But such inquiry becomes the inductive method science only when those gappy laws are themselves supported, not simply as spontaneous inductions, but there is a background theory, a generic law about laws, that provides for them antecedent inductive support deriving from other, related areas.
It follows that such a position can never be fully articulated each time one attempts to articulate the broad multiverse conception one must employ a background theory but since one is a pluralist about that background theory this pass at using the broad multiverse to articulate the conception does not do the conception full justice.
Another common reason is that the axiomatic theory in question intends to capture a particular non-classical semantics of truth, for which a classical background theory may prove unsound.
Hilbert's consistency demonstrations in FG are all demonstrations of relative consistency, which is to say that in each case the consistency of a set AX of geometric axioms is reduced to that of a familiar background theory B, demonstrating that AX is consistent if B is.
Of course, if Putnam is willing to use a stronger background theory to prove his theorem e.g., ZFC + "there exists an inaccessible cardinal"—then he can evade these kinds of criticisms.
One can certainly take the pluralist stance and try to gesture toward or exhibit the view that one intends by provisionally settling on a particular background theory but then advocate pluralism regarding that when pressed.
In this paper, we aimed to stress that the specific set-up of empirical-ethical research necessitates a comprehensive reflection with regard to the selection of an ethical background theory.
