In my recent posts on Badiou’s method I am making no unusual or unduly metaphysical claims about the logic of necessity or the nature of reality..
I am merely starting out from the famous « layer-cake » model of testing starting with observational theories (I say observational « theories because there are no pure observations) going upwards via more and more conceptually elaborated auxiliary theories and ending with some very general speculative theory. The constitutive principles of each theoretical stratum are mutually exclusive, because of the time factor.
Note: this is not a logical necessity but a pragmatic one.
As various observational and auxiliary theories (concerning instrumentation, experimental set-ups, and more or less low level regional laws) are already in place it would be very surprising if a new theory at the speculative level were to be able to generate all the lower-level theories compatible with its concepts – and all at the same time – and able to replace the already entrenched theories.
This is why I talk in terms of « research programmes » (sort of a de-dogmatised Kuhnian paradigms). It takes time to build a new research programme and to fill in all the intermediate levels.
The example of Galileo’s heliocentric theory and the associated auxiliary theories needed to support it, but coming only much later (e.g. a theory of the telescope’s construction, functioning, and conditions of reliability) already illustrates this time-sensitivity in dealing with incommensurable theories layered in terms of differing degrees of generality and differing degrees of observationality.
Thus I make no absolute claims about the « real world » but talk about a theory as being able to « deal with the real world » if it has testable content in terms of this model.
This dealing with the world (or not) can only be evaluated from within a particular truth procedure.