According to the Incommensurability Thesis (IT) superseding scientific theories (paradigms) are incommensurable. Unlike many authors we do not discuss whether there is a relationship of this kind. We take for granted that this may be the case, and see the problem in the endeavour to establish the domain of validity of the IT. The notion incommensurability (Ic) is derivative from the concepts of scientific paradigm (P) and scientific revolution (R). There are several concepts of P, as well as various conceptions (...) of R. The Ic concept also has more than one meaning. The validity of the IT is restricted to a subset of P, R, and Ic. From the viewpoint of P this may be the case with (a) substantially different competing general conceptions not reformulated with a view to make them comparable, as well as with (b) scientific communities dogmatically committed to such conceptions. From the viewpoint of R this takes place when we have to do with big revolutions, i.e. superseding conceptions with prevailing discontinuity. Lastly, from the point of view of Ic proper: when it is meant a weak Ic, i.e. a particular incomparability (incompatibility) between the conceptions in question. (shrink)