In spite of successful tests, the standard cosmological model, the $$\varLambda$$ CDM model, possesses the most problematic concept: the initial singularity, also known as the big bang. In this paper—by adopting the Kantian difference between to think of an object and to cognize an object—it is proposed a degree of scientificity using fuzzy sets. Thus, the notion of initial singularity will not be conceived of as a scientific issue because it does not belong to the fuzzy set of what is (...) known. Indeed, the problematic concept of singularity is some sort of what Kant called the noumenon, but science, on the other hand, is constructed in the phenomenon. By applying the fuzzy degree of scientificity in cosmological models, one concludes that cosmologies with a contraction phase before the current expansion phase are potentially more scientific than the standard model. At the end of this article, it is shown that Kant’s first antinomy of pure reason indicates a limit to our cosmological models. (shrink)