WHAT IS NON-CLASSICAL SCIENCE?

I make an attempt at specifying methodological features under which a theory may be avowed to be non-classical with respect to the extant scientific knowledge. One such feature is the case when a theory suggests a systematic description of objects that display a paradoxical, or unexpected behaviour (usually dubbed 'non-classical objects'), and another, when it proposes a radically new conceptual approach for grasping the nature of familiar phenomena. The first case is realized in quantum theories, and we are faced with the second in the theory of relativity, or in genetics. The "sociological" role of scientific communities is also taken into account. It is shown in the end that some Para science could eventually turn into non-classical science, only if it could be embraced by some consistent methodology of scientific growth. If not, this is an argument for it to be referred to the realm of pseudo-science.