But the basic resemblance between these concepts is their open texture. In elucidating them, certain (paradigm) cases can be given, about which there can be no question as to their being correctly described as "art" or "game," but no exhaustive set of cases can be given. I can list some cases and some conditions under which I can apply correctly the concept of art but I cannot list all of them, for the all-important reason that unforeseeable or novel conditions are always forthcoming or envisageable.
A concept is open if its conditions of application are emendable and corrigible; i.e., if a situation or case can be imagined or secured which would call for some sort of decision on our part to extend the use of the concept to cover this, or to close the concept and invent a new one to deal with the new case and its new property. If necessary and sufficient conditions for the application of a concept can be stated, the concept is a closed one. But this can happen only in logic or mathematics where concepts are constructed and completely defined. It cannot occur with empirically-descriptive and normative concepts unless we arbitrarily close them by stipulating the ranges of their uses.