Question

At one point I heard from you a solution to the sorites paradox, according to which one should free oneself from binary logic and move to a fuzzier logic. According to this, the concept of a “heap” is not absolute but graded: there is a heap at the level of 0.1, 0.2, and so on. That is how the logical contradiction in the paradox is resolved.

Following that, I thought that indeed in many of our definitions of concepts there is a broad range. You yourself mentioned the distinction between poetry and prose: there are theoretical endpoints, but in practice there are different degrees of “poeticness” as opposed to “prosaicness.” Still, there are definitions that seem binary. For example, the definition of “Jew” — either you are a Jew or you are not. There is no “Jew to degree 0.4.” Though it may be that with respect to certain laws there are gradations or overlapping boundaries; I don’t know.

In any case, assuming there are binary kinds of definitions as opposed to graded ones, the question arises: why does linguistic or conceptual reality sometimes behave one way and sometimes another? Intuitively I thought that perhaps this is connected to the distinction between a “directive definition” and a “constitutive definition”. As you explained with regard to the game of chess — which is a constitutive system in which the rules themselves define the game — as opposed to soccer, whose rules are directive toward an existing intuitive substrate.

And perhaps accordingly: when the definition is directive (that is, it describes a concept that already exists in intuition), a broad range and different degrees of realization emerge, as with poetry or beauty. By contrast, when the definition is constitutive — as with “Jew” — there is no scale, because there is no prior intuition on which it rests; the definition itself creates the concept.

What do you think of this distinction?