As mentioned above, parthood, as opposed to the set-theoretic notion of membership, is transitive: if a is a part of b and b is a part of c, then a is a part of c. Neither the system Leonard and Goodman present in their 1940 article, nor the version in Goodman’s A Study of Qualities, nor the calculus he uses in The Structure of Appearance, take “part” as primitive. Rather, it is in all three cases defined based on the sole primitive notion adopted: overlap in SA, and discreteness in the other two systems. Overlap can pre-systematically be understood as sharing a part in common; discreteness as sharing no part in common. All three systems indeed define parthood so that these two pre-systematic understandings come out as theorems.