Formal mereology and ordinary language - Reply to Varzi

Achille Varzi ends his note [10] on my paper [6] by saying: “Parthood is transitive, φ-parthood—for many values of ‘φ’—is not.” Let me call this view ‘the (Simons/Casati/Varzi) predicate modifier account’ of non-transitive parthood relations [9, 2]. As summarized in this quotation, I agree with it here, and did agree with it in the paper Varzi criticizes. It is puzzling to me why he surrounds his specific comments on subsumption, relative products, and functions with statements such as “we end up with a reinforcement of the standard defense of transitivity on behalf of classical mereology” ([10], abstract). I have not questioned this transitivity, and until reading Varzi’s reply thought that I had made this perfectly clear in my paper. Rather, my thoughts about the intransitivity examples have led me to the view that they bring sharply to the fore a more general problem: what does the relation between classical formal mereology and the parthood predicates used in science and ordinary language look like. My paper ends with “a warning: be careful if you try to apply the transitivity axiom of binary mereology to parthood predicates found in areas outside mereology proper. Such predicates might very well be intransitive, non-transitive or fall outside the scope of any natural definition of transitivity ([6], p. 180).” Perhaps an analogy can illuminate what my warning amounts to. In undergraduate courses in logic, students are taught how to transform sentences in ordinary language into sentences in first order predicate logic. Sometimes this can be done smoothly, but sometimes it is hard and sometimes not even possible. In my opinion, when mereology is applied in ontological engineering, similar situations can obtain: as formalizations of ordinary language can be problematic, “mereologizations” of ordinary language can be problematic. Since computer and information scientists have to relate themselves to pre-existing predicates that in ordinary life are used as means to talk about the world, I think this view of mine is quite relevant to what has given this journal its name: Applied Ontology. It is good for authors and developers of all domain-specific computer ontologies such as the Gene Ontology (GO) [4] and the Foundational Model of Anatomy (FMA) [3], which contain (proper) parthood relations, to know (i) whether “their” parthood relations (which I think are φ-parthoods) are in general transitive or not, and, (ii) if not, whether these relations are nonetheless transitive in some specific area that is important for the practical purposes at hand. Now to the more specific issues in Varzi’s paper (note: the section numbers below do not mirror Varzi’s).