The Square of Individuals

Coordinate, plural and predicative constructions of noun phrases are common and highly productive in natural languages. They are also related in intricate ways: conjunctive coordination is one of the simple means to form plural NP’s from singular ones; many coordinate and plural NP’s appear naturally in predicative positions. Any theory of grammar and semantic interpretation should account for these facts. The present paper is a contribution to the semantic part of the theory. Following Partee’s programmatic article “Noun phrase interpretation and type shifting principles” (1987) we will further explore and substantiate the paradigm of Type Flexibility. Extending the treatment in Winter (1994) to plural and predicative NP’s, it will be shown how the long-standing puzzle surrounding “intersective” vs. “collective” conjunction can be not only resolved, but also lead to a more comprehensive theory of flexibility. The conjunctive coordinator and is uniformly treated as standard Boolean intersection, eliminating the common stipulation about its ambiguity. It will be proposed that one underlying property of Boolean domains, called The Principal Filter Property governs the apparent “non-Boolean” behaviour of conjunction. This property will lead to an extension of Partee’s flexibility diagram (“The Partee Triangle”) into a polymorphic scheme, The Square of Individuals. The advantages of this extended mechanism in treating coordination, plurality and predication will be exemplified.