Further beyond the Frege boundary

avant propos This paper is basically Keenan (1992) augmented by some new types of properly polyadic quantification in natural language drawn from Moltmann (1992), Nam (1991) and Srivastav (1990). In addition I would draw the reader's attention to recent mathematical studies of polyadic quantiicationz Ben-Shalom (1992), Spaan (1992) and Westerstahl (1992). The first and third of these extend and generalize (in some cases considerably) the techniques and results in Keenan (1992). Finally I would like to acknowledge the stimulating and constructive discussions ofthe earlier paper with many scholars, notably Dorit Ben-Shalom, Jaap van der Does, Hans Kamp, Uwe Mormich, Arnim von Stechow, Mats Rooth, and Ede Zimmermann. And I repeat here the acknowledgment in the earlier paper to Jim Lambek, Ed Stabler and two anonymous referees for Linguistics and Philosophy (the latter responsible for substantial improvements in the proofs - see footnote 10).