Speaker: Danny Fox (MIT)
Time: Friday, May 7, 2010, 3:30pm-5pm
Location: 32-141 (Stata Center)
Title: Negative Islands and Maximization Failure
The goal of this talk is to discuss various questions that arise in the context of attempts to reduce a class of weak islands to Maximization Failure (Fox and Hackl 2006, Fox 2007, Abrusan 2007, in press, Nouwen 2008, Abrusan and Spector 2008, in press, Shimoyama and Schwarz 2010). The basic idea that guides these attempts is that the the relevant islands arise from a maximality requirement that cannot be met on semantic/logical grounds.
The questions we will discuss pertain to the possible sources of this Maximization Failure (MF). According to Fox and Hackl, the source in certain degree constructions is the density of degree domains. However, in later work, it was pointed out that some of the results could be derived if alternative sources of MF are postulated, and Abrusan and Spector (A&S) present arguments for one specific alternative that I will be focusing on (quantification over degree intervals).
The more specific goals of this talk are the following: (a) to argue that density is necessary despite various observations made by A&S that seem to argue for intervals, and (b) to argue that there is yet another source for MF beyond those identified in recent literature and that this source for MF is responsible for another weak island observed in Spector (2008), and could also account for A&S’s observations.