Inaccessible worlds: A possible worlds narrative analysis of select modernist texts

This thesis is an examination of three themes across three modernist novels. I look at Father's Suicide, Spurned Union and Birth as Death as they take place (or fail to take place) in Ford Madox Ford's Parade's End, Virginia Woolf's To the Lighthouse and James Joyce's Ulysses. As a framework, I have adopted Marie Laure-Ryan's Possible Worlds Theory as laid out in her Possible Worlds, Artificial Inteligence and Narrative Theory. This allows me to discuss the aforementioned themes as products of various modal systems (axiological, epistemic, deontic), which in turn allows me to examine the way the three novels relate to each other and to their common modernist milieu. Advisor: Sebastian Knowle

The modal logic of set-theoretic potentialism and the potentialist maximality principles

We analyze the precise modal commitments of several natural varieties of set-theoretic potentialism, using tools we develop for a general model-theoretic account of potentialism, building on those of Hamkins, Leibman and L\"owe, including the use of buttons, switches, dials and ratchets. Among the potentialist conceptions we consider are: rank potentialism (true in all larger $V_\beta$); Grothendieck-Zermelo potentialism (true in all larger $V_\kappa$ for inaccessible cardinals $\kappa$); transitive-set potentialism (true in all larger transitive sets); forcing potentialism (true in all forcing extensions); countable-transitive-model potentialism (true in all larger countable transitive models of ZFC); countable-model potentialism (true in all larger countable models of ZFC); and others. In each case, we identify lower bounds for the modal validities, which are generally either S4.2 or S4.3, and an upper bound of S5, proving in each case that these bounds are optimal. The validity of S5 in a world is a potentialist maximality principle, an interesting set-theoretic principle of its own. The results can be viewed as providing an analysis of the modal commitments of the various set-theoretic multiverse conceptions corresponding to each potentialist account.Comment: 36 pages. Commentary can be made about this article at http://jdh.hamkins.org/set-theoretic-potentialism. Minor revisions in v2; further minor revisions in v