Philosophy

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    TOPIC SENSITIVE BELIEF REVISION
    (2009) Parsia, Bijan; Horty, John F; Philosophy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    When asked to change one's beliefs in the face of new information, or to revise a book given errata, we commonly strive to keep our changes relevant, that is, we try to restrict the beliefs (or chapters) we change to those that bear some content relation to the new information. One kind of relevance, topicality, is interesting for two reasons: First, topicality tends to be strongly encapsulating, e.g., we shouldn't make any off-topic changes. Second, topicality tends to be weaker than strict relevance. Consider a panel of three papers on the topic of Kant's life and works. It would be entirely possible for each of the papers to have no bearing on the truth of any sentence in any of the other papers, and yet for all of the papers to be on topic. In this dissertation, I explore theories of logical topicality and their effect on formal theories of belief revision. Formal theories of belief revision (in the Alchourrón, Gärdenfors, and Makinson (AGM) tradition) model the object of change (my beliefs, a book) as a collection of formulae in a supra-classical logic and provide a set of postulates which express constraints on the sorts of change that are, in principle, formally rational. In 1999, Rohit Parikh proposed that signature disjointness captured a reasonable notion of topicality but that taking topicality into account required changes in the standard AGM postulates (and thus, the notion of rational change). He, and subsequent theorists, abandoned this notion of topicality in order to deal with the revision of inconsistent objects of change. In this thesis, I show 1) that a disjoint signature account of topicality does not require changes to the AGM rationality postulates and 2) a disjoint signature account of topicality can apply to inconsistent objects of change. Additionally, I argue that signature disjointness has a strong claim to being at least a sufficient condition of logical topicality.
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    Quantification and Second-Order Monadicity
    (Blackwell, 2003) Pietroski, Paul
    The first part of this paper reviews some developments regarding the apparent mismatch between the logical and grammatical forms of quantificational constructions like 'Pat kicked every bottle'. I suggest that (even given quantifier-raising) many current theories still posit an undesirable mismatch. But all is well if we can treat determiners (words like 'every', 'no', and 'most') as second-order monadic predicates without treating them as predicates satisfied by ordered pairs of sets. Drawing on George Boolos's construal of second-order quantification as plural quantification, I argue that we can and should view determiners as predicates satisfied (plurally) by ordered pairs each of which associates an entity with a truth-value (t or f). The idea is 'every' is satisfied by some pairs iff every one of them associates its entity with t. It turns out that this provides a kind of explanation for the "conservativity" of determiners. And it lets us say that concatenation signifies predicate-conjunction even in phrases like 'every bottle' and 'no brown dog'.