University of Connecticut OpenCommons@UConn Doctoral Dissertations University of Connecticut Graduate School 8-8-2018 Applications of Non-Classical Logic Andrew Tedder University of Connecticut - Storrs,
[email protected] Follow this and additional works at: https://opencommons.uconn.edu/dissertations Recommended Citation Tedder, Andrew, "Applications of Non-Classical Logic" (2018). Doctoral Dissertations. 1930. https://opencommons.uconn.edu/dissertations/1930 Applications of Non-Classical Logic Andrew Tedder University of Connecticut, 2018 ABSTRACT This dissertation is composed of three projects applying non-classical logic to problems in history of philosophy and philosophy of logic. The main component concerns Descartes’ Creation Doctrine (CD) – the doctrine that while truths concerning the essences of objects (eternal truths) are necessary, God had vol- untary control over their creation, and thus could have made them false. First, I show a flaw in a standard argument for two interpretations of CD. This argument, stated in terms of non-normal modal logics, involves a set of premises which lead to a conclusion which Descartes explicitly rejects. Following this, I develop a multimodal account of CD, ac- cording to which Descartes is committed to two kinds of modality, and that the apparent contradiction resulting from CD is the result of an ambiguity. Finally, I begin to develop two modal logics capturing the key ideas in the multi-modal interpretation, and provide some metatheoretic results concerning these logics which shore up some of my interpretive claims. The second component is a project concerning the Channel Theoretic interpretation of the ternary relation semantics of relevant and substructural logics. Following Barwise, I de- velop a representation of Channel Composition, and prove that extending the implication- conjunction fragment of B by composite channels is conservative.