-- "Deontic Logic in the Lambeth Fragments of Anselm of Canterbury"

Sara L. Uckelman, ILLC, suckelma@illc.uva.nl

Fragmentary notes of Anselm, Archbishop of Canterbury, which were compiled and organized shortly after his death in 1109 contain modal analyses of certain Latin verbs, including facere `to do', velle `to will', and posse `to be able'. His primary focus is on facere, with his analyses of velle and posse being modelled after the analysis of facere for the most part. In discussing facere, Anselm makes clear that there is a difference between the usus proprie `proper use' and the usus improprie or usus loquendi `improper, common use' of a term. Normally, the logician is interested in proper usage and leaves investigations of improper or common usage to the grammarian. However, Anselm points out that in many cases, terms used in scripture are not used in their proper, logical sense but are used improperly, or according to common usage. Since understanding scripture is something which everyone should strive towards, Anselm points out that the logician should be interested in the common usage of terms because in many cases it can be explained by the logical or proper usage. An agentive modal logic can be extracted from his analysis of the logical usage of facere: It is the non-normal modal logic EMCT. But embedded within his analysis of agency there is, not explicitly, also a deontic theory, where he connects his analysis of agency with issues in obligation and good and evil as they are found in scripture. A formal analysis of these issues results in a robust mutli-agent deontic logic with good and evil predicates for both actions and agents. Such a logic gives a formal justification for Anselm's informal arguments that improper uses of agentive and deontic terms in scripture can be explained via proper, logical usage. The resulting logic is of interest both historically, as perhaps one of the earliest examples of a deontic logic, and logically, as in order to model uniquely theological aspects such as God it is essentially different from many standard modern deontic logics. In this paper, we present some of the historical background to the work, discuss Anselm's motivations for appropriate agency as he does and provide a syntax and semantics for his agentive logic, and then augment this logic with the deontic concepts required to model his analysis of scriptural usage of doing, obligation, and goodness. --