Programme
Davide Falessi
University of Lucerne
Ockham on Formal Contingency
Whereas other logicians such as Peter of Spain and William of Shyrewood do not provide a clear demarcation between contingency and possibility, William of Ockham provides a clear definition of propositions de contigenti by the application of De Morgan’s rules at the case of possibility and necessity. My presentation will try to outline how contingency can be distinguished from the so-called two sided possibility and what is relationship between ontological definition of contingency and its formal transcription in a conjunction of propositions de possibili. These will be the main questions: what is the logical semantics of contingency? What happen when we deny a proposition de contigenti? Since providing a formal definition of a modal operator means also to set up all the logical relations with the other operators and this means in turn to set up a modal square, one then can reasonably ask: is it possible to set up a modal square involving proposition de contigenti?
It is well known that during the XIV century there were set forth different modal squares using not only modalities but also quality and quantity of propositions. Ockham provides three different squares in his Expositio in librum Perihermenias. None of them involves contingency. However, one of them, which involves propositions de possibili and de necessario, which are both related to the definition of contingency, can be re-write as a possible extension of modal squares. Looking both at the Summa Logicae and at this modal square provided in the Expositio in librum Perihermenias, we shall finally outline the modal hexagon involving contingency, possibility and necessity: following Ockham we can draw step by step the so-called modal hexagon that has been discovered only starting from 1950s.