The Modal Logic of Albert of Saxony - Ely, Pamela (My University, 1981)
This work is an exegetical account of the modal logic of Albert of Saxony, a 14th century logician and scientist. The text used was the 1522 Venice edition of the Perutilis logica. As there is no critical edition of the text, a "working edition" of the pertinent sections (tract III, chapter iv and tract IV, chapters v-vi, xii-xviii) accompanies the dissertation as an appendix.
Aristotle's modal logic which served as a basis for modal logic in the Middle Ages is briefly reviewed. Albert's non-modal propositional logic, onto which the modal logic is grafted, is then presented informally.
Albert's chapter on the semantic and syntactic considerations for a modal logic (III,iv) is analyzed in detail as are his chapters on modal consequences (IV, v-vi) and his chapters on modal syllogisms (IV, xii-xviii). In these chapters, Albert makes the distinction between modal propositions in sensu composito and in sensu diviso, and gives the truth conditions for each type of modal proposition. He goes on to state the rules which govern what can be inferred from the two sorts of propositions and finally examines syllogisms constructed from modal propositions following the Aristotelian classification of figures and moods. While he mentions the modes of knowing, doubting, etc., he primarily is interested in the modes of possibility and necessity and, to a lesser extent, the mode of contingency.
In the concluding chapter, Albert's system is briefly compared with modern systems and the ground work for a semantic model is laid, i.e., considerations concerning the truth of modal propositions which the formal logician must take into account for the construction of such a model are put forward. Further, a brief comparison between Albert, Aristotle, and Ockham is made concerning certain aspects of necessity.
For the purposes of clarity and convenience, standard quantified modal predicate calculus is used.
Pertinent findings include the fact that Albert's system encompasses the modern T system and an argument can be made that it includes the 55 system as well.
More importantly, Albert ultimately wishes to distinguish four different sorts of necessity: a necessity concerning how an attribute applies to an individual, a necessity concerning the relationship between the subject and predicate terms, an 'hypothetical' necessity concerning an event once it has occurred, and finally, it is argued, a necessity concerning the relationship of the subject and predicate terms not on the basis of their denotata but on the basis of their signification, i.e., their meaning.
Though Albert does not succeed in constructing an unmbiguous formal logical system, he does bring to light some aspects of the nature of necessity and possibility and the ways in which the terms "necessary" and "possible" are used in natural language.