Peter Abaelard's birth around 1079 coincided with the promulgation by Pope Gregory VII of a decree instructing his bishops to ensure that all clerics were trained in the liberal arts, and Abaelard's life was shaped by the consequent increase in the number and importance of teaching masters. These early twelfth century teachers commented on the works of what would later be called the logica vetus, including from Aristotle only the Categories and De Interpretatione. Abaelard also had some access to the Sophistical Refutations and, indeed, seems to have known a little about the Prior Analytics. The latter work, however, played no role in the development of thinking about modal propositions in the period to be considered here. Rather it was Aristotle's remarks on the proper placing of the negative particle in forming the contradictory of a given modal proposition in de Interpretatione 12, and 13, and a distinction made by Boethius between different forms of modality in his De Syllogismis Hypotheticis that prompted early twelfth century philosophers to investigate the nature of modal propositions.

Ancient Sources

The general problem for the De Interpretatione is to characterise the logical relationship of opposition in truth-value. Aristotle has no notion of negation as a propositional operator and proceeds, rather, syntactically, to consider where the negative particle is to be inserted into each form of categorical proposition to produce the desired opposite. This leads him in chapters 12 and 13 to the question of the proper negations of, and logical relations between, propositions involving nominal modes. For the Latin writers we are to consider here these are propositions such as ‘(For) Socrates to be a man is possible’ (‘Possibile est Socratem esse hominem’) and ‘(For) Socrates not to be a stone is necessary’ (‘Necesse est Socratem non esse lapidem’). Aristotle holds that negation is an operation on terms which takes the narrowest possible scope. For modalities this entails, he concludes, that it must be applied to the modal adjective to yield, for example, ‘not necessary to be’ as the negation of ‘necessary to be’. In chapter 13 of De Interpretatione he summarises his results in a set of four tables of equipollent combinations of mode and quality which were the starting point of early twelfth century discussions of modal sentences.