Mediaeval logicians inherited from Boethius an account of conditional propositions and the syllogisms which may be constructed using them. In the following paper it is shown that there are considerable difficulties with Boethius' account which arise from his failure to understand the nature of compound propositions and in particular to provide for their negation. Boethius suggests that there are two different conditions which may be imposed for the truth of a conditional proposition but he really gives no adequate account of (...) how such propositions may be obtained. The true greatness of Peter Abaelard as a philosophical logician is revealed in what he is able to do with the material which he found in Boethius. It is shown that he developed a precise theory of conditionals giving an account of how true conditionals may be obtained and principles which may be used to reject others as false. Unlike Boethius Abaelard properly appreciates that conjunctions must be treated as logical units. Even he, however, falls victim to difficulties which arise when this connective is brought into contact with negation and the conditions which he lays down for the truth of a conditional. (shrink)

This thesis focuses on Abelard’s solution to the problem of understanding universals as presented in the Tractatus de Intellectibus. He examines this issue by asking what is understood when we consider the term ‘man’, a problem I call the ‘homo intelligitur [man is understood]’ problem. This is an important question, since earlier in the Treatise, Abelard states that understandings paying attention [attendens] to things otherwise than they are are empty, and thus, cannot be true. The challenge is therefore to explain (...) how understandings about universals, such as genera and species, can be sound, given that Abelard is a nominalist and, as such, does not believe in the existence of universal entities. His own answer to the problem is that such understandings attend to natures. However, since natures are, on his view, nothing more than the individuals they belong to, it is unclear how his solution is intended to work. I propose two ways to understand Abelard’s solution to the ‘homo intelligitur’ problem, identifying their respective merits and drawbacks. The first one is to treat ‘nature’ as meaning ‘status’. I explore this solution in Chapters 2 and 3, and conclude that while it has the advantage of establishing links between De Intellectibus and previous logical works by Abelard, it has some significant drawbacks, most notably that it is unclear how we can have epistemic access to status given that status are not things, which renders unclear how the criteria for the soundness of understandings can be met. The second one involves treating natures as referring to behaviors typical of members of a given genus or species. These behaviors come from the particular essential forms possessed by individuals, i.e. their differentiae understood as analogous to nuclear tropes in Peter Simons’ trope theory. I conclude that this solution is more intuitive than the first one and has the advantage of not depending on a specific interpretation of the evolution of Abelard’s thought. However, it is unclear how to treat behaviors and regularities in his ontology. (shrink)