Peter Abelard (1079 – 21 April 1142) [‘Abailard’ or ‘Abaelard’ or ‘Habalaarz’ and so on] was the pre-eminent philosopher and theologian of the twelfth century. The teacher of his generation, he was also famous as a poet and a musician. Prior to the recovery of Aristotle, he brought the native Latin tradition in philosophy to its highest pitch. His genius was evident in all he did. He is, arguably, the greatest logician of the Middle Ages and is equally famous as (...) the first great nominalist philosopher. He championed the use of reason in matters of faith (he was the first to use ‘theology’ in its modern sense), and his systematic treatment of religious doctrines are as remarkable for their philosophical penetration and subtlety as they are for their audacity. Abelard seemed larger than life to his contemporaries: his quick wit, sharp tongue, perfect memory, and boundless arrogance made him unbeatable in debate — he was said by supporter and detractor alike never to have lost an argument — and the force of his personality impressed itself vividly on all with whom he came into contact. His luckless affair with Héloïse made him a tragic figure of romance, and his conflict with Bernard of Clairvaux over reason and religion made him the hero of the Enlightenment. For all his colourful life, though, his philosophical achievements are the cornerstone of his fame. (shrink)

Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of ontological commitment to real (...) numbers. (shrink)

According to the aspect theory of instantiation, a particular A instantiates a universal B if and only if an aspect of A is cross-count identical with an aspect of B. This involves the assumption that both particulars and universals have aspects, and that aspects can mediate between different ways of counting things. I will ask what is new about this account of instantiation and, more importantly, whether it is an improvement on its older relatives. It will turn out that the (...) part of it that is new is the notion of cross-count identity among aspects. As I will show, this notion is both dubious and unnecessary. I will end by presenting a simplified aspect theory of instantiation that does not involve cross-count identity. (shrink)