SCIENCE AND OTHER COMMON NOUNS: FURTHER IMPLICATIONS OF ANTI-ESSENTIALISM

The term “science” is a common noun that is used to designate a whole range of activities. If Reeves is right—and I think he is—that there is no essence to these activities that allows them to be objectively identified and demarcated from nonscience, then what qualifies as science is determined by communities. It becomes much more difficult on this antiessentialism position to identify and dismiss pseudo-science. I suggest we might find a way forward, though, by engaging a philosophical tradition that has largely been neglected in English-speaking science and religion studies, and by articulating a theory of consensus along the lines of Oreskes (2019).     

The independence of the parallel postulate and development of rigorous consistency proofs

I trace the development of arguments for the consistency of non-Euclidean geometries and for the independence of the parallel postulate, showing how the arguments become more rigorous as a formal conception of geometry is introduced. I analyse the kinds of arguments offered by Jules Hoüel in 1860–1870 for the unprovability of the parallel postulate and for the existence of non-Euclidean geometries, especially his reaction to the publication of Beltrami's seminal papers, showing that Beltrami was much more concerned with the existence of non-Euclidean objects than he was with the formal consistency of non-Euclidean geometries. The final step towards rigorous consistency proofs is taken in the 1880s by Henri Poincaré. It is the formal conception of geometry, stripping the geometric primitive terms of their usual meanings, that allows the introduction of a modern fully rigorous consistency proof.     

Dialectic in the eleventh and twelfth centuries: garlandus compotista

Dialectic is a standard and important part of the logica vetus (or old logic) in medieval philosophy. It has its ultimate origins in Aristotle's Topics,its fundamental source in Boethius's De topicis differentiis,and its flowering in its absorption into fourteenth-century theories of consequences or conditional inferences. The chapter on Topics in Garlandus Compotista's logic book is the oldest scholastic work on dialectic still extant. In this paper I show the differences between Boethius's Theory of Topics and Garlandus's in order to illustrate the role of Topics in early scholastic logic. I argue that for Garlandus Topics are warrants for the inference from the antecedent to the consequent in a conditional proposition and that he is interested in Topics because of his overriding interest in hypothetical syllogisms. I conclude by discussing briefly the relationship between Garlandus's use of Topics and twelfth-century accounts.