George Berkeley is known as “The Good Bishop,” a name celebrating his faith, pastoral ministry and earnest commitment to his philosophical views. To mathematicians, he is known for his agitated performance in his 1734 critique of fluxions, The Analyst. That work and its petulant tone were occasioned by (i) his “philo-mathematical” opponents’ alleged admonitions on religious mysteries’ lack of logical respectability and (ii) what Berkeley saw as a related public appetite for reformist and deist religious movements. This paper questions Berkeley’s (...) saintly reputation by outlining the hostility and flippancy in his handling of Jacob Walton’s contributions to the debate. Berkeley’s interactions with Walton bear many of the hallmarks of contemporary “trolling” culture and this paper emphasises and explains these parallels. Finally, given Berkeley’s theological and political agenda in his mathematical interactions, I argue that we should not read his mathematical rhetoric as straightforwardly representing his philosophical views. (shrink)

The ArgumentThis paper is a study of the role of language in scientific activity. It recommends that language be viewed as a community's means of patterning its affairs. Language represents where the boundaries of the community are and who is entitled to speak within it, and it displays the structures of authority in the community. Moreover, language precipitates the community's view of what the world is like, such that linguistic usages can be taken as referring to that world. Thus, language (...) connects on the one side to a community's practical life, and, on the other, to the reality on which it “reports.”The example treated is Robert Boyle's view of the language proper for experimental practice, and his arguments against the value and legitimacy of mathematical representations within the experimental community. Boyle argued that the use of mathematics was inappropriate because (i) it would restrict the number of potential participants; (ii) it would give rise to unwarranted expectations of the certainty and accuracy to be expected of real physical inquiries; (iii) it would suggest views of natural law and God's relations with the natural world which were incorrect and possibly dangerous; and because (iv) the world upon which the experimentalist operated was not such as was represented by mathematical idealizations. I try to establish that decision about the appropriate language for the experimental community was a moral choice. (shrink)

ABSTRACTThis paper responds to two issues in interpreting George Berkeley’s Analyst. First, it explains why the text contains no discussion of religious mysteries or points of faith, despite the claims of the text's subtitle; I argue that the subtitle must be understood, and its success assessed, in conjunction with material external to the text. Second, it’s unclear how naturally the arguments of the Analyst sit with Berkeley’s broader views. He criticizes the methodology of calculus and conceptually problematic entities, and the (...) extent to which they require one to bend the rules of classical mathematics. Yet, elsewhere, Berkeley’s opinion of classical mathematics and its intelligibility is low, and he defends a pragmatic approach to word meaning that should not find fault with so functionally successful a theory. The ad hominem intention of the text makes it difficult to discern to what extent Berkeley is committed to the sincerity of these criticisms. This component of the text is rarely discussed, but I argue that when trying to decide what Berkeley’s true position is in the Analyst, we should treat its ad hominem component as its primary intention. (shrink)