This paper discusses George Boole’s two distinct approaches to the explanatory relationship between logical and psychological theory. It is argued that, whereas in his first book he attributes a substantive role to psychology in the foundation of logical theory, in his second work he abandons that position in favour of a linguistically conceived foundation. The early Boole espoused a type of psychologism and later came to adopt a type of anti-psychologism. To appreciate this invites a far-reaching reassessment of his philosophy (...) of logic. (shrink)

Scholars in both digital humanities and media studies have noted an apparent disconnect between computation and the interpretive methods of the humanities. Alan Liu has argued that literary scholars employing digital methods encounter a “meaning problem” due to the difficulty of reconciling algorithmic methods with interpretive ones. Conversely, the media scholar Friedrich Kittler has questioned the adequacy of hermeneutics as a means of studying computers. This paper argues that that this disconnect results from a set of contingent decisions made in (...) both humanistic and mathematical disciplines in the first half of the nineteenth century that delineated, with implications that continue to resonate in the present day, which aspects of human activity would come to be formalized in algorithms and which would not. I begin with a discussion of Nicolas de Condorcet, who attempted, at the height of the 1789 revolution, to turn algebra into a universal language; his work, I argue, exemplifies the form of algorithmic thinking that existed before the Romantic turn. Next, I discuss William Wordsworth’s arguments about the relationship of poetry and science. While Wordsworth is sometimes viewed as a critic of science, I argue that his polemic is specifically targeted at highly politicized projects like Condorcet’s that sought to supplant existing modes of thought with scientific rationality. Finally, I demonstrate the importance of Romantic thought for George Boole, creator of the logic system that would eventually form the basis of digital electronics. The reason Boole was able to succeed where Condorcet had failed, I argue, was that Romantic notions of culture enabled him to reconcile a mechanical view of mathematical reasoning with an organic view of the development of meaning—a dichotomy that remains a key assumption of computer interfaces in the twenty-first century. (shrink)

In this paper I consider three mathematicians who allowed some role for menial processes in the foundations of their logical or mathematical theories. Boole regarded his Boolean algebra as a theory of mental acts; Cantor permitted processes of abstraction to play a role in his set theory; Brouwer took perception in time as a cornerstone of his intuitionist mathematics. Three appendices consider related topics.

In his influential Laws of Thought , the mathematician George Boole presented a formulation of logic using algebraic expressions and manipulations. His widow, Mary Everest Boole, undertook an ambitious project of disseminating his ideas by introducing lay audiences to the law of pulsation, a prescription for correct reasoning that incorporates two of his fundamental insights. Contemporary scholarship presents a fragmented picture of Mary Boole, regarding her largely as a source of information on the religio-psychological impetus for her husband's contributions to (...) logic, among other matters. Some studies rightly acknowledge that her better-known commentary on educational reform relates to a promotion of the Laws of Thought, yet these typically fail to expand on how she articulated such relationships for readers. This paper provides a more complete understanding of her efforts by examining texts on various subjects motivated by a dedication to propagating as much as fulfilling the intellectual legacy she associated with her husband. In doing so it considers her interventions – like those undertaken by other Victorian women who sought to cultivate scientific enterprises – within a contextual framework broad enough to include strategic responses to cultural realities and possibilities. (shrink)

(1993). Thomas solly (1816–1875):an unknown pioneer of the mathematization of logic in england, 1839. History and Philosophy of Logic: Vol. 14, No. 2, pp. 133-169.

The goal of this paper is to provide a detailed reading of John Venn's Logic of Chance as a work of logic or, more specifically, as a specific portion of the general system of so-called ‘material’ logic developed in his Principles of Empirical or Inductive Logic and to discuss it against the background of his Boolean-inspired views on the connection between logic and mathematics. It is by means of this situating of Venn 1866 [The Logic of Chance. An Essay on (...) the Foundations and Province of the Theory of Probability. With Especial Reference to Its Application to Moral and Social Science, London: Macmillan] within the entirety of his oeuvre that it becomes both possible to revisit and necessary to re-articulate its place in the history of the frequency interpretation of probability. For it is clear that if Venn's approach to logic not only allowed him to establish its foundations on the basis of a process of idealization and define it as consisting of so-called hypothetical infinite series, bu.. (shrink)