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)

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)

(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.

Symbolic logics tend to be too mathematical for the philosophers and too philosophical for the mathematicians; and their history is too historical for most mathematicians, philosophers and logicians. This paper reflects upon these professional demarcations as they have developed during the century.

Few have entertained the idea that Georg Cantor, the creator of set theory, might have influenced Edmund Husserl, the founder of the phenomenological movement. Yet an exchange of ideas took place between them when Cantor was at the height of his creative powers and Husserl in the throes of an intellectual struggle during which his ideas were particularly malleable and changed considerably and definitively. Here their writings are examined to show how Husserl's and Cantor's ideas overlapped and crisscrossed in the (...) areas of philosophy and mathematics, arithmetization, abstraction, consciousness and pure logic, psychologism, metaphysical idealism, new numbers, and sets and manifolds. (shrink)

This paper is an attempt to convince anti-realists that their correct intuitions against the metaphysical inflationism derived from some versions of mathematical realism do not force them to embrace non-standard, epistemic approaches to truth and existence. It is also an attempt to convince mathematical realists that they do not need to implement their perfectly sound and judicious intuitions with the anti-intuitive developments that render full-blown mathematical realism into a view which even Gödel considered objectionable. I will argue for the following (...) two theses: that realism, in its standard characterization, is our default position, a position in agreement with our pre-theoretical intuitions and with the results of our best semantic theories, and that most of the metaphysical qualms usually related to it depends on a poor understanding of truth and existence as higher-order concepts. (shrink)