The Australasian Journal of Logic

Understanding Christine Ladd-Franklin's Logic

2023-05-31T08:33:57+00:00

In the late 19th century Christine Ladd-Franklin proposed a new logical system in the algebraic tradition championed by Boole, Jevons, Schröder, and her teacher Charles Sanders Peirce. This new logic was at the time celebrated as providing a novel and complete characterization of the valid syllogisms, although Ladd-Franklin’s work was largely forgotten until recently. Here we present a careful reconstruction of Ladd-Franklin’s work, concentrating on her characterization of the valid syllogisms, and we clear up some earlier confusions regarding how this novel logical system works.

Christine Ladd-Franklin and the progress of formal logic

2023-05-30T11:38:47+00:00

I want to highlight Christine Ladd-Franklin's contribution to logic, by placing her technical contribution to the algebra of logic in the broader context of her philosophical contribution to logic in general, concerning her view of the nature of logic and its role in philosophy. First, I will present the sense in which her algebra of logic means a progress within formal logic towards a higher level of formality. Second, I will focus on the contrast between the new symbolic form of logic and the traditional non-symbolic form of logic. Third, I will focus on the contrast between the symbolic form of logic and the "mathematical" form of symbolic logic that Russell and his ilk were trying to impose.

Being a woman and wanting to be a woman

2024-10-30T15:22:04+00:00

In this paper I provide a new way of thinking of questions using an expanded space of FDE-worlds/state space. This allows both for non-exclusive and non-exhaustive answers to questions concerning one's gender identity. Further, and most crucially for the purposes of this paper, it allows for a new, more general definition of question inclusion that allows for the identification of a new form of hermeneutical injustice. This form of injustice, I argue, affects trans people by keeping them in a prolonged state of gender questioning and confusion in which they only grasp the part of the question Am I X gender identity? that corresponds to the question Do I want to be X gender identity?.

Rethinking Negation for Transformative Models of Identity-Thinking

2023-05-28T21:23:12+00:00

Negation often reinforces problematic habits of othering, but rethinking negation can make good on feminist hopes for logic as a transformative space for inclusion. As Plumwood argues in her 1993 paper, not all uses of negation in the context of social identity are inherently problematic, but the widespread implicit use of classical negation has limited our options with respect to representing difference, ultimately reinforcing dualisms that essentialize social differences in problematic ways. In response to these limitations, I take inspiration from Dembroff's recent work on the metaphysics of genderqueer identity to build models of social identity using the Heyting-Brouwer logic developed by Rauszer in her 1974 paper. Ultimately, I argue that these models demonstrate both how classical negation reinforces problematic habits of othering and how alternative forms of negation can transform our treatment of social identity altogether.