Jitka Kadlečíková

This introduction sets the stage for the special issue of the Journal of Logic, Language, and Information entitled "Variable-Sharing Properties (and Their Discontents)." We first record the details of the corresponding workshop held at Rensselaer Polytechnic Institute held on November 14–16, 2024, describing the events and the motivations that led to its organization. We then provide an overview of the contents of the special issue and how each paper’s contents tie into the unifying theme of variable-sharing properties.

Although many fields of study have been radically reshaped by feminist critiques, formal a priori disciplines like mathematics and computer science have proven more intransigent; feminist critiques have largely emphasized goals like increasing enrollment or participation in these fields, stopping short of proposing radical critiques of their theoretical foundations. In this paper, we discuss how Valerie Plumwood’s work on reading classical logic as a logic of domination can be extended to provide grounds for authentic feminist theories of mathematics. We argue that the relevant arithmetic $$\mathsf{R}^{\sharp}$$ described by Plumwood’s collaborator Robert K. Meyer satisfies the criteria characteristic of a Plumwoodian critique of arithmetic. The setting of $$\mathsf{R}^{\sharp}$$ is finally used to investigate several consequences of such an approach, including the degree to which such an arithmetic parts ways with classical mathematics as regards arithmetical truths.