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Mangraviti, Franci. The Liberation Argument for Inconsistent Mathematics
2023 2023, The Australasian Journal of Logic, 20 (2): 278-317
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Added by: Franci Mangraviti and Viviane Fairbank
Abstract: Val Plumwood charged classical logic not only with the invalidity of some of its laws, but also with the support of systemic oppression through naturalization of the logical structure of dualisms. In this paper I show that the latter charge - unlike the former - can be carried over to classical mathematics, and I propose a new conception of inconsistent mathematics - queer incomaths - as a liberatory activity meant to undermine said naturalization.

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Rahman, Shahid, Carnielli, Walter. The Dialogical Approach to Paraconsistency
2001 2001, Synthese 125 (1-2):201-232
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Added by: Franci Mangraviti
Abstract:

Being a pragmatic and not a referential approach to semantics, the dialogical formulation of paraconsistency allows the following semantic idea to be expressed within a semi-formal system: In an argumentation it sometimes makes sense to distinguish between the contradiction of one of the argumentation partners with himself (internal contradiction) and the contradiction between the partners (external contradiction). The idea is that external contradiction may involve different semantic contexts in which, say A and not A have been asserted. The dialogical approach suggests a way of studying the dynamic process of contradictions through which the two contexts evolve for the sake of argumentation into one system containing both contexts. More technically, we show a new, dialogical, way to build paraconsistent systems for propositional and first-order logic with classical and intuitionistic features (i.e. paraconsistency both with and without tertium non-datur) and present their corresponding tableaux.

Comment: This paper would fit well in a course on dialogical formulations of logic (as either main or further reading, depending on the time dedicated to Lorenz-style approaches), or in a course on paraconsistent logic (as an alternative way of thinking about paraconsistency); both topics are introduced in an accessible enough way. If students have no familiarity with tableaux systems, sections 4 and 5.2 can be skipped.

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Sinclair, Rebekah. Exploding Individuals: Engaging Indigenous Logic and Decolonizing Science
2020 2020, Hypatia, 35, pp. 58–74
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Added by: Franci Mangraviti
Abstract:

Despite emerging attention to Indigenous philosophies both within and outside of feminism, Indigenous logics remain relatively underexplored and underappreciated. By amplifying the voices of recent Indigenous philosophies and literatures, I seek to demonstrate that Indigenous logic is a crucial aspect of Indigenous resurgence as well as political and ethical resistance. Indigenous philosophies provide alternatives to the colonial, masculinist tendencies of classical logic in the form of paraconsistent—many-valued—logics. Specifically, when Indigenous logics embrace the possibility of true contradictions, they highlight aspects of the world rejected and ignored by classical logic and inspire a relational, decolonial imaginary. To demonstrate this, I look to biology, from which Indigenous logics are often explicitly excluded, and consider one problem that would benefit from an Indigenous, paraconsistent analysis: that of the biological individual. This article is an effort to expand the arenas in which allied feminists can responsibly take up and deploy these decolonial logics.

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