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Bobzien, Susanne. Stoic Syllogistic
1996, Oxford Studies in Ancient Philosophy 14: 133-92.
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Added by: Berta Grimau, Contributed by: Giada Fratantonio
Abstract: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental rules which establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (cut type rules and antilogism). The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed (similar to tableau methods). The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented, and similarities to relevance logic are pointed out.

Comment: This paper can be used as specialised/further reading for an advanced undergrad or postgraduate course on ancient logic or as a primary reading in an advanced undergrad or postgraduate course on Stoic logic. Alternatively, given that the text argues that there are important parallels between Stoic logic and Relevance logic, it could be used in a course on Relevance logic as well. It requires prior knowledge of logic (in particular, proof theory).

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Eckert, Maureen, Donahue, Charlie. Towards a Feminist Logic: Val Plumwood’s Legacy and Beyond
2020, In Dominic Hyde (ed.), Noneist Explorations II: The Sylvan Jungle - Volume 3 (Synthese Library, 432). Dordrecht: pp. 424-448
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Added by: Franci Mangraviti
Abstract:

Val Plumwood’s 1993 paper, “The politics of reason: towards a feminist logic” (hence- forth POR) attempted to set the stage for what she hoped would begin serious feminist exploration into formal logic – not merely its historical abuses, but, more importantly, its potential uses. This work offers us: (1) a case for there being feminist logic; and (2) a sketch of what it should resemble. The former goal of Plumwood’s paper encourages feminist theorists to reject anti-logic feminist views. The paper’s latter aim is even more challenging. Plumwood’s critique of classical negation (and classical logic) as a logic of domination asks us to recognize that particular logical systems are weapons of oppression. Against anti-logic feminist theorists, Plumwood argues that there are other logics besides classical logic, such as relevant logics, which are suited for feminist theorizing. Some logics may oppress while others may liberate. We provide details about the sources and context for her rejection of classical logic and motivation for promoting relevant logics as feminist.

Comment (from this Blueprint): This is an ideal companion piece to Plumwood's paper: it provides an accessible summary, and discusses both objections to the paper and possible responses.

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Plumwood, Val. The Politics of Reason: Towards a Feminist Logic
1993, Australasian Journal of Philosophy, 71(4): 436-462
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Added by: Franci Mangraviti
Abstract:

The author argues that there is a strong connection between the dualisms that have strengthened and naturalized systematic oppression across history (man/woman, reason/emotion, etc.), and "classical" logic. It is suggested that feminism's response should not be to abandon logic altogether, but rather to focus on the development of alternative, less oppressive forms of rationality, of which relevant logics provide an example.

Comment (from this Blueprint): This is a seminal text of feminist logic, and thus a natural pick for any course wanting to discuss the topic. It could however also be assigned in a course on relevant logics interested in discussing particular applications, especially if such a course has previously spent time on the arguments in Plumwood's "False laws of logic" (or more generally, in Sylvan&co's "Relevant logics and their rivals"). Eckert and Donahue's "Towards a Feminist Logic" is a useful reading companion.

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Routley, Richard, Routley, Val. Negation and Contradiction
1985, Revista Columbiana de Mathematicas:201--231
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Added by: Franci Mangraviti
Abstract:

The problems of the meaning and function of negation are disentangled from ontological issues with which they have been long entangled. The question of the function of negation is the crucial issue separating relevant and paraconsistent logics from classical theories. The function is illuminated by considering the inferential role of contradictions, contradiction being parasitic on negation. Three basic modelings emerge: a cancellation model, which leads towards connexivism, an explosion model, appropriate to classical and intuitionistic theories, and a constraint model, which includes relevant theories. These three modelings have been seriously confused in the modern literature: untangling them helps motivate the main themes advanced concerning traditional negation and natural negation. Firstly, the dominant traditional view, except around scholastic times when the explosion view was in ascendency, has been the cancellation view, so that the mainstream negation of much of traditional logic is distinctively nonclassical. Secondly, the primary negation determinable of natural negation is relevant negation. In order to picture relevant negation the traditional idea of negation as otherthanness is progressive) refined, to nonexclusive restricted otherthanness. Several pictures result, a reversal picture, a debate model, a record cabinet (or files of the universe) model which help explain relevant negation. Two appendices are attached, one on negation in Hegel and the Marxist tradition, the other on Wittgenstein's treatment of negation and contradiction.

Comment: Can be used in a course on relevant logic or on negation. The emphasis on comparing different models makes it ideal for discussion. No familiarity with relevant logic is required.

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Routley, Richard, Routley, Val. The Semantics of First Degree Entailment
1972, Noûs 6 (4):335-359
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Abstract:

From the introduction: "we argue that the semantics of the first degree paradox-free implication system FD supports the claim it is superior to strict implication as an analysis of entailment at the first degree level. The semantics also reveals that Disjunctive Syllogism, [...] far from being a paradigmatic entailment, is invalid, and allows the illegitimate suppression of tautologies"

Comment: The paper introduces some of the central ideas in the relevance logic literature, e..g the connection between suppression and sufficiency, and the modeling of negation via the Routley star. It is a natural pick for a specialized course on relevance logic, but it can also be used as an introduction to (or further reading about) relevance logic in a general course on non-classical logics. Some familiarity with classical and modal logic (in particular, the notion of strict implication) is required.

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Russell, Gillian. Logic: A Feminist Approach
2020, In Garchar, Kimberly K. and Shew, Melissa M. (Ed.). Philosophy for girls: An invitation to a life of thought, pp. 79-98
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Added by: Franci Mangraviti
Abstract:

This chapter asks whether there is any such thing as feminist logic. It defines feminism and logic, and then goes on to present and evaluate four possible views, introducing and critiquing the work of Andrea Nye, Val Plumwood, and Susan Stebbing. It argues that Stebbing’s approach—on which feminism is one among many political applications of logic—is correct, but that feminist logic could do more, by providing a formal framework for the study of social hierarchies, much as it presently provides a formal framework for the study of numbers and similarity rankings among possible worlds.

Comment: Ideal for an intro course to either feminist philosophy or logic, to introduce possible interactions between the fields. More advanced courses (in either direction) might want to adopt G. Russell's "From Anti-Exceptionalism to Feminist Logic" instead, which covers the same topic in a lot more detail.

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