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Added by: Jie GaoPublisher’s Note:
Formal languages are widely regarded as being above all mathematical objects and as producing a greater level of precision and technical complexity in logical investigations because of this. Yet defining formal languages exclusively in this way offers only a partial and limited explanation of the impact which their use (and the uses of formalisms more generally elsewhere) actually has. In this book, Catarina Dutilh Novaes adopts a much wider conception of formal languages so as to investigate more broadly what exactly is going on when theorists put these tools to use. She looks at the history and philosophy of formal languages and focuses on the cognitive impact of formal languages on human reasoning, drawing on their historical development, psychology, cognitive science and philosophy. Her wide-ranging study will be valuable for both students and researchers in philosophy, logic, psychology and cognitive and computer science.Dutilh Novaes, Catarina. The Dialogical Roots of Deduction: Historical, Cognitive, and Philosophical Perspectives on Reasoning2020, Cambridge University Press.-
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Added by: Fenner Stanley TanswellPublisher’s Note:
This comprehensive account of the concept and practices of deduction is the first to bring together perspectives from philosophy, history, psychology and cognitive science, and mathematical practice. Catarina Dutilh Novaes draws on all of these perspectives to argue for an overarching conceptualization of deduction as a dialogical practice: deduction has dialogical roots, and these dialogical roots are still largely present both in theories and in practices of deduction. Dutilh Novaes' account also highlights the deeply human and in fact social nature of deduction, as embedded in actual human practices; as such, it presents a highly innovative account of deduction. The book will be of interest to a wide range of readers, from advanced students to senior scholars, and from philosophers to mathematicians and cognitive scientists.Comment (from this Blueprint): This book by Dutilh Novaes recently won the coveted Lakatos Award. In it, she develops a dialogical account of deduction, where she argues that deduction is implicitly dialogical. Proofs represent dialogues between Prover, who is aiming to establish the theorem, and Skeptic, who is trying to block the theorem. However, the dialogue is both partially adversarial (the two characters have opposite goals) and partially cooperative: the Skeptic’s objections make sure that the Prover must make their proof clear, convincing, and correct. In this chapter, Dutilh Novaes applies her model to mathematical practice, and looks at the way social features of maths embody the Prover-Skeptic dialogical model.
Eckert, Maureen, Donahue, Charlie. Towards a Feminist Logic: Val Plumwood’s Legacy and Beyond2020, 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 MangravitiAbstract:
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.
Eckert, Maureen. De-centering and Genderqueering Val Plumwood’s Feminist Logic2024, In R. Cook and A. Yap (eds.), Feminist Philosophy and Formal Logic. University of Minnesota Press-
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Added by: Franci Mangraviti and Viviane FairbankAbstract:
The strongest and, until recently, least-explored approach to feminist logic holds that some formal logics have structural features that perpetuate sexism and oppression, whereas other logics are helpful for resisting and opposing these social phenomena. Our choice of logics may not be purely formal on this view: for example, some logics are preferrable to others on the grounds of feminist commitments. This strong account of feminist logic was first articulated by Val Plumwood. We will critically engage salient features of her view, especially her critique of classical logic and the centering and dominating functions she believes classical negation has. We will see that her understanding of classical negation captures neither the development of Intersectional Feminism, nor the position the concept of centering holds in transformative justice. However, Plumwood's critique of classical negation does lead us to a deeper insight regarding which logics to apply in social justice contexts. Robin Dembroff's analysis of genderqueer as a critical gender kind helps us delineate a non-classical context in which a four-valued logic, such as FDE, can structurally account for the critical feature of this gender kind in a way classical logic cannot. We will also observe how four-valued logics precisely capture the destabilization of, and resistance to, the exclusive and exhaustive gender binary categories Dembroff describes.Comment:
available in this Blueprint
Edgington, Dorothy. On Conditionals1995, Mind 104(414): 235-329.-
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Added by: Emily Paul, Contributed by: Helen De Cruz
Summary: Examines the theory of conditionals and whether it's possible to have a unified theory of them.Comment: Great core text as there are many important discussion points here, and Edginton uses lots of helpful examples. Could set students the task of coming up with their own conditionals, and analysing these in the would/will sense. This definitely requires a background in beginner's logic.
Edgington, Dorothy. Indicative Conditionals2001, In The Stanford Encyclopedia of Philosophy (Fall 2020 Edition), Edward N. Zalta (ed.)-
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Added by: Franci MangravitiAbstract:
The chapter is an introduction to logical treatments of indicative conditionals, comparing truth-functional, non-truth-functional, and suppositional approaches. Some of the topics discussed are truth conditions, conditional belief, assertability, and issues with compounds of conditionals.
Comment: This page can be used in a course focused on the philosophy of conditionals, as an introduction/overview of the basic logical issues; or in any logic course wishing to spend more time on this particular notion.
Eichler, Lauren. Sacred Truths, Fables, and Falsehoods: Intersections between Feminist and Native American Logics2018, APA Newsletter on Native American and Indigenous Philosophy, 18(1).-
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Added by: Franci MangravitiAbstract:
From the newsletter's introduction: "Lauren Eichler [...] examines the resonances between feminist and Native American analyses of classical logic. After considering the range of responses, from overly monolithic rejection to more nuanced appreciation, Eichler argues for a careful, pluralist understanding of logic as she articulates her suggestion that feminists and Native American philosophers could build fruitful alliances around this topic."
Comment:
available in this Blueprint
Ficara, Elena. The Form of Truth: Hegel’s Philosophical Logic2020, De Gruyter-
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Added by: Franci MangravitiPublisher’s Note:
This book is a consideration of Hegel’s view on logic and basic logical concepts such as truth, form, validity, and contradiction, and aims to assess this view’s relevance for contemporary philosophical logic. The literature on Hegel’s logic is fairly rich. The attention to contemporary philosophical logic places the present research closer to those works interested in the link between Hegel’s thought and analytical philosophy, Koch 2014, Brandom 2014, 1-15, Pippin 2016, Moyar 2017, Quante & Mooren 2018 among others). In this context, one particularity of this book consists in focusing on something that has been generally underrated in the literature: the idea that, for Hegel as well as for Aristotle and many other authors, logic is the study of the forms of truth, i.e. the forms that our thought can assume in searching for truth. In this light, Hegel’s thinking about logic is a fundamental reference point for anyone interested in a philosophical foundation of logic.
Comment: The book could be used in any course on Hegel's logic, either as a main textbook (if focusing on the author's overall interpretation) or as further reading. The latter approach is facilitated by the structure of the book, since each part is focused on a distinct logical notion (logic, logical form, truth, validity, contradiction). Given the author's thesis that Hegel can be considered as a genuine interlocutor of philosophical logic as it is understood today, one might even try discussing some chapters in a course focusing on a particular logical notion.
Fisher, Jennifer. On the Philosophy of Logic2007, Cengage Learning.-
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Added by: Berta Grimau, Contributed by: Matt Clemens
Publisher's Note: Jennifer Fisher's On the Philosophy of Logic explores questions about logic often overlooked by philosophers. Which of the many different logics available to us is right? How would we know? What makes a logic right in the first place? Is logic really a good guide to human reasoning? An ideal companion text for any course in symbolic logic, this lively and accessible book explains important logical concepts, introduces classical logic and its problems and alternatives, and reveals the rich and interesting philosophical issues that arise in exploring the fundamentals of logic.Comment: This book provides an introduction to some traditional questions within philosophy of logic. Moreover, it presents some non-classical logics. It includes an introduction to formal classical logic, so no previous technical knowledge is required. Adequate for a first course on philosophy of logic, either as main or further reading.
Francois, Karen, Vandendriessche, Eric. Reassembling Mathematical Practices: a Philosophical-Anthropological Approach2016, Revista Latinoamericana de Etnomatemática Perspectivas Socioculturales de la Educación Matemática, 9(2): 144-167.-
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Added by: Fenner Stanley TanswellAbstract:
In this paper we first explore how Wittgenstein’s philosophy provides a conceptual tools to discuss the possibility of the simultaneous existence of culturally different mathematical practices. We will argue that Wittgenstein’s later work will be a fruitful framework to serve as a philosophical background to investigate ethnomathematics (Wittgenstein 1973). We will give an overview of Wittgenstein’s later work which is referred to by many researchers in the field of ethnomathematics. The central philosophical investigation concerns Wittgenstein’s shift to abandoning the essentialist concept of language and therefore denying the existence of a universal language. Languages—or ‘language games’ as Wittgenstein calls them—are immersed in a form of life, in a cultural or social formation and are embedded in the totality of communal activities. This gives rise to the idea of rationality as an invention or as a construct that emerges in specific local contexts. In the second part of the paper we introduce, analyse and compare the mathematical aspects of two activities known as string figure-making and sand drawing, to illustrate Wittgenstein’s ideas. Based on an ethnomathematical comparative analysis, we will argue that there is evidence of invariant and distinguishing features of a mathematical rationality, as expressed in both string figure-making and sand drawing practices, from one society to another. Finally, we suggest that a philosophical-anthropological approach to mathematical practices may allow us to better understand the interrelations between mathematics and cultures. Philosophical investigations may help the reflection on the possibility of culturally determined ethnomathematics, while an anthropological approach, using ethnographical methods, may afford new materials for the analysis of ethnomathematics and its links to the cultural context. This combined approach will help us to better characterize mathematical practices in both sociological and epistemological terms.Comment (from this Blueprint): Francois and Vandendriessche here present a later Wittgensteinian approach to “ethnomathematics”: mathematics practiced outside of mainstream Western contexts, often focused on indigenous or tribal groups. They focus on two case studies, string-figure making and sand-drawing, in different geographic and cultural contexts, looking at how these practices are mathematical.
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Dutilh Novaes, Catarina. Formal Languages in Logic: A Philosophical and Cognitive Analysis
2012, Cambridge: Cambridge University Press
Comment: This book addresses important questions about formal languages: why formalization works and the limitations of formalization. The questions are answered from cognitive, historical and logical points of view. It is a good introductory material for teaching on formal language and psychology of reasoning.