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Added by: Jamie Collin
Summary: Introduction to mathematical nominalism, with special attention to Chihara's own development of the position and the objections of John Burgess and Gideon Rosen. Chihara provides an outline of his constructibility theory, which avoids quantification over abstract objects by making use of contructibility quantifiers which instead of making assertions about what exists, make assertions about what sentences can be constructed.Chimakonam, Jonathan O,. Ezumezu: A System of Logic for African Philosophy and Studies2019, Cham, Switzerland: Springer Verlag-
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Added by: Franci MangravitiPublisher’s Note:
The issue of a logic foundation for African thought connects well with the question of method. Do we need new methods for African philosophy and studies? Or, are the methods of Western thought adequate for African intellectual space? These questions are not some of the easiest to answer because they lead straight to the question of whether or not a logic tradition from African intellectual space is possible. Thus in charting the course of future direction in African philosophy and studies, one must be confronted with this question of logic. The author boldly takes up this challenge and becomes the first to do so in a book by introducing new concepts and formulating a new African culture-inspired system of logic called Ezumezu which he believes would ground new methods in African philosophy and studies. He develops this system to rescue African philosophy and, by extension, sundry fields in African Indigenous Knowledge Systems from the spell of Plato and the hegemony of Aristotle. African philosophers can now ground their discourses in Ezumezu logic which will distinguish their philosophy as a tradition in its own right. On the whole, the book engages with some of the lingering controversies in the idea of (an) African logic before unveiling Ezumezu as a philosophy of logic, methodology and formal system. The book also provides fresh arguments and insights on the themes of decolonisation and Africanisation for the intellectual transformation of scholarship in Africa. It will appeal to philosophers and logicians—undergraduates and post graduate researchers—as well as those in various areas of African studies.
Comment: Can be used as a main reference textbook for a course on African logic, insofar as Part I provides an (opinionated) survey of the field, and Part II develops a particular proposal in extensive detail. The chapters in Part I can be accompanied by many of the primary sources in "Logic and African Philosophy: Seminal Essays on African Systems of Thought", edited by the same author. Chapters 6-8, which introduce Ezumezu, can be used in a general course on logic or African philosophy wanting to discuss this particular system and philosophy thereof. While familiarity with Part I is helpful, it is not strictly required. Can be used as a main reference textbook for a course on African logic, insofar as Part I provides an (opinionated) survey of the field, and Part II develops a particular proposal in extensive detail. The chapters in Part I can be accompanied by many of the primary sources in "Logic and African Philosophy: Seminal Essays on African Systems of Thought", edited by the same author. Chapters 6-8, which introduce Ezumezu, can be used in a general course on logic or African philosophy wanting to discuss this particular system and philosophy thereof. While familiarity with Part I is helpful, it is not strictly required.
Clerbout, Nicolas, McConaughey, Zoe. Dialogical Logic2022, "Dialogical Logic", The Stanford Encyclopedia of Philosophy (Fall 2022 Edition), Edward N. Zalta & Uri Nodelman (eds.)-
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Added by: Franci MangravitiAbstract:
This entry presents the framework of « dialogical logic » in the initial Lorenzen and Lorenz tradition. The rules for the game and for building strategies are provided with step by step examples, helping the reader understand how the dialogue tables reflect a dynamic process of interaction between the players. Various logics are presented within this pluralistic framework: intuitionist logic, classical logic, and modal logics, with references to various other logics. In a second part of the entry, objections against the framework are considered, together with answers provided by the « Immanent Reasoning » variant, which stays within the Lorenzen and Lorenz tradition, and by the « Built-In Opponent » variant first developed by Catarina Dutilh Novaes, which develops a different dialogical tradition.
Comment: Obvious overview choice for any course involving dialogical logic. Familiarity with first-order languages is a prerequisite.
Dalla Chiara, Maria Luisa. Logical Self Reference, Set Theoretical Paradoxes and the Measurement Problem in Quantum Mechanics1977, International Journal of Philosophical Logic 6 (1):331-347.-
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Added by: Sara Peppe
Introduction: From a logical point of view the measurement problem of quantum mechanics, can be described as a characteristic question of 'semantical closure' of a theory: to what extent can a consistent theory (in this case 2R) be closed with respect to the objects and the concepfs which are described and expressed in its metatheory?Comment: This paper considers the measurement problem in Quantum Mechanics from a logical perspective. Previous and deep knowledge of logics and Quantum Mechanics' theories is vital.
De Toffoli, Silvia. Groundwork for a Fallibilist Account of Mathematics2021, The Philosophical Quarterly, 71(4).-
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Added by: Fenner Stanley TanswellAbstract:
According to the received view, genuine mathematical justification derives from proofs. In this article, I challenge this view. First, I sketch a notion of proof that cannot be reduced to deduction from the axioms but rather is tailored to human agents. Secondly, I identify a tension between the received view and mathematical practice. In some cases, cognitively diligent, well-functioning mathematicians go wrong. In these cases, it is plausible to think that proof sets the bar for justification too high. I then propose a fallibilist account of mathematical justification. I show that the main function of mathematical justification is to guarantee that the mathematical community can correct the errors that inevitably arise from our fallible practices.Comment (from this Blueprint): De Toffoli makes a strong case for the importance of mathematical practice in addressing important issues about mathematics. In this paper, she looks at proof and justification, with an emphasis on the fact that mathematicians are fallible. With this in mind, she argues that there are circumstances under which we can have mathematical justification, despite a possibility of being wrong. This paper touches on many cases and questions that will reappear later across the Blueprint, such as collaboration, testimony, computer proofs, and diagrams.
De Toffoli, Silvia, Giardino, Valeria. An Inquiry into the Practice of Proving in Low-Dimensional Topology2015, in From Logic to Practice, Gabriele Lolli, Giorgio Venturi and Marco Panza (eds.). Springer International Publishing.-
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Added by: Fenner Stanley TanswellAbstract:
The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three theses will be defended. First, the representations used in the practice are an integral part of the mathematical reasoning. As a matter of fact, they convey in a material form the relevant transitions and thus allow experts to draw inferential connections. Second, in low-dimensional topology experts exploit a particular type of manipulative imagination which is connected to intuition of two- and three-dimensional space and motor agency. This imagination allows recognizing the transformations which connect different pictures in an argument. Third, the epistemic—and inferential—actions performed are permissible only within a specific practice: this form of reasoning is subject-matter dependent. Local criteria of validity are established to assure the soundness of representationally heterogeneous arguments in low-dimensional topology.Comment (from this Blueprint): De Toffoli and Giardino look at proof practices in low-dimensional topology, and especially a proof by Rolfsen that relies on epistemic actions on a diagrammatic representation. They make the case that the many diagrams are used to trigger our manipulative imagination to make inferential moves which cannot be reduced to formal statements without loss of intuition.
Dick, Stephanie. AfterMath: The Work of Proof in the Age of Human–Machine Collaboration2011, Isis, 102(3): 494-505.-
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Added by: Fenner Stanley TanswellAbstract:
During the 1970s and 1980s, a team of Automated Theorem Proving researchers at the Argonne National Laboratory near Chicago developed the Automated Reasoning Assistant, or AURA, to assist human users in the search for mathematical proofs. The resulting hybrid humans+AURA system developed the capacity to make novel contributions to pure mathematics by very untraditional means. This essay traces how these unconventional contributions were made and made possible through negotiations between the humans and the AURA at Argonne and the transformation in mathematical intuition they produced. At play in these negotiations were experimental practices, nonhumans, and nonmathematical modes of knowing. This story invites an earnest engagement between historians of mathematics and scholars in the history of science and science studies interested in experimental practice, material culture, and the roles of nonhumans in knowledge making.Comment (from this Blueprint): Dick traces the history of the AURA automated reasoning assistant in the 1970s and 80s, arguing that the introduction of the computer system led to novel contributions to mathematics by unconventional means. Dick’s emphasis is on the AURA system as changing the material culture of mathematics, and thereby leading to collaboration and even negotiations between the mathematicians and the computer system.
Dizadji-Bahmani, Foad, Frigg, Roman, Hartmann, Stephan. Confirmation and reduction: A bayesian account2011, Synthese,79(2): 321-338.-
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Added by: Laura Jimenez
Abstract: Various scientific theories stand in a reductive relation to each other. In a recent article, the authors argue that a generalized version of the Nagel-Schaffner model (GNS) is the right account of this relation. In this article, they present a Bayesian analysis of how GNS impacts on confirmation. They formalize the relation between the reducing and the reduced theory before and after the reduction using Bayesian networks, and thereby show that, post-reduction, the two theories are confirmatory of each other. They ask when a purported reduction should be accepted on epistemic grounds. To do so, they compare the prior and posterior probabilities of the conjunction of both theories before and after the reduction and ask how well each is confirmed by the available evidenceComment: This article is an interesting reading for advanced courses in philosophy of science or logic. It could serve as further reading for modules focused on Bayesian networks, reduction or confirmation. Previous knowledge of bayesianism is required for understanding the article. No previous knowledge of thermodynamics is needed.
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.
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Chihara, Charles. Nominalism
2005, in The Oxford Hanbook of Philosophy of Mathematics and Logic, ed. S. Shapiro. New York: Oxford University Press.
Comment: This chapter would be a good primary or secondary reading in a course on philosophy of mathematics or metaphysics. Chihara is very good at conveying difficult ideas in clear and concise prose. It is worth noting however that, despite the title, this is not really an introduction to nominalism generally but to Chihara's own (important) development of a nominalist philosophy of mathematics / metaphysics.