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Added by: Berta Grimau, Contributed by: Giada FratantonioSummary: A comprehensive introduction to ancient (western) logic from the 5th century BCE to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians. Topics include pre-Aristotelian logic, Aristotelian logic, Peripatetic logic, Stoic Logic and a note on Epicureans and their views on logic.
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Added by: Franci MangravitiAbstract:
This chapter begins with a discussion of humanist criticisms of scholastic logic. It then discusses the evolution of the scholastic tradition and the influence of Renaissance Aristotelianism, Descartes and his influence, the Port-Royal Logic, the emergence of a logic of cognitive faculties, logic and mathematics in the late 17th century, Gottfried Wilhelm Leibniz's role in the history of formal logic, and Kant's influence on logic.
Comment: Useful for a history of logic course. Familiarity with Aristotelian syllogistic is assumed.
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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.
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Added by: Franci MangravitiAbstract:
This chapter gives a survey of the field of philosophy where the philosophical foundations of modern logic were discussed and where such themes of logic were discussed that were on the borderline between logic and other branches of the philosophical enterprise, such as metaphysics and epistemology. The contributions made by Gottlob Frege and Charles Peirce are included since their work in logic is closely related to and also strongly motivated by their philosophical views and interests. In addition, the chapter pays attention to a few philosophers to whom logic amounted to traditional Aristotelian logic and to those who commented on the nature of logic from a philosophical perspective without making any significant contribution to the development of formal logic.
Comment: Could be used in a history of logic course, as an overview of developments at the turn of the century. It spends a lot of time contextualizing and comparing Frege and Husserl's philosophies of logic, so it could also be a good further reading for a course focusing on either of them. The text assumes almost no previous knowledge of logic, or of the authors in question.
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Added by: Simon Fokt, Contributed by: Alexander YatesAbstract: Controversy remains over exactly why Frege aimed to estabish logicism. In this essay, I argue that the most influential interpretations of Frege's motivations fall short because they misunderstand or neglect Frege's claims that axioms must be self-evident. I offer an interpretation of his appeals to self-evidence and attempt to show that they reveal a previously overlooked motivation for establishing logicism, one which has roots in the Euclidean rationalist tradition. More specifically, my view is that Frege had two notions of self-evidence. One notion is that of a truth being foundationally secure, yet not grounded on any other truth. The second notion is that of a truth that requires only clearly grasping its content for rational, a priori justified recognition of its truth. The overarching thesis I develop is that Frege required that axioms be self-evident in both senses, and he relied on judging propositions to be self-evident as part of his fallibilist method for identifying a foundation of arithmetic. Consequently, we must recognize both notions in order to understand how Frege construes ultimate foundational proofs, his methodology for discovering and identifying such proofs, and why he thought the propositions of arithmetic required proof.
Comment: A nice discussion of what sort of epistemic status Frege thought axioms needed to have. A nice historical example of foundationalist epistemology - good for a course on Frege or analytic philosophy more generally, or as further reading in a course on epistemology, to give students a historical example of certain epistemological subtleties.
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Added by: Franci MangravitiPublisher’s Note:
Is logic masculine? Is women's lack of interest in the "hard core" philosophical disciplines of formal logic and semantics symptomatic of an inadequacy linked to sex? Is the failure of women to excel in pure mathematics and mathematical science a function of their inability to think rationally? Andrea Nye undermines the assumptions that inform these questions, assumptions such as: logic is unitary, logic is independenet of concrete human relations, and logic transcends historical circumstances as well as gender. In a series of studies of the logics of historical figures--Parmenides, Plato, Aristotle, Zeno, Abelard, Ockham, and Frege--she traces the changing interrelationships between logical innovation and oppressive speech strategies, showing that logic is not transcendent truth but abstract forms of language spoken by men, whether Greek ruling citizens, or scientists.
Comment: available in this Blueprint
Comment: This paper would be ideal as an introductory overview for a course on ancient logic. Alternatively, it could serve as an overview for a module on ancient logic within a more general course on the history of logic. No prior knowledge of logic is required; formalisms are for the most part avoided in the paper. Note that this is a SEP entry, so it's completely accessible to students.