This contributed volume collects papers related to the Logic in Question workshop, which has taken place annually at Sorbonne University in Paris since 2011. Each year, the workshop brings together historians, philosophers, mathematicians, linguists, and computer scientists to explore questions related to the nature of logic and how it has developed over the years. As a result, chapter authors provide a thorough, interdisciplinary exploration of topics that have been studied in the workshop. Organized into three sections, the first part of the book focuses on historical questions related to logic, the second explores philosophical questions, and the third section is dedicated to mathematical discussions. Specific topics include:
• logic and analogy
• Chinese logic
• nineteenth century British logic (in particular Boole and Lewis Carroll)
• logical diagrams
• the place and value of logic in Louis Couturat’s philosophical thinking
• contributions of logical analysis for mathematics education
• the exceptionality of logic
• the logical expressive power of natural languages
• the unification of mathematics via topos theory
Logic in Question will appeal to pure logicians, historians of logic, philosophers, linguists, and other researchers interested in the history of logic, making this volume a unique and valuable contribution to the field.
Table of Content
Inference in nineteenth century British logic .- The representation of negative terms with Euler diagrams .- Logical hylemorphism in the 13th Latin century .- What is the relation between Peirce’s logic and his philosophy of logic? .- Boole’s symbolized laws of thought facing empiricism .- Lewis Carroll’s almost diagrammatic notation .- Boole’s untruth tables: The formal conditions of meaning before the emergence of propositional logic .- What is “ancient Chinese logic”? .- Husserlian pure logic from the standpoint of intentionality .- Definition and inference in Leśniewski’s logic .- The place and value of logic in Louis Couturat’s philosophical thinking .- Frege’s silence about Bolzano .- Symbolism and unintepretability in Boole .- Tabular notations .- Identity, equality in logic, mathematics and politics .- Logic and metaphysics .- Can logic be cartesian?.- Images and their ability to negate .- What does “best explaining’ mean? Explanatory virtues and the role of context in IBE .- What does a concept entail? .- The analytic and the synthetic from homology to heterology .- About all and nothing. Meinongian views of all and nothing as maximal and minimal objects of thought .- On dichotomy and analogy: A question on the next ‘unbloody’ revolution in logic .- Logic and analogy .- A Carnapian logic of conceivability .- No, no and no .- Philosophical logic = philosophy + logic? .- ‘Grammar is not a mechanism’ (Wittgenstein) or what could an anthropology of mathematics? .- Existential Presupposition and Logical Square .- The unification of mathematics via topos theory .- Quasi-topological structuring of extensions within logic of typicals and atypicals (LTA) .- Contributions of logical analysis for mathematics education .- A categorical aspect of the analogy between quantifiers and modalities .- The relevance logic program: Failed or just stalled? .- Is logic relevant to classifications? .- Logic and theory of representation .- Back and forth in positive logic.
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