Alex Oliver is Reader in Philosophy at Cambridge University and a Fellow of Gonville and Caius College, UK. Jonathan Lear is the John U. Nef Distinguished Service Professor at the Committee on Social Thought and in the Department of Philosophy at the University of Chicago, USA.

• Preface Acknowledgments 1. Philosophy in and out of the armchair, Kwame Anthony Appiah 2. Restricted quantifiers and logical theory, Thomas Baldwin 3. Logical form, James Cargile 4. The Socratic elenchus: no problem, James Doyle 5. What makes mathematics mathematics?, Ian Hacking 6. Smiley’s distinction between rules of inference and rules of proof, Lloyd Humberstone 7. Relative validity and vagueness, Rosanna Keefe 8. The force of irony, Jonathan Lear 9. The matter of form: logic’s beginnings, Alex Oliver 10. Abstractionist class theory: is there any such thing?, Michael Potter 11. A case of mistaken identity?, Graham Priest 12. Inferential semantics for first-order logic: motivating rules of inference from rules of evaluation, Neil Tennant List of contributors Bibliography of works by Timothy Smile Index

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