Gerhard Gentzen (1909–1945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called “proof theory” but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today. The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945. Particular emphasis in the book is put on the conditions of scientific research, in this case mathematical logic, in National Socialist Germany, the ideological fight for “German logic”, and their mutual protagonists. Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an indispensable source of information on this important mathematician, his work, and his time. The volume is completed by two deep substantial essays by Jan von Plato and Craig Smoryński on Gentzen's proof theory; its relation to the ideas of Hilbert, Brouwer, Weyl, and Gödel; and its development up to the present day. Smoryński explains the Hilbert program in more than the usual slogan form and shows why consistency is important. Von Plato shows in detail the benefits of Gentzen's program. This important book is a self-contained starting point for any work on Gentzen and his logic. The book is accessible to a wide audience with different backgrounds and is suitable for general readers, researchers, students, and teachers.

Gerhard Gentzen (1909-1945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called ''proof theory'' but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today. The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945. Particular emphasis in the book is put on the conditions of scientific research, in this case mathematical logic, in National Socialist Germany, the ideological fight for ''German logic'', and their mutual protagonists. Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an indispensable source of information on this important mathematician, his work, and his time. The volume is completed by two deep substantial essays by Jan von Plato and Craig Smorynski on Gentzen's proof theory; its relation to the ideas of Hilbert, Brouwer, Weyl, and Godel; and its development up to the present day. Smorynski explains the Hilbert program in more than the usual slogan form and shows why consistency is important. Von Plato shows in detail the benefits of Gentzen's program. This important book is a self-contained starting point for any work on Gentzen and his logic. The book is accessible to a wide audience with different backgrounds and is suitable for general readers, researchers, students, and teachers. Information for our distributors: Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.

Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They underlie modern developments in computer science such as automated theorem proving and type theory.

From breakout stand-up comedian Iliza Shlesinger comes a subversively funny collection of essays and observations on the secret genius of irrational behavior. Have you ever been pissed because you're not pretty enough, and then gotten even more pissed that someone didn't find you as pretty as you think you are? Have you ever obsessed over the size of your thighs while eating dessert, all the while saying you'll work out extra tomorrow? Or spent endless hours wondering why you have to bear the brunt of other people's insecurities? I mean, after all, I'm pretty great. Why cope with insecurities I don't already have? That last one's just me? All right, then. But if the rest sounds familiar, you are experiencing Girl Logic: a characteristically female way of thinking that appears contradictory and circuitous but is actually a complicated and highly evolved way of looking at the world. You end up considering every repercussion of every choice (about dating, career, clothes, lunch) before making a move toward what you really want. And why do we attempt these mental hurdles? Well, that's what this book is all about. The fact is, whether you're obsessing over his last text or the most important meeting of your career, your Girl Logic serves a purpose: It helps push you, question what you want, and clarify what will make you a happier, better person. Girl Logic can be every confident woman's secret weapon, and this book shows you how to wield it.

An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.

Infectious Liberty traces the origins of our contemporary concerns about public health, world population, climate change, global trade, and government regulation to a series of Romantic-era debates and their literary consequences. Through a series of careful readings, Robert Mitchell shows how a range of elements of modern literature, from character-systems to free indirect discourse, are closely intertwined with Romantic-era liberalism and biopolitics. Eighteenth- and early-nineteenth century theorists of liberalism such as Adam Smith and Thomas Malthus drew upon the new sciences of population to develop a liberal biopolitics that aimed to coordinate differences among individuals by means of the culling powers of the market. Infectious Liberty focuses on such authors as Mary Shelley and William Wordsworth, who drew upon the sciences of population to develop a biopolitics beyond liberalism. These authors attempted what Roberto Esposito describes as an “affirmative” biopolitics, which rejects the principle of establishing security by distinguishing between valued and unvalued lives, seeks to support even the most abject members of a population, and proposes new ways of living in common. Infectious Liberty expands our understandings of liberalism and biopolitics—and the relationship between them—while also helping us to understand better the ways creative literature facilitates the project of reimagining what the politics of life might consist of. Infectious Liberty is available from the publisher on an open-access basis.