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Modal Homotopy Type Theory
"The old logic put thought in fetters, while the new logic gives it wings." For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory. Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its mo...
Towards a Philosophy of Real Mathematics
In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.
Power and the Professions in Britain 1700-1850
The modern professions have a long history that predates the development of formal institutions and examinations in the nineteenth century. Long before the Victorian era the emergent professions wielded power through their specialist knowledge and set up informal mechanisms of control and self-regulation. Penelope Corfield devotes a chapter each to lawyers, clerics and doctors and makes reference to many other professionals - teachers, apothecaries, governesses, army officers and others. She shows how as the professions gained in power and influence, so they were challenged increasingly by satire and ridicule. Corfield's analysis of the rise of the professions during this period centres on a discussion of the philosophical questions arising from the complex relationship between power and knowledge.
Making and Breaking Mathematical Sense
In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical,...
The Georgians
A comprehensive history of the Georgians, comparing past views of these exciting, turbulent, and controversial times with our attitudes today The Georgian era is often seen as a time of innovations. It saw the end of monarchical absolutism, global exploration and settlements overseas, the world’s first industrial revolution, deep transformations in religious and cultural life, and Britain’s role in the international trade in enslaved Africans. But how were these changes perceived by people at the time? And how do their viewpoints compare with attitudes today? In this wide-ranging history, Penelope J. Corfield explores every aspect of Georgian life—politics and empire, culture and society, love and violence, religion and science, industry and towns. People’s responses at the time were often divided. Pessimists saw loss and decline, while optimists saw improvements and light. Out of such tensions came the Georgian culture of both experiment and resistance. Corfield emphasizes those elements of deep continuity that persisted even within major changes, and shows how new developments were challenged if their human consequences proved dire.
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