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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.
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...
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 World Is Badly Made
When the palace of Arabesque’s aide d’camp, a cat named the Tremblees, stumbles upon a translation of an ancient language that reveals the existence of a fabled stone, he vows to find it for reasons of greed and vengeance.With a dead dog stuck to a car bonnet, some burst luggage, a blind bus driver and an enormous number of olives, it becomes a race for Oscar, his colleague Meesha and the Tieress of Arabesque to prevent the Tremblees plunging Arabesque back into the Era of Bedlam, a horror that plagued the land a thousand years ago.“Corfield blurs the boundary between rubbish and garbage, and does justice to neither.” - Aiden White, Barrington Points Lighthouse Keeper.“The plot is only held together by the book’s tangled and convoluted sentences.” - Tiffany Parlek, Mortal Goddess.“A two-in-the-morning page turner, but only because each one’s so hard to get through.” – Pannel Norbit, Curator of Exotic Fungal Infections.
The Alchemists Of Vra
When Oscar stumbles across an arrogant bard named the Dodosette and the beautiful cat Vaasi-Vee, he unearths a plot to plunge the world into darkness. After some begging, a lot of snow and an industrial-sized vat of soup, the three animals argue all the way to the infamous land of Vra to do something about it.They did not, however, anticipate having to fight invisible Rottweilers, smash kitchens to pieces, lick frozen cars or fund taxi drivers’ sisters' eye operations. Although, for Oscar Teabag-Dooven, such things are not unusual.
Foundations of Bayesianism
This is an authoritative collection of papers addressing the key challenges that face the Bayesian interpretation of probability today. The volume includes important criticisms of Bayesian reasoning and gives an insight into some of the points of disagreement amongst advocates of the Bayesian approach. It will be of interest to graduate students, researchers, those involved with the applications of Bayesian reasoning, and philosophers.
The Purging Of Ruen - Abridged
When assigned to determine the cause of brewing tensions in the exclusive seaside city of Ruen, Oscar Teabag-Dooven discovers it’s on the brink of tearing itself apart. Things become complicated when it appears those responsible are in charge of running the place. Drawn into a scandalous plot of insanity and greed, Oscar befriends the Dervy, a young revolutionary, by throwing her off a cliff, and Horace, an elderly doctor with a phobia of worming ointments.Together they battle the ruthless genius of Sedervitz Tappen-Noo and the grievous insanity of the Pyjami, in an attempt to save a beautiful city from certain destruction.But things don’t go according to plan. Principally because they don’t have one.
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