Philosophical Uses Of Categoricity Arguments
Download Philosophical Uses Of Categoricity Arguments full books in PDF, epub, and Kindle. Read online free Philosophical Uses Of Categoricity Arguments ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : Penelope Maddy |
| Publisher | : Cambridge University Press |
| Total Pages | : 75 |
| Release | : 2023-12-21 |
| Genre | : Philosophy |
| ISBN | : 1009432915 |
This Element addresses the viability of categoricity arguments in philosophy by focusing with some care on the specific conclusions that a sampling of prominent figures have attempted to draw – the same theorem might successfully support one such conclusion while failing to support another. It begins with Dedekind, Zermelo, and Kreisel, casting doubt on received readings of the latter two and highlighting the success of all three in achieving what are argued to be their actual goals. These earlier uses of categoricity arguments are then compared and contrasted with more recent work of Parsons and the co-authors Button and Walsh. Highlighting the roles of first- and second-order theorems, of external and internal theorems, the Element concludes that categoricity arguments have been more effective in historical cases that reflect philosophically on internal mathematical matters than in recent questions of pre-theoretic metaphysics.
| Author | : Sophia Arbeiter |
| Publisher | : Springer Nature |
| Total Pages | : 526 |
| Release | : |
| Genre | : |
| ISBN | : 3031584252 |
| Author | : A. C. Paseau |
| Publisher | : Cambridge University Press |
| Total Pages | : 153 |
| Release | : 2024-02-29 |
| Genre | : Science |
| ISBN | : 100922199X |
The Euclidean Programme embodies a traditional sort of epistemological foundationalism, according to which knowledge – especially mathematical knowledge – is obtained by deduction from self-evident axioms or first principles. Epistemologists have examined foundationalism extensively, but neglected its historically dominant Euclidean form. By contrast, this book offers a detailed examination of Euclidean foundationalism, which, following Lakatos, the authors call the Euclidean Programme. The book rationally reconstructs the programme's key principles, showing it to be an epistemological interpretation of the axiomatic method. It then compares the reconstructed programme with select historical sources: Euclid's Elements, Aristotle's Posterior Analytics, Descartes's Discourse on Method, Pascal's On the Geometric Mind and a twentieth-century account of axiomatisation. The second half of the book philosophically assesses the programme, exploring whether various areas of contemporary mathematics conform to it. The book concludes by outlining a replacement for the Euclidean Programme.
| Author | : Richard Samuels |
| Publisher | : Cambridge University Press |
| Total Pages | : 100 |
| Release | : 2024-02-07 |
| Genre | : Philosophy |
| ISBN | : 100905967X |
This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views within mainstream number cognition research, along with the central challenges these views face. Third, it identifies and critically assesses a series of core philosophical assumptions often adopted by number cognition researchers. Finally, the Element articulates and defends a novel version of pluralism about number concepts.
| Author | : Graham Priest |
| Publisher | : |
| Total Pages | : 82 |
| Release | : 2024-04-16 |
| Genre | : Philosophy |
| ISBN | : 1009089269 |
Mathematical pluralism is the view that there is an irreducible plurality of pure mathematical structures, each with their own internal logics; and that qua pure mathematical structures they are all equally legitimate. Mathematical pluralism is a relatively new position on the philosophical landscape. This Element provides an introduction to the position.
| Author | : Neil Barton |
| Publisher | : Cambridge University Press |
| Total Pages | : 122 |
| Release | : 2024-06-30 |
| Genre | : Philosophy |
| ISBN | : 1009227254 |
Many philosophers are aware of the paradoxes of set theory (e.g. Russell's paradox). For many people, these were solved by the iterative conception of set which holds that sets are formed in stages by collecting sets available at previous stages. This Element will examine possibilities for articulating this solution. In particular, the author argues that there are different kinds of iterative conception, and it's open which of them (if any) is the best. Along the way, the author hopes to make some of the underlying mathematical and philosophical ideas behind tricky bits of the philosophy of set theory clear for philosophers more widely and make their relationships to some other questions in philosophy perspicuous.
| Author | : Leon Horsten |
| Publisher | : A&C Black |
| Total Pages | : 647 |
| Release | : 2011-08-04 |
| Genre | : Philosophy |
| ISBN | : 144115423X |
A single volume reference guide to the latest work and potential future directions in Philosophical Logic, written by an international team of leading scholars.
| Author | : Leon Horsten |
| Publisher | : Bloomsbury Publishing |
| Total Pages | : 657 |
| Release | : 2014-09-25 |
| Genre | : Philosophy |
| ISBN | : 1472522737 |
Logical methods are used in all area of philosophy. By introducing and advancing central to topics in the discipline, The Bloomsbury Companion to Philosophical Logic emphasizes the crucial role logic plays in understanding philosophical problems. Covering stages in the history of logic and of modern logic, this comprehensive Companion looks ahead to new areas of research and explores issues pertaining to classical logic and its rivals, semantics for parts of natural language, and the application of logic in the theory of rationality. Experts in the field provide a mix of technical chapters that offer excellent encyclopaedias of results in the area and chapters of philosophical discussions that survey a range of philosophical positions. To facilitate further study, this volumes also includes a series of research tools such as a detailed index, an up-to-date list of resources and an annotated bibliography. Balancing technical exposition with philosophical discussion, The Bloomsbury Companion to Philosophical Logic not only provides students and lecturers with the basis of a course in philosophical logic, it offers anyone working in this key area of contemporary philosophy a valuable research resource.
| Author | : John T. Baldwin |
| Publisher | : Cambridge University Press |
| Total Pages | : 365 |
| Release | : 2018-01-25 |
| Genre | : Mathematics |
| ISBN | : 1107189217 |
Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.
| Author | : Vincent F. Hendricks |
| Publisher | : Automatic Press Vip |
| Total Pages | : 368 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : |
Interviews of more than two dozen scholars about the philosophy of mathematics, their interests in the field, and their ideas about future developments.
