MIT Press
Lectures on the Philosophy of Mathematics
Key Metrics
- Joel David Hamkins
- MIT Press
- Paperback
- 9780262542234
- 9 X 6.9 X 0.6 inches
- 1.45 pounds
- Mathematics > History & Philosophy
- English
Secure TransactionBook Description
In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
Author Bio
Joel David Hamkins is Professor of Logic at Oxford University and Sir Peter Strawson Fellow in Philosophy at University College, Oxford. He has published widely in refereed research journals in mathematical logic and set theory and is the creator of the popular blog Mathematics and Philosophy of the Infinite.
He is a prominent contributor to MathOverflow, where he has posted more than 1,000 mathematical arguments.
When teaching logic, I aim to show students the enormous breadth of the subject — it encompasses truth, meaning, definability, provability, possibility, computability, and more — while also helping to develop the student’s ability to engage with sometimes technical ideas, ultimately using the power they provide to express oneself clearly and precisely. In an honest back-and-forth exchange, I aim that we arrive together at a deeper understanding of the topic.
Research Interests
My research program spans diverse topics in logic, including mathematical and philosophical logic, especially set theory and the philosophy of set theory, as well as modal logic, computability theory and the logic of games; more specifically, I seek to explore aspects of infinity in all these realms.
In my current work on potentialism, for example, I am analyzing various potentialist conceptions in arithmetic and set theory, bringing a modal-logic perspective to the classical problem of actual versus potential infinity. My mathematical work has focused on large cardinals, those strong axioms of infinity, and their interaction with forcing, the set-theoretic method of constructing alternative mathematical worlds, often exhibiting alternative mathematical truths. Indeed, I have become deeply interested in and involved with the debate on pluralism in the philosophy of set theory and the rise of multiverse perspectives in the foundations of mathematics.
I have worked in infinitary comput ability on the theory of infinite time Turing machines. In more playful recent work, I have been investigating infinitary game theory, and this work has led to several fun projects in infinite chess, infinite Go and infinite Sudoku.
Source: University College Oxford
Videos
Community reviews
Write a ReviewNo Community reviews