Joel David Hamkins
Sir Peter Strawson Fellow and Praelector in Philosophy; Professor of Logic
I am new to Oxford from New York, but I look forward to teaching at University College.
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.
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.
Joel David Hamkins and Øystein Linnebo. “The modal logic of set-theoretic potentialism and the potentialist maximality principles”. Review of Symbolic Logic (2018). (http://wp.me/p5M0LV-1zC)
Victoria Gitman and Joel David Hamkins. “Open determinacy for class games”. In: Foundations of Mathematics, Logic at Harvard, Essays in Honor of Hugh Woodin’s 60th Birthday. Ed. by A. E. Caicedo, et al. AMS Contemporary Mathematics, 2016. (http://jdh.hamkins.org/open-determinacy-for-class-games)
Joel David Hamkins and Makoto Kikuchi. “Set-theoretic mereology”. Logic and Logical Philosophy, special issue “Mereology and beyond, part II” 25.3 (2016). Ed. by A. C. Varzi and R. Gruszczynski, pp. 285–308. (http://jdh.hamkins.org/set-theoretic-mereology)
Gunter Fuchs, Joel David Hamkins, and Jonas Reitz. “Set-theoretic geology”. Annals of Pure and Applied Logic 166.4 (2015), pp. 464–501. (http://jdh.hamkins.org/set-theoreticgeology)
Joel David Hamkins. “Is the dream solution of the continuum hypothesis attainable?” Notre Dame J. Formal Logic 56.1 (2015), pp. 135–145. (http://jdh.hamkins.org/dream-solution-of-ch)
C. D. A. Evans and Joel David Hamkins. “Transfinite game values in infinite chess”. Integers 14 (2014), Paper No. G2, 36. (http://jdh.hamkins.org/game-values-in-infinite-chess)
Joel David Hamkins. “The set-theoretic multiverse”. Review of Symbolic Logic 5 (2012), pp. 416–449. (http://jdh.hamkins.org/themultiverse)
Joel David Hamkins and Benedikt Löwe. “The modal logic of forcing”. Trans. AMS 360.4 (2008), pp. 1793–1817. (http://wp.me/p5M0LV-3h)
Joel David Hamkins and Andy Lewis. “Infinite time Turing machines”. J. Symbolic Logic 65.2 (2000), pp. 567–604. (http://jdh.hamkins.org/ittms)
Joel David Hamkins and Barbara Montero. “Utilitarianism in infinite worlds”. Utilitas 12.1 (2000), pp. 91–96. (http://jdh.hamkins.org/infiniteworlds)
See a complete list of my publications on my blog: jdh.hamkins.org/publications