My research primarily focuses on the philosophy of mathematics, logic, and the history of analytic philosophy. I am particularly interested in the incompleteness theorems and their philosophical implications, and in the work of Kurt Gödel more broadly. I am also interested in the philosophy of language and metaphysics (particularly metametaphysics). You can find links to the articles I've written in these areas below (all of them are available with open access).
I'm currently working on several projects in collaboration with other philosophers. My incompleteness-related work is continuing with Joel David Hamkins (Notre Dame). We are writing an article on the relationship between the Gödelian process of extending a given theory of arithmetic with a new true assertion about the numbers, and the Cantorian process of extending a given countable approximation to the real numbers with a new real number.
Alexander Paseau (Oxford) and I have also been contracted by Cambridge University Press to write a monograph for their Elements in the Philosophy of Mathematics series. We are writing about the Euclidean Programme, the philosophy of mathematics according to which the discipline is simply the deduction of new theorems from self-evident axioms. As far as we know, this will be the first book in the analytic tradition devoted to this historically dominant view of the subject. We are also preparing an accompanying paper relating our work to that of Imre Lakatos, who coined the term 'Euclidean Programme', and is one of the few philosophers in recent history to have devoted any serious attention to the view.
Books
Paseau, A.C. and W. Wrigley (forthcoming in 2023). The Euclidean Programme. Monograph under contract with Cambridge University Press for their Elements in the Philosophy of Mathematics series.
Articles
3. Wrigley, W. (2022). 'Gödel's Disjunctive Argument.' Philosophia Mathematica 30.3: 306-342.
Available with open access: doi.org/10.1093/philmat/nkac013
A digest of this article, 'Infinite Reasoning and Arithmetical Undecidability', was published in The Reasoner 16.7: 64-65. Available online at www.thereasoner.org/
2. Wrigley, W. (2022), 'Gödelian Platonism and Mathematical Intuition.' The European Journal of Philosophy 30.2: 578-600.
Available with open access: doi.org/10.1111/ejop.12671
1. Wrigley, W. (2018), 'Sider's Ontologese Introduction Instructions'. Theoria 84.4: 295-308.
Available with open access: doi.org/10.1111/theo.12153
I'm currently working on several projects in collaboration with other philosophers. My incompleteness-related work is continuing with Joel David Hamkins (Notre Dame). We are writing an article on the relationship between the Gödelian process of extending a given theory of arithmetic with a new true assertion about the numbers, and the Cantorian process of extending a given countable approximation to the real numbers with a new real number.
Alexander Paseau (Oxford) and I have also been contracted by Cambridge University Press to write a monograph for their Elements in the Philosophy of Mathematics series. We are writing about the Euclidean Programme, the philosophy of mathematics according to which the discipline is simply the deduction of new theorems from self-evident axioms. As far as we know, this will be the first book in the analytic tradition devoted to this historically dominant view of the subject. We are also preparing an accompanying paper relating our work to that of Imre Lakatos, who coined the term 'Euclidean Programme', and is one of the few philosophers in recent history to have devoted any serious attention to the view.
Books
Paseau, A.C. and W. Wrigley (forthcoming in 2023). The Euclidean Programme. Monograph under contract with Cambridge University Press for their Elements in the Philosophy of Mathematics series.
Articles
3. Wrigley, W. (2022). 'Gödel's Disjunctive Argument.' Philosophia Mathematica 30.3: 306-342.
Available with open access: doi.org/10.1093/philmat/nkac013
A digest of this article, 'Infinite Reasoning and Arithmetical Undecidability', was published in The Reasoner 16.7: 64-65. Available online at www.thereasoner.org/
2. Wrigley, W. (2022), 'Gödelian Platonism and Mathematical Intuition.' The European Journal of Philosophy 30.2: 578-600.
Available with open access: doi.org/10.1111/ejop.12671
1. Wrigley, W. (2018), 'Sider's Ontologese Introduction Instructions'. Theoria 84.4: 295-308.
Available with open access: doi.org/10.1111/theo.12153