Tim Gowers's Blog

I just stumbled upon this blog by Tim Gowers, a mathematician at Cambridge with interests in the philosophical side of things. It's been running since September, and there are some interesting posts up here, as well as some interesting comments by interesting people. If you're a philosopher interested in maths, and haven't seen it yet, I can recommend a peek.

Explanation Book Proposal

I've just finished and sent off the book proposal for my planned book Explanation in Philosophical Theories. The book will assess the prospects of what might be called 'explanationism' in various areas of philosophy, especially metaphysics and metaphilosophy. Comments welcome, of course.

Backwards Explanation

UPDATE: A little sibling for Backwards E! Our paper 'Liar-like Paradox and Object-Language Features' is now forthcoming in American Philosophical Quarterly. It argues that you can get Liar-like paradoxes without much at all in the object language (in particular, without anything like a truth-predicate, reference to truth-bearers, or negation) so it's a mistake to suppose that these sorts of object-language features are to blame, or that you're safe as long as you ban them. We'll get a final draft online soon ...

Daniel and Carrie are pleased to announce the forthcoming arrival of their first joint project, a healthy 7000-word metaphysics paper which they have named Backwards Explanation.

Backwards Explanation is still in incubation, and will not be fully developed until its appearance in a special issue of Philosophical Studies containing papers from this year's enjoyable and fertile BSPC.

Carrie and Daniel are doing well, and hoping that 'Backwards E', as it is affectionately known, will soon have lots of little brothers and sisters to play with. Following the delivery Carrie will have an Erdős number of 6.

Paranormality Again

UPDATE II: I've just heard that this reply will be appearing in Analysis after Caret and Cotnoir's piece (which I believe is scheduled for the July 2008 issue).

UPDATE: I've now drafted a more thorough reply.

Caret and Cotnoir's reply to my Analysis paper on Beall's 5-valued approach to the Liar is now online. Their main contention is that it is not a requirement on Beall's model that designation should be expressible in the model language. They make lots of helpful clarifications, but I am not convinced by the main thrust of the paper, which I'll just say a little bit about here.

They say:
"Jenkins has provided no argument for the requirement that 'untruth' be expressible; but the requirement appears to be based on an unwarranted assumption, namely that 'true' in English is a classical notion ... it comes as no surprise that classically bivalent notions will yield inconsistency."

I disagree with Caret and Cotnoir that because designation in Beall's model is a 'model-dependent, instrumental notion', it is no problem for the model if its language cannot, on pain of Liar-like paradox, include any predicate expressing it. I don't see how helpful a model can be, with regard to resolving the Liar, if there are any semantic facts about the way the model works that cannot, on pain of Liar-like paradox, be expressed in its language. It's certainly not that I'm assuming that 'true' in English is classical. It's just that it seems to me that the problem the Liar presents is the apparent impossibility of our language's being capable of expressing certain kinds of claim about its own semantics which it seems to be able to express. Models which embrace the inexpressibility of key semantic claims don't satisfy me as ways towards a resolution of that problem.

I'm planning to write up a proper reply soon.