Metapost

I just added a feed from my Google Reader account in the sidebar. I'll use it to share items of interest that I don't have time to post about. I'll keep it as long as I can get into the routine of updating it regularly (and given that you don't find it annoying---I did remove the Snap function after feedback from unhappy readers).

John P. Burgess: Philosophical Logic

John P. Burgess (Princeton) has a the manuscript of a forthcoming book, entitled Philosophical Logic, on his homepage (216 p). The book is intended as a volume in the Foundations of Twenty-First Century Philosophy Series (Princeton University Press, ed. Scott Soames). Browsing through the manuscript, I find that it promises material on classical logic, temporal logic, modal logic, conditional logic, intuitionistic logic, and relevant logic. Now, my gut reaction is that isn't really taking philosophical logic into the 21st Century. Of course, the author has particular readers in mind, and it looks from the preface to be a very conscious choice of topics. A brief passage:

The temptation to include topics of great technical interest but doubtful philosophical relevance has been resisted. The center of gravity of ‘philosophical logic’ today lies in theoretical computer science, but not the center of gravity of this book. Among the more technically-oriented a ‘logic’ no longer means a theory about which forms of argument are valid, but rather means any formalism, regardless of its intended applications, that resembles a logic in this original sense enough to allow it to be usefully studied by similar methods. In this book I unashamedly take seriously philosophical questions of logic in the original sense (such as the question which modal systems gives the right account of the formal logic of modal notions, or whether relevantists were right in claiming certain classical forms of argument invalid) in a way the more technically-oriented would regard as reactionary or quaint.

What I would like to see, rather, is someone facing the challenge of bringing philosphical logic up to speed with contemporary logic. This is not a task accomplished (nor promised) by this book. That being said, I can't criticize a book I have yet to read, so I'll leave it at that, hoping that I'll have chance to take a close look later on.

HT: Semantics etc

Ideals of Proof

A collaboration of French universities have started an interesting project funded by the Agence Nationale de la Recherche, reports Theorem(e). The new project, entitled 'Ideals of Proof', features inaugural lectures by Michael Detlefsen and an inaugural symposium with Detlefsen and Dag Prawitz. I'm very sad to miss it, but if you're around in Paris in the coming weeks, make sure to be there (more info here).

A project description is here (excerpt below), and info about research fellowship possibilities are here.

The term 'ideals' in the title has two intended senses. The first concerns the aims and virtues of proof considered as justificative norms for mathematical practice generally. The second concerns the use of so-called "ideal" elements or methods as means of pursuing these aims.

Ideals in the first sense include not only such traditional standards as rigor, certainty, apriority, purity and explanatory gain, but also such "collective" or systemic virtues as (various types of) completeness, closure, efficiency and freedom. Generally speaking, we want to improve our understanding of why such conditions and constraints as have figured as ideals of proof in the history of mathematics have so figured and whether they are truly deserving of such regard.

Ideals in the second sense include such things as the introduction of "infinites" (both large and small), imaginary and complex numbers in algebra and analysis, the use of Kummer ideals in number theory and the use of points, lines and planes at infinity in projective geometry.

We're concerned with ideals in both of the above senses. We're also interested in the relationships between them and are especially concerned to determine how the use of ideals in the second sense may either support or run contrary to realization of the ideals in the first sense. More generally we want to identify and understand the contributions ideal elements or methods have made and may yet make to the larger enterprises of mathematical proof and knowledge.

Congratulations: Danish Formal Philosopher Wins Prestigious Award

I just found out that Danish philosopher, logician and Editor-in-Chief of Synthese, Vincent F. Hendricks, has been awarded the Elite Research Prize by the Danish Minister of Science, Technology and Innovation and Her Majesty, Crown Princess Mary.

Congratulations to Vincent! No doubt it is a very good thing for philosophy and logic to get this kind of publicity in Denmark and elsewhere. In fact, the award-winner has recently given some suggestions on visibility in philosophy, so perhaps Vincent has been following his own advice.

HT: Lemmings

Thanks to the Cambridge Philosophers: Conference Report

And everyone else who helped make the Cambridge Graduate Conference such a success. Special thanks to Luca and Tim for organising the much-needed event, probably the first philosophy of logic and math only graudate conference in the UK (at least this is what we concluded during the conference). Speaking at this conference was a pleasure: very nice atmosphere, with just the right sort of interested and informed audience. Personally, I'm very happy with the feedback I got on my own talk, questions, and suggestions. Helpful comments from my respondent, Florian Steinberger, were especially appreciated. A whole-hearted request that the Cambridge philosophers make sure this event is made into an annual one!

Our keynotes speakers, Dorothy Edgington and Alan Weir, contributed with interesting talks. The former's was a response to Williamson (2000). where her (1985) approach to the Church-Fitch paradox is famously criticized by the author.

The latter made a brave attempt at reviving formalism---in the shape of so-called neo-formalism---borrowing from Thomae and the Hilbert of The Foundations of Geometry, yet aspiring to justify some sort of content to mathematical utterances. (I'm quite keen on this project myself, especially the Thomae part---a philosopher who has been left with little honour due to Frege's onslaught.) Interesting was Weir's suggestion on how to avoid the old incompleteness challenge to the formalist projects (his has its own worries, not unrelated to those of Hilbert's Programme). Aligning himself with some recent suggestions by one of my supervisors, Stephen Read, Alan Weir suggests that we avoid incompleteness by allowing the ω-rule to make a comeback in the formal system. I'm not very keen on the approach, but I'll leave any elaborate comment for later; suffices to say that it is unclear what sort of contribution an infinitary rule makes to the holistic Hilbertian semantics Weir has in mind.

Although I won't take time to go through all graduate talks, let me just give a couple of links. Peter Smith, who responded to Elia Zardini's vagueness paper entitled 'A Model of Tolerance', has a longish post on his blog, Logic Matters, about the exchange. Over at Joe Salerno's Knowability there is a post about another of the grad papers: Julien Murzi and Salvatore Florio's 'The Paradox of Idealization'.

Chalmers and the Philosophy Teams

I think this post by Chalmers is worth a link. Check out the comments too.

Job possibilities in Arché

Good news for Arché at the start of the year: The AHRC application on Intuitions and Philosophical Methodology was accepted. This means that while we are still in the process of looking for two new 4-year post docs on Contextualism and Relativism, we now also need more people for the Methodology project. See below for details:

UNIVERSITY OF ST ANDREWS

School of Philosophical, Anthropological and Film Studies

Arché: Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology

2 Research Fellows

Salary – £27,857 per annum

We are seeking to appoint two research fellows for up to four years. You will commence on 1 September 2008, or as soon as possible thereafter. You will conduct research within the scope of the AHRC funded research project ‘Intuitions and Philosophical Methodology’.

We encourage applicants working in any area of philosophy who have a genuine interest in methodological issues. You must have a PhD in Philosophy by the time of appointment and be capable of demonstrating outstanding research potential in the areas of the project. A track record of high quality publications will be an advantage. Please include with your application a CV, research proposal (1000 word max) and recent writing sample (5000 word max.).

Please quote ref: ME097/08 Closing date: 15 February 2008

Application forms and further particulars are available from Human Resources, University of St Andrews, College Gate, North Street, St Andrews, Fife KY16 9AJ, tel: 01334 462571, by fax 01334 462570 or by e-mail Jobline@st-andrews.ac.uk. The advertisement and further particulars and a downloadable application form can be found at http://www.st-andrews.ac.uk/employment/.

The University is committed to equality of opportunity.

A travel letter: Truth and Paradox

Dear reader,

Currently making my way back from the Kingdom of Norway, flying over a stormy North Sea. [Actually, this post was written some time ago---at the time of posting I'm back in St Andrews. So much for a dramatic opening.] In my lap is a copy of Hartry Field's review of Tim Maudlin's Truth and Paradox: Solving the Riddles (2006) [Oxford Scholarship Online]. Why? you say. Next semester the Arché Philosophy of Logic seminar is setting off a good three months to work with truth and paradox, more precisely Truth after Kripke (that's the overarching theme of the seminar). Before the break we agreed to start off with Tim Maudlin's book and then proceed to a series of articles by Field (most of these are online on his webpage). If time allows, we'll proceed to work with more formal aspects of Kripke's theory: Reinhardt, Halbach, etc. (Tentative seminar schedule here.)

So far I haven't started reading the book, but on my supervisor's recommendation gone immediately to Field's review. And not without reason. Hartry Field's review starts as follows: "Tim Maudlin's Truth and Paradox is terrific." And ends, "for anyone interested in the paradoxes this is a must-read book." Without sliding into a review of a review, let me use Field to introduce some of the book's topics that interest me.

What is perhaps most striking about Field's review is that it suggests an alternative reading of the book---a reading which appears quite contrary to the authors intentions. Let me explain. The review starts by outlining the Liar and proposing the three following solutions: (i) accept the contradiction and endorse a non-explosive logic; (ii) reject one or both of the T-inferences (the upward T-inference from A to T[A] or the downward from T[A] to A); (iii) reject reductio ad absurdum. Setting aside the first option (endorsed by dialetheists such as Graham Priest and JC Beall), Field agrees with Maudlin that the real game is between (i) and (ii). According to Field, Maudlin presents his solution as an option (iii) solution, whereas it ought to be presented as an option (ii) solution.

How is it possible to disagree as radically on the correct upshot of the theory? The reason ties in with the following observation by Field: "A virtue of Maudlin's book is that it isn't concerned only with the semantics of languages with truth predicates, but also with their inferential structure." (1) Needless to say, someone with my inferentialist sympathies is only too happy to see that the inferential perspective is maintained in the analysis of the Liar. But, tinkering with the inference rules for the truth predicate is nothing new in the Liar literature; what is interesting (if not new) in Maudlin is that there is, according to Field, two notions of validity in play---one semantic and one inferential. What is the difference? Semantic validity is something like the well-known (necessary, i.e., over all cases) truth-preservation; inferential validity is by Field described as a doxastic relation---believing the premises commits you to believing the conclusion.

In Maudlin's theory, importantly, semantic validity does not entail inferential validity. Maudlin himself describes the theory as one in which reductio is (semantically) invalid while the T-rules are valid. Field, on the other hand, prefers to describe the theory as one in which the upward T-inference is (inferentially) invalid while reductio is valid.

Consider this just a teaser. I'll return to the topic when I've read the first chapters of the book. But already now I'm confident that the discussion is fertile ground for a subject close to my heart: disagreement about logic. Systematic reasons for revising inferential rules, and which rules to pick, is a dreadfully understudied area, although much of contemporary discussion of paradoxes, vagueness, philosophy of mathematics deals unhesitatingly with such revisions. It is a bonus that the Field-Maudlin debate also makes it clear that disagreement about validity is not as unequivocal as is sometimes assumed.


Yours provably,
Ole

Ten Signs a Claimed Mathematical Breakthrough is Wrong

Quite amusing. And not entirely without relevance for logic and philosophy. Without further ado: Ten Signs a Claimed Mathematical Breakthrough is Wrong. (Through Shtetl-Optimized. Thanks Lene.)

Philosophy vs Scottish Common Sense

I just came across this article over at Philosophy, et cetera. Apparently, philosophy is on the rise in Scottish schools, so much, in fact, that it has brought out a whole new market for my department. The following is from The Herald:

However, the increasing popularity of the subject has created an unforeseen problem. Because there is currently no secondary teaching certificates for philosophy as a specialist subject, some schools are struggling to cope with the new found demand. The situation has prompted St Andrews University to offer a new online course for teachers involving elements of philosophy such as ethical issues, reasoning and knowledge, mind and reality.

The course has been designed by Dr Lisa Jones, a teaching fellow for the university's department of philosophy, after a request from a teacher at a local secondary school.

Richard Chappel (Philosophy, et cetera) noticed that, unfortunately, the comments on the article are overwhelmingly negative towards the tendency. I think my favorite is the following response:

All this philosophy undermines plain Scottish Common Sense in my opinion.

Take the health service, for example. Every right thinking Scot knows fine well that hospitals should be near to where you live. It means you can be rushed there quickly in an ambulance, and more importantly, people can visit you easily and bring bunches of grapes. It's philosophers with their fancy new ideas that propose concentrating hospitals far away just so the doctors can get more experience and do a better job. How will people be visited and brought bunches of grapes then?

Thank goodness the new Scottish Government talks plain old Scottish Common Sense.

Here's a fancy new idea: Beware of Scottish Common Sense (what's with the caps?).