Links

Just a couple of links:

• There is a new metaphysics blog called Matters of Substance with a very top heavy team of contributors. Among them are Archéans Elizabeth Barnes, Ross Cameron, Dan López de Sa, Jonathan Schaffer, and Robbie Williams.
• Over at Richard Zach's LogBlog there is info about some up-coming summer schools in logic.
• Aaron Cotnoir over at Condundrum writes about UConn and the PGR here.
• In other news: I've added a Twitter feed to the side bar for those who need to know what I'm doing absolutely all the time. However, I do not guarantee to keep the tweets phil logic relevant.
  

PGR 2009: St Andrews

It's that time of year again. Well, it's really biennial, but it feels like every year week. The new Philosophical Gourmet Report (2009) is out. We've seen previews on the Leiter Report for some time already, so no need to rehearse the generals. I try not to get too involved in the heated debate about the value and content of the PGR, but I've generally linked to ranking info in the Elsewhere in the Blogosphere section (see sidebar). This post, of course, is nothing but a shameless little plug for the St Andrews department. Actually, a shameless plug for the joint St Andrews/Stirling effort, since the two departments rank together (for reasons I won't dwell with). It's cheating, basically.

In the overall ranking for the English speaking world the programme is ranked shared 17th, which is no real change from the last PGR. I think we ought to be pretty satisfied with this; it brings us into the same bracket as CUNY, Notre Dame, and Toronto. In the UK ranking we stay ranked as number two, reasonably enough far behind Oxford (2nd overall), but ahead of Cambridge. Without selling my home institution short, I do perhaps think that Cambridge is underrated. At any rate, they probably perform better against St Andrews and Stirling individually.

In the Philosophical Logic speciality St Andrews is placed in the 4th bracket with a mean of 3.75. I believe this is a drop from last PGR, probably due to Crispin's NYU move. This is similar to the situation with the Philosophy of Mathematics speciality (mean 4.0). In Mathematical Logic we score a mean of 3.5. All scores appear reasonable, but I do hope we'll improve now that the FLC project has officially started. Once two new post doctoral researchers are in place there will certainly be more activity. Yet, any real advance must be preceded by a senior appointment, and with the current financial situation it does not appear all too likely.

A score that is really good news is our 1st place in The History of Analytic Philosophy (incl. Wittgenstein) - mean score 4.5. Clearly we are here helped by a significant research presence in Stirling.

Although I don't belong to the ranking skeptics (I believe that the rankings do serve a useful purpose for potential grad students), a lesser worry might be useful to raise. As the Report itself notes, some of specialities have a very limited number of evaluators (e.g., Phil of Math with 6; contrast Philosophy of Language with 52). Considering the potentially large area of research covered by one PGR-speciality this might be unhealthy. Even more worrying, perhaps, is the fact that so few people in these specialities choose to participate in the evaluation. True, there are fewer experts available in philosophy of mathematics than in language, but the above ratio probably misrepresents the situation.

Conference on Non-Classical Mathematics

Browsing through the info for this year's LOGICA, I noticed that there is an adjacent event in Hejnice this summer. Just before LOGICA there is a conference on non-classical mathematics (June 18th-22nd). There is a cfp on the website together with some more information. Here is the list of invited speakers.

• Chris Mortensen (University of Adelaide, Australia).
• Greg Restall (University of Melbourne, Australia).
• Giovanni Sambin (University of Padua, Italy).
• Kazushige Terui (Kyoto University, Japan).

Brandom on inference rules

The following passage is from Brandom's Articulating Reason, p. 62-63

Gentzen famously defined connectives by specifying introduction rules, or inferentially sufficient conditions for the employment of the connective, and elimination rules, or inferentially necessary consequences of the employment of the connective. [...]

What corresponds to an introduction rule for a propositional content is the set of sufficient conditions for asserting it, and what corresponds to an elimination rule is the set of necessary consequences of asserting it, that is, what follows from doing so.

(See Stephen Read's paper 'Harmony and modality' (forthcoming in On Dialogues, Logics and other Strange Things, ed. C. Dégremont, et al.) for a brief criticism of this way of construing the inferential rules.)

I want to suggest an alternative way of looking at it, inspired by Smiley (1996). The idea is well-known: We introduce assertion and rejection as primitive signs on the wffs of the language (+A and -A respectively). In the enriched structural language, we can then express conditions not only for asserting but for rejecting. This two-dimensional view on inferential rules changes the story. The intro-rules for a rejection-signed formula are characterising the sufficient conditions for rejection of a proposition. So, assuming that the rejection sign behaves like a non-embeddable negation (albeit not in the object language), i.e., -A is correct iff A is false (correspondingly, +A is correct iff A is true), we can think of the rejection-sign intro-rule as a sort of contraposition of an assertion-signed elim-rule. In other words, rejection-signed intro rules can also be seen as giving necessary conditions for assertion!

Let me give you an example. Normally 'From A, infer A or B' and 'From B, infer A or B' are both expressions of sufficient conditions for asserting 'A or B'. With a rejection as a sign, we can say 'From -A and -B, infer -(A or B)', thus giving a reversed intro-rule which states that rejecting both A and B is sufficient for rejecting 'A or B'. Given the above assumption about rejection, this amounts to giving the last line of a truth-table definition of disjunction: falsity of A, B yields falsity of 'A or B'. Put differently, it's a necessary assertion-condition on 'A or B' that you either assert A or assert B. Of course, the standard elim-rule for disjunction doesn't mimic this directly since it doesn't employ multiple conclusion. But in a multiple conclusion framework we can give the rule 'From 'A or B', infer A, B' where the comma operates as a disjunction at the structural level (think sequent calculus).

In other words, with an enriched structural language for the proof-system, new light might be shed on Brandom's remark.

Zalabardo on logical consequence in the Tractatus

José Zalabardo (UCL) has a forthcoming paper on his website called 'The Tractatus on Logical Consequence'.

ABSTRACT: I discuss the account of logical consequence advanced in Wittgenstein’s Tractatus. I argue that the role that elementary propositions are meant to play in this account can be used to explain two remarkable features that Wittgenstein ascribes to them: that they are logically independent from one another and that their components refer to simple objects. I end with a proposal as to how to understand Wittgenstein’s claim that all propositions can be analysed as truth functions of elementary propositions.

HT: Methods of Projection

IF Logic

Hintikka's The Principles of Mathematics Revisited is one of those books I've had in my shelf for way too long without reading. For those with a similar problem there is now a new SEP entry for Independence Friendly Logic, the logical system proposed in the book.

Humberstone on logical pluralism

The March 2009 issue of AJP has a new review by Lloyd Humberstone of Greg Restall and JC Beall's book Logical Pluralism. The review deals with some technical issues in the book that might be worth revisiting. But, more importantly, I suspect that Humberstone gets Greg and JC's philosophical theory right, in contrast to a number of other commentators. As a bonus there are some short comments on the assertion/denial framework from a favourite paper of mine, Greg's 'Multiple Conclusion' (preprint).

HT: Julien Murzi

Cambridge revisited

An overdue note on the 2nd Cambridge Graduate Conference in the Philosophy of Logic and Mathematics. I can't praise Florian and Luca enough for this wonderful event. Other participants and myself have systematically tried to pressure them to continue the tradition, and hopefully they'll find new grad students to organise it in the years to come.

Julien and myself presented our joint paper on the categoricity problem, followed by excellent comments from Peter Smith (comments are also online on Logic Matters). Hannes Leitgeb's very interesting keynote paper on "On Formal and Informal Provability" is unfortunately not online, but it is forthcoming in New Waves in Philosophy of Mathematics. Most of the other papers in the volume can be found as preprints here. Williamson gave a solid paper on second-order modal logic and Barcan-related formulae. Paper can be found here.