A Plea for a Reprint

I need to echo what Logic Matters said a long time ago. Shoesmith and Smiley's Multiple-Conclusion Logic (1978) is an awesome book: it's comprehensive and elegant on topics discussed few other places in the literature. As I'm working with categoricity issues for logical constants (something Smiley discusses briefly in his 1996 Analysis paper called 'Rejection'), I decided to read the book in detail, especially the chapters on many-valued logics. Rarely have I been so captivated by the "narrative" of a logic book. Unfortunately, as Peter Smith pointed out, the typesetting is hopeless and somewhat detracts from the reading experience. Also, and here's the real killer, if you're library doesn't have a copy, you're in trouble. The only copy I've found online is $295 on Amazon - used.

Now for the plea. Did anyone say Dover?

Update: From the comments, here is a somewhat cheaper alternative.

First issue of the Review of Symbolic Logic

The following was recently announced. The journal has been on its way for a while, and now finally the first issue is here. My good friend Luca Incurvati has a paper entitled 'On Adopting Kripke Semantics in Set Theory'. Archean Graham Priest contributes with 'The Closing of the Mind: How the Particular Quantifier Became Existentially Loaded Behind Our Backs'. And there is much more -- follow the link in the announcement for a list contents.

The Association of Symbolic Logic (ASL) has just launched a new journal, the Review of Symbolic Logic (RSL). It is published by Cambridge University Press. The first issue has just appeared and you can see the table of contents and download articles from the journal's CUP homepage at:

http://journals.cambridge.org/action/displayIssue?jid=RSL&volumeId=1&issueId=01#

RSL is devoted to philosophical and non-classical logics and their applications, history and philosophy of logic, and philosophy and methodology of mathematics. Submissions are welcome.

Conference: The Foundations of Mathematics

Just a little update on the phil of math conference in NYU. The dates have been changed; the conference will now be held from 10th-12th of April 2009. Good for me since that increases my chances of going over to see the talks.

Conference page here.

HT: Aidan

WCP4 Report

I'm just now getting 0rganised in my new hometown, Melbourne, running between libraries trying to find the books I need for my stay, etc. In between, I've been to the 4th World Congress in Paraconsistent Logic, hosted by the Melbourne Philosophy Department. It's been great meeting many friends again here, both Archeans and people I've met at other events. The conference has had an amazing turn out and an impressive line up of paraconsistent logicians from all generations, from the old school Bob Meyer and Ross Brady to the "youngens" such as Francesco Berto, João Marcos, and many more. (The list of abstracts is still online here.)

The conference has seen a number of different approaches to paraconsistenty: adaptive logic, preservationism, dialetheism, the Brazilian school, etc. The Ghent logicians showed up in impressive number and made a considerable impact on the conference with their research on adaptive logic. I've always been intrigued by watching Batens talks before, and this time was no exception. For a family of logics which is relatively little known in the philosophy community, it is astonishing how sophisticated, diverse, and, not to mention, useful the adaptive logics are. I look forward to the day I have time to read a bit more of the details. (For readers new to the logics, a basic idea of adaptive logics is that they are dynamic, i.e., not only can something underived become derived, something derived may also become underived!) Among the many contributions here in Melbourne, Joke Meheus gave a solid talk on adaptive logics as a tool for dealing with normative conflicts. She presented an adaptive, paraconsistent deontic logic MI^m which validates some problematic inferences that cannot be delivered by standard systems.

One of my clear favourites was Patrick Allo's talk on ambiguity in logical connectives. Non-dialetheic paraconsistentists, like my supervisor Stephen Read (1981; JStor required), employ a notion of ambiguity in the logical connectives to avoid endorsing true contradictions. (Aside: considering its linguistic baggage, I'm not sure that 'ambiguity' is the most happy label for what is going on here, but it seems to be well established.) Stephen worked with the idea of having an disjunctive connective 'OR' that is ambiguous over the extensional and the intensional disjunction. Patrick takes this idea seriously and provides a logic of ambiguity where the limited information about which connective is in play affects the logical consequence relation. Where FORM^amb is the language with the ambiguous connectives and FORM is the equivocal language with both extensional and intensional connectives, let tr^e: FORM → FORM^amb be a translational surjective mapping from one language to the other where equivocal connectives are simply replaced by their ambiguous counterparts. Then a consequence relation is defined as follows: Γ |-_amb A iff for each Γ' ∈ FORM which contains for each B ∈ Γ a B' s.t. tr^e(B') = B, there is an A' that satisfies tr^e(A') = A and Γ' |- A'.

Patrick's work has a series of interesting ramifications. One is that we might be able to say something about reasoning with imperfect information about the logic of our interlocutor; another is that we could rethink the nature of disagreement about logic in a framework of ambiguity. I'm looking forward to see the finished paper.

To round things up: Thanks to the organisers and speakers who made this a memorable event. A couple of pictures from the event and the conference wine trip:

Ormond College, University of Melbourne

Greg Restall

Organisers Graham Priest and Ricki Bliss

New Editorial team for the Journal of Philosophical Logic

This just out on the AAL list:

The Journal of Philosophical Logic is proud to announce its new editorial team at the ESSLLI 2008 Summer School in Hamburg, Germany. We warmly invite you to a reception on Monday August 11th, starting at 18.45. With special thanks to the ESSLLI organizing committee and to Springer Verlag for their support.

Information on ESSLLI: http://www.illc.uva.nl/ESSLLI2008/
The reception: http://www.illc.uva.nl/ESSLLI2008/social.html
The Journal of Philosophical Logic: http://www.springer.com/philosophy/logic/journal/10992

Melbourne

Yours truly is off to Melbourne. Currently at London Heathrow waiting for my plane. I'll surface again in time for the World Congress in Paraconsistent Logic in Melbourne.

Philosophers' Football in St Andrews

The annual Moral Philosophy vs Logic & Metaphysics football game was recently played in St Andrews. Following up good play from the last two years, Logic & Metaphysics yet again stole the title, albeit with a narrow win: 2-1. A nasty comparison of Logic & Metaphysics with Chelsea has circulated, but there is not truth to the accusation that Arché PhDs has a clause in their scholarship contracts demanding football skills. In fact, we have a clause not allowing us to talk about it.

Congratulations to the team. I'm not sure how many years we need to win to catch up with Moral Philosophy (they had an unprecedented winning streak in the 90's), but the recent tendency is praiseworthy.

The 2008 Logic & Metaphysics Team

Captain Björn with players

New Arché Project: Foundations of Logical Consequence

If you don't subscribe to Arché's news feed, it's about time you start. That aside, there are some astounding news: Arché has just been awarded its fourth AHRC project grant. And, that not being enough, the title is Foundations of Logical Consequence. The project has been in the offing for quite some time, and I'm thrilled to see it finally become a reality. We've spent an incredible amount of time preparing the application and doing pilot research to prepare the ground, so it's hard to express exactly how relived I am. There can be no doubt that this will significantly boost Arché's phil of logic side. Some of the formal but project-less students who were left after the vagueness and math project ended now have a new home!

Many people have asked about the project application in the last weeks, at Logica and other places, so it's with particular joy that we now see the start of a collaboration with a great international network of researchers. If you want details about the content of the project or the upcoming positions and scholarships, have a look here. I'll be posting more as we get started.

LOGICA 2008, part II w/ pictures

Some more words on LOGICA. And, an opportunity to share a couple of pictures from the event. There are a couple of talks I want to mention in particular. As I said in the last post, the first day was something of a proof-theoretic semantics extravaganza, with Prawitz kicking off the event. What made it so enjoyable was that I finally got to meet a couple of people that I knew were writing their thesis (or had been writing their thesis) on topics closely related to my own.

Theodora Achourioti's gave a paper entitled 'Justification and Harmony', with observations very similar to those I made in my own conference contribution. Among her points is that the alleged meaning-theoretic importance of harmony is made dubious by the fact that harmony is a property of a presentation of a logic. (Note that she understands harmony as normalization/subformula property.) Importantly, global properties of a natural deduction system can affect the result, e.g., although, famously, classical logic "isn't" harmonious, a multiple-conclusion version of natural deduction for classical logic is. (Cf. Boricic 1985, Read 2000.)

A personal favourite of mine was Jarda Peregrin's 'Inferentializing semantics and consequence'. Behind the general title was a very neat collection of results about the expressive power of a range of proof-theoretic system (for propositional logics). With the basic idea that a proof-system can determine the truth-conditional content of logical constant, we might want to ask whether or not a particular system has the resources to rule out certain valuations (say, valuation that flatly violate the satisfaction clauses of the connectives). One such valuation, first discussed by Carnap, is the trivial one: every wff is taken to the value 1. Interestingly, an ordinary natural deduction system for classical logic cannot rule out this valuation. If it is added to the class of valuations, every inference rule will still be valid (i.e., truth-preserving in every valuation). However, with a multiple-conclusion system, one can rule out this valuation by using an empty consequence set. (See for example Smiley 1996, Rumfitt 1997.) Peregrin's contribution is to map out a hierarchy of different calculi in order of their ability to proof-theoretically distinguish between valuations in this sense. Unsurprisingly, at the very top is a system which allows both infinite (and empty) premise sets and infinite (and empty) conclusion sets. As I've recently been writing about related material with Julien Murzi, I'm sure I'll have more to say about this stuff in the near future.

Nils Kurbis, another proof-theoretic semanticist, offered a diagnosis of modal operators where the lack of a harmonious rules is proposed as evidence for a more radical understanding of their role in the Dummett-Prawitz programme. Modal notions, Kurbis suggests, have a more direct relation to the concept of logical consequence than your average logical notion. The concept of logical consequence in turn is taken to be primitively modal. Gillman Payette gave a critical analysis of logical pluralism and JC Beall and Greg Restall's attempt at sharpening the position. Catarina Dutilh Novaes, one of Arché's upcoming visitors this semester, made an interesting comparison of Brandom's 'game of giving and asking for reasons' and medieval obligationes. (In fact, obligationes has been the topic of St Andrews's reading group in medieval logic this semester.)

I could go on and on about the many great topics, but I'll rather end with a couple of pictures. I'm looking forward to meeting some of the people again in Melbourne in a week's time. Meanwhile, I'll post an update if any of the videos comes online on the conference pages.

Dag Prawitz

Gillman Payette

Jarda Peregrin

Bob Brandom