Arché seminars 2007: Philosophy of Logic

Last semester, my first semester in Arché, I recall asking one of my seniors how we were supposed to find time to write a thesis with all these research seminars, workshops and conferences. Fortunately, I was told not to worry: "Next semester", he said, "things will calm down."

Well, what can one say. After seeing the new Arché schedule, I realise of course that I was duped. In fact, it doesn't calm down at all. In addition to the epistemology seminar, the vagueness/math seminar, the Grundgesetze seminar, the relativism seminar, and the Arché Logic Group, Arché now finally decided (after a substantial amount of lobbying) to start a new philosophy of logic seminar which I'll have the honour of convening. Additionally, our new Arché Professors, Herman Cappelen and Jessica Brown, have put together a Knowledge and Language seminar, which will start with some sessions on assertion. In other words, the truth of it is that the thesis will be written in the fourth year ... of a three-year PhD.

Some of my readers will perhaps recall that last semester we started the ALG, the Arché Logic Group, working through Graham Priest's An Introduction to Non-Classical Logic, and proof-reading the forthcoming second volume (dealing with first-order non-classical logics). This semester the group will continue, changing its focus to proof-theory. For now we've decided to read through the Troelstra & Swichtenberg textbook, Basic Proof Theory. Needless to say, this will greatly benefit my work.

And speaking of seminars that benefit my work, the discussion topics for the philosophy of logic have more or less been agreed upon. What more can a poor philosopher of logic wish for? Here are the topics we'll work with this semester:

1. What is logic?
   
2. What is a logical constant?
3. Logical consequence
4. Inferentialism
5. Logical pluralism
6. Disagreement about logic
7. Unrestricted quantification
8. Truth makers for logical laws
   

The full schedule, with the texts that we will be working with, can be found here. In due time, the research seminar will start concentrating on more particular issues, and it will provide plenty of room for Arché members and visitors to present their work within the broad scope of philosophy of logic. I'll keep my readers updated on the discussions as they take form. (That's not a promise. In the blogosphere, as some of you already know, the speech-act of promising fails by default. So let's just call it a prediction.)

UNILOG 2007, Xi'an, China

A busy year ahead. Here's one of the major events that I hope to visit in 2007.


UNILOG 2007 (16-19 August, Xi'an, China)

Ok, so it's a long way to go for a conference. But I've set my mind on this one, not only was the first UNILOG, in Montreux 2005, a tremendous success, this year's event promises great things. Firstly, some highly interesting philosophers/logicians will contribute to the first week of tutorials; secondly, the topic the contest announced on the web page is translation of logics, so there will be several talks closely related with my current work.

Even more so, the list of tutorials has everything I could ask for: (1) Peter Schröder-Heister, one of my heroes, is giving a tutorial on proof-theoretic semantics (I'll bet you this is the first time in history - at least outside Sweden - anyone has ever given a full tutorial on this topic); (2) in addition to the tutorial on translation between logics with Ítala M. Loffredo D'Ottaviano, Alexandre Costa-Leite has a tutorial on combinations of logic; (3) Vincent Hendricks has a tutorial on modal operators, focusing on formal epistemology (an aside: there's a new book by Vincent Hendricks available, Thought 2 Talk, a basic course in argumentative analysis and logical method. For anyone like me, who has struggled with bad books in courses mixing informal and formal logic, this is definitely worth a look.); (4) logical pluralism gets its own tutorial; and (5) I finally get a chance to update my knowledge about category theory in 'Category theory for logics'. And all this even before the conference starts. Now my only problem is that some of these tutorials are bound to collide.

In the conference part, a few of the invited speakers are worth mentioning: Hartry Field, Wilfrid Hodges, and Jean-Yves Béziau. Of course, I await wild speculations on who the secret speaker will be. At the first UNILOG it turned out to be Saul Kripke - how does one top something like that?

New Arché PhD studentships

Arché is now advertising six new PhD studentships in epistemology and the philosophy of language commencing in September 2007. The new PhD students will be working on the Arché projects together with Arché Professors Jessica Brown, Herman Cappelen, and Crispin Wright. Two of the studentships are directly related to the new Basic Knowledge project. The deadline is the 30th of April. Further details can be found here.

If you're interested and would like to speak to some current PhD students in Arché, don't hesitate to contact Andreas or me.

More on Hartry Field

As I never quite got around to saying something about the interesting bit in this paper (that is, 'Metalogic and modality' (1991)), I give myself a second chance. Going Back to a famous paper by Georg Kreisel, 'Informal Rigor and Completeness Proofs' (1967), Hartry Field wants to investigate whether there are advantages with taking the notions of consistency and (logical) implication as primitives instead of treating them in the traditional Tarskian manner. (Kreisel's point was about how to understand completeness in light of such primitive notions.)

What does Field mean by primitive in this context? Here is a first helpful hint: "The claim that consistency should be regarded as a primitive notion does involve the claim that we can't clarify its meaning by giving a definition of it in more basic terms." (p. 5) In other words, anything like a reductive approach (e.g., defining consistency in terms of truth-in-structures) is excluded. In fact, Field points to what he perceives to be an analogy to other basic logical notions:

Similarly, logical notions like 'and', 'not', and 'there is' are primitive. We don't learn these notions by defining them in more basic terms. Rather, we learn them by learning to use them in accordance with certain rules; and we clarify their meaning by unearthing the rules that govern them. (p. 5)

Stuff like this is music in the ears of anyone inclined towards inferentialism. Yet, Field takes it a step further, promising to expand the inferentialistic approach to consistency and consequence as well.

The same holds for consistency and implication, I claim: there are "procedural rules" governing the use of these terms, and it is these rules that give the terms the meaning they have, not some alleged definitions, whether in terms of models or of proofs or of substitution instances." (ibid.)

This undeniably smacks of a more full-blown proof-theoretic semantics, where core meta-logical notions are associated with 'procedural rules'. Unfortunately, Field does not deliver anything resembling such a semantics. Rather, the "two intuitive principles" that he takes to govern our understanding of 'consistency' are not procedural in any interesting way. Let's take a closer look at them: The first is intuitively the sufficient condition for Gamma being consistent, the model-theoretic possibility principle:

(MTP) If there is a model in which Gamma is true, then Gamma is consistent.

Likewise, there is a necessary condition, called "modal soundness".

(MS) If Gamma is consistent, it is formally irrefutable in F (where F is some particular proof-system).

Note that 'consistency' here appears completely uninterpreted; our understanding of the notion derives from its occurrence in these intuitive principles. Field himself ensures us that under this explication, "consistency is neither a proof-theoretic notion nor a model-theoretic notion." (p. 6) True, Field is correct in saying that model- and proof-theory now is on par, but the analogy to the inferential approach to logical connectives is not as obvious as before. The principles are not inferential, so the rule-talk disappears in something more like an axiomatic approach.

Fortunately, it's no cost to the theory to restate the principles in rule-form. By doing this, Field would also emphasize the point that his 'procedural rules' are supposed to capture our use of the notion - a fact that is made clear by his insistence that the principles are connected to the revisability of logic. What Field seems to have in mind is something like harmony for the rules for 'consistency' and 'implication' respectively, mimicking the harmony of introduction- and elimination-rules for logical constants. In particular, he entertains the thought that the former rule-sets might "be found to conflict", thus opening for revision.

Congratulations

Congratulations to Lene Sælen who started the new year by publishing her first physics paper called 'The N-dimensional Coulomb problem: Stark effect in hyperparabolic and hyperspherical coordinates', co-authored with R. Nepstad, J. P. Hansen, and L. B. Madsen.

Carnegie Mellon Summer School in Logic and Formal Epistemology

This just in over the PT list.

Carnegie Mellon Summer School in Logic and Formal Epistemology In the summer of 2007, the Department of Philosophy at Carnegie Mellon University will hold a three-week summer school in logic and formal epistemology for promising undergraduates in philosophy, mathematics, computer science, linguistics, and other sciences.

The goals are to:

• introduce students to cross-disciplinary fields of research at an early stage in their career; and
• forge lasting links between the various disciplines.

The summer school will be held from Monday, June 11 to Friday, June 29, 2007. There will be morning and afternoon lectures and daily problem sessions, as well as planned outings and social events.

The summer school is free. That is, we will provide

• full tuition, and
• dormitory accommodations on the Carnegie Mellon campus.

So students need only pay round trip travel to Pittsburgh and living expenses while there. There are no grades, and the courses do not provide formal course credit.

Instructions for applying can be found on the summer school web page,

http://www.phil.cmu.edu/summerschool

Materials must be received by the Philosophy Department by March 15, 2007.

This year's topics are:
Causal and Statistical Inference
Monday, June 11 to Friday, June 15
Instructor: David Danks

Logic and Formal Verification
Monday, June 18 to Friday, June 22
Instructor: Jeremy Avigad

Decisions and Games
Monday, June 25 to Friday, June 29
Instructor: Teddy Seidenfeld

The summer school is open to undergraduates, as well as to students who will have just received their undergraduate degrees. Applicants need not be US citizens.

Inquiries may be directed to Jeremy Avigad (avigad@cmu.edu).

Snap

Just found a neat new feature through the search engine Snap. The links in my posts now appear with small boxes pre-viewing the page that is linked to. Although I'm not quite convinced that it's necessary, I'm willing to give it a shot. I appreciate any comments if it turns out to be a nuisance. I'm aware that I sometimes put up links without any description of what it's about, so perhaps this will make it easier to avoid links you're not really interested in. And for those of you who liked the surprise of an incognito link - sorry, I've spoiled it.

If you're interested in trying this on your own blog, take a look here (literally).

Corus continued

Since we've just had the first off-day in the Corus 2007 tournament, let me briefly recap. After four games, the "Baby from Baku" (yes, that's the place Kasparov's from as well), GM T. Radjabov (2729), is in the lead with the solid 3.5/4.0. Topalov is in a clear second with 3.0, followed by the rest of the big guns on 2.0 - Anand, Aronian, and Svidler. That being said, Radjabov has yet to play against any of his most formidable opponents; in fact, all his points have been scored against the low seeded players. Still, a win against Shirov is not to be ignored. Whether or not he can keep up the lead, Radjabov's performance has been impressive.

Unfortunately, the same cannot be said about GM Carlsen: after four rounds and meeting opponents from the lower half of the list, he has only managed a disappointing 1.0/4.0. Here are the rounds one by one:

G1 S. Tiviakov - M. Carlsen. A rather uneventful draw with the black pieces in an Alapin Sicilian - quick exchanges led to a draw in 24 moves.

G2 M. Carlsen - D. Navara. The day of blood, only one game ended with a draw. Carlsen had GM Navara pressured in the Exchange Grünfeld White, but according to the expert was just letting him off the hook when Navara suddenly blundered on move 31. Carlsen missed the one-move win and went on the lose the game by overextending the c-pawn in the endgame. This is the type of psychologically decisive games that could ruin the tournament for Carlsen. Navara has continued his good run, making a 2.5 before the break, playing at +101.

G3 R. Ponomariov - M. Carlsen. After letting the win slip the day before, Carlsen didn't play up to his full strenght and let Ponomariov run him into early difficulties. Carlsen got crushed in a 30-move Slav, where his Queen was involuntarily sacrificed as early as move 16. No one else to blame than himself. We can see the silhouettes of a disasterous tournament.

G4 M. Carlsen - V. Anand. Facing one of the favourites on a bad day is never good. Carlsen kept it together and made an early draw to gain time to recover.

Carlsen is now entering a difficult part of the tournament, playing some of the highest seeded players, meeting Aronian, Topalov, and the leader Radjabov with black. Fingers crossed.

Hartry Field's 'Metalogic and Modality'

Reading Hartry Field's paper 'Metalogic and Modality' (Philosophical Studies 62: 1-22, (1991)), I came over some comments reminding me of an argument against a proof-theoretic account of logical consequence that has always bothered me. In fact, I first read it in Etchemendy's The Concept of Logical Consequence, but I recall seeing it elsewhere as well. And now - in Field's article. But first, here is the Etchemendy quote:

It has long been acknowledged that the purely syntactic approach does not yield a general analysis of the ordinary notion of consequence, and in principle cannot. The reason for this is simple. It is obvious, for starters, that the intuitive notion of consequence cannot be captured by any single deductive system. For one thing, such a system will be tied to a specific set of rules and a specific language, while the ordinary notion is not so restricted. Thus, by “consequence” we clearly do not mean derivability in this or that deductive system. But neither do we mean derivability in some deductive system or other, for any sentence is derivable from any other in some such system. So at best we might mean by “consequence” derivability in some sound deductive system. But the notion of soundness brings us straight back to the intuitive notion of consequence. (Etchemendy [1990, p. 2-3])

Similarly, Hartry Field provides the following line of thoughts:

These model-theoretic definitions [Tarskian] are much more natural than proof-theoretic definitions of implication and consistency - for instance, a proof-theoretic definition proceeds in terms of some definite proof procedure, but it seems prette arbitrary which proof procedure one picks, and it isn't very satisfying to rest ones definitions of fundamental metalogical concepts on such highly arbitrary choices. (p. 2)

In my master thesis, I argued that although this type of criticism - that a proof-theoretic account turns on a specific proof-system, and thus a specific language - applies to some out-of-date approaches, in particular, Hilbert's attempt at giving an axiomatic definition of logical consequence (whether or not Hilbert actually thought of himself is not all that relevant; Tarski certainly read something like this into the axiomatic project), the criticism is not applicable to semantic accounts framed in proof-theory, i.e., proof-theoretic semantics. The problem here is that many authors appear to be associating proof-theory merely with syntax, refusing it any semantic capacities. However, the tradition allowing 'proof' as a semantic notion (e.g., Prawitz, Dummett, Schröder-Heister, Wansing, Sundholm, Restall) typically appreciates proof-theory as something more than simply a collection of particular systems/languages.

Central notions in proof-theoretic semantics, such as proof-condition, harmony, normalizability, cut-elimination, recursiveness, etc., are all applicable to a wide range of systems, just as the rival notions, model, truth-in-a-model, truth-condition, satisfaction, etc. To take an example, Prawitz's definition of logical consequence in terms of the former notions fare no worse than Tarski's model-theoretic definition in terms of langauge-dependence. Another issue althogether is that the model-theoretic definition is more frequently applied, and thus has a wider range of actual appliactions. This, however, does not reflect on the potential.

If you're interested in the details of Prawitz's definition, here are some of his papers on the topic:

• "Ideas and results in proof theory", in: Proceedings of the 2. Scandinavian Logic Symposium, pp 237-309, J. Fenstad (ed), North-Holland, 1971.
• "On the idea of a general proof theory", Synthese 27, 1974, pp 63-77.
• "Remarks on some approaches to the concept of logical consequence", Synthese 62, 1985, pp 153-71.
• "Meaning approached via proofs", Synthese 148:507–524, 2006.

Wijk aan Zee 2007

The Corus tournament in Wijk aan Zee is over us yet again. I recall mentioning that Magnus Carlsen will be playing in the A field this year. In other words, he'll be meeting large sharks such as Anand, Topalov, Kramnik, Svidler, Aronian, and his arch-enemy Karjakin (who just turned 17). You can find the full list of players including the schedule on Chessbase.

The games start today, and GM Carlsen is black against Dutch GM S. Tiviakov, a game he cannot lose if he wants to make it in this field. In fact, a win today wouldn't be too much to ask from the Norwegian. Tiviakov (2682) is among the four players in the 14 players strong field who is seeded below Carlsen. However, among the more exciting games today are Ponomariov vs Anand and Karjakin vs Kramnik.

Needless to say, many on-lookers are waiting to see how Kramnik, the new FIDE champion, will do in this category 19 tournament. Kramnik is typically held to be more a one-on-one player than a round-robin player. With Topalov, on the other hand, it's vice versa. Unfortunately, however, the two won't meet until the 12th game, so the scandals will have to wait.

As usual The Daily Dirt Chess Blog gives the unofficial perspective on the tournament, with an ever-growing thread of comments.

Would a modern-day Wittgenstein contribute to this debate?

As the counter-factual speculations about Wittgenstein spin out of control, I take the opportunity of giving readers who haven't stumbled over the debate a quick guide. I'm not going to add anything here, I consider myself done with the discussion - at least until Stanley posts again.

Summary: When Leiter posted on the "changing sociology of the philosophy profession", Aidan McGlynn wrote a comment where he raised en passant an old question once raised by Dummett: Would Wittgenstein get a job in professional philosophy with today's practice? (The full quote from Dummett can be found here.) In response, Jason Stanley wrote a characteristically modest post on Leiter Report, calling the claim that Wittgenstein wouldn't get a job today, the 'Wittgenstein Fallacy'. Aidan's reply with a thread of comments can be found here. Stanley has some comments in this thread, and so do I. However, we're still awaiting Stanley's proper reply, which was promised here.

In addition, here's a refreshing aside by Carrie Jenkins.

Random Dummett quotes

Following Shawn and Aidan, I give you this little gem which surely isn't quoted frequently enough:

"Philosophy is, after all, a craft, as plumbing is."
- The Logical Basis of Metaphysics, p. 19