Turning the page

After three days and three written exams, I have now surfaced on the other side. Leaving behind ethics, metaphysics, epistemology and philosophy of mind, I am now finally ready to do what I want. If the results of the essays and exams are according to the plan (and they better be, Patrick!), this autumn will signal the start of my three-year long, research-only , PhD (who wants to be in America, Aidan ;) ). How exactly will I exploit my new freedom? I will be working with proof-theoretical semantics for logical consequence together with Stephen Read. During the summer I'll be working with the same topic in my M.Litt dissertation, so there's bound to be some posts on this in the coming weeks.

Of course, after a long year in St. Andrews there are plenty of people who deserve thanks for making all this worth while. However, in true von Trier spirit, first things first: There are some people I need to forgive. I forgive my room mates Richard and John for waking me up in the middle of the night with their reckless partying, I forgive my friend Tord for beating me in a winning position, I forgive Prof. Sullivan for frowning at my Quine project, I forgive James for not inviting me to his party (you break my heart), I forgive the American students in my class for taking up all the time with useless questions, I forgive the girl behind the counter in the gym (whose name I do not know) for complaining about my shoes, I forgive Dan for kissing me, I forgive the people at Tesco (their mistakes are too numerous to mention), I forgive Marcus for doing what I should have been doing, Yin for constantly understating his potential, and Raffles for leaving us, I forgive the Norwegians in St. Andrews for their event, I forgive the University for its greed, the department for its many administrational shortcuts, and myself for forgetting the only thing that matters. I forgive you all.

Then, to the thanking. First of all I want to thank the Department and especially Patrick Greenough for putting up the Philosophy of Logic course on the student's request. Patrick turned this into the best philosophy course I've ever done. I also need to thank Dr. Clark for all his kind help with applications, and for his wonderful course in meta-theory - only Dr. Clark can embed an advanced logic course in excellent narration. Moreover, I want to thank Prof. Shapiro for teaching us that "this is connected, for everything is" - the origins of analytic philosophy course was a great success. Then, of course, I want to thank some of my future room mates: thanks to Andri for his Turing machine abilities, thanks to Ralf for his unsurpassable fighting spirit and valuable English lessons, and thanks to Andreas for his lovable intellectual elitism, and teaching us that "they can keep their filthy money". Finally, thanks to a great philosophy department and its faculty, and thanks to the ORS and the University of St. Andrews for funding for my PhD.

M-Tel Masters 2006

This years M-Tel Masters, held in Sofia, Bulgaria, claims to be the strongest tournament in the world with a breath-taking average Elo of 2747. The two only players in the world ranked above 2800, Topalov and Anand (no. 1 and no. 2, respectively) will join Svidler, Ponomariov, Bacrot and Kamsky in a double round robin tournament. Even if one ignores the quality of the players, there are several reasons to expect this to be a particularly demanding tournament. Firstly, the tournament has ten playing days in a row without break; secondly, due to the unorthodox rule that no player can offer a draw, the games are bound to be longer than usual; and, thirdly, one of the tie breakers is actually number of moves taken, so there will be plenty of reason to keep on playing. However, as we all know, exhausted players perform accordingly.

At the moment of writing, the second round is just about to end. Two out of three games have ended with a decisive score. Yesterday's opening round saw one decisive game, two draws, but by no standard a boring start. Although the broadcast was a bit unstable on Chessbase, most kibitzers managed to make time pass by discussing some of the interesting battles promised by this tournament. First up, of course, is the one-on-one between the two greatest players in the world (Kasparov notwithstanding), Anand and Topalov. Since only one (!) point separate the two, it is hard to say anything determinate about their relative strength. True, Topalov has dominated the big tournaments lately, but that said, not by outplaying Anand. Rather, Topalov's success owes largely to scoring more points against the other players than Anand does. There is nothing disreputable in that, although it leaves us with some unanswered questions.

And if anyone doubted that Anand had it in him to challenge the FIDE champion, they got their beliefs revised today. Already yesterday, Anand got a running start by beating Bacrot with the black pieces. However, everyone knew that this would not materialise into anything substantial before today's match against Topalov. And what a match it turned out to be. Due to Topalov's outstanding play lately, and Anand's rather anonymous performances, I guess most people had their money on Topalov today. A bit of history, however, should inform us that not so long ago it was Anand who was the favoured second behind Kasparov; Topalov was but a promising top ten. At any rate, today Anand proved that he is without doubt Topalov's toughest opponent in the Championship, and a worthy contender for the throne. He actually made it look easy to beat Topalov, outplaying him by penetrating a tactical position the way only Anand and computers can. To the amazement of all kibitzers armed with computers, Anand found a deep trap in the end position, winning a piece and heading into an easy endgame. A few moves later, Topalov resigned. So, this leaves the question wide open: Who will be the 2007 FIDE Champion?

Whereas Topalov and Anand are both directly qualified for the final tournament for the title (due to the results in San Luis where Topalov took the title and Anand came in second (however, if Topalov loses against Kramnik in the upcoming match, he'll also lose his place to Kramnik)), most of the other players have fought their way toward the tournament, either through the Cup or by achieving high enough Elo. A noticable exception is Svidler: the Russian is in something of an inbetween position. Though he is by few thought to be as good as Topalov and Anand, he clearly doesn't belong with the rest. Coming in third in San Luis, he is also directly qualified, and has at his best played well enough to challenge even the winner. This tournament could be his chance to convince his critics. So far, by beating youngster Ponomariov in the second round, he has not at all started poorly.

That leaves us with "the rest". Kamsky, Ponomariov, and Bacrot all played in the Cup to secure places in the candidate matches. Some of you, perhaps, will remember Kamsky and Bacrot as the two (only) players who beat Magnus Carlsen. The latter should have won against the French Bacrot, but had an unlucky blunder in the final game. Kamsky won quite convincingly, in what will be remembered as his come-back tournament. However, none of them could match Ponomariov, who came in second behind Aronian. Obviously, for all of them, this will be an opportunity to show that they belong in the final eight player tournament for the title. So far, Bacrot has lost one game, and so has Ponomariov. Kamsky seems to be the only one with an acceptable start, drawing the first, and it appears he has winning chances in today's game against Bacrot (still not finished).


Categories: Chess

The Development of Mathematical Logic from Russell to Tarski: 1900-1935

Richard Zack has recently uploaded a very interesting manuscript on his homepage. 'The Development of Mathematical Logic from Russell to Tarski: 1930-1935' is a book-length article to appear in Leila Haaparanta, ed., The History of Modern Logic. New York and Oxford: Oxford University Press. The article is co-authored with Paolo Mancosu and Calixto Badesa. Here is the abstract:

Abstract: The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim and Skolem. Itinerary V surveys the work in logic connected to the Hilbert school, and itinerary V deals specifically with consistency proofs and metamathematics, including the incompleteness theorems. Itinerary VII traces the development of intuitionistic and many-valued logics. Itinerary VIII surveys the development of semantical notions from the early work on axiomatics up to Tarski's work on truth.

Through Théorème.


Categories: Logic, Philosophy, Model-theory

Game Theory

Following the success of the format of Formal Philosophy, the concept has been expanded to the field of game theory. Although it is chiefly associated with economic theory, game theory has had a large impact on logic and epistemology through its contribution to concepts such as common knowledge, rational agents, and information. Game Theory, edited by Vincent F. Hendricks and Pelle Guldborg Hansen, is a collection of answers by some of the most prominent researches on the field. They answer questions on the aim and scope of game theory, plus the future direction of the field.

Check it out here.


Categories: Philosophy, Logic, Game-theory

Moral Philosophy vs. Logic and Metaphysics 1-8

As is well known to the students and faculty of St. Andrews, our philosophy department has traditionally been split in two: one department for Moral Philosophy (MP) and one for Logic and Metaphysics (LM). Yet in the later years the departments have been merged into one, and now only a few things remind us of the venerable old distinction; the two entries of Edgecliffe with their MP and LM signs respectively, the occasional turbulence in the seminar rooms between the champions of times past, and, of course, the annual football match (I assume that my American readers manage to figure this one out). Playing for the LM team, it is with great pleasure that I present a little report from this Sunday's clash. I sincerly hope that the outcome will reflect on the ensuing battle in the seminars.

On an excellent day for football, the match started after the compulsory whining from the MP team. Apparently, as in professional football, being 'moral' means arguing about player transactions, blaming the weather, questioning the referee, etc. Whereas the simple logic of things, on the other hand, is that the team with the most goals gets to carry home the trophy. And, fortunately for us, scoring goal seems to be precisely the agenda of the day for LM star par excellence, Philip. Quickly taking the LM team to a score of three to nothing, the stage was set for a one man show.

No threats materialised from the MP team before the second half when the referee without warning decided to penalise our token Texan Trey for being larger than his opponents. The resulting penalty kick was professionally executed by MP captain Brian. No doubt this discrepancy was due to the telepathic influence of the managers. As reported by photographer Elizabeth, "Crispin and Tim are engaged in a fierce battle of the wills as they control their pawns".


Nevertheless, the powerful mind control could not alter the inevitable. The second half saw more LM domination, and our team could set the final score to 8-1 in favour of all that is sound.

Here is the proud LM team (aka Crispin's Army of Light), unsuccessfully hiding their shameless gloating after defeating the archrivals.


Categories: Philosophy, St. Andrews

The 3rd Arché Graduate Conference in Analytic Philosophy

17th-19th November 2006 the Arché centre in St. Andrews will hold its 3rd Graduate Conference. Call for papers is here. The announced keynote speakers are:

Prof. Graham Priest (Melbourne)
Prof. Diana Raffman (Toronto)
Prof. Jason Stanley (Rutgers)

The deadline for submission is 16th of August.


Categories: Arché, Philosophy, Conferences

The argument from vagueness

In his book Four-Dimensionalism: An Ontology of Persistence and Time, Ted Sider presents an improved version of David Lewis's argument from vagueness (from On the Plurality of Worlds). The argument has generated a lot of attention (see links in the end) because of its powerful metaphysical conclusion, i.e., four-dimensionalism (or, in Lewis's version, universalism for mereological composition), and its rather innocent-looking premises about vagueness.

For brevity, let us here ignore the more complicated argument for four-dimensionalism, and just focus on Lewis's version with an important strengthening made by Sider (if you want to see Sider's full argument, here is a preprint of an article called 'Four-dimensionalism'). The argument is roughly as follows: There are three broad positions on mereological composition: (i) nihilism, no non-empty set of objects form a mereological sum, i.e., a fusion; (ii) universalism, all non-empty set of objects form a mereological sum; and (iii) retrictivism, some non-empty set of objects form a mereological sum.

Now, our intuitions tell in favour of (iii). Some objects, like the particles of my hand, form another object, namely my hand. However, some sets of objects, like the set of my left hand, a deck of card, and the planet Saturn, does not form a fusion. As pointed out by Lewis, distance, cohesion and other criteria decide whether or not we believe that some objects have a fusion. But, he continues, these criteria cannot be stated non-vaguely. To see this, imagine that we take all the particles of my hand and move them all 0,00001 nanometer in different directions. Due to the insignificance of the distance, the object will still form a hand. Then move them all again, and a third time, and a fourth, etc. The question becomes: When are the particles too scattered to form a hand?

We find ourselves in a sorites paradox. There is no sharp cut-off where the particles n nanometers apart form a hand, but at n+0000,1 nanomets they seize to form a hand. So, according to Lewis and Sider, the criteria for restrictive composition would have to be vague. Furthermore, they both agree that ontic vagueness is simply untenable (this is an assumption, if you like ontic vagueness, you shouldn't be worried by the argument), so if there is any vagueness it has to be linguistic vagueness, i.e., vagueness owing to the terms involved in formulating the criteria. (Sider also brings up and rejects epistemicism as an answer (see Sider's book, pp. 130-132).)

However, to which terms should we attribute the vagueness? Lewis argues that all that is needed to formulate the criteria is classical first-order logic with identity and a special predicate for identity of overlap. But, Lewis claims, none of these terms are candidates for vagueness, thus there cannot be linguistic vaguness. Consequently, restrictivism is impossible. We are left with nihilism and universalism. Both are counter-intuitive positions, but Lewis and Sider opt for the latter (ibid., ch. 5.6 for the case against nihilism).

There are many weaknesses to the argument, and I will not list them here (although see the papers listed at the end). What I am interested in is the crux of the argument, namely the alleged non-vagueness of the terms listed by Lewis. Of course, some commentators prone to believe that logical terms (including identity) are non-vague, made the case for the vagueness of the notion of identity of overlap. This term is surely the weakest link in the argument, and Sider admits that this needs fixing. Fortunately, however, he has a brilliant way of embedding Lewis's claim into strictly logical language.

For, how we set the restrictions on composition will affect the overall number of objects in the domain. (The domain Sider has in mind is the quantication domain of the 'absolutely' unrestricted quantification. Whether such a quantifier can be stabilised is a widely debated topic. See here for a paper by Williamson and here for a paper by Rayo. Sider has responded to critics in the paper 'Against vague existence' here. See also a recent post by Carrie Jenkins.) More precisely, the number of simple objects (atomic, if you like) and the criteria for composition will determine the number of existing objects. Sider's idea is to argue that since the number of existing things (i.e., the size of the domain D) can be expressed in first-order logic with identity (but without the special predicate for identity of overlap), it cannot be vague. Because if it were, that would entail that some of the logical terms would be vague.

Assuming that Sider is right that logical terms are non-vague, it seems that he has entrenched Lewis's result. Restrictivsm fails, and the only options are nihilism and universalism. Personally, I think the issue hinges on whether Sider can make a convincing case for the non-vagueness of the quantifiers, something which rests heavily on the intelligibility of unrestricted quantification. This discussion, however, I will put off for some other time. The issue I want to raise, rather, is the relation between the formulation of the criteria for composition and the number of existing things. Why is that the indeterminacy transmits from the former to the latter?

Note first of all that this is not due to logical consequence. Although the number of existing things is a logical consequence of the number of simpels and criteria for composition, it is not in general the case that indeterminacy transmits through logically valid inferences. The most obvious examples are those in which the conclusion is a logical truth (and thus follows from anything, including vague premises). Of course, it is tempting to reply that in these examples the premises don't really do any work, while in Sider's argument they are crucial. However, by the model-theoretic definition of logical consequence, the number of existing things (in the unrestricted domain) is precisely an instance of a logical truth. (See Etchemendy 1990)

Nevertheless, our intuition still tells us that Sider is correct that vagueness will transmit from the number of simples and criteria of composition to the number of existing things. What is it then that ensures us of this. My best guess is that this is connected to mathematics rather than logic. Whereas the number of simples, being determinate, is non-vague, the criteria for composition is in a sense a (set-theoretically) fuzzy function. It takes a determinate number of things as functional argument but yields an indeterminate number of things as functional value.

This is just a proposal. In general I am interested in how indeterminacy transmits through arguments, so any comments would be appreciated. Here, as promised, is a list of relevant literature:

Achille C. Varzi 'Change, Temporal Parts, and the Argument from Vagueness', Dialectica, 59 (2005), 485-498 (preprint).

Daniel Nolan 'Vagueness, Multiplicity, and Parts', forthcoming in Noûs.

Daniel Z. Korman 'Unrestricted composition and the argument from vagueness' (unpublished).

Ned Markosian 'Two arguments from Sider's Four-Dimensionalism', Phil. and Phen. Research, 68 (2004), 665-673.

A more complete bibliography can be found in Korman's paper.


Categories: Philosophy, Logic, Metaphysics, Vagueness

News from Arché

Good news from Arché today: The new reseach project on epistemic warrant has received funding for three years.

Epistemic Warrant: Collaborative Research Project with the Australian National University and the University of Oxford. Crispin Wright (Arché), Daniel Stoljar (ANU) and Martin Davies (Oxford) have secured a Discovery Grant from the Australian Research Council for a three-year collaborative research project on Epistemic Warrant.

Good news for everyone at the St. Andrews department, and especially good news for those who are interested in epistemology.

Categories: Arché, Philosophy

Chess Oscar

Yesterday, Veselin Topalov, current FIDE Champion, received the Chess Oscar 2005. The Oscar is awarded annually to the player who gets the highest score from expert judges. Anand, the runner-up, wasn't even close to Topalov's remarkable score; but this is no surprise. Out of 361 scoregivers, 219 awarded Topalov the 1st place on their list; in comparison, Anand was 1st on 31 lists. As I've said before, this is truly Topalov's year.

So, rather than ranting on about his impressive performance, let us look at some other players. Levon Aronian makes a well earned appearance as no. 3, followed by Svidler and Leko. The two latter are frequent in this context, but Aronian is fresh blood on the list. The 3rd place is witness to the fact that after his victory in the Linares super-GM tournament, Aronian has settled himself in the top five. And, arguably, the Armenian GM still has a lot to prove. Incidentally, since he won the Championship Cup in Sibir a few months ago, he will have ample opportunity to do exactly that at the end of the year. He is set to meet GM Magnus Carlsen in the first candidate match.

And speaking about the young Wizard, guess who made it into the top 10 in the Oscar competition? For Carlsen, this is another astonishing feat, this time getting ahead of several other young super-GMs (e.g., such as Karjakin). That he is ranked fifty spots over his FIDE ranking shows the rampant expectations of the chess world. Luckily, he continues to live up to them: Today he won a one-on-one against dutch GM Loek van Wely. However, as much as I want to congratulate him on the win, I am anxious to see him play against better opposition, preferably someone in the top 10.


Categories: Chess