|Friday, Dec 8 |
|14.30–16.30||Friedericke Moltmann: “ ‘The Number of Planets’ ”|
|16.30–17.00||Tea and Coffee|
|17.00–19.30||Symposium: Higher-Order Logic |
|Saturday, Dec 9 |
|10.00–12.30||Symposium: Implicit Defintions |
|13.30–16.00||Symposium: Impredicativity & Bad Company |
|16.00–16.30||Tea and Coffee|
|16.30–19.30||Extensions to Real and Complex Analysis and Set Theory |
with: Jeffrey Ketland, Paul McCallion, Peter Simons, Robert Williams
Stewart Shapiro on Set Theory
|Sunday, Dec 10 |
|10.00–12.30||Conspectus Round Table & Neo-Fregean Responses |
with responses by Bob Hale and Crispin Wright
|12.30||End of the workshop|
Sunday, November 26, 2006
John Hawthorne 'Epistemic Modals'
Martin Davies 'Two Purposes of Arguing and Two Epistemic Projects'
Duncan Pritchard 'Knowledge and Value'
Timothy Williamson 'Knowing When You Probably Don't'
Jason Stanley 'Knowledge and Certainty'
Although there was certainly enough post-worthy talks (and responses) at the workshop, I've chosen to write about Besson's paper. Not only was the talk quite impressive, it also helped me find some crucial connections between my own work with proof-theoretic semantics and more or less free-floating epistemological considerations I've been entertaining about logic. One Quinean concession is called for immediately: I'm certainly no champion of epistemology, meaning that not only do I have many half-digested beliefs about epistemological problems, but hopefully I also still have some pre-theoretic intuitions left (although nothing rests on this). So, I cannot pretend to give full justice to the epistemological debate that Besson's paper touches on - I'll more or less confine myself to presenting the basics of her talk, and then relating it to some issues in the philosophy of logic. I also want to mention briefly that Elia Zardini gave a brilliant response to Besson, emphasizing several of the worries that I myself had with the argument. I hope to outline some of these thoughts as well, with appropriate acknowledgement of Elia's six page handout(!).
Here is the aim of Besson's paper as formulated in the handout: "Show that the possibility of constructing Gettier cases for the a priori knowledge of logical rules refutes what I call the 'Understanding Account' - according to which a priori knowledge of a basic rule of logic is grounded on semantic or conceptual understanding."
I'll just assume that my readers are familiar with Gettier cases, and focus on the speical case of Gettiered logical knowledge. First, however, let me briefly say something about the so-called Understanding Account (UA). UA appears in the talk as a rather broad position (as many of the commentators pointed out), and it is associated with philosophers such Boghossian, Peacocke, Wright and Hale. A good place to look up the details of their positions would be the following volume on the A Priori, New Essays on the A Priori, eds. Boghossian & Peacocke. The central claim that Besson attaches to this position is from Boghossian: 'A statement is 'true by virtue of its meaning' provided that grasps of its meaning alone suffices for justified belief in its truth.' ('Analyticity Reconsidered', Noûs 30, 1996: p. 363. An aside: Carrie Jenkins has a new paper on Boghossian here.). This paper is a famous attempt at revitalizing the notion of analyticity after the Quinean onslaught. The above claim, however, attaches these considerations about meaning and analyticity directly to epistemic concepts, i.e., justified belief and understanding. When applied to logic, the idea is that grasping some logical rules is sufficient for having a priori knowledge that they're valid. Unsurprisingly, the rules thought to display this epistemic property are the so-called meaning-conferring rules, say, introduction-rules for classical connectives, e.g., implication-introduction. Besson's wants to show that by introducing an element of luck, also logical cases of this can be Gettiered so as to take apart knowledge (in this case apriori) from true, justified belief.
Here is the example reworked in my words. Say that two language users, Jean-Yves and Alfred, have a conversation about logic. It turns out that Alfred has no notion of material implication, so Jean-Yves sets out to help him with the concept. However, being something of a trickster, Jean-Yves wants to have some fun with Alfred: introducing the material implication by perverted rules, say rules that allow for affirming the consequent. But, as luck would have it, the proverbial "strange atmospheric conditions" interfere so that when Jean-Yves presents his perverse rules, what he actually gives Alfred is the correct rules for material implication. Now, on the Gettier analysis, the idea is that Alfred, going on to use material implication to everyone's satisfaction (well, perhaps not to Jean-Yves's, the trickster's, satisfaction) has a true, justified belief, but it still isn't knowledge. The intuition is, I gather, that just minor changes to the situation (i.e., in a close world with normal atmospheric conditions) would have led to Alfred applying the perverse rules, thus failing to grasp the concept.
What is the upshot if the Gettier example goes through? The UA is Gettiered in the sense that the example puts a wedge in between justification and knowledge: grasping the rule isn't sufficient for knowledge, it's only sufficient for justification. Let me couch this in langauge a bit closer to my own my own field of study. The idea advocated by for example Dummett and Prawitz was that the introduction-rules had a special status; not only did they confer meaning to the involved logical constant, since they had this definitorial feature they were also self-justificatory. Although Dummett never wrote explicitly about these epistemological issues, it seems fair to assume that he would assent to expanding this talk into talk about subjective justification, that is, if someone grasps the self-justificatory rule she/he has immediate justification. If anyone has references to passages where Dummett talks directly about knowledge of logic in this context, I would be glad to know. Because, undoubtedly, there is a temptation to go on to claim that the self-justificatory nature of the rule makes it a candidate for a priori knowledge. It is this move, however, that is denied by Besson.
To evaluate precisely how Besson's point affects UA is not all that easy. In fact, as I myself suspected, and Elia pointed out in the response, it is not all clear that the proponents of UA are at talking about knowledge; most of the discussion turns around justification (Elia also adds, or entitlement). Granted, for all I know the discussion by Boghossian et al. might be confused on whether or not knowledge is involved, but perhaps they can recourse to just claiming that justification is what they want. The important point for me to make, at any rate, is that for proof-theoretic semantics, nothing obviously hinges on knowledge. For both inferentialism and the larger project of a proof-theoretic account of logical consequence, it suffices that our grasping of the rules is tied up with justification (what has been at stake has always been 'justification of deduction', not 'knowledge of deduction'). By attaching these logical concepts to justification (or entitlement), the prospect is that we end up with a semantics sensitive to the connection between epistemology and language - precisely what Dummett worried that the classical account lacked (I'm thinking about manifestation and aquisition here).
Furthermore, both Elia and John Hawthorne stressed that Besson's argument failed to make some important distinctions between knowing-that and knowing-how, or more precisely, belief in a logical statement and behaviour according to a logical practice. It is unclear that logical knowledge could consist in anything else than the type of competence that Alfred, in the above example, undeniably displays after grasping the rules. If such distinctions could be employed to refute Besson's argument, then perhaps UA propoenents and, thus, proof-theoretic semanticists could incorporate knowledge of logic into their theory after all.
As a final remark, I think it is decisive to appreciate that for proof-theoretic semantics, the notion of proof is first and foremost a justificatory notion, and only secondly related to knowledge.
Saturday, November 25, 2006
Synthese - An International Journal for Epistemology, Logic and Philosophy of Science hosts its first annual conference at the Carlsberg Academy in Copenhagen, October 3- 5 , 2007. The conference is sponsored by PHIS - The Danish Research School in Philosophy, History of Ideas and History of Science and Springer.
Title / Between Logic and Intuition: David Lewis and the Future of Formal Methods in Philosophy
Abstract / David Lewis is one of the most important figures in contemporary philosophy. His approach balances elegantly between the use of rigorous formal methods and sound philosophical intuitions. The benefit of such an approach is reflected in the substantial impact his philosophical insights have had not only in many core areas of philosophy, but also in neighboring disciplines ranging from computer science to game theory and linguistics. The interplay between logic and intuition to obtain results of both philosophical and interdisciplinary importance makes Lewis' work a prime example of formal philosophy. Lewis' work exemplifies the fruitful interplay between logic and intuition that is central to contemporary philosophy. This conference serves as a tribute to Lewis and as a venue for adressing questions concerning the relationship between logic and philosophical intuition. This first Synthese Annual Conference is the venue for discussing the future of formal methods in philosophy.
Invited Speakers / John Collins, Alan Hajek, Hannes Leitgeb, Rohit Parikh, L.A. Paul, Brian Weatherson
Program Committee and Conference Chairs / Johan van Benthem, Vincent F. Hendricks, John Symons (SYNTHESE) , Stig Andur Pedersen (PHIS)
Conference Manager / Pelle Guldborg Hansen
Call for papers / Synthese invites papers on the work of David Lewis and formal philosophy in accordance with the conference abstract. The final papers should be sent electronically to Editor-in-Chief, Vincent F. Hendricks at firstname.lastname@example.org, using "SAC"-submission in the subject entry. The deadline for submitting a paper for consideration is April 1, 2007. Notification of acceptance for presentation at the conference is August 1, 2007.
Publication / A selection of the best papers will be published as an anthology in the Synthese Library book series.
Thursday, November 23, 2006
The Graduate Conference was a definite success: smoothly administered and with some excellent talks. Thanks to both the organisers and the speakers for an interesting weekend. Unfortunately, I didn't have time to go to all the talks, so I can't give any complete report. All I want to do is mention two talks in particular: Dilip Ninan's (MIT) 'Imagination: Inside and out' and Pablo Cobreros's 'Supervaluation and Logical Consequence' (at the moment, both talks are available here). The former offered us an insight into the semantics of imagination reports, turning on the distinction between 'imagining from the inside' and 'imagining from the outside'. An aside: To my surprise it was established, contrary to what I used to believe, that I cannot imagine myself to be Napoleon 'from the outside'. Well, that is, assuming that I'm not actually Napoleon. Some dreams are hard to maintain, I guess.
Cobreros's claim was that the supervaluationist (see here if you're unfamiliar with the position) could recourse to local validity (i.e., standard validity for modal logics), rather than opting for global validity, i.e., A is a global logical consequence of Gamma iff for all structures, if for every world w, all the gamma in Gamma are true in w, then A is true in w. Famously, Williamson argued in his book that due to the supervaluationists' equation between truth and supertruth, the local validity didn't work since it preserved truth, not supertruth. Equally famously, Williamson then went on to present a range of difficulties for supervaluationism cum global validity. To avoid difficulties connected to this globality, but still preserve the spirit of supervaluationism, Cobrero submitted another alternative: regional validity.
- A is a logical consequence iff for all structures, for all worlds: if every world w' s.t. wRw', all members of Gamma are true, then for every world w' s.t. wRw', A is true.
After spending over a year in St. Andrews, I've learned that giving vagueness talks in this town is never easy. There's a lot of competence on the field because of the Arché project, so any claim about vagueness will meet with massive resistance from the local faculty. And, as a matter of fact, Cobrero's proposal proved to be not all that popular either. Firstly, Shapiro, who was the designated respondent, raised a worry about the conceptual content of regional validity. It might prove difficult to provide a notion of validity relativized to admissible sharpenings a plausible story that fits the (supervaluationist) intuitions about vagueness. Secondly, Priest noted that some of the technical results, more precisely the validity of the inference 'phi |- D(phi)', hinged on the logic being single-conclusion. Thirdly, Elia Zardini suggested that the alleged solution to the paradox of higher-order vagueness had more to do with the mode of presentation in the Graff formulation, than with the actual intuition driving the paradox. Read more here.
Graham Priest also had an entertaining talk about logic for relativism. Not himself a relativist (Priest is accused of being many strange things which he's not), Priest gave a seven-valued (!) logic in an attempt to solve some traditional worries for the relativist: (i) the self-refutation problem, that is, the relativist's own position appears to be absolute, but ex hypothesi it cannot be; (ii) the relativist must relativize all claims with something like a 'from a perspective it is the case that...' operator, but even claims with the operator must be relativized, so we're thrown into an infinite regress. Since I don't have notes nor a handout from the talk I can't provide any details here. However, Carrie Jenkins has an interesting post on the second problem.
Wednesday, November 22, 2006
Herman Cappelen, Norwegian philosopher of languge, currently Fellow of Somerville College, Oxford, just accepted an offer from Arché. There are two immediate consequences: (i) the philosophy of language part of Arché will be significantly strengthened, and the relativism seminar has a new spearhead member; (ii) I am no longer the only Norwegian Archean. We all know they only want us because of the oil money, but it's still flattering.
Cappelen is co-author of Insensitive Semantics together with Ernie Lepore. Here is some further information about Cappelen, together with a list of publications. The announcement on Leiter Reports is here.
Saturday, November 18, 2006
The last two weeks, Moscow has been the scene for a category 20 GM tournament commemorating Mikhail Tal. Although none of the top three participated (Topalov, Anand, Kramnik), the event had an impressive starting line: Svidler, Morozevich, Mamedyarov, Shirov, Gelfand, Aronian, Leko, Grischuk, Ponomariov, and our very own Carlsen. It's been some time since I last wrote about the 15-year old Norwegian super-GM, so let me remind the readers: still a young teenager, the Mozart of chess ("official" nick name) is now among the top 25 chess players in the world, and still climbing. He is also qualified for the candidate matches to play for the FIDE title (now held by Kramnik) in the 2007 cycle, where he is to face Aronian (that is, if FIDE ever gets around to sponsoring these matches).
So, back to the tournament. Why haven't I written about it so far? To be honest, the chess played just haven't been that inspiring. In fact, there was a 69% draw rate, three joint winners at the modest +2 score, and a rather depressing performance by Magnus Carlsen. Altogether, not the kind of chess I care to write about. That being said, there was of course some good fighting chess; it just rarely ended in anything conclusive. Nevertheless, even if I could forgive the players for trying and failing, the scandalous last day of the tournament merely emphasized my antipathy. Why would every single player decide that the last day, when everything is up for grabs (with a multitude of players having good practical chances of winning), to take the day completely off, and offer an yawn-provoking draw before move 25? At any rate, let me en passant mention that the three winners were Aronian, Leko, and Ponomariov. I don't know how the tie break is, and, quite frankly, I couldn't give a damn.
Over to GM Carlsen. According to Chessbase, Carlsen's explicit aim for the tournament was to win one game. Although he was the only player ranked below 2700, this was a rather modest goal, not characteristic for the ambitious youngster. And perhaps it jinxed him, because he certainly didn't achieve his one win - indeed, three losses and the rest draw landed him behind everyone but Morozevich (number five in the world, but known as a very unstable player). Of course, it would be a bit optimistic to hope that Carlsen would win or even come close in a category 20 tournament, but we're just all so spoiled by his achievements. Moreover, if he wants to make it in the candidate matches, he has to do a lot better than this. The blundered loss against Aronian was a taste of what he' s up against when he meets the Armenian again in a one-on-one.
Fortunately for Carlsen, he's not out of opportunities: today the Blitz part of the tournament is starting, where he is automatically ready for the final together with the rest of the original field and invited players Anand, Karpov and Polgar. Anand is, of course, the top seed for the Blitz part, but as some of you probably remember, Carlsen defeated Anand in a blitz game not long ago.
Posted by Ole Hjortland at 8:32 am
Friday, November 03, 2006
Through LogBlog, I just learned that Leon Henkin, esteemed logician, died earlier this week on the 1st of November. Leon Henkin was known for several important contributions to mathematical logic, among them Henkin-completeness, a variant of Gödel's famous proof, and Henkin-semantics, a non-standard semantics for second-order logic.