Between Logic and Intuition David Lewis and the Future of Formal Methods in Philosophy

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SYNTHESE ANNUAL CONFERENCE BETWEEN LOGIC AND INTUITION DAVID LEWIS AND THE FUTURE OF FORMAL METHODS IN PHILOSOPHY

INVITED SPEAKERS CONFERENCE CHAIRS Johan van Benthem John Collins Vincent F. Hendricks Alan Hajék John Symons Hannes Leitgeb Stig Andur Pedersen

Rohit Parikh CONFERENCE MANAGER L.A. Paul Pelle Guldborg Hansen

THE CARLSBERG ACADEMY COPENHAGEN OCTOBER 3-5, 2007 SYNTHESE AN INTERNATIONAL JOURNAL FOR EPISTEMOLGY, LOGIC AND PHILOSOPHY OF SCIENCE

Editors-in-Chief: Johan van Benthem Vincent F. Hendricks John Symons

The Synthese Annual Conference is sponsored by PHIS - The Danish Research School in Philosophy, History of Ideas and History of Science and Springer. 1 CONTENTS Between Logic and Intuition: David Lewis and the Future of Formal MethodsinPhilosophy...... 3 InvitedSpeakers...... 4 Speakers...... 4 GuestofHonor...... 4 Schedule...... 5 TitlesandAbstracts...... 6 ProgramCommittee...... 10 ConferenceChairs...... 10 ConferenceManager...... 10 Registration...... 10 ConferenceDinner...... 11 Sight-SeeingTour...... 11 Publication...... 11 ConferenceVenue...... 12 ConferenceHotel...... 14 Synthese...... 15 3 SYNTHESE ANNUAL CONFERENCE Synthese hosts its ﬁrst annual conference at the Carlsberg Academy in Copen- hagen, October 3—5, 2007. The conference is sponsored by PHIS — The Dan- ish Research School in Philosophy, History of Ideas and History of Science and Springer.

Cambridge Blue Pub in Cambridge, 2001. Photo by Hugh Mellor

Between Logic and Intuition: David Lewis and the Future of Formal Methods in Philosophy 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 benefitofsuchanapproachisreflected 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. 4

This ﬁrst Synthese Annual Conference is also the venue for discussing the future of formal methods in philosophy.

Invited Speakers John Collins (Columbia University) •

Alan Hajék (Australian National University) •

Hannes Leitgeb (University of Bristol) •

Rohit Parikh (CUNY Graduate Center) •

L.A. Paul (University of Arizona) •

Speakers Brit Brogaard and Joe Salerno (Australian National University) •

John Cantwell (Royal Institute of Technology, Sweden) •

Vladan Djordjevic (University of Alberta) •

Ulrich Meyer (Colgate University) •

Neil Tennant (Ohio State University) •

Guest of Honor Stephanie Lewis • 5 Schedule

Wednesday Thursday Friday October 3 October 4 October 5

09:00—9:30 Registration

09:30—9:45 Welcome Coﬀee Coﬀee

Chair Hendricks Symons Pedersen

09:45—11:00 Collins Leitgeb Hajék

11:00—11:15 Coffee Coffee Coffee

11:15—12:30 Tennant Cantwell Meyer

12:30—13:30 Lunch Lunch Lunch

Chair van Benthem Hendricks

13:30—14:45 Brogaard / Synthese Djordjevic Salerno Board Meeting [13:30—17:00] 14:45—15:15 Coﬀee Coﬀee Sight-Seeing Tour 15:15—16:30 L.A. Paul Parikh

16:30—16:40 Closing

19:00 Conference Dinner 6

David Lewis at the age of nine, teaching school to his younger siblings Ellen and Donald in their home in Oberlin, Ohio, in November of 1950. Courtesy of Stephanie Lewis.

Titles and Abstracts Formal and Informal Models of Belief / John Collins • David Lewis once fished an old offprint out of his filing cabinet for me, apologizing as he did so: “I’m sorry, this was published before I taught my- self how to write without using subscripts.” Technical notation is a familiar aspect of philosophy in the formal mode, but an inessential one. Lewis invented a non-technical way of writing formal philosophy, a prose style of a clarity that matched his thought. His philosophical writing is at once direct, unfussy, razor keen, colloquial, and jaunty. It is easy to overlook Lewis’s considerable literary achievement; the later papers and monographs are no less “formal” for the lack of subscripts. Lewis once described decision theory as “a systematic exposition of the consequences of ceratin well-chosen platitudes about belief, desire, preference and choice ... the core of our common-sense theory of persons, dissected out and elegantly systematized.” This passage says much about Lewis’s own approach to the philosophical enterprise. The present paper examines formal and informal accounts of the concept of belief. 7

Lewis Meets Hegel: A Tribute to David Lewis, and Two Dialectics on • Formal Methods/ Alan Hajék This talk is partly a tribute to David Lewis, partly a homily on the value of formal methods in philosophy. I will begin with some fond personal reminiscences of David. I will then give a brief intellectual biography of him, tracing some of his main influences, especially with an eye to his use of formal methods, which was exemplary. This will segue to more general reflections on the value of such methods, presented in the form of two dialectics (complete with thesis, antithesis, and synthesis), and laced with frequent references to David’s work. A Probabilistic Semantics for Counterfactuals / Hannes Leitgeb • It is suggested that subjunctive conditionals obey a probabilistic semantics. This semantics is made precise and studied in three different versions which are related to each other by means of representation theorems. The results of this investigation are used to shed light on two philosophical theses: (i) Most counterfactuals are false (as claimed by Hawthorne and Hájek). (ii) The conditional analysis of dispositions is bound to fail (as claimed by Martin and Bird). Sentences, Propositions, and Group Knowledge / Rohit Parikh • The current period in formal epistemology begins with two books. One by Hintikka on Knowledge and Belief,andonebyDavidLewisonConvention. While both of these sources have been tremendously valuable, they have also raised some issues which have been largely left to one side. One is the issue of logical omniscience, according to which agents know all logical truths and all consequences of what they know. These assumptions do not seem valid, and in certain colloquial senses of the word "know" they are obviously false. A second issue is that of common knowledge, a notion invented by Lewis, and independently by Schiffer. This notion is supposed to explain co-ordinated action, whether in terms of common understanding of a sentence, or two agents playing the same Nash equilibrium. But again the notion is quite implausible, because it requires finite minds to entertain an infinite hierarchy of statements like "i knows that k knows that p knows that it is raining." There are other strains, like Frege’s problem raising the issue of whether a person who knows that the Evening Star is shining also knows that the Morning Star is. And finally there is the issue of what it is that animals (if we disagree with Descartes that they are not mere au- tomata) know or believe. Actually all these strains can be brought together into a single comprehensive, and even simple framework hich relates to the ideas of Ramsey, Savage and Hayek. We will explain what it is. 8

Puzzles with Preemption and Overdetermination / L.A.Paul (University • of Arizona) I critically examine some of the methods employed by Lewis and others in interpreting and responding to counterexamples to counterfactual analyses of causation.

Princeton University, 1998. Courtesy of Stephanie Lewis.

Remarks on Counterpossibles / Brit Brogaard and Joe Salerno • Subjunctive conditionals with impossible antecedents (or counterpossibles) are standardly treated as vacuously true–the classical lore being that if an impossibility were to obtain, anything would follow. We however oﬀer and defend a non-vacuous reading of some counterpossibles. An advantage to the approach is that allows us to capture the intuitive diﬀerence between essence and necessity.

Can Conditionals Play a Role in Causal Decision Theory? / John Cantwell • The question whether conditionals can play a role in Causal Decision The- ory (CDT) is reopened. A semantics for the indicative conditional in a branching-time framework is proposed. It is then showed that such a conditional is suitable for a version of CDT given in terms of probabilities of conditions. The semantics builds on, and reﬁnes, familiar ideas of David Lewis, Robert Stalnaker and Richard Thomason and Anil Gupta. It is argued that the semantics has an independent linguistic plausibility. It is 9

also shown how the basic framework can be extended with operators such as “It is possible that A” and “The objective chance that A is x”andthat these operators interact in a natural way with the indicative conditional. Similarity and Cotenability / Vladan Djordjevic • This is an investigation into the relation between the two notions. It results in a counterexample to Lewis’s theory. The counterexample is meant to show that absolute similarity, which is a crucial notion of the theory, leads to unsolvable problems. Modal Comprehension / Ulrich Meyer • To define new property terms, we combine already familiar ones by means of certain logical operations. Given suitable constraints, these logical operations may presumably include the resources of standard first-order logic: truth-functional connectives and quantification over objects. What is less clear is whether we can also use modal operators for this purpose. This paper clarifies what is involved in this question, and argues in favour of modal property definitions. Parts, Classes and Parts of Classes / Neil Tennant • This study is in two parts. In the first part, various important princi- ples of classical extensional mereology are derived on the basis of a nice axiomatization involving ‘part of’ and fusion. All results are proved here with full Fregean (and Gentzenian) rigor. They are chosen because they are needed for the second part. In the second part, this natural-deduction framework is used in order to regiment David Lewis’s justification of his Division Thesis, which features prominently in his combination of mereology with class theory. The Division Thesis plays a crucial role in Lewis’s informal argument for his Second Thesis in his book Parts of Classes. In order to present Lewis’s argument in rigorous detail, an elegant new principle is offered for the theory that combines class theory and mereology. The new principle is called the Canonical Decomposition Thesis. It secures Lewis’s Division Thesis on the strong construal required in order for his argument to go through. The exercise illustrates how careful one has to be when setting up the details of an adequate foundational theory of parts and classes. The main aim behind this investigation is to determine whether an anti-realist, inferentialist theorist of meaning has the resources to exhibit Lewis’s argument for his Second Thesis–which is central to his marriage of class theory with mereology–as a purely conceptual one. The formal analysis shows that Lewis’s argument, despite its striking appearance to the contrary, can be given in the constructive, relevant logic IR.Thisis the logic that the author has argued, elsewhere, to be the correct logic from an anti-realist point of view. The anti-realist is therefore in a position to regard Lewis’s argument as purely conceptual. 10 Program Committee Johan van Benthem (University of Amsterdam / Stanford University) • Horacio Arlo-Costa (Carnegie Mellon University) • Vincent F. Hendricks (Roskilde University) • John Symons (University of Texas at El Paso) • Stig Andur Pedersen (Roskilde University) • Conference Chairs Johan van Benthem ([email protected]) • Vincent F. Hendricks ([email protected]) • John Symons ([email protected]) • Stig Andur Pedersen ([email protected]) • Conference Manager Pelle Guldborg Hansen ([email protected]) • Registration Please write conference manager Pelle Guldborg Hansen to register:

Department of Philosophy and Science Studies Roskilde University, P6 P.O. Box 260 DK4000 Roskilde, Denmark Phone: (+45) 4674 2540 Cell: (+45) 2334 2175 Fax: (+45) 4674 3012 Email: [email protected]

A conference fee is to be paid cash upon finalregistration(Wednesday,October 3, 2007). The conference fee is 150,00 Danish kroner a day, thus participation for the entire duration of the conference (Thursday, October 3 — Saturday 5, 2004) is 450,00 Danish kroner. The conference fee covers the lunches with free beverages, conference booklet, tea and coffee during the breaks. NOTICE: Please remember exact amount. Deadline for registration Monday, October 1, 2007. If email is used include ‘SAC 2007’ in the subject entry. All questions per- taining to registration and accommodations should be directed to Pelle Guldborg Hansen. 11 Conference Dinner A conference dinner is scheduled for Thursday, October 4 at 19:00,Restau- rant Madklubben in the center of Copenhagen. The dinner costs 400,00 Dkr and includes a three course meal and wine. Only a limited number of seats is available. More detailed information on this arrangement will be available at the conference. Participants interested in conference dinner participation should notify Pelle Guldborg Hansen no later than Monday morning, October 1, 2007.Please let it be known whether you are vegetarian. Only cash payments are accepted and no later than upon final conference registration during Thursday, October 3. Undue cancellation of participation or conference dinner orders is subject to full charge.

Sight-Seeing Tour A sight-seeing tour of either Copenhagen or the Carlsberg brewery (depending on the weather) is planned for Thursday, October 4. The tour will cost 50,00 Dkr which includes transportation, guides and passes. Signing up for the tour is, as for the lunch and dinner arrangements, no later than Monday, October 1, 2007, and payment is due no later than upon ﬁnal registration. Notice: Again, please remember exact amounts.

Publication A selection of the best papers will be published as an anthology in the Synthese Library book series as Between Logic and Intuition: David Lewis and the Future of Formal Methods in Philosophy, edited by Johan van Benthem, Vincent F. Hendricks, John Symons and Stig Andur Pedersen. Dordrecht: Springer, 2008. Preliminary Table of Contents

Introduction / Johan van Benthem, Vincent F. Hendricks, John • Symons and Stig Andur Pedersen

Invited papers

Formal and Informal Models of Belief / John Collins • Lewis Meets Hegel: A Tribute to David Lewis, and Two Dialectics on • Formal Methods / Alan Hajék

A Probabilistic Semantics for Counterfactuals / Hannes Leitgeb • Sentences, Propositions, and Group Knowledge / Rohit Parikh • Puzzles with Preemption and Overdetermination / L.A.Paul • Submitted papers 12

Remarks on Counterpossibles / Brit Brogaard and Joe Salerno • Can Conditionals Play a Role in Causal Decision Theory? / John Cantwell • Similarity and Cotenability / Vladan Djordjevic • Modal Comprehension / Ulrich Meyer • Parts, Classes and Parts of Classes / Neil Tennant • Submitted papers (not presented) Social Goals / Giulia Andrighetto • On counterfactuals, indeterminism, and quantum mechanics / Tomasz • Bigaj Imaging, Recognizing and Diﬀerentiating / Bence Nanay • How to Lewis a Kripke-Hintikka / Alessandro Torza • Index Conference Venue The conference venue is Niels Bohr’s honorary mansion at The Carlsberg Academy Gamle Carlsberg Vej 15 DK2500 Valby

The Carlsberg Academy – garden view 13

One may find it difficult to enter the Carlsberg Academy. This is due to the fact that the Academy is located on the compound of the Carlsberg Brewery, which is a declared ‘customs free area’. Thus the area is usually not accessible to the public. The entrance for conference site is in circled in blue below. When you arrive you will have to pass two gates. In order to do this you will have to press the code ‘B0052’ on the intercom at each gate (unless otherwise stated on these). You will then have to await the conference staff letting you in to the compound. This will most probably be a procedure to be followed each time entering and leaving the Academy, why it s obviously a good idea to come on time. Please be patient and repeat the procedure until you are let in, though. The staff might be juggling the morning coffee and Danish while also handling the intercom.

Map of the Carlsberg Academy 14 Conference Hotel

Comfort Hotel Espladen, Copenhagen

TheconferencehotelfortheSynthese Annual Conference is Comfort Hotel Esplanaden Bredgade 78 Copenhagen, Denmark K 1260 Phone: (45) 33 48 10 00 Fax: (45) 33 48 10 66 Website: www.choicehotels.dk/hotels/dk007 Please contact Director Henriette Kibsgaard ([email protected]) for booking. Reduced rates available for conference participants. 15 Synthese An International Journal for Epistemology, Methodology and Philosophy of Sci- ence

Editors-in-Chief

Johan van Benthem • Vincent F. Hendricks • John Symons • Area Editors Computability and computer science / Luciano Floridi Epistemology / Horacio Arló-Costa History of early analytic philosophy / Paolo Mancosu Language and linguistics / Robert van Rooij Logic and mathematics / Gabriel Sandu Metaphysics / Achille Varzi Methodology and general philosophy of science / Paul Humphreys Psychology and neuroscience / John Bickle Social philosophy and the social sciences / Raymond Dacey Technology, biology and artiﬁcial life / Mark Bedau

Synthese publishes articles in all the fields covered by the subtitle. These include: the theory of knowledge; the general methodological problems of science, such as the problems of scientific discovery and scientific inference, of induction and prob- ability, of causation and the role of mathematics, statistics and logic in science; the methodological and foundational problems of different sciences. Insofar as they have philosophical interest: those aspects of symbolic logic and of the foundations of mathematics which are relevant to the philosophy and methodology of science; and those facets of the ethics, history and sociology of science which are important for contemporary topical pursuits. Special attention is paid to the role of mathematical, logical and linguistic methods in the general methodology of science and the foundations of the different sciences.

Special section Knowledge, Rationality and Action,editedbyWiebe van der Hoek. The aim of the section is to provide a platform for researchers interested in a formal approach to the process comprising rational behaviour: from gathering and representing information, via reasoning and decision making up to acting. Consequently, the journal will address topics related to: 16

Knowledge — Gathering information, reasoning about knowledge, belief, • uncertainty, and information about changing situations: belief revision and updates, dynamics epistemic logic, security and authorisation. Rationality — Decision making, bounded rationality and resource bounded • reasoning, optimal and satisfycing behaviour, preferences, cooperative and competitive behaviour, logic and game theory, solution concepts of games, computational models of rational behaviour, planning, theories of norms. Action — Theories of action, theories of belief and action, rational agency, • social structures, logic for action and change, sensing, temporal reasoning, re-planning, veriﬁcation of dynamic systems, logic programming, the frame problem, action and cognition.

The scope of Knowledge, Rationality and Action is interdisciplinary: it will be of interest to researchers in the ﬁelds of artiﬁcial intelligence, agents, computer science, knowledge representation, game theory, economics, logic, philosophy, mathematics, cognitive science, cryptography, and auction theory, as well as to application specialists using formal and mathematical methods and tools.

Abstracted/Indexed in: Academic Abstracts, Arts & Humanities Citation In- dex, Current Contents/Arts and Humanities, Current Index to Statistics, Family & Society Studies Worldwide, Internationale Bibliographie fur Österreichische Philosophie, ISI Alerting Services, Linguistics and Language Behavior Abstracts, Mathematical Reviews, MLA International Bibliography, Referativnyi Zhurnal, SCOPUS, Social Science Citation Index (SSCI), Social SciSearch, Sociological Abstracts, Zentralblatt Math.

ISSN: 0039-7857 (print version) ISSN: 1573-0964 (electronic version) Journal no. 11229 Springer Netherlands

The Synthese Annual Conference is jointly sponsored by PHIS — The Danish Re- search School in Philosophy, History of Ideas and History of Science and Springer. c 2007 Johan° van Benthem, Vincent F. Hendricks, John Symons, Stig Andur Pedersen and Springer http://www.springer.com/journal/11229