2-4 September 2010, British Logic Colloquium (BLC 2010), Birmingham, U.K.

The British Logic Colloquium exists to support, promote, and foster the study of logic (especially, but not exclusively, formal and mathematical logic) in Britain. It embraces diverse aspects of logic, from the studies of traditional formal systems to philosophical logic and the modern applications in artificial intelligence, computer science and linguistics; above all, it aims to encourage communication between logicians working in related fields.

The annual meeting of The British Logic Colloquium will take place from
2-4 September 2010 in Birmingham. The aim of this meeting is to present current topics in all areas of logic. BLC 2010 is supported financially by the London Mathematical Society and by the British Logic Colloquium.

The workshop featured the following speakers and talks:

David Christensen (Brown) “Rational Reflection”
The main question of the paper concerned the relationship between what it is rational for one to believe and what it is rational for one to believe about what it is rational for one to believe. Christensen approached the issue mainly in the context of graded belief.  He formulated a rational reflection principle: Cr (A/Pr(A)=n)=n, where Cr stands for the agent’s credences, and Pr stands for the credences that would be maximally rational for someone in that agent’s epistemic situation. Christensen showed how this prima facie plausible principle leads to some puzzling results and explored a number of different reactions to the puzzling cases.

Peter Milne (Stirling) “Belief, Degrees of Belief, and Assertion”
On the basis of an in-depth discussion of the role of assertion and the relationship between assertion and belief, Milne went on to discuss two puzzling issues: The first concerned the assertion of indicative conditionals.   Much recent research in the psychology of reasoning supports two theses: that people ascribe to the indicative conditional the so-called “defective truth-table” in which an indicative conditional with false antecedent is deemed neither true nor false; and that people assign as probability to an indicative conditional, the (conditional) probability of consequent conditional upon antecedent.  The second issue Milne discussed concerned the relationship between assertion and degrees of belief. Certain well known cases suggest that a high degree of belief is neither necessary nor sufficient for a willingness to assert.

Brian Weatherson (Rutgers/Arche) “Rational Belief and Rational Action”
Weatherson discussed the principle, defended by Jeremy Fantl and Matthew McGrath, that if S’s belief that p is justified, then it is permissible for S to use p as a premise in practical reasoning. Weatherson argued that the principle is false. In cases where the agent has some rational beliefs and some irrational beliefs, it might be that justification is insufficient to ground action. Weatherson went on to discuss a novel suggestion regarding the relationship between rational beliefs and rational degrees of belief.

Alan Hájek (ANU) “Staying Regular”
Hájek first reviewed several arguments for regularity as a norm of rationality. There are two ways an agent could violate this norm: by assigning probability zero to some doxastic possibility, and by failing to assign probability altogether to some doxastic possibility. Williamson and Easwaran have argued forcefully that the former kind of violation may be unavoidable. Hájek’s discussion focused on violations of the second kind. Both kinds of violations of regularity have serious consequences for traditional Bayesian epistemology, in particular conditional probability, conditionalization, probabilistic independence and decision theory.

Carl Hoefer (Barcelona) “Connecting Objective and Subjective probability:  How to Justify the Principal Principle”
Hoefer focused on David Lewis’s Principal Principle and the claim that “Truth is to belief as agreement with objective chance is to degree of belief.”
The plausibility and defensibility of these theses depend, clearly, on how we understand objective chance.  The paper introduced an account of objective chance: a Humean/reductive account closely related to Lewis’ own.  One of the key virtues of this account of chance is that it allows us to demonstrate that the PP is indeed a requirement of rationality. Hoefer also argued for a second thesis on which agreement with actual frequencies, rather than chances, serves as the core virtue for degrees of belief.

Branden Fitelson (Berkeley) & Kenny Easwaran (USC) “Partial Belief, Full Belief, and Accuracy-Dominance”
The paper had two main aims: (1) to make some (cautionary) remarks about the set-up and interpretation of some recent accuracy-dominance based arguments for probabilism (with respect to partial beliefs), and (2) to discuss some interesting (formal and informal) analogies (and disanalogies) between partial belief and full belief, when it comes to the phenomenon of accuracy-dominance. In particular, Fitelson and Easwaran discussed the case of an extremal agent (who can only assign degrees of belief 0 or 1) and showed that there are non-probabilistic extremal functions that are not even weakly dominated by any probabilistic extremal function (using the Brier score).

Philip Ebert & Martin Smith

Opening the conference, Hans Kamp (University of Stuttgart) tackled the issue of the relation between mental representations and meaning of utterances and discourse. Successful communication is based on similarity between the mental representations of the utterer and of the audience, i.e. on a shared understanding of the relation between words and thoughts. However, Hans elaborated on the crucial fact that, in order to obtain successful communication, background information has to be commonly understood and represented as well. Paul Egre (Institute Jean Nicod, Paris) reported on work on vagueness led in collaboration with Pablo Cobreros (Navarra), David Ripley (IJN) and Robert van Rooij (ILLC Amsterdam). The semantic framework put forth by Paul accounts for the principle that, if x is P, then y is also P if y is similar enough to x. To account for the principle, classical truth nicely interacts with two further notions of consequence defined in terms of the classical one. The semantic framework provides a solution of the sorites paradox and its relation to paraconsistent truth was discussed. In his contribution, Wilfried Sieg (Carnegie Mellon University) investigated the inner workings of the mathematical mind by looking at the relation between mathematical arguments and rigorous proofs. The analysis was tackled from the points of view of (abstract) axiomatic method, on the one hand, and (concrete) proof construction as directed by proof theory, on the other, providing a rich picture that touched on computer and cognitive science alike. Rohit Parikh (City University of New York) talk on “Behavior and Belief” offered a new perspective on realistic formal models for epistemic reasoning. The desideratum is a notion of belief that does not entail logical omniscience and that can accommodate, among other things, the inconsistencies and incompleteness characterizing human epistemic performance. Rather than tweak existing systems of epistemic and doxastic logic, Rohit proposes to adopt a “Ramseyian” approach, deriving belief from observed behavior and agents’ perferences. The talk explored three ways in which agents revise their belief ascriptions: through observed actions, heard sentences and performed inferences. The multi-agent case was also tackled in the talk. Questions pointed out possible asymmetries between behavior-based attributions and actual mental states, also due to the complexity of interpretation of behavior as in case, for instance, of the conjunction fallacy. Brian Skyrms (UC Irvine and Stanford University) presented new work on “The concepts of information and deception in signaling games.” Adding probabilities to standard Lewisian signaling games (and leaving open its intended interpretation), Brian analyzed of the informational content of signals according to the intuition that a signal is informative insofar as it moves the probability of states. After discussing examples, the talk went on to cover deception. Contrary to Kant’s claim that universal deception is self-contradictory or practically impossible, Brian showed there are signaling games in which all players saying ‘half-truths’ (interpreted as partial pooling of states in one signal) constitutes an equilibrium. Questions revolved around the measure used for the informativity of signals and the relationship between the dynamics of signaling and information flow in networks. Oliver Schulte (Simon Fraser) gave a talk on his recent research on relational (as opposed to single-table) data. To account for relational data tables, Oliver uses parametrized Bayes nets where nodes are construed as functions. After describing the hurdles faced by knowledge-based  models constructed on such machinery, and explained how Markov logic networks can overcome them, Oliver described a very fast and accurate new algorithm for learning causal graphs in such models. In his dense philosophical talk, James Woodward (University of Pittsburgh) investigated the relationship between two accounts of causation, dubbed “geometrical” (think collisions, pushing etc.) and “difference-making” (comparative, counterfactual-based). The connectedness necessary to the GM account is not necessary for DM, and it is also not sufficient (a physical connection is not enough). Experiments about perception of causal link were also reported.

Stephan Hartmann (University of Tilburg) opened the second day with a provoking Bayesian account of confirmation and reduction. Stephan offered a Bayesian formalization of Schaffner-Nagel reductionism, arguing that the Bayesian network framework helps represent relations of conditional independence and hence simplify calculations relative to confirmative evidence. Some of the numerous questions were concerned with how the model deals with confirmation of bridge laws and with the relation between Schaffner-Nagel’s philosophical account and its Bayesian formalization. Branden Fitelson (UC Berkely, from Fall: Rutgers University), reporting on joint work with Jim Hawthorne (University of Oklahoma), attacked the problem of irrelevant conjunction: if some evidence confirms a hypothesis, then the same evidence confirms also the same hypothesis in conjunction with an arbitrary X, which, however, need not lend plausibility to the hypothesis H. Branden’s proposed solution is to consider X irrelevant if it is independent of the evidence given the hypothesis. Questions brought up qualitative alternative solutions based on non-monotonic logic, and the problematic case in which both H and X entail the evidence. After lunch, the audience were treated to Hannes Leitgeb’s (Bristol University, from Fall: Ludwig-Maximilians University Munich) “peace project,” aiming at the unification of qualitative and probabilistic beliefs. Recognizing that both kinds of belief serve important purposes in epistemology, Hannes provided axioms for both types, bridge principles linking them together and a representation theorem. The theorem validates the left-to-right direction of the “Lockean thesis” that p is qualitatively believed iff its probability is higher than a given threshold, while the other direction can be (partially) obtained by adding further axiomatic constraints on qualitative belief. Applications are of course wide-ranging, from the lottery paradox to a probabilistic analysis of Duhem’s problem, from Ramsey test and the logic of conditionals, to the possibility of re-uniting logical and probabilistic techniques in accounts of inductive reasoning. Jim Joyce (University of Michigan) defended the use of imprecise probabilities in inference and decision-making. Jim reviews a counterexample to the idea of imprecise credal states due to Roger White, undermining White’s conclusion against imprecise probability and positively arguing about a solution to the counterexample based on Seidenfeld and Wasserman’s notion of dilation. Jim then went on discussing, against White, the implication of imprecise credal states for decision-making. Teddy Seidenfeld (Carnegie Mellon University) reviewed three approaches on how a decision maker might frame her probability space: (i) assess precise probabilities for the random variable of interest only; (ii) choose “wisely” the set of events to which precise probabilities can be assigned; (iii) bite the bullet and choose an incoherent prior, then use Bayesian learning to update to a less incoherent posterior, minimizing loss. Teddy’s talk was as usual rich in theoretical implications. E.g, the analysis of (ii) revealed that de Finetti’s coherence conditions do not entail that the decision-maker have determinate probabilities over the entire space, but only over a subset determined by the decision problem at hand. Wolfgang Spohn (University of Konstanz) concluded the line-up of invited talks with a tutorial on ranking theory—Wolfgang’s theory of degrees of belief that avoids some of the pitfalls of Bayesianism (for instance, the lottery paradox). The talk highlighted applications of ranking theory in philosophy of science, for instance analyzing the relation between Bayesian nets and ranking nets.

The two day celebration ended with a round table discussion on formal epistemology moderated by Horacio Arló Costa and featuring panelist from various geographical and academic backgrounds: philosophers from South (Eleonora Cresto, University of Buenos Aires) and North America (Frederick Eberhardt, Washington University, Kishida Kohei, University of Pittsburgh, Jeff Helzner, Columbia University, Giacomo Sillari, University of Pennsylvania, Mike Titelbaum, Wisconsin-Madison) as well as philosophers and computer scientists from Europe (Eric Pacuit, Tilburg University, Choh Man Teng and Greg Wheeler, CENTRIA, Lisbon).

Giacomo Sillari

Second Call for Registration

Arch ‘Logic or Logics?’ Mini-course and Workshop

27 September – 1 October, 2010, University of St Andrews

The Arch ‘Logic or Logics?’ Mini-course and Workshop are organised by the members of the AHRC funded Foundations of Logical Consequence project. The Mini-Course is intended for graduate students and younger researchers (postdocs and junior faculty) working on related topics. The aim is to provide intensive graduate-level instruction on the latest thinking about pluralism and revision in logic. Topics will include the revision of logic debate, logical pluralism vs. absolutism (or monism), and combining logics. The week will conclude with a Workshop dedicated to contemporary research on the same theme.

The speakers for the Mini-course are:
       – JC Beall (University of Connecticut)
       – Carlos Caleiro (Instituto Superior Tcnico, Portugal)
       – Joo Marcos (DIMAp / UFRN, Brazil)
       – Graham Priest (University of Melbourne/CUNY)
       – Greg Restall (University of Melbourne)
       – Gillian Russell (Washington University, St Louis)
       – Johan van Benthem (University of Amsterdam

We invite interested parties to register here: http://tinyurl.com/2wtxkp6
For the full programme see the event website here: http://www.standrews.ac.uk/~arche/events/event?id=398
Any further inquiries should be directed to arche@st-andrews.ac.uk
Messages to the list are archived at http://listserv.liv.ac.uk/archives/philos-l.html.
Prolonged discussions should be moved to chora: enrol via http://listserv.liv.ac.uk/archives/chora.html.
Other philosophical resources on the Web can be found at http://www.liv.ac.uk/pal.

Kosta Dosen spoke about the perspectives in general proof theory, in particular about the categorial approach to proof theory. He tried to show how the categorial perspective enables us to formulate the criteria for identity of meaning of propositions. The role of propositions in inferences seems to be crucial for their identity.

Hannes Leitgeb showed that given reasonable assumptions it is possible to provide a definition of belief simpliciter in terms of subjective probability. Both quantitative and qualitative belief turns out to be governed by one unified theory. A new semantics for conditionals emerges form this approach.

The lecture of Hans Rott focused on the problem of the Ramsey test and the question whether it can serve as a viable analysis of nested conditionals. He proposed that conditionals should be studied with the help of constructive models of iterated theory change. From this point of view, the problem of nested conditionals (e.g. A -> (B -> C)) can be clarified.

Conditionals were considered also by Libor Behounek and Ondrej Majer (Academy of Sciences of the Czech Republic) who reformulated Lewis’ definition of counterfactuals in the framework of formal fuzzy logic. From many other topics presented and discussed at the symposium let us mention only a few examples: Tarsikan theory of truth (Shawn Standefer, University of Pittsburgh and also Theodora Achourioti, University of Amsterdam), the procedural character of the notion of concept (Pavel Materna, Academy of Sciences of the Czech Republic), different kinds of weak negation (David Ripley, University of Melbourne), logic based on incompatibility (Jaroslav Peregrin, Academy of Sciences of the Czech Republic), logic of Moore’s paradox (Igor Sedlar, Comenius University in Bratislava), logic of falsification (Andreas Pietz, University of Barcelona), Bolzano’s view on logical notions (Stefan Roski, VU University Amsterdam), the relation between the set theoretic and the semantics paradoxes (Giulia Terzian, University of Bristol).

Generally the themes of the papers were in line with the traditional aim of the symposium which is to concentrate on issues that are interesting both for philosophically and for mathematically oriented logicians.

Vít Puncochar

The square is a simple picture describing relations between three notions of opposition. It is useful to understand many concepts as clearly explained by Robert Blanché in his book “Structures intellectuelles” (Vrin, Paris, 1966), where he proposes also a hexagon as an improvement of the square.

This event with about 70 people from all round the world was a very good platform to exchange ideas about the square. Corte is a little town at the middle of Corsica with magnificent surroundings providing a relaxing atmosphere.

After the first congress on the square organized in Montreux in 2007 a special issue of the journal Logica Universalis (vol.2, n.1, 2008) was published and also a book New perspectives on the square of opposition (Peter Lang, Bern, 2010). After the event in Corsica more publications will be released. The square is a very fruitful source of inspiration for thinkers.

We are projecting to organize a third world congress on the square in 2012 in Crete.

http://www.square-of-opposition.org

Jean-Yves Beziau

A spectacular landscape and an at times unbereably hot weather could not stop deontic logicians to attend three days of both technical and interdisciplinary talks.

The conference was moreover connected to a multiplicity of ‘satellite workshops’ on Deontic Logic:

- iComply, the First Workshop on Law Compliancy Issues in Organisational Systems and Strategies;
- the “Norm Compliance” Workshop;
- the 10th Augustus De Morgan Workshop on Deontic Logic.

Remarkably the latter discussed, among the other subjects, the editing of a forthcoming “Handbook on deontic logic and normative systems”.

The purpose of the conference, in the editors’ intentions (Guido Governatori and Giovanni Sartor), was to “promote international cooperation amongst scholars interested in deontic logic and its use in computer science”.

Definitely I have heard talks ranging from artificial intelligence, philosophical logic, game theory, law. All probably holding a different view concerning what it should be, which is ultimately what DEON is about.

I believe the invited speakers where representative of the different areas constituting DEON community. Marek Sergot, from the Department of Computing of the Imperial College in London, discussed Norms, Action and Agency in Multi-Agent Systems; Leon van der Torre, from the Faculty of Sciences, Technology and Communication of University of Luxembourg, discussed the challenge of Deontic Redundancy, showing one more application for input-output logic; Michele Taruffo could not be there but was replaced, amazingly on the fly, by Jörg Hansen, who talked about defaults and priorities. Last but not least, Rosaria Conte, from the Institute of Cognitive Science and Technologies of the Italian National Research Council who presented a theory of norm adoption showing computer simulation results.

The talks where articulated into sections that more or less reflected the invited speakers topics.

- “Preferences and Contrary to Duties” where the problems related to Contrary to Duties structures and Preference priorities was discussed. Here the work by van Benthem, Grossi and Liu (University of Amsterdam the first two and of Tsinghua the last) on a correspondence between contrary to duty structures and preference orders over possible worlds raised interesting questions concerning the nature of contrary to duties structure. When there are plenty of contrary to duty obligations how is the preference order that they induce on worlds supposed to be represented?

- “Input-ouput logic and norm change” dealing with the dynamic aspects of normative system change. Dynamic logic type of formalisms turned out to be first choice of many deontic logicians interested in studying norm change.
Here Antonino Rotolo, University of Bologna, discussed the fascinating phenomenon of Retroactive Legal Changes by means of Theory Revision in Defeasible Logic. Reatroactive Legal Changes suggest the possibility of a legal branching past, usually ruled out by temporal accounts of action. Rotolo’s account instead incorporates this fact in a sophisticated model, involving the use of defeasible logic. What the best way could be of modelling the way a system at a certain time ‘sees itself’ in the past was one of the central questions following the talk.

- “Deontic logic and Argumentation” where the conflicting reasons for accepting a certain rule or to deal with conflicting rules were discussed.

Here the work by Phan Ming Dung and Giovanni Sartor (Asian Institute of Technology and University of Bologna) was presented. It is an integration of two seemingly disconnected disciplines: argumentation theory, born in computer science to account for conflicting pieces of information to be selected and the study Private International Law. The central idea is that pieces of Private International Laws among countries can be inconsistent if put together. Here the use of argumentation theory to provide feasible answers for lawyers.

- “Agents, Institutions and Deontic Logic” instead collected contributions interested in understanding the role of social interaction in determining norms.

In this section Rosja Mastop (University of Eindhoven) presented his contribution on collective responsibility, what he calls “the problem of many hands”. Given that a state of the world is brought about, who is accountable for it, if this state of the world is result of a collective choice? Apart from the inner interest of this question, a connection could be drawn with the “principle of absence of moral luck” discussed by Marek Sergot in his invited talk. There is no moral luck when agents are individually and not collectively responsible for a certain damage. I thought Mastop’s contribution as a natural exploration in the realm of moral luck.

Apart from the talks themselves, I found the discussion with the public to be most inspiring, especially when conflicting views were put forward, e.g. technical versus conceptual. I strongly believe DEON to be an instructive arena as long as different areas come together to discuss about what it should be.

Paolo Turrini

- Traditional analysis of cryptographic protocols divides participants into honest parties that follow the protocol even if it is not to their best interest, and dishonest parties, with arbitrary malicious behavior. Under the headline rational cryptography, cryptographers have more recently begun analyzing protocols under the assumption that parties are rational. It has been subject to some controvery which game theoretic solution concepts are relevant for such analysis.

- In formal methods, a well established methodology is the modeling of reactive systems using infinite duration two-player zero-sum games and the minimax solution concept and the computation of the minimax as a prescriptive solution. A recent trend is to consider modeling and analysing such systems using multi-player general-sum games. Again, which solution concepts are relevant for such analysis is a subject of discussion.

- In computational game theory, there has been a surge of interest into the computation of solution concepts beyond minimax and Nash, such as the Stackelberg solutions and equilibrium refinements.

The workshop brought together computer scientists from these three groups with experts on game theory, with a overweight on epistemic game theorists (i.e., experts on what solution concepts really mean), with the explicit purpose of making the two communities draw on the expertise and be inspired by each other.

The workshop featured presentations by Geir Asheim (University of Oslo), Christian W. Bach (Maastricht University), Jing Chen (M.I.T.), Edith Elkind (NTU, Singapore), Kousha Etessami (University of Edinburgh), Janos Flesch (Maastricht University) Ronen Gradwohl (Northwestern) Erich Grädel (Aachen), Josh Letchford (Duke), Silvio Micali (M.I.T.), Peter Bro Miltersen (Aarhus), Moni Naor (Weizmann), Jesper Buus Nielsen (Aarhus), Andres Perea (Maastricht University), Rafael Pass (Cornell), Alon Rosen (Herzliya) Rahul Santhanam (University of Edinburgh), Abhi Shelat (University of Virginia), Troels Bjerre Sorensen (Warwick), Bernhard von Stengel (London School of Economics), and Carmine Ventre (Liverpool).

The workshop concluded with a panel discussion, chaired by Jesper Buus Nielsen and with the entire audience being the panel, attempting to shed new lights on the controversies motivating the workshop. The discussion made it clear that while the issues are still subject to discussion, the purpose of initiating interaction between the groups was indeed accomplished.

Abstracts of the talks given can be found on the workshop website.

• Julie Hunter (IJN Paris & Philosophy, Texas-Austin) presented a model for presuppositional character, an alternative to Kaplan’s model for the reference-fixing content of indexicals which purports to mend the gap between indexicals and definite descriptions assumed by previous presuppositional accounts.

Maria Aloni’s noted that this account still requires a Kaplan-style notion of context. She highlighted differences in projection between indexicals and standard presuppositions (already noted by Beaver et al. (2010)), and she inquired about the non-descriptiveness of indexical’s reference-fixing meaning.

• Isidora Stojanovic (IJN Paris) proposed a relativist definition of truth and validity to give a pragmatic account of entailments between utterances with indexical anchors and their non-indexicalised counterparts, and to explain the seeming tautologicity of certain self-referring utterances.

Lucian Zagan challenged the need for a relativist approach given that MacFarlane’s contextual view on truth and validity does not initialise all parameters at once, and he disputed as well the notion of logical validity underlying Stojanovic’s proposal.

• Michael Murez (IJN, Paris) introduced an agentive propositional attitude, “control” in order to provide better accounts for situations of agentive feeling in which belief, desire, and intention are not entirely adequate.

Inés Crespo praised this embodied perspective on agency. She also raised issues regarding the propositional character of this attitude, supported by Maria Aloni’s suggestion to consider
an ontology of actions for this attitude, as in the semantics for imperatives.

• Alexandra Arapinis (IHPST, Paris) defined the class of terms referring to institutional entities, she showed its systematic polysemy, and accounted for this adapting Pustejovsky’s (1995) notion of dot-types to define the structure of ontological counterparts for these terms via “dot-objects”.

Ana Aguilar Guevara referred to coordination of predicates applying to ‘coerced’ objects and to dot-objects as a possible difficult case for this approach, and she introduced weak definites and bare singulars as phenomena seemingly related to institutional terms.

• Fabrice Correia (Philosophy, Geneva) defended a presentist stance with respect to eternalist discouse by providing adequate translations using non-proxy reductions. Non-proxy paraphrasing of eternalist discourse does make use of presentistically acceptable proxies or surrogates to translate eternalist statements. He then put forward a metric method, different from available ones such as Peacock’s, Vlach’s and Fine’s.

Jonathan Shaheen challenged Correia’s objection to the Peacockean and Vlachian methods. He also argued that modalists like Forbes can better account for expressions quantifying over time.

• Fred Landman (Linguistics, Tel-Aviv & ILLC, Amsterdam) presented his “Prolegomena to a Theory of Mass Nouns”. To analyse the fact that objects in a mass denotation cannot be counted in terms of the parts of the object that are minimal elements of the denotation, he proposed a theory based on overspecification: mass denotations have too many minimal elements. He provided supporting data from both English and Chinese, and he developed in some details the details to obtain the right kind of set underlying the quantification in mass counting.

• David Ripley (IJN, Paris & Melbourne) argued that to treat denial as a sort of speech act, parallel to assertion, we should accept an operator that embeds denial. This led to understand the assertion of a negation as a denial, and to defend a paracoherentist approach to disagreement.

Catarina Dutilh Novaes explained why she considers embedding of speech-acts a category mistake. She also inquired about the suggested parallelism between assertion and denial, especially in view of the reduction of denial to the assertion of negation.

• Henri Galinon (IHPST, Paris) investigated how the truth predicate helps us in obtaining knowledge otherwise inaccessible to us. With his idea of “reflexive consequence”, inspired by G ”odel’s (1964) remarks about ZF, he supported the crucial expressive role of truth, ultimately defending deflationism against than Shapiro’s and Ketland’s attempts.

Theodora Achourioti highlighted an apparent transcendental step in Galinon’s argumentation, and she then contended the argument by pointing out that Peano’s axioms can also be justified via a derivation of their second order version. In the audience, Frank Veltman asked whether infinite conjunctions could play the role that Galinon claimed for the truth predicate.

• Johannes Stern (Philosophy, Geneva) argued for treating modalities such as truth, necessity, and knowledge as predicates and he constructed a possible world semantics for this syntactical modal logic. To avoid well-known paradoxes, he relied on quotation names.

Stefan Wintein objected the exclusion of Kripke’s minimal fixed point in the model theory for Stern’s logic. More generally, he contended Stern’s abidance by Gupta’s adequacy conditions for semantics, and he invited the author to re-consider Kripke’s adequacy conditions.

• David Etlin (Philosophy, Leuven) identified the problem of vagueness as a matter of vagueness of our intentions, and suggested to find a solution for the Sorites paradox by adapting Schicks explanation of the “money pump” puzzle. Agents do not need to act according to the non-dominance principle of choice (choose whatever is not dispreferred), as they can be informed by context.

Raquel Fernández Rovira inquired about the essential differences between the adaptation of a Schick’s solution of the “money pump” puzzle, and Delia Graff Fara’s approach to the Sorites, and she wondered about the substantial gain in this choice-theoretic stance on vagueness.

• Fabio Del Prete (IJN, Paris) presented linguistic evidence for truth value transitions for future contingents from true to false and from false to true, a richer view on truth value change than the relativist (like MacFarlane), and he presented a Branching Time model to account for this.

Katrin Schulz made critical remarks on whether the empirical data indeed fits in the logical form that the theory then proposes to handle. She also proposed definitions to simplify the formal apparatus to deal with the data that Del Prete wanted to account for.

• Frank Veltman’s talk, based on a joint paper with Harald Bastiaanse, introduced a framework for dealing with conflicting default rules. The semantics is framed within circumscription theory, given in a language of monadic first order logic that translates a default rule such as “Ps are normally Qs” by including an “abnormality clause that excludes all objects that behave abnormally with respect to the given rule. A class of models satisfying constraints of exemption and inheritance can accommodate defeasible arguments and other pieces of non-monotonic reasoning. Inheritance networks satisfying minimal and equivalence constraints are the right syntactic support for the information flow achieved via models in the circumscription theory, as they are sound and complete with respect to the semantics.

In the question round after the talk, David Ripley inquired whether this framework can represent hierarchies of default rules, i.e., dominance or priority relations among rules in a set. Furthermore, the questions clarified that the notion of “normally” that this approach purports to model is not reducible to frequency or recurrence patterns, and it is instead a normative notion.

Inés Crespo and Lucian Zagan

On the 25th and 26th of June, the LSE hosted its third Philosophy of Probability Graduate Conference. As in previous years, the philosophy and foundations of probability proved to be a common concern for philosophy of physics, decision theory, epistemology, and philosophy of language.

Our first keynote address was given by Professor Dorothy Edgington (Birkbeck) who talked on “Estimating conditional chances and evaluating counterfactuals”. She offered a way to evaluate counterfactuals in terms of conditional probabilities which avoids various problems with problems these accounts typically face. The first of our graduate speakers was Isabel Guerra (Complutense/LSE) who gave us several reasons to doubt the claims made by “Quantum Bayesians”. These revolved around the fact that the “Lüder’s rule”, while formally analogous to standard conditionalisation, cannot perform the conceptual role of conditionalisation. After lunch, Jonny Blamey (KCL) criticised a common assumption in decision theory, particularly in the discussion of Dutch book arguments: “Stake Size Invariance”. Jonny’s positive suggestion was that modelling agents as having a “bid-ask spread” was preferable to the standard point probabilies of standard treatments of degrees of belief. Richard Bradley, commenting on Jonny’s paper, suggested that the contentious supposition might not be shared by all justifications of probability theory. The first day of the conference was rounded off by our second keynote speaker, Mauricio Suárez (Complutense). The topic of his talk was “Propensities and a Pragmatism”. Mauricio explained how a return to C.S. Peirce’s conception of propensities was preferable to the current Popper-influenced paradigm. A minor modification to Peirce’s view was offered: a move from “long-run” propensities to “single-case” propensities.

We started the second day of the conference with our final keynote address from Antony Eagle (Oxford). The topic under consideration was “The epistemic value of agreement”. How should agreement and disagreement with one’s epistemic peers affect one’s degrees of belief? The suggestion offered here is that it shouldn’t affect one’s degrees of belief directly, but should change the stability or resilience of those beliefs. Our next graduate speaker was Sylvia Wenmackers (KU Leuven) talking on “Probability and epistemology of denumerable lotteries using non-standard analysis”. Her claim was that extending analysis to include infinitesimals of a particular kind (numerosities) allows you to solve problems with infinite lotteries and countable addivity as well as blocking the preface paradox. Matt Parker suggested two worries for the non-standard analysis approach: first the inequalities are sensitive to choice of ultrafilter, and second that the results conflict with our intuition that sets of the same size can be put in one-to-one correspondence with each other. After lunch Julia Staffel (University of Southern California) showed how Dutch books can be used to measure degrees of incoherence. Her approach involved getting an agent to bet once on each event in the algebra, and Julia showed how this approach avoided the “double counting” problem that a similar attempt faced. Rory Smead commented that there was a possiblty unintuitive consequence to Julia’s approach: that unrelated beliefs could lessen the extent of one’s degree of incoherence. The final talk of the conference was by Chris Clarke (Bristol) who presented a more general representation theorem, motivated by a kind of pragmatism. The idea was to weaken parts of the standard theorem to allow a more general result to be proved. So instead of assuming that agents are necessarily utility maximisers one places weaker constraints on their decision theory. Luc Bovens presented some computer simulations that seem to agree with Chris’ argument and situated Chris’ argument within a general space with Savage’s theorem as a special case.

The conference organisers would like to thank British Society for the Philosophy of Science, the Institute of Philosophy and the LSE philosophy department for financial support. Thanks also to all the speakers and commentators!

Seamus Bradley (LSE), Foad Dizadji-Bahmani (LSE), Conrad Heilmann (LSE)