MCMP – Mathematical Philosophy (Archive 2011/12)

Stephan Hartmann is regarded as one of the leading scholars in the fields of formal epistemology and philosophy of science, and he became a member of the Faculty of Philosophy at LMU last October. Later today (8 May, 2013), at a ceremony in Berlin, Hartmann will officially receive Germany’s most generously endowed prize for distinguished contributions to research, the Alexander von Humboldt Professorship, that brought him back to the land of his birth. Hartmann now holds the Chair of Philosophy of Science at LMU‘s Munich Center for Mathematical Philosophy (MCMP) and, together with his colleague Hannes Leitgeb, who occupies the Chair of Logic and Philosophy of Language and also holds a Humboldt Professorship, he is actively engaged in extending the interdisciplinary reach of his subject in often surprising directions. The basic goal of the MCMP is to apply advanced mathematical methods to a range of complex philosophical problems. Born in 1968, Hartmann studied Philosophy and Physics, and has held professorships at the London School of Economics and Political Science (LSE) and, prior to his move to LMU, at Tilburg University in the Netherlands, where he served as Founding Director of the Tilburg Center for Logic and Philosophy of Science. Hartmann is the fourth Humboldt Professor at LMU. The honor had previously been accorded to systems biologist Ulrike Gaul, astrophysicist Georgi Dvali and Hannes Leitgeb. The prestigious awards, administered by the Alexander von Humboldt Foundation and financed by the Federal Ministry for Research, are intended to enable internationally recognized scholars and scientists to carry out long-term, groundbreaking projects at research institutions and universities in Germany. (LMU press release, Munich, 8 May 2013)

The MCMP is proud to present over 250 videos on iTunes U! Thanks for all your contributions in the last two years! In 2013 we are introducting 4 new channels: "Logic", "Epistemology", "Philosophy of Science", "Metaphysics and Philosophy of Language". Have fun exploring!

Craig Callender (UCSD) gives a talk at the MCMP/MCTS Workshop on Laws of Nature (17 December, 2012) titled "Building a Better System". Abstract: In this talk I'll sketch the central motivating idea behind Humean approaches to lawhood, namely, that modality arises from bodies of knowledge, not the world (see, e.g., Putnam 1962). Keeping one's eyes firmly focused on this motivation is the key to developing so-called "system" approaches to lawhood. I'll claim that it will suggest particular ways of formulating the best system theory and also replies to recent criticisms. But it will also invite many open questions, such as why do creatures like us modalize at all?

Markus Schrenk (Köln) gives a talk at the MCMP/MCTS Workshop on Laws of Nature (17 December, 2012) titled "Trouble with Properties for Better Best Systems". Abstract: In Lewis' original best system account, the mosaic of point-sized, intrinsic, quiddistic, perfectly natural, fundamental properties is the ultimate material on which everything else, laws of nature in particular, supervenes. While better best system competitions (BBSCs) for different, separate special science property sets aim to apply the same mechanism as Lewis's to get the laws from the distributions of properties (balancing simplicity, strength and fit) it is not so clear: (i) which features properties of the special science have (they are clearly not fundamental, maybe not natural but also not-quiddistic, etc.), (ii) in which kind of entities they are instantiated (clearly not singular space-time points), (iii) how BBSCs deal with vague and extensionless properties, (iv) and what the boundaries are for the different sets of properties which BBSCs take as raw material for allegedly separate competitions. This paper will show that (i) - (iv) are not easy to answer for (us) better best system advocates.

Michael Esfeld (Lausanne) gives a talk at the MCMP/MCTS Workshop on Laws of Nature (17 December, 2012) titled "Humeanism and dispositionalism in physics". Abstract: The paper sets out to make a case for a natural philosophy or naturalized metaphysics that treats physics and metaphysics as inseparable. It examines how Humeanism and dispositionalism about laws of nature fare with respect to classical as well as quantum physics. In particular, I argue that, despite widespread claims to the contrary, Lewis' metaphysics of Humean supervenience is applicable to non-relativistic quantum mechanics and that its application even removes the charge of quidditism. However, this position faces considerable difficulties once physics abandons the assumption of a background system of geometrical relations unifying the world. Against this background, I indicate reasons to prefer dispositionalism to Humeanism.

Helen Beebee (Manchester) gives a talk at the MCMP/MCTS Workshop on Laws of Nature (17 December, 2012) titled "Ramsey vs. Lewis on conditionals and causation". Abstract: In this paper, I explore the prospects for a (very roughly sketched) broadly Pricean perspectivalist account of causation. The ingredient I add to the mix is the thought, familiar from Lewis and others, that causal claims express conditional relationships – except that here the relevant conditional is to be understood in Ramseyan, non-truth-apt terms rather than in terms of Lewis’s machinery of possible worlds. I argue that this approach is much better able than the standard counterfactual approach to account for the close connection between causation and inference.

Mathias Frisch (Maryland) gives a talk at the MCMP/MCTS Workshop on Laws of Nature (17 December, 2012) titled "Why Physics Can't Explain Everything". Abstract: Barry Loewer and David Albert have argued for a view on laws that is at once pragmatic (and takes nomic regularities are summaries of aspects of the Humean mosaic that are useful for beings like us) and 'imperialistic' or foundationalist. I argue in this paper that there is a deep tension between the two planks of the account and suggest that it is the pragmatism and not the foundationalism that is worth keeping.

Stathis Psillos (Athens) gives a talk at the MCMP Colloquium (13 December, 2012) titled "Making Contact with Molecules: On Perrin's Argument for Realism". Abstract: Between roughly 1908 and 1912, there was a turn in the scientific community in favour of the atomic hypothesis. Jean Perrin’s theoretical and experimental work on the causes of Brownian motion played a major role in this shift. When Perrin received the Nobel Prize for physics in 1926, it was noted in the presentation speech that he “put a definite end to the long struggle regarding the real existence of molecules”. The aim of this talk is to cast light on the reasons that explain the shift of opinion concerning the reality of atoms and molecules in the beginning of the twentieth century. The story told will have some rather interesting repercussions concerning the scientific realism debate. After presenting the philosophical debate concerning the role and status of explanatory hypotheses c.1900, (focusing on the work of Ostwald, Poincaré and Boltzmann), I will examine in detail Perrin’s theoretical account of the molecular origins of Brownian motion and explain the structure and the strength of Perrin’s argument for the reality of molecules.

Giovanni Valente (Pittsburgh) gives a talk at the MCMP Colloquium (06 December, 2012) titled "Local Disentanglement in Relativistic Quantum Field Theory". Abstract: In their paper on "Entanglement and Open Systems in Algebraic Quantum Field Theory", Clifton and Halvorson (2001) raised the question whether entanglement between quantum systems can be destroyed by means of local operations and claimed that, contrary to non-relativistic quantum mechanics, this can never be the case in relativistic quantum field theory. In this talk I will argue that Clifton and Halvorson's no-go result applies only to a special kind of local operations, and thereby I will reject their conclusion. In fact, after providing sufficient conditions for local disentanglement to be achieved, I will show that, if the split property holds, there exists a class of local operations which disentangle all states across any pair of spacelike separated quantum field systems.

Peter Adamson (LMU) gives a talk at the MCMP Colloquium (22 November, 2012) titled "Logic as an Instrument in Greek and Arabic Philosophy". Abstract: As is well known, the Aristotelian works on logic were collectively referred to in antiquity as the Organon, meaning "instrument". Ancient Aristotelians took this seriously: for them, logic is not a part of philosophy but only a tool or instrument which one should ideally learn before embarking on the study of philosopher proper. This view was not universally adopted in antiquity, however. The Stoics made logic one of three broad areas of philosophy (along with ethics and physics), and thought of these areas as closely interrelated "parts". In this paper I explore the philosophical consequences of this apparently rather superficial disagreement; for instance, it bears on the question of the extent to which logic was perceived in the ancient world as a "formal" discipline. I also pursue the part vs. instrument debate into the Arabic tradition. There, we find adherents of Aristotle torn between their desire to agree that logic is a mere instrument, and not a part, of philosophy, and their desire to show the importance of logic against its detractors.

Mikael Cozic (Paris) gives a talk at the MCMP Colloquium (22 November, 2012) titled "On Representation Theorems". Abstract: Contemporary decision theory attaches much importance to representation theorems. Representation theorems are mathematical results which establish the equivalence between criteria of preferences and choices among options (e.g., expected utility) and axioms on preferences (e.g., transitivity or independence). Distinct roles can be assigned to these results. One of them is semantic: according to this view, representation theorems allow one to define decision-theoretic involved in the criteria of evaluation (e.g., subjective probability and utility on outcomes for the criterion of expected utility). The aim of this paper is to assess this semantic function by relying on philosophical views on the meaning of theoretical terms.

Thomas Müller (Utrecht) gives a talk at the MCMP Colloquium (21 November, 2012) titled "Toward a formal account of substance via case-intensional logic". Abstract: Things - concrete individuals persisting through time, or more traditionally speaking, substances - are a central ontological category of our commonsensical as well as of our scientific worldview. There is, however, no satisfactory formal account of substance, or so I will argue - despite a plethora of systems of modal and temporal logic available in the literature. I will indicate some of the shortcomings of available accounts by contrasting them with what I take to be a more adequate formal approach. In my talk, which for a large part is based on joint work with Nuel Belnap (Journal of Philosophical Logic, forthcoming), I will introduce a general logical framework for modality and quantification, called "Case-intensional first-order logic" (CIFOL). CIFOL combines first-order quantification and a universal S5 modality in a straightforward way and is meant to provide a neutral formal framework for discussing various metaphysical and scientific arguments. CIFOL's generality is made possible by an innovation due to Aldo Bressan: All terms (including definite descriptions, variables and constants) have an extension in each case (where the interpretation of the cases is left open; they do not need to be thought of as "possible worlds"), and an intension, which is the function from cases to the case-relative extensions. Predication is intensional (i.e, whether a predicate applies, may depend on more than what is so in a single case). This makes it possible to define a class of so-called absolute predicates, which allow the tracing of a thing from case to case without building into the logical framework metaphysical assumptions about "rigid designation" or "trans-world identity" to handle the reidentification of things. Concrete individuals are thereby seen to be represented not by extensions, as in standard quantified modal logic (in which one tends to think in terms of "inhabitants of possible worlds"), but by intensions. This approach leaves the nature of the extensions completely unspecified - their only systematic role is to figure in case-relative identity statements. In the second part of the talk, I will switch to specific formal structures of cases that are adequate for representing indeterminism: branching history structures. I will argue that CIFOL based on these structures allows for a detailed discussion of formal aspects of things (substances) and their qualities, and thereby provides a useful formal framework within which, e.g., problems of the identity of substances can be formulated and discussed.

Francesco Paoli (Cagliari) gives a talk at the MCMP Colloquium (14 November, 2012) titled "Semantic minimalism for logical constants". Abstract: In a 2003 paper ("Quine and Slater on paraconsistency and deviance", J. Phil. Log. 32, 2003, pp. 531-548), I defended a minimalist account of meaning for logical constants as a way to ward off Quine's meaning variance charge against deviant logics. Its key idea was that some deviant propositional logics share with classical logic the operational meanings of all their connectives, as encoded in their sequent calculus operational rules, yet validate different sequents than classical logic; therefore, we can have genuine rivalry between logics without meaning variance. In his PhD thesis, Ole Hjortland levelled several objections at this view. The aim of this talk is to address these criticisms, highlighting at the same time the role played by logical consequence in this version of semantic minimalism.

Michael De (Utrecht) gives a talk at the MCMP Colloquium (14 November, 2012) titled "Classical negation and expansions of FDE" (joint work with Hitoshi Omori (Kobe University, Japan & CUNY, New York)). Abstract: It is sometimes said that classical negation can be recaptured in some systems of non-classical logic. But what exactly *is* classical negation? We endorse and defend one such characterization of classical negation in the context of FDE. We then provide an expansion FDE+ of FDE by this classical negation and show it sound and complete with respect to its intended semantics. Along the way we show that other candidate classical negations to be undefinable in FDE+.

Fabrice Correia (Neuchâtel) gives a talk at the MCMP Colloquium (15 November, 2012) titled "Logical Grounds". Abstract: Philosophers have recently displayed a strong interest in the idea that some facts or truths hold in virtue of - or, as they say, are grounded in - others facts or truths. Grounding come in various sorts, and my talk will focus on logical grounding as opposed to e.g. metaphysical or normative grounding. I will (i) offer a proof-theoretic characterisation of the concept relative to propositional and first-order languages, (ii) show that so characterised, the concept can be used to characterise some notions of truth-in-a-model and various semantic consequence relations, and finally (iii) connect my concept of logical grounding with the notion of groundedness put forward by Kripke in his "Outline of a Theory of Truth".

Benjamin Schnieder (Hamburg) gives a talk at the MCMP Colloquium (15 November, 2012) titled "On Ground and Consequence". Abstract: The notion of grounding has proven to be a fruitful tool for philosophical analysis. While traditionally, many explications of core philosophical notions proceeded in purely modal terms, explications in terms of grounding often yield more adequate results. In my talk I will explore a new application of grounding and develop a notion of logical consequence in terms of grounding.

Harvey M. Friedman (OSU) gives a talk at the MCMP Colloquium (30 October, 2012) titled "Transcendental Proofs". Abstract: We discuss our Transcendental Proofs project, spanning approximately 45 years, which aims to uncover mathematically fundamental, rich, and diverse subareas of athematics which can only be developed by going well beyond the usual ZFC axioms for mathematics. The discussion will have mathematical, computational, and philosophical components.The mathematical component focuses on long finite sequences, adjacent amsey theorems, finite trees and graphs, continuous maps between countable sets, Borel diagonalization and selection, Boolean Relation Theory, and Embedded Maximal Cliques. The computational component focuses on predictions from higher infinities of the result of actual computations. The philosophical component focuses on various formulations of the project, involving measures of simplicity and naturalness, as well as prospects for confirmation of the validity of transcendental methods.

Harvey M. Friedman (OSU) gives a talk at the MCMP Colloquium (31 October, 2012) titled "Concept Calculus". Abstract: Concept Calculus develops theories in first and second order predicate calculus arising from the analysis of various commonsense notions. The systems arising in this way are shown to closely correspond to various well known systems arising in the foundations of mathematics - via mutual interpretations. Initial work on Concept Calculus focused on the general notions of better than and much better than. More recent developments surround a basic notion of universe, based on a principle of plenitude. Universes correspond to Peano Arithmetic. ZFC, and various extensions by large cardinals arise from the axiomatization of various basic kinds of explosions of universes. We discuss some further contexts for Concept Calculus, including the evolutionary universe, and various comparison notions. We believe that any informal conceptual context leads to the natural formulation of axiomatic principles which are mutually interpretable with a range of standard formal systems ranging from PA and fragments, through type theory and ZFC, and the usual strong systems extending ZFC.

Kit Fine (NYU) gives a talk at the Workshop on Groundedness (26-27 October, 2012) titled "Ground and Partial Content". Abstract: I provide a ground-theoretic account of partial content.

Jönne Speck (Birkbeck) gives a talk at the Workshop on Groundedness (26-27 October, 2012) titled "Grounding Class Theory". Abstract: In this talk, I propose a conception of proper class. It brings together two separate strands of research: metaphysical and semantical groundedness. On the one hand, I use the *metaphysical* concept of grounding. Whether or not something is a member of a class, I will argue, must be grounded in other facts. On the other hand, the method of *semantical* groundedness will provide a formal theory that captures this conception of class.

Denis Bonnay (Paris) gives a talk at the Workshop on Groundedness (26-27 October, 2012) titled "Dependence and Groundedness". Abstract: In this talk, I will discuss whether the notion of groundedness can be analyzed directly in terms of dependence upon non-semantic states of affairs or whether a detour via truth and falsity is always necessary.

Luca Incurvati (Cambridge) gives a talk at the Workshop on Groundedness (26-27 October, 2012) titled "That's it, you're grounded!". Abstract: I will begin by reviewing and further defending the minimalist approach to sets which I advanced in earlier work. Then, I will consider the prospects for extending the minimalist approach to the case of semantics. I will conclude by examining whether a minimalist approach prevents us from giving a common account of grounding assumptions in set theory and semantics.

Patrick Suppes (Stanford) gives a talk at the Workshop on Groundedness (26-27 October, 2012) titled "Neuroscience Perspective on the Foundations of Mathematics". Abstract: I mainly ask and partially answer three questions. First, what is a number? Second, how does the brain process numbers? Third, what are the brain processes by which mathematicians discover new theorems about numbers? Of course, these three questions generalize immediately to mathematical objects and processes of a more general nature. Typical examples are abstract groups, high dimensional spaces or probability structures. But my emphasis is not on these mathematical structures as such, but how we think about them. For the grounding of mathematics, I argue that understanding how we think about mathematics and discover new results is as important as foundations of mathematics in the traditional sense.

Jon Erling Litland (Oslo) gives a talk at the Workshop on Groundedness (26-27 October, 2012) titled "Pure Logic of Iterated Ground". Abstract: The presently existing logics of ground have not had anything to say about iterated grounding claims, that is, claims of the form: "A grounds that (B grounds C)". I develop a pure logic of iterated ground providing a systematic account of such iterated grounding claims. The logic is developed as a Prawitz style natural deduction system; the grounding operators are provided with both introduction and elimination rules, and normalization can be proved. The resulting logic is a conservative extension of Kit Fine's Pure Logic of Ground.

Øystein Linnebo (Birkbeck/Oslo) gives a talk at the Workshop on Groundedness (26-27 October, 2012) titled "Towards a theory of grounded properties". Abstract: I outline some desiderata for a theory of properties and then examine some attempts to develop an account of 'grounded' properties.

Toby Meadows (Bristol) gives a talk at the Workshop on Groundedness (26-27 October, 2012) titled "Local Dependence". Abstract: The purpose of this paper is to lay out some groundwork for a general understanding of relationships between: notions of dependence and groundedness; and notions of complexity and cardinality. We commence by sketching a pleasing framework linking dependence with the theory of inductive definitions. We pose a kind of problem for this framework and attempt to explain why this is interesting using a case study from the semantic theory of truth literature. We then attempt to formulate a definition of local dependence which addresses this issue. Finally, we consider limitations of this definition and consider possibilities for its further generalisation.

Caspar Storm Hansen (Aberdeen/Oslo) gives a talk at the Workshop on Groundedness (26-27 October, 2012) titled "Alternative Supervaluation for Kripke's Theory of Truth". Abstract: I will present a method of supervaluation for Kripke's theory of truth. It is different from Kripke's own method in that it employs trees, results in a compositional semantics, assigns the intuitively correct truth values to the sentences of a particularly tricky example of Gupta's, and is acceptable as an explication of the correspondence theory of truth.

Brendan Balcerak Jackson (Cologne) gives a talk at the MCMP Colloquium (25 October, 2012) titled "Defusing Easy Arguments for Numbers". Abstract: Pairs of sentences like the following pose a problem for ontology: (1) Jupiter has four moons. (2) The number of moons of Jupiter is four. (2) is intuitively a trivial paraphrase of (1). And yet while (1) seems ontologically innocent, (2) appears to imply the existence of numbers. Thomas Hofweber proposes that we can resolve the puzzle by recognizing that sentence (2) is syntactically derived from, and has the same meaning as, sentence (1). Despite appearances, the expressions ‘the number of moons of Jupiter’ and ‘four’ do not function semantically as singular terms in (2). Hofweber’s primary evidence for this proposal concerns differences in the focus-related communicative functions of (1) and (2). In this paper I raise several serious problems for Hofweber’s proposal, and for his attempt to support it by appeal to focus-related phenomena. I conclude by offering independent evidence for an alternative, purely pragmatic resolution of the ontological puzzle.

Erich Reck (UCR) gives a talk at the MCMP Colloquium (18 October, 2012) titled "Explicating Dedekind: Existential Axiomatics or Logicist Abstration?". Abstract: In recent years, there has been renewed interested in Richard Dedekind as a philosopher of mathematics, especially in connection with structuralist views about the content of mathematics. In this talk, I will juxtapose two ways of interpreting Dedekind's structuralism, or better, two explications (in Carnap's sense) of his position, that seem most promising to me. One of them is Hilbertian, leading to a reading of Dedekind as a precursor of Hilbert's "existential axiomatics"; the other is neo-Fregean or neo-logicist, in the sense of being based on a distinctive kind of "abstraction principles" that can be seen as underlying Dedekind's position. I will argue that, besides being more defensible on interpretive grounds, the second explication of Dedekind points in a direction for developing mathematical structuralism that deserves further attention today.

Elliott Sober (Wisconsin) gives a talk at the MCMP Colloquium (24 October, 2012) titled "Time and Knowability in Evolutionary Processes".

Elliott Wagner (Amsterdam) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "The long-run stability of collective action".

Ittay Nissan-Rozen (Jerusalem) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "Moral uncertainty and normative requirements of indifference".

Constanze Binder (Rotterdam) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "Social Choice and Comparative Justice: Correcting for Parochial Values".

Justin P. Bruner (UCI) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "Diversity, Tolerance and the Social Contract".

Simon Huttegger (UCI) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "The Evolution of Norms in Structured Populations".

Conrad Heilmann (Rotterdam) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "Weighting Value".

Campbell Brown (Edinburgh) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "Minding the Is-Ought Gap".

Gillman Payette (Calgary) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "Normative Consistency: an (X)stit account".

Shyam Nair (USC) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "Consequences of Reasoning with Conflicting Obligations".

Felix Pinkert (St Andrews) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "Inductive Proofs for Many-Hands Cases in Ethics ".

Gerhard Schurz (Düsseldorf) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "Formal Versions of Hume's Is-Ought Thesis".

Mathieu Beirlaen (Ghent) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "Dynamic Proof Theories for Reasoning with (Conditional) Norms".

Hlynur Orri Stefansson (LSE) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "Fairness and Counterfactuals".

Ralf M. Bader (Oxford) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "Separability and admissible factorisations".

Nathan Robert Howard (Toronto) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "The Good Samaritan Paradox".

John Horty (University of Maryland) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "Common Law Reasoning".

Paul McNamara (New Hampshire) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "Toward a Formal Framework for Some Fundamental Common Moral Statuses".

Gert-Jan C. Lokhorst (Delft) gives a talk at the MCMP Formal Ethics Workshop (11-13 October, 2012) titled "Mally's Deontic Logic (1926)".

Branden Fitelson (Rutgers) and Richard Pettigrew (Bristol) discuss philosophical approaches to coherence, differing perspectives, and formal/conceptual common grounds in part 2 ("Truth Table") of the MCMP Round Table on Coherence (20 July, 2012). Abstract: Recent arguments for probabilistic norms have attempted to justify coherence requirements for (sets of) degrees of confidence solely by appeal to considerations involving their accuracy. Richard Pettigrew, Bristol, and Branden Fitelson, Rutgers, (and their collaborators) have worked extensively on various arguments of this sort. This public MCMP event is to bring their differing approaches and perspectives to one table.

David Etlin (Groningen) comments on Hans Rott's "Two concepts of plausibility in default reasoning" at the 9th Formal Epistemology Workshop (Munich, May 29–June 2, 2012).