Five Years MCMP: Quo Vadis, Mathematical Philosophy?
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Program

Room Arrangement

DateAddress
2 & 3 June Südliches Schlossrondell 23
D-80639 Munich
4 June Lecture Hall A120
Geschwister-Scholl-Platz 1
D-80539 Munich

Day 1 (2 June, 2016)

TimeTopic
09:00 - 09:30 Registration.
09:30 - 10:00 Opening: Hannes Leitgeb, Stephan Hartmann, Martin Wirsing (LMU Vicepresident).
10:00 - 10:30 Roland Poellinger: "Five Years: Looking Back" (Watch online)
Chair: Stephan Hartmann & Hannes Leitgeb 
10:30 - 11:00 Coffee Break.
11:00 - 11:20 Johannes Korbmacher: "What is Truthmaker Semantics?" (Watch online)
Chair: Alexander Reutlinger
11:20 - 11:40 Chloé de Canson: "How Bayesianism Addresses the Problem(s) of Induction" (Watch online)
Chair: Alexander Reutlinger 
11:40 - 12:00 Radin Dardashti: "What Are No-Go Theorems Good for?" (Watch online)
Chair: Alexander Reutlinger 
12:30 - 14:00 Lunch.
14:00 - 14:20 Huimin Dong: "Open Reading for Free Choice Permission: A Perspective in Substructural Logics" (Watch online)
Chair: Gil Sagi 
14:20 - 14:40 Liam Kofi Bright: "Valuing Questions" (Watch online)
Chair: Gil Sagi 
14:40 - 15:00 Ilaria Canavotto: "A Math-Philosophical Approach to Deontic Concepts" (Watch online)
Chair: Gil Sagi 
15:00 - 15:30 Discussion
15:30 - 16:00 Coffee Break.
16:00 - 17:30 Anne Siegetsleitner: "Ethics and Morality in the Vienna Circle" (Watch online)
Chair: Hannes Leitgeb 
17:30 - 19:00 General Discussion.
Chair: Hannes Leitgeb 

Day 2 (3 June, 2016)

TimeTopic
09:00 - 10:30 The Ideas Session.
Chair: Hannes Leitgeb 
10:30 - 11:00 Coffee Break.
11:00 - 11:20 Catrin Campbell-Moore: "Self-Referential Probability" (Watch online)
Chair: Adam Caulton 
11:20 - 11:40 Laurenz Hudetz: "Towards an Adequate Criterion of Structural Equivalence of Theories" (Watch online)
Chair: Adam Caulton 
11:40 - 12:00 Rossella Marrano: "Degrees of Truth Explained Away" (Watch online)
Chair: Adam Caulton 
12:30 - 14:00 Lunch.
14:00 - 14:20 Lavinia Picollo: "Formal Methods in the Study of Truth" (Watch online)
Chair: Gregory Wheeler 
14:20 - 14:40 Silvia de Toffoli: "Notations and Diagrams in Algebra" (Watch online)
Chair: Gregory Wheeler 
14:40 - 15:00 Thomas Schindler: "A Deflationary Account of Classes" (Watch online)
Chair: Gregory Wheeler 
15:30 - 16:00 Coffee Break.
16:00 - 17:30 Hannes Leitgeb: "Mathematical Empiricism" (Watch online)
Chair: Stephan Hartmann 
17:30 - 19:00 General Discussion.
Chair: Stephan Hartmann 
19:30 Workshop Dinner (Schwaige Nymphenburg).

Day 3 (4 June, 2016)

TimeTopic
11:30 - 11:50 Marta Sznajder: "Inductive Reasoning with Conceptual Spaces: A Proposal for Analogy" (Watch online)
Chair: Martin Fischer 
11:50 - 12:10 Hans-Christoph Kotzsch: "On Some Recent Developments in the Categorical Semantics of Modal Logic"
Chair: Martin Fischer 
12:10 - 12:30 Discussion.
Chair: Martin Fischer 
12:30 - 14:00 Lunch.
14:00 - 14:20 Kristina Liefke: "Relating Theories of Intensional Semantics: Established Methods and Surprising Results" (Watch online)
Chair: Lavinia Picollo 
14:20 - 14:40 Thomas Meier: "Quo Vadis Mathemetical Philosophy - An Application from The Philosophy of Linguistics"
Chair: Lavinia Picollo 
14:40 - 15:00 Discussion.
Chair: Lavinia Picollo 
15:00 - 15:30 Coffee Break.
15:30 - 17:00 André Carus: "Mathematical Philosophy and Leitgeb’s Carnapian Big Tent: Past, Present, Future" (Watch online)
Chair: Norbert Gratzl 
17:00 - 18:30 General Discussion.
Chair: Norbert Gratzl 

Abstracts

Liam Kofi Bright (CMU Pittsburgh): Valuing Questions

If all scientists seek the truth, will they agree on how this search should be carried out? Social epistemologists have alleged that were scientists to be truth seekers they would display an unwelcome homogeneity in their choice of what projects to pursue. However, philosophers of science have argued that the injunction to seek the truth is incapable of providing any guidance to scientific project selection. Drawing on theories of the semantics of questions to construct a model of project selection, I argue that the injunction to seek the truth can guide choice through a philosophcially well motivated decision theory, but may indeed discourage division of cognitive labour. I end by discussing methods of maintaining heterogeneity among a community of inquirers, even veritistic ones, in light of my results.top

Catrin Campbell-Moore (University of Cambridge/MCMP): Self-Referential Probability

In this talk we consider situations where what someone believes can affect what happens, for example: Bettie will be able to jump across a river just if she's confident that she'll be able to do so. These situations can cause problems in formal epistemology: what beliefs are rational for such agents? Such situations bear a close relationship to sentences that say something about their own truth, such as the liar paradox, and the vast amount of work in mathematical philosophy on theories of truth can give insights into how to think about these more realistic situations too. Instead of studying type-free truth, then, we think about type-free (subjective) probability, but there are very similar considerations. This therefore provides a traditional area of mathematical philosophy a new and exciting application.top

Ilaria Canavotto (LMU Munich/MCMP): A Math-Philosophical Approach to Deontic Concepts

The aim of this talk is to present relevant open lines of research in deontic logic, especially in deontic logic of actions (ought-to-do logic), so as to provide evidence of the potential that mathematical philosophy has in the analysis of prescriptive concepts. I will do this by first making explicit what I take mathematical philosophy to be, at least ideally. I will then consider to what extent dynamic deontic logic (DDL) approaches the proposed model, and suggest that DDL represents a promising starting point to further investigate themes and address problems which are central both to action logic and deontic logic, including the distinction between action and ability, the characterization of a proper notion of action negation and the problem of accounting for normative conflicts without incurring in a trivialization of the system.top

André W. Carus: Mathematical Philosophy and Leitgeb’s Carnapian Big Tent: Past, Present, Future

Hannes Leitgeb’s conception of mathematical philosophy, reflected in the success of the MCMP, is characterized by a pluralism — a Big Tent program — that shows remarkable continuity with the Vienna Circle, as now understood. But logical empiricism was notoriously opposed to metaphysics, which Leitgeb and other recent scientifically-oriented philosophers, such as Ladyman and Ross, embrace to varying degrees. So what, if anything, do these new, post-Vienna scientific philosophies exclude? Ladyman and Ross explicitly exclude much of recent analytic metaphysics, decrying it — very much in the logical empiricist spirit of critical Enlightenment — as vernacular “domestication” of counter-intuitive science. But it turns out, in the light of recent research on Carnap’s later thought, that Leitgeb’s Big Tent conception, though it excludes less than Ladyman and Ross, adheres more closely to Carnap’s Enlightenment ideal.top

Radin Dardashti (LMU Munich/MCMP): What Are No-Go Theorems Good for?

No-go Theorems in physics have often been construed as impossibility results with respect to some goal. These results usually have had two effects on the field. Either, the no-go result effectively stopped that research programme or one or more of the assumptions involved in the derivation were questioned. In this talk I address some general features of no-go theorems and try to address the question how no-go results should be interpreted. The way they should be interpreted differs significantly from how they have been interpreted in the history of physics. More specifically, I will argue that no-go theorems should not be understood as implying the impossibility of a desired result, and therefore do not play the methodological role they purportedly do, but that they should be understood as a rigorous way to outline the methodological pathways in obtaining the desired result.top

Cloé de Canson (University of Cambridge): How Bayesianism Addresses the Problem(s) of Induction

The paper seeks to argue that Bayesian Confirmation Theory is the right kind of theory to account for confirmation. More precisely, a thorough (non-Bayesian) analysis of the paradox of the raven is used to show that (i) propositions play the role of evidence; (ii) there are two relations involved in confirmation, a logical one whose relata are propositions, and an epistemic one whose antecedent is a learning event; (iii) background knowledge is highly relevant; (iv) the logical relation is non-monotonic. The paper then shows that, unlike the hypothetico-deductive method and broadly Carnapian approaches, Bayesian Confirmation Theory satisfies all these criteria, and concludes that it is the right sort of theory to account for confirmation.top

Silvia de Toffoli (Stanford University): Notations and Diagrams in Algebra

The aim of this talk is to investigate the roles of Commutative Diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that, differently from other mathematical diagrams, CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation, that goes beyond the traditional bipartition of mathematical representations into graphic and linguistic. It will be argued that one of the reasons why CDs form a good notation is that they are highly ‘mathematically tractable’: experts can obtain valid results by ‘calculating’ with CDs. These calculations, take the form of a ‘diagram chase’. In order to draw inferences, experts move algebraic elements around the diagrams. These diagrams present a dynamic nature. It is thanks to their dynamicity that CDs can externalize the relevant reasoning and allow experts to draw conclusions directly by manipulating them. Lastly, it will be shown that CDs play essential roles in the context of proof as well as in other phases of the mathematical enterprise, such as discovery and conjecture.top

Huimin Dong (University of Bayreuth): Open Reading for Free Choice Permission: A Perspective in Substructural Logics

This talk proposes a new solution to the well-known free choice permission para- dox [2], combining ideas from substructural logics and non-monotonic reasoning. Free choice permission is intuitively understood as “if it is permitted to A or B then it is permitted to do A and it is permitted to do B.” Yet one of its logically equivalent form allows the following inference which seems clearly unacceptable: if it is permitted to order a lunch then it is permitted to order a lunch and not pay for it [2]. The challenge for a logic of free choice permission is to exclude such counter-intuitive consequences while not giving up too much deductive power. We suggest that the right way to do so is using a family of substructural logics augmented with principles borrowed from non-monotonic reasoning. Our semantic strategy to face the challenge of free choice permission as a follow-up research proposed in [1].top

Laurenz Hudetz (University of Salzburg): Towards an Adequate Criterion of Structural Equivalence of Theories

My aim in this talk is to provide a general and adequate explication of structural equivalence of scientific theories. I will first give a brief overview of the recent debate about criteria for structural equivalence and highlight the main problems of the criteria proposed so far. I argue that an adequate criterion of equivalence should explicitly take into account morphisms between the models of theories. The criterion of categorical equivalence does this and has been frequently considered recently (cf. Weatherall, 2015; Barrett, Rosenstock and Weatherall, 2015; Hudetz, 2015; Halvorson, 2016; Barrett and Halvorson, 2016; Weatherall, 2016; Halvorson and Tsementzis, 2016). Yet, it is not free of problems. I show that categorial equivalence is much too wide as a criterion of structural equivalence of theories. Then I will propose a solution to this problem by specifying a strengthening of categorical equivalence, which I call 'definable categorical equivalence'. This strengthened criterion employs the model-theoretic notion of definability. I argue that definable categorical equivalence is neither too wide nor too narrow.top

Johannes Korbmacher (LMU Munich/MCMP): What is Truthmaker Semantics?

The aim of this short programmatic talk is to try to clear up some fundamental concepts of truthmaker semantics. Among the questions that will be addressed are: What is special about truthmaker semantics? What is the concept of truthmaking in truthmaker semantics? What is the concept of truthmakers in truthmaker semantics? The result of the talk will be a list of questions I think proponents of truthmaker semantics should address in the future. What is Truthmaker Semantics?

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Hans-Christoph Kotzsch (LMU Munich/MCMP): On Some Recent Developments in the Categorical Semantics of Modal Logic

We describe a new, more refined, approach to modelling modal logic in a topos. It is slightly more flexbile, but compatible, with the one studied earlier. We outline some of its consequences and uses, including topological completeness of higher-order modal logic.
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Hannes Leitgeb (LMU Munich/MCMP): Mathematical Empiricism. A Methodological Proposal

I will propose a way of doing (mathematical) philosophy which I am calling 'mathematical empiricism'. It is the proposal to rationally reconstruct language, thought, ends, decision-making, communication, social interaction, norms, ideals, and so on, in conceptual frameworks. The core of each such framework will be a space of "possibilities", however, these "possibilities" will consist of nothing else than mathematical structures labeled by empirical entities. Mathematical empiricism suggests to carry out (many) rational reconstructions in such mathematical-empirical conceptual frameworks. When the goal is to rationally reconstruct a part of empirical science itself (which is but one philosophical goal amongst many others), it will be reconstructed as "taking place" within such frameworks, whereas the frameworks themselves may be used to rationally reconstruct some of the presuppositions of that part of empirical science. While logic and parts of philosophy of science study such frameworks from an external point of view, with a focus on their formal properties, metaphysics will be embraced as studying such frameworks from within, with a focus on what the world looks like if viewed through a framework. When mathematical empiricists carry out their investigations in these and in other areas of philosophy, no entities will be postulated over and above those of mathematics and the empirical sciences, and no sources of epistemic justification will be invoked beyond those of mathematics, the empirical sciences, and personal and social experience (if consistent with the sciences). And yet mathematical empiricism, with its aim of rational reconstruction, will not be reducible to mathematics or empirical science. When a fragment of science is reconstructed in a framework, the epistemic authority of science will be acknowledged within the boundaries of the framework, while as philosophers we are free to choose the framework for reconstruction and to discuss our choices on the metalevel, all of which goes beyond the part of empirical science that is reconstructed in the framework. There is a great plurality of mathematical-empirical frameworks to choose from; even when ultimately each of them needs to answer to mathematical-empirical truth, this will underdetermine how successfully they will serve rational reconstruction. In particular, certain metaphysical questions will be taken to be settled only by our decisions for or against conceptual frameworks, and these decisions may be practically expedient for one purpose and less so for another. The overall hope will be to take what was good and right about the distinctively Carnapian version of logical empiricism, and to extend and transform it into a more tolerant, less constrained, and conceptually enriched logical-mathematical empiricism 2.0.top

Kristina Liefke (LMU Munich/MCMP): Relating Theories of Intensional Semantics: Established Methods and Surprising Results

Formal semantics comprises a plethora of ‘intensional’ theories which model propositional attitudes through the use of different ontological primitives (e.g. possible/impossible worlds, partial situations, unanalyzable propositions). The ontological relations between these theories are, today, still largely unexplored. In particular, it remains unclear whether the basic objects of some of these theories can be reduced to objects from other theories (s.t. phenomena which are modeled by one theory can also be modeled by the other theories), or whether some of these theories can even be reduced to ontologically ‘poor’ theories (e.g. extensional semantics) which do not contain intensional objects like possible worlds.

This talk surveys my recent work on ontological reduction relations between the above theories. This work has shown that – more than preserving the modeling success of the reduced theory – some reductions even improve upon the theory’s modeling adequacy or widen the theory’s modeling scope. Our talk illustrates this observation by two examples: (i) the relation between Montague-/possible world-style intensional semantics and extensional semantics, and (ii) the relation between intensional semantics and situation-based single-type semantics. The relations between these theories are established through the use of associates from higher-order recursion theory (cf. (i)) and of type-coercion from programming language theory (cf. (ii)).

Part of this work is joined with Markus Werning (RUB Bochum) and Sam Sanders (LMU Munich/MCMP).top

Rossella Marrano (Scuola Normale Superiore Pisa): Degrees of Truth Explained Away

The notion of degrees of truth arising in infinite-valued logics has been the object of long-standing criticisms. In this paper I focus on the alleged intrinsic philosophical implausibility of degrees of truth, namely on objections concerning their very nature and their role, rather than on objections questioning the adequacy of degrees of truth as a model for vagueness. I suggest that interpretative problems encountered by the notion are due to a problem of formalisation. On the one hand, indeed, degrees of truth are artificial, to the extent that they are not present in the phenomenon they are meant to model, i.e. graded truth. On the other hand, however, they cannot be considered as artefacts of the standard model, contra what is sometimes argued in the literature. I thus propose an alternative formalisation for graded truth based on comparative judgements with respect to the truth. This model provides a philosophical underpinning for degrees of truth of structuralist flavour: they are possible numerical measures of a comparative notion of truth. As such, degrees of truth can be considered artefacts of the model, thus avoiding the aforementioned objections.top

Thomas Meier (LMU Munich/MCMP): Quo Vadis Mathemetical Philosophy - An Application from The Philosophy of Linguistics

I will show and discuss some examples of my doctoral (and postdoctoral) research, mainly from the philosophy of science, applied to the debate on structural realism, the dynamics of theories and to linguistics. Furthermore, there will be some metaphilosophical questions at the end.top

Lavinia Picollo (LMU Munich/MCMP): Formal Methods in the Study of Truth

The nature of truth has been an issue in philosophy since ancient times. Several theories have been proposed, the most popular of which is correspondentism, the idea that truth bearers are true as long as they correspond to certain chunks of reality. At the beginning of the XX century a rival theory emerged: deflationism. Unlike correspondentists, deflationists put forward an explanation of truth in logical terms. This leads to the formulation of formal truth systems, which requires the application of mathematical methods. First, I briefly introduce correspondentism and deflationism, and indicate how the latter prompts the search for formal systems. Second, I show why the obvious system cannot work and propose another way of constructing truth theories based on relative interpretations.top

Roland Poellinger (LMU Munich/MCMP): Five Years: Looking Back

In this presentation I will speak about the MCMP's outreach and line up some of the center's achievements in the last five years. I will put special emphasis on our media output since many of our activities are mirrored in our media-related efforts such as our video channels on iTunes U, our Coursera online courses, and our publication database on the MCMP's web portal.
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Thomas Schindler (University of Cambridge/MCMP): A Deflationary Account of Classes

Charles Parsons claims that the introduction of the notion of class answers to a need to generalise on predicate places. Similarly, the notion of truth answers to a need to generalise on sentence places. Deflationism about truth is the view that truth is no more than that. This suggests that we should also consider deflationism about classes. I'll start by exploring some consequences of a deflationary account of classes. In the second part of the talk I'll present a type-free theory of classes in which a substantial amount of mathematics can be reconstructed.top

Anne Siegetsleitner (University of Innsbruck): Ethics and Morality in the Vienna Circle

In my talk I will present key aspects of a long-overdue revision of the prevailing view on the role and conception of ethics and morality in the Vienna Circle. This view is rejected as being too partial and undifferentiated. Not all members supported the standard view of logical empiricist ethics, which is held to be characterized by the acceptance of descriptive empirical research, the rejection of normative and substantial ethics as well as an extreme non-cognitivsm. Some members applied formal methods, some did not. However, most members shared an enlightened and humanistic version of morality and ethics. I will show why these findings are still relevant today, not least for mathematical philosophers.top

Marta Sznajder (University of Groningen/MCMP): Inductive Reasoning with Conceptual Spaces: A Proposal for Analogy

In his late work on inductive logic Carnap introduced the conceptual level of representations – i.e. conceptual spaces – into his system. Traditional inductive logic (e.g. Carnap 1950) is a study of inductive reasoning that belongs to the symbolic level of cognitive representation (in the three-level view of representations presented by Gärdenfors (2000)). In the standard, symbolic approach the confirmation functions are functions applied to propositions defined with respect to a particular formal language. In my project I investigate alternative approach that is a step towards modelling inductive reasoning directly on the conceptual spaces: considering probability densities (or distributions) over the set of points in a conceptual space rather than traditional credences over propositions.

I will present one way in which analogical effects can enter inductive reasoning, using the tools of Bayesian statistics and building up from Carnap’s idea that analogical dependencies between predicates can be read off conceptual spaces via the distances that encode similarity relations between predicates. I consider a quasi-hierarchical Bayesian model in which the different hypotheses considered by the agent are probability distributions over a one-dimensional conceptual space, representing possible distributions of the particular qualities among a studied population.