How Bayesianism Adresses the Problem(s) of Induction

Thomas Schindler (University of Cambridge/MCMP) gives a talk at the Workshop on Five Years MCMP: Quo Vadis, Mathematical Philosophy? (2-4 June, 2016) titled "A Deflationary Account of Classes". Abstract: 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.

Lavinia Picollo (LMU/MCMP) gives a talk at the Workshop on Five Years MCMP: Quo Vadis, Mathematical Philosophy? (2-4 June, 2016) titled "Formal Methods in the Study of Truth". Abstract: 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.

Chloé de Canson (University of Cambridge) gives a talk at the Workshop on Five Years MCMP: Quo Vadis, Mathematical Philosophy? (2-4 June, 2016) titled "How Bayesianism Addresses the Problem(s) of Induction". Abstract: 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.

Johannes Korbmacher (LMU/MCMP) gives a talk at the Workshop on Five Years MCMP: Quo Vadis, Mathematical Philosophy? (2-4 June, 2016) titled "What is Truth-Maker Semantics?". Abstract: 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?

Laurenz Hudetz (University of Salzburg) gives a talk at the Workshop on Five Years MCMP: Quo Vadis, Mathematical Philosophy? (2-4 June, 2016) titled "Towards an Adequate Criterion of Structural Equivalence of Theories". Abstract: 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.

Catrin Campbell-Moore (University of Cambridge/MCMP) gives a talk at the Workshop on Five Years MCMP: Quo Vadis, Mathematical Philosophy? (2-4 June, 2016) titled "Self-Referential Probability". Abstract: 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.

Ilaria Canavotto (LMU/MCMP) gives a talk at the Workshop on Five Years MCMP: Quo Vadis, Mathematical Philosophy? (2-4 June, 2016) titled "A Math-Philosophical Approach to Deontic Concepts". Abstract: 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.

Huimin Dong (University of Bayreuth) gives a talk at the Workshop on Five Years MCMP: Quo Vadis, Mathematical Philosophy? (2-4 June, 2016) titled "Open Reading for Free Choice Permission: A Perspective in Substructural Logics". Abstract:

André W. Carus (LMU) gives a talk at the Workshop on Five Years MCMP: Quo Vadis, Mathematical Philosophy? (2-4 June, 2016) titled "Mathematical Philosophy and Leitgeb’s Carnapian Big Tent: Past, Present, Future". Abstract: 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.

Kristina Liefke (LMU/MCMP) gives a talk at the Workshop on Five Years MCMP: Quo Vadis, Mathematical Philosophy? (2-4 June, 2016) titled "Relating Theories of Intensional Semantics: Established Methods and Surprising Results". Abstract: 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).