MCMP – Epistemology LudwigMaximiliansUniversität München

 Philosophy
Mathematical Philosophy  the application of logical and mathematical methods in philosophy  is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.
The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.
Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logicalmathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.

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New Responses to Some Purported Counterexamples to Likelihoodist Principles
Colloquium Mathematical Philosophy, Greg Gandenberger (Pittsburgh) gives a talk at the MCMP Colloquium (22 April, 2015) titled "New Responses to Some Purported Counterexamples to Likelihoodist Principles". Abstract: The Likelihood Principle is important because the frequentist statistical methods that are most commonly used in science violate it, while rival likelihoodist and Bayesian methods do not. It is supported by a variety of arguments, including several proofs from intuitively plausible axioms. It also faces many objections, including several purported counterexamples. In this talk, I provide new responses to four purported counterexamples to the Likelihood Principle and its nearcorollary the Law of Likelihood that are not adequately addressed in the existing literature. I first respond to examples due to Fitelson and Titelbaum that I argue are adequately addressed by restricting the Law of Likelihood to mutually exclusive hypotheses. I then respond to two counterexamples from the statistical literature. My responses to these latter examples are novel in that they do not appeal to prior probabilities, which is important for attempts to use the Likelihood Principle to provide an argument for Bayesian approaches that does presuppose the permissibility of using prior probabilities in science.

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A Pragmatic Vindication of Epistemic Utility Theory
Colloquium Mathematical Philosophy, Ben Levinstein (Oxford) gives a talk at the MCMP Colloquium (6 May, 2015) titled "A Pragmatic Vindication of Epistemic Utility Theory". Abstract: Traditionally, probabilism and other norms on partial belief have been motivated from a pragmatic point of view. For instance, as Frank Ramsey long ago showed, if you're probabilistically incoherent, then you're subject to a set of bets each of which you consider fair but which are jointly guaranteed to result in a net loss. Since Joyce's seminal 1998 paper, some epistemologists have shifted course and have tried to establish norms on epistemic states without any recourse to practical rationality. I use a theorem from Schervish to bridge the gap between these two approaches. We can either take standard measures of accuracy to be formalizations of purely epistemic value, or we can generate them from what are at base practical foundations. Even if we opt for this latter approach, I show we can mostly cordon off the epistemic from the practical while ultimately grounding epistemic norms in purely practical rationality.

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An Axiomatization of Individual and Social Updates
Colloquium Mathematical Philosophy, Denis Bonnay (Paris Quest/IHPST) gives a talk at the MCMP Colloquium (30 April, 2015) titled "An Axiomatization of Individual and Social Updates". Abstract: In this talk, I will consider update rules, which an agent may follow in order to update her subjective probabilities and take into account new information she receives. I will consider two different situations in which this may happen: (1) individual updates: when an agent learns the probability for a particular event to have a certain value. (2) social updates: when an agent learns the probability an other agent's gives to a particular event. Jeffrey's conditioning and weighted averaging are two famous update rules, in individual and social situations respectively. I will show that both can be axiomatized by means of one and the same invariance principle, related to Carnap's use of invariance in his work on probabilities.

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Collective Accuracy: Agent Based & Emergent vs Statistical and Assumed
Conference on AgentBased Modeling in Philosophy, Scott Page (Michigan) gives a talk at the Conference on AgentBased Modeling in Philosophy (1113 December, 2014) titled "Collective Accuracy: Agent Based & Emergent vs Statistical and Assumed". Abstract: In this talk, I describe two broad classes of models that can explain collective accuracy, what is more commonly referred to as the wisdom of crowds. The first model is based on statistical/law of large numbers logic. Accuracy emerges from the cancellation of random errors. The second model has roots in computer science and psychology. It assumes that predictions come from models. Different predictions arise because of different model. I then describe how in agent based models the amount model diversity, and therefore the accuracy of the collective emerges. It is possible to write difference equations that explain average diversity levels. The talk will summarize papers written with Lu Hong, Maria Riolo, PJ Lamberson, and Evan Economo.

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Agentbased Models and Confirmation Theory
Conference AgentBased Modeling in Philosophy, Michael Weisberg (Pennsylvania) gives a talk at the Conference on AgentBased Modeling in Philosophy (1113 December, 2014) titled "Agentbased Models and Confirmation Theory". Abstract: Is it possible to develop a confirmation theory for agentbased models? The are good reasons to be skeptical: Classical confirmation theory explains how empirical evidence bears on the truth of hypotheses and theories, while agentbased models are almost always idealized and hence known to be false. Moreover, classical ideas about confirmation have been developed for relatively simple hypotheses, while even the simplest agentbased models have thousands of variables. Nevertheless, we can draw on ideas from confirmation theory in order to develop an account of agentbased model confirmation. Theorists can confirm hypotheses about model/world relations, and they can also use a variety of techniques to investigate the reliability of model results. This paper is an exploration of these possibilities.

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I Believe I don't Believe. (And So Can You!)
Colloquium Mathematical Philosophy, Aidan Lyon (Maryland, MCMP) gives a talk at the MCMP Colloquium (13 November, 2014) titled "I Believe I don't Believe. (And So Can You!)". Abstract: Contemporary epistemology offers us two very different accounts of our epistemic lives. According to Traditional epistemologists, the decisions that we make are motivated by our desires and guided by our beliefs and these beliefs and desires all come in an allornothing form. In contrast, many Bayesian epistemologists say that these beliefs and desires come in degrees and that they should be understood as subjective probabilities and utilities. What are we to make of these different epistemologies? Are the Tradionalists and the Bayesians in disagreement, or are their views compatible with each other? Some Bayesians have challenged the Traditionalists: Bayesian epistemology is more powerful and more general than the Traditional theory, and so we should abandon the notion of allornothing belief as something worthy of philosophical analysis. The Traditionalists have responded to this challenge in various ways. I shall argue that these responses are inadequate and that the challenge lives on.