Stephan Hartmann

Some naturalistic philosophers of mind subscribing to the predictive processing theory of mind have adopted a realist attitude towards the results of Bayesian cognitive science. In this paper, we argue that this realist attitude is unwarranted. The Bayesian research program in cognitive science does not possess special epistemic virtues over alternative approaches for explaining mental phenomena involving uncertainty. In particular, the Bayesian approach is not simpler, more unifying, or more rational than alternatives. It is also contentious that the Bayesian approach is overall better supported by the empirical evidence. So, to develop philosophical theories of mind on the basis of a realist interpretation of results from Bayesian cognitive science is unwarranted. Naturalistic philosophers of mind should instead adopt an anti-realist attitude towards these results and remain agnostic as to whether Bayesian models are true. For continuing on with an exclusive focus and praise of Bayes within debates about the predictive processing theory will impede progress in philosophical understanding of scientific practice in computational cognitive science as well as of the architecture of the mind.

We present a Bayesian analysis of the epistemology of analogue experiments with particular reference to Hawking radiation. Provided such experiments can be externally validated via universality arguments, we prove that they are confirmatory in Bayesian terms. We then provide a formal model for the scaling behaviour of the confirmation measure for multiple distinct realisations of the analogue system and isolate a generic saturation feature. Finally, we demonstrate that different potential analogue realisations could provide different levels of confirmation. Our results thus provide a basis both to formalise the epistemic value of analogue experiments that have been conducted and to advise scientists as to the respective epistemic value of future analogue experiments.

Deliberation is a standard procedure to make decisions in not too large groups. It has the advantage that the group members can learn from each other and that, at the end, often a consensus emerges that everybody endorses. But a deliberation procedure also has a number of disadvantages. E.g., what consensus is reached usually depends on the order in which the different group members speak. More specifically, the group member who speaks first often has an unproportionally high impact on the final decision: She anchors the deliberation process. While the anchoring effect undoubtably appears in real deliberating groups, we ask whether it also appears in groups whose members are truth-seeking and rational in the sense that they take the information provided by their fellow group members properly into account by updating their beliefs according to plausible rules. To answer this question and to make some progress towards explaining the anchoring effect, a formal model is constructed and analyzed. Using this model, we study the anchoring effect in homogenous groups, for which we provide analytical results, and in inhomogeneous groups, for which we provide simulation results.

A widely shared view in the cognitive sciences is that discovering and assessing explanations of cognitive phenomena whose production involves uncertainty should be done in a Bayesian framework. One assumption supporting this modelling choice is that Bayes provides the best approach for representing uncertainty. However, it is unclear that Bayes possesses special epistemic virtues over alternative modelling frameworks, since a systematic comparison has yet to be attempted. Currently, it is then premature to assert that cognitive phenomena involving uncertainty are best explained within the Bayesian framework. As a forewarning, progress in cognitive science may be hindered if too many scientists continue to focus their efforts on Bayesian modelling, which risks to monopolize scientific resources that may be better allocated to alternative approaches.

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. This paper presents a case study of a new type of intertheoretic relation that is inspired by Montague’s analysis of the linguistic syntax-semantics relation. The paper develops a simple model of this relation. To motivate the adoption of our new model, we show that this model extends the scope of application of the Nagelian models and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework.

This paper focuses on the question of how to resolve disagreement and uses the Lehrer-Wagner model as a formal tool for investigating consensual decision-making. The main result consists in a general definition of when agents treat each other as epistemic peers (Kelly 2005; Elga 2007), and a theorem vindicating the “equal weight view” to resolve disagreement among epistemic peers. We apply our findings to an analysis of the impact of social network structures on group deliberation processes, and we demonstrate their stability with the help of numerical simulations.

It is often claimed that the greatest value of the Bayesian framework in cognitive science consists in its unifying power. Several Bayesian cognitive scientists assume that unification is obviously linked to explanatory power. But this link is not obvious, as unification in science is a heterogeneous notion, which may have little to do with explanation. While a crucial feature of most adequate explanations in cognitive science is that they reveal aspects of the causal mechanism that produces the phenomenon to be explained, the kind of unification afforded by the Bayesian framework to cognitive science does not necessarily reveal aspects of a mechanism. Bayesian unification, nonetheless, can place fruitful constraints on causal–mechanical explanation. 1 Introduction2 What a Great Many Phenomena Bayesian Decision Theory Can Model3 The Case of Information Integration4 How Do Bayesian Models Unify?5 Bayesian Unification: What Constraints Are There on Mechanistic Explanation?5.1 Unification constrains mechanism discovery5.2 Unification constrains the identification of relevant mechanistic factors5.3 Unification constrains confirmation of competitive mechanistic models6 ConclusionAppendix.

Inductive Logic is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration.

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. In this paper, we present a model of a new type of intertheoretic relation, called 'Montague Reduction', which is assumed in Montague's framework for the analysis and interpretation of natural language syntax. To motivate the adoption of our new model, we show that this model extends the scope of application of the Nagelian (or related) models, and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework.

Der Begriff ‘Modell’ leitet sich vom Lateinischen ‘modulus’ (das Maß) ab, im Italienischen existiert seit dem 16. Jh. ‘modello’ und R. Descartes verwendet im 17. Jh. ‘modèlle’. Während der Begriff in Architektur und Kunst schon seit der Renaissance gängig ist, wird er in den Naturwissenschaften erst im 19. Jh. verwendet.1 Dort greifen wissenschaftliche Modelle die für eine gegebene Problemstellung als wesentlich erachteten Charakteristika (Eigenschaften, Beziehungen, etc.) eines Untersuchungsgegenstandes heraus und machen diesen so einem Verständnis bzw. einer weiterführenden Untersuchung zugänglich. Es ist üblich, zwischen Skalenmodellen, Analogmodellen und theoretischen Modellen zu unterscheiden.

Here P is the density operator of the system under consideration, and σ ± and σ 3 are the usual Pauli matrices, acting on atom i whose states are |1 > or |0 >, representing, respectively, the atom being in an excited state or in the ground state. B and C are appropriate decay constants and s has been called the pumping parameter [1]. It varies from s = 0 for pure damping to s = 1 for full laser action. To solve the corresponding quantum master equations, three approaches have been taken: First, one focuses on the case of one atom. Second, one truncates eq. (1) and derives semi-classical models. Third, one employs numerical simulation methods such as the quantum trajectory method. While the latter method is very popular, it should be noted that the numerical complexity of the problem increases exponentially with the number of atoms, and so numerical methods soon become unfeasible.

In a famous experiment by Tversky and Kahneman (Psychol Rev 90:293–315, 1983), featuring Linda the bank teller, the participants assign a higher probability to a conjunction of propositions than to one of the conjuncts, thereby seemingly committing a probabilistic fallacy. In this paper, we discuss a slightly different example featuring someone named Walter, who also happens to work at a bank, and argue that, in this example, it is rational to assign a higher probability to the conjunction of suitably chosen propositions than to one of the conjuncts. By pointing out the similarities between Tversky and Kahneman’s experiment and our example, we argue that the participants in the experiment may assign probabilities to the propositions in question in such a way that it is also rational for them to give the conjunction a higher probability than one of the conjuncts

A federal assembly consists of a number of representatives for each of the nations (states, Länder, cantons,...) that make up the federation. How many representatives should each nation receive? What makes this issue worth quibbling about is that the model of representation that is instituted will have an impact on the welfare distribution over the nations in the federation that will ensue over due course. We will investigate what models of representation yield welfare distributions that score higher on a utilitarian measure. First, we construct a continuum of models of representation ranging from equal to proportional representation. In between these extremes are models of degressive proportionality. We run a Monte-Carlo simulation in which a large number of motions are voted up or down within different contexts of evaluation and investigate how well the resulting welfare distributions score on the utilitarian measure. Subsequently, we will provide matching analytical results for a slightly idealized case. We conclude with a discussion of the significance of our results and of the role of simulations and analytical results and point to further work.

There is a long philosophical tradition of addressing questions in philosophy of science and epistemology by means of the tools of Bayesian probability theory (see Earman (1992) and Howson and Urbach (1993)). In the late '70s, an axiomatic approach to conditional independence was developed within a Bayesian framework. This approach in conjunction with developments in graph theory are the two pillars of the theory of Bayesian Networks, which is a theory of probabilistic reasoning in artificial intelligence. The theory has been very successful over the last two decades and has found a wide array of applications ranging from medical diagnosis to safety systems for hazardous industries.

The variety of evidence thesis in confirmation theory states that more varied supporting evidence confirms a hypothesis to a greater degree than less varied evidence. Under a very plausible interpretation of this thesis, positive test results from multiple independent instruments confirm a hypothesis to a greater degree than positive test results from a single instrument. We invoke Bayesian Networks to model confirmation on grounds of evidence that is obtained from less than fully reliable instruments and show that the variety of evidence thesis is not sacrosanct when testing is conducted with less than fully reliable instruments: under certain conditions, a hypothesis receives more confirmation from evidence that is obtained from one rather than from more independent instruments. In the appendix, we prove certain convergence results for large numbers of positive test results from single versus multiple less than fully reliable instruments.

The aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on the same propositions has recently drawn much attention. Seemingly reasonable aggregation procedures, such as propositionwise majority voting, cannot ensure an equally consistent collective conclusion. The literature on judgment aggregation refers to such a problem as the \textit{discursive dilemma}. In this paper we assume that the decision which the group is trying to reach is factually right or wrong. Hence, we address the question of how good the various approaches are at selecting the right conclusion. We focus on two approaches: distance-based procedures and a Bayesian analysis. They correspond to group-internal and group-external decision-making, respectively. We compare those methods in a probabilistic model, demonstrate the robustness of our results over various generalizations and discuss their applicability in different situations. The findings vindicate (i) that in judgment aggregation problems, reasons should carry higher weight than conclusions and (ii) that considering members of an advisory board to be highly competent is a better strategy than to underestimate their advice.".

Models are a principle instrument of modern science. They are built, applied, tested, compared, revised and interpreted in an expansive scientific literature. Throughout this paper, I will argue that models are also a valuable tool for the philosopher of science. In particular, I will discuss how the methodology of Bayesian Networks can elucidate two central problems in the philosophy of science. The first thesis I will explore is the variety-of-evidence thesis, which argues that the more varied the supporting evidence, the greater the degree of confirmation for a given hypothesis. However, when investigated using Bayesian methodology, this thesis turns out not to be sacrosanct. In fact, under certain conditions, a hypothesis receives more confirmation from evidence that is obtained from one rather than more instruments, and from evidence that confirms one rather than more testable consequences of the hypothesis. The second challenge that I will investigate is scientific theory change. This application highlights a different virtue of modeling methodology. In particular, I will argue that Bayesian modeling illustrates how two seemingly unrelated aspects of theory change, namely the (Kuhnian) stability of (normal) science and the ability of anomalies to over turn that stability and lead to theory change, are in fact united by a single underlying principle, in this case, coherence. In the end, I will argue that these two examples bring out some metatheoretical reflections regarding the following questions: What are the differences between modeling in science and modeling in philosophy? What is the scope of the modeling method in philosophy? And what does this imply for our understanding of Bayesianism?

In his entry on "Quantum Logic and Probability Theory" in the Stanford Encyclopedia of Philosophy, Alexander Wilce (2012) writes that "it is uncontroversial (though remarkable) the formal apparatus quantum mechanics reduces neatly to a generalization of classical probability in which the role played by a Boolean algebra of events in the latter is taken over the 'quantum logic' of projection operators on a Hilbert space." For a long time, Patrick Suppes has opposed this view (see, for example, the paper collected in Suppes and Zanotti (1996). Instead of changing the logic and moving from a Boolean algebra to a non-Boolean algebra, one can also 'save the phenomena' by weakening the axioms of probability theory and work instead with upper and lower probabilities. However, it is fair to say that despite Suppes' efforts upper and lower probabilities are not particularly popular in physics as well as in the foundations of physics, at least so far. Instead, quantum logic is booming again, especially since quantum information and computation became hot topics. Interestingly, however, imprecise probabilities are becoming more and more popular in formal epistemology as recent work by authors such as James Joye (2010) and Roger White (2010) demonstrates.