The purpose of this survey is twofold: (1) to place some centralthemes of epistemic logic in a general epistemological context,and (2) to outline a new framework for epistemic logic developedjointly with S. Andur Pedersen unifying some key ``mainstream''epistemological concerns with the ``formal'' epistemologicalapparatus.

A number of philosophers of science and statisticians have attempted to justify conclusions drawn from a finite sequence of evidence by appealing to results about what happens if the length of that sequence tends to infinity. If their justifications are to be successful, they need to rely on the finite sequence being either indefinitely increasing or of a large size. These assumptions are often not met in practice. This paper analyzes a simple model of collecting evidence and finds that the (...) practice of collecting only very small sets of evidence before taking a question to be settled is rationally justified. This shows that the appeal to long run results can be used neither to explain the success of actual scientific practice nor to give a rational reconstruction of that practice. (shrink)

Recently, Rueger and Sharp (1996) and Koperski (1998) have been concerned to show that certain procedural accounts of model confirmation are compromised by non‐linear dynamics. We suggest that the issues raised are better approached by considering whether chaotic data analysis methods allow for reliable inference from data. We provide a framework and an example of this approach.

We propose strategic games wherein the strategies consist of players asking each other questions and answering those questions. We study simplifications of such games wherein two players simultaneously ask each other a question that the opponent is then obliged to answer. The motivation for our research is to model conversation including the dynamics of questions and answers, to provide new links between game theory and dynamic logics of information, and to exploit the dynamic/strategic structure that, we think, lies implicitly inside (...) epistemic models for epistemic languages, and to make that structure an explicit subject of logical study. Our main contributions are: the notion of a two-person question-answer game with information goals, the existence and computation of equilibria for these games, the correspondence with Bayesian games and their equilibria, and a connection between logic and game theory namely the existence of equilibria for positive goal formulae. (shrink)

Various proposals have suggested that an adequate explanatory theory should reduce the number or the cardinality of the set of logically independent claims that need be accepted in order to entail a body of data. A (and perhaps the only) well-formed proposal of this kind is William Kneale’s: an explanatory theory should be finitely axiomatizable but it’s set of logical consequences in the data language should not be finitely axiomatizable. Craig and Vaught showed that Kneale theories (almost) always exist for (...) any recursively enumerable but not finitely axiomatizable set of data sentences in a first order language with identity. Kneale’s criterion underdetermines explanation even given all possible data in the data language; gratuitous axioms may be “tacked on.” Define a Kneale theory, T, to be logically minimal if it is deducible from every Kneale theory (in the vocabulary of T) that entails the same statements in the data language as does T. If they exist, minimal Kneale theories are candidates for best explanations: they are “bold” in a sense close to Popper’s; some minimal Kneale theory is true if any Kneale theory is true; the minimal Kneale theory that is data equivalent to any given Kneale theory is unique; and no Kneale theory is more probable than some minimal Kneale theory. I show that under the Craig-Vaught conditions, no minimal Kneale theories exist. (shrink)

Standard models of statistical explanation face two intractable difficulties. In his 1984 Salmon argues that because statistical explanations are essentially probabilistic we can make sense of statistical explanation only by rejecting the intuition that scientific explanations are contrastive. Further, frequently the point of a statistical explanation is to identify the etiology of its explanandum, but on standard models probabilistic explanations often fail to do so. This paper offers an alternative conception of statistical explanations on which explanations of the frequency of (...) a property consist in the derivation of that frequency from a statistical specification of the mechanism by which instances of the relevant property are produced. Such explanations are contrastive precisely because they identify the determinate causal etiologies of their explananda. (shrink)

Bogen and Woodward (1988) advance adistinction between data and phenomena. Roughly, theformer are the observations reported by experimentalscientists, the latter are objective, stable featuresof the world to which scientists infer based onpatterns in reliable data. While phenomena areexplained by theories, data are not, and so theempirical basis for an inference to a theory consistsin claims about phenomena. McAllister (1997) hasrecently offered a critique of their version of thisdistinction, offering in its place a version on whichphenomena are theory laden, and hence (...) on which theempirical support for inferences to theories is also,unavoidably, theory laden. In this commentary I arguethat McAllister and Bogen and Woodward are mistaken inthinking that the distinction is necessary, and thatthe empirical support for inferences to theories isnot necessarily theory laden in the way McAllister'saccount entails they are. (shrink)

Words, Thoughts and Theories arguesthat infants and children discover the physical and psychological featuresof the world by a process akin to scientific inquiry, more or less asconceived by philosophers of science in the 1960s (the theory theory).This essay discusses some of the philosophical background to analternative, more popular, ``modular'''' or ``maturational'''' account ofdevelopment, dismisses an array of philosophical objections to the theorytheory, suggests that the theory theory offers an undeveloped project forartificial intelligence, and, relying on recent psychological work oncausation, offers (...) suggestions about how principles of causal inference mayprovide a developmental solution to the ``frame problem''''. (shrink)

This paper discusses the possibility of modelling inductive inference (Gold 1967) in dynamic epistemic logic (see e.g. van Ditmarsch et al. 2007). The general purpose is to propose a semantic basis for designing a modal logic for learning in the limit. First, we analyze a variety of epistemological notions involved in identification in the limit and match it with traditional epistemic and doxastic logic approaches. Then, we provide a comparison of learning by erasing (Lange et al. 1996) and iterated epistemic (...) update (Baltag and Moss 2004) as analyzed in dynamic epistemic logic. We show that finite identification can be modelled in dynamic epistemic logic, and that the elimination process of learning by erasing can be seen as iterated belief-revision modelled in dynamic doxastic logic. Finally, we propose viewing hypothesis spaces as temporal frames and discuss possible advantages of that perspective. (shrink)

Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. Diachronic norms of theory change, as studied in belief revision, restrict how one should change one’s current beliefs in light of new information. Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning, we explicate inductive truth conduciveness in terms of optimally direct (...) convergence to the truth, where optimal directness is explicated in terms of reversals and cycles of opinion prior to convergence. Concerning, we explicate Ockham’s razor and related principles of choice in terms of the information topology of the empirical problem context and show that the principles are necessary for reversal or cycle optimal convergence to the truth. Concerning, we weaken the standard principles of agm belief revision theory in intuitive ways that are also necessary for reversal or cycle optimal convergence. Then we show that some of our weakened principles of change entail corresponding principles of choice, completing the triangle of relations between,, and. (shrink)

Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. Diachronic norms of theory change, as studied in belief revision, restrict how one should change one’s current beliefs in light of new information. Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning, we explicate inductive truth conduciveness in terms of optimally direct (...) convergence to the truth, where optimal directness is explicated in terms of reversals and cycles of opinion prior to convergence. Concerning, we explicate Ockham’s razor and related principles of choice in terms of the information topology of the empirical problem context and show that the principles are necessary for reversal or cycle optimal convergence to the truth. Concerning, we weaken the standard principles of agm belief revision theory in intuitive ways that are also necessary for reversal or cycle optimal convergence. Then we show that some of our weakened principles of change entail corresponding principles of choice, completing the triangle of relations between,, and. (shrink)

Both early analytic philosophy and the branch of mathematics now known as topology were gestated and born in the early part of the 20th century. It is not well recognized that there was early interaction between the communities practicing and developing these fields. We trace the history of how topological ideas entered into analytic philosophy through two migrations, an earlier one conceiving of topology geometrically and a later one conceiving of topology algebraically. This allows us to reassess the influence and (...) significance of topological methods for philosophy, including the possible fruitfulness of a third conception of topology as a structure determining similarity. (shrink)

This paper discusses Kevin Kelly’s recent attempt to justify Ockham’s Razor in terms of truth-finding efficiency. It is argued that Kelly’s justification fails to warrant confidence in the empirical content of theories recommended by Ockham’s Razor. This is a significant problem if, as Kelly and many others believe, considerations of simplicity play a pervasive role in scientific reasoning, underlying even our best tested theories, for the proposal will fail to warrant the use of these theories in practical prediction.

Interest in the computational aspects of modeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by explaining the significance of error management strategies for the rational reconstruction of scientific practice. To this end, we first characterize the role and nature of modeling error in relation to a recipe for model construction known as Euler’s recipe. We then describe a general model (...) that allows us to assess the quality of numerical solutions in terms of measures of computational errors that are completely interpretable in terms of modeling error. Finally, we emphasize that this type of error analysis involves forms of perturbation analysis that go beyond the basic model-theoretical and statistical/probabilistic tools typically used to characterize the scientific method; this demands that we revise and complement our reconstructive toolbox in a way that can affect our normative image of science. (shrink)

Philosophers cannot agree on whether the rule of Countable Additivity should be an axiom of probability. Edwin T. Jaynes attacks the problem in a way which is original to him and passed over in the current debate about the principle: he says the debate only arises because of an erroneous use of mathematical infinity. I argue that this solution fails, but I construct a different argument which, I argue, salvages the spirit of the more general point Jaynes makes. I argue (...) that in Jaynes’s objective Bayesianism we might have good reasons to adopt Countable Additivity, and some of the major problems this adoption is known to entail need not worry us. In particular, I propose to adopt this new angle on Countable Additivity in Jon Williamson’s version of objective Bayesianism. (shrink)

Say that an agent is "epistemically humble" if she is less than certain that her opinions will converge to the truth, given an appropriate stream of evidence. Is such humility rationally permissible? According to the orgulity argument : the answer is "yes" but long-run convergence-to-the-truth theorems force Bayesians to answer "no." That argument has no force against Bayesians who reject countable additivity as a requirement of rationality. Such Bayesians are free to count even extreme humility as rationally permissible.

In Part I, we presented and motivated a new formulation of Humean Supervenience about Laws of Nature (HS). Here in Part II, we present an epistemological argument in defense of HS, thus formulated. Our contention is that one can combine a modest realism about laws of nature with a proper recognition of the importance of empirical testability in the epistemology of science only if one accepts HS.

Earman (1993) distinguishes three notions of empirical indistinguishability and offers a rigorous framework to investigate how each of these notions relates to the problem of underdetermination of theory choice. He uses some of the results obtained in this framework to argue for a version of scientific anti- realism. In the present paper we first criticize Earman's arguments for that position. Secondly, we propose and motivate a modification of Earman's framework and establish several results concerning some of the notions of indistinguishability (...) in this modified framework. Finally, we interpret these results in the light of the realism/anti- realism debate. (shrink)

I propose a framework for pragmatic reliability in-the-limit criteria, extending the epistemic reliability framework. I identify some common scientific contexts that complicate the application or i...

In a recent essay, John Norton proposes a material theory of induction, according to which all justification for inductive inference ultimately stems from the particular facts of the case at hand. Despite being sympathetic to the pluralistic spirit of this proposal, I argue that central controversies among leading theories of inductive inference turn not on material facts but upon normative judgments regarding the proper standards and aims of induction. Thus, a pluralistic approach to induction can be successfully developed only given (...) an explanation of how the choice of such aims and standards depends on features of particular cases. (shrink)

We present a framework that provides a logic for science by generalizing the notion of logical (Tarskian) consequence. This framework will introduce hierarchies of logical consequences, the first level of each of which is identified with deduction. We argue for identification of the second level of the hierarchies with inductive inference. The notion of induction presented here has some resonance with Popper's notion of scientific discovery by refutation. Our framework rests on the assumption of a restricted class of structures in (...) contrast to the permissibility of classical first-order logic. We make a distinction between deductive and inductive inference via the notions of compactness and weak compactness. Connections with the arithmetical hierarchy and formal learning theory are explored. For the latter, we argue against the identification of inductive inference with the notion of learnable in the limit. Several results highlighting desirable properties of these hierarchies of generalized logical consequence are also presented. (shrink)

The sensitivity condition on knowledge says that one knows that P only if one would not believe that P if P were false. Difficulties for this condition are now well documented. Keith DeRose has recently suggested a revised sensitivity condition that is designed to avoid some of these difficulties. We argue, however, that there are decisive objections to DeRose’s revised condition. Yet rather than simply abandoning his proposed condition, we uncover a rationale for its adoption, a rationale which suggests a (...) further revision that avoids our objections as well as others. The payoff is considerable: along the way to our revision, we learn lessons about the epistemic significance of certain explanatory relations, about how we ought to envisage epistemic closure principles, and about the epistemic significance of methods of belief formation. (shrink)

Science advances by means of argument and debate. Based on a formal model of complex argumentation, this article assesses the interplay between evidential and inferential drivers in scientific controversy, and explains, in particular, why both evidence accumulation and argumentation are veritistically valuable. By improving the conditions for applying veritistic indicators , novel evidence and arguments allow us to distinguish true from false hypotheses more reliably. Because such veritistic indicators also underpin inductive reasoning, evidence accumulation and argumentation enhance the reliability of (...) inductive inference, for example, inference to the best explanation. 1 Introduction2 Theory of Dialectical Structures3 Debate Simulations4 From Evidence and Arguments to Truth: The First Route5 From Evidence to Truth: The Second Route6 Conclusion. (shrink)

Taking Backward Induction as its running example, this paper explores avenues for a logic of information-driven social action. We use recent results on limit phenomena in knowledge updating and belief revision, procedural rationality, and a ‘Theory of Play’ analyzing how games are played by different agents.

Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of dynamic-probabilistic (...) logics as well. Finally, we discuss how our basic update rule can be parameterized for different update policies, or learning methods. (shrink)

Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of dynamic-probabilistic (...) logics as well. Finally, we discuss how our basic update rule can be parameterized for different update policies, or learning methods. (shrink)

The twin goals of this essay are: to investigate a family of cases in which the goal of guaranteed convergence to the truth is beyond our reach; and to argue that each of three strands prominent in contemporary epistemological thought has undesirable consequences when confronted with the existence of such problems. Approaches that follow Reichenbach in taking guaranteed convergence to the truth to be the characteristic virtue of good methods face a vicious closure problem. Approaches on which there is a (...) unique rational doxastic response to any given body of evidence can avoid incoherence only by rendering epistemology a curiously limited enterprise. Bayesian approaches rule out humility about one’s prospects of success in certain situations in which failure is typical. (shrink)

Bayesians often assume, suppose, or conjecture that for any reasonable explication of the notion of simplicity a prior can be designed that will enforce a preference for hypotheses simpler in just that sense. But it is shown here that there are simplicity-driven approaches to curve-fitting problems that cannot be captured within the orthodox Bayesian framework.

Bayesians often assume, suppose, or conjecture that for any reasonable explication of the notion of simplicity a prior can be designed that will enforce a preference for hypotheses simpler in just that sense. Further, it is often claimed that the Bayesian framework automatically implements Occam's razor—that conditionalizing on data consistent with both a simple theory and a complex theory more or less inevitably favours the simpler theory. But it is shown here that there are simplicity-driven approaches to curve-fitting problems that (...) cannot be captured within the orthodox Bayesian framework and that the automatic razor does not function for such problems. (shrink)

A piece of folklore enjoys some currency among philosophical Bayesians, according to which Bayesian agents that, intuitively speaking, spread their credence over the entire space of available hypotheses are certain to converge to the truth. The goals of the present discussion are to show that kernel of truth in this folklore is in some ways fairly small and to argue that Bayesian convergence-to-the-truth results are a liability for Bayesianism as an account of rationality, since they render a certain sort of (...) arrogance rationally mandatory. (shrink)

We build a model of the reflective equilibrium method to better understand under what conditions a community of agents would achieve a shared equilibrium. We find that, despite guaranteeing that agents individually reach equilibrium and numerous constraints on how agents deliberate, it is surprisingly difficult for a community to converge on a small number of equilibria. Consequently, the literature on reflective equilibrium has underestimated the challenge of coordinating intrapersonal convergence and interpersonal convergence.

De Finetti would claim that we can make sense of a draw in which each positive integer has equal probability of winning. This requires a uniform probability distribution over the natural numbers, violating countable additivity. Countable additivity thus appears not to be a fundamental constraint on subjective probability. It does, however, seem mandated by Dutch Book arguments similar to those that support the other axioms of the probability calculus as compulsory for subjective interpretations. These two lines of reasoning can be (...) reconciled through a slight generalization of the Dutch Book framework. Countable additivity may indeed be abandoned for de Finetti's lottery, but this poses no serious threat to its adoption in most applications of subjective probability. Introduction The de Finetti lottery Two objections to equiprobability 3.1 The ‘No random mechanism’ argument 3.2 The Dutch Book argument Equiprobability and relative betting quotients The re-labelling paradox 5.1 The paradox 5.2 Resolution: from symmetry to relative probability Beyond the de Finetti lottery. (shrink)

The underdetermination thesis poses a threat to rational choice of scientific theories. We discuss two arguments for the thesis. One draws its strength from deductivism together with the existence thesis, and the other is defended on the basis of the failure of a reliable inductive method. We adopt a partially subjective/objective pragmatic Bayesian epistemology of science framework, and reject both arguments for the thesis. Thus, in science we are able to reinstate rational choice called into question by the underdetermination thesis.

Stalnaker, 169–199 2006) introduced a combined epistemic-doxastic logic that can formally express a strong concept of belief, a concept of belief as ‘subjective certainty’. In this paper, we provide a topological semantics for belief, in particular, for Stalnaker’s notion of belief defined as ‘epistemic possibility of knowledge’, in terms of the closure of the interior operator on extremally disconnected spaces. This semantics extends the standard topological interpretation of knowledge with a new topological semantics for belief. We prove that the belief (...) logic KD45 is sound and complete with respect to the class of extremally disconnected spaces and we compare our approach to a different topological setting in which belief is interpreted in terms of the derived set operator. We also study belief revision as well as belief dynamics by providing a topological semantics for conditional belief and belief update modalities, respectively. Our setting based on extremally disconnected spaces, however, encounters problems when extended with dynamic updates. We then propose a solution consisting in interpreting belief in a similar way based on hereditarily extremally disconnected spaces, and axiomatize the belief logic of hereditarily extremally disconnected spaces. Finally, we provide a complete axiomatization of the logic of conditional belief and knowledge, as well as a complete axiomatization of the corresponding dynamic logic. (shrink)

The paper discusses Bayesian convergence when the truth is excluded from the analysis by means of a simple coin-tossing example. In the fair-balance paradox a fair coin is tossed repeatedly. A Bayesian agent, however, holds the a priori view that the coin is either biased towards heads or towards tails. As a result the truth is ignored by the agent. In this scenario the Bayesian approach tends to confirm a false model as the data size goes to infinity. I argue (...) that the fair-balance paradox reveals an unattractive feature of the Bayesian approach to scientific inference and explore a modification of the paradox. (shrink)

One of our more fundamental beliefs is that causal chains are continuous in time: we believe that every influence from the past upon the future runs through the present. I argue that this tenet, given certain data, can force conceptual changes upon us. I attempt to formulate a heuristic for discovery, based as explicitly as possible upon this tenet, and illustrate it by means of several examples, one of which is Mendel's discovery of genes.

Thoroughgoing relativists typically dismiss the realist conviction that competing theories describe just one definite and mind-independent world-structure on the grounds that such theories fail to be relatively translatable even though they are equally correct. This line of argument allegedly brings relativism into direct conflict with the metaphysics of realism. I argue that this relativist line of reasoning is shaky by deriving a theorem about relativistic inquiry in formal epistemology—more specifically, in the approach Kevin Kelly has dubbed “logic of reliable inquiry”. (...) According to the theorem, two scientists, who share some background knowledge but follow different appropriately reliable methods, will converge to relatively formally translatable competing theories, even if meaning, truth, logic and evidence are allowed to vary in time depending on each scientist’s conjectures, actions, or conceptual choices. Some final remarks on the relevance of the theorem to the incommensurability thesis that has vexed twentieth century philosophy of science are adduced. (shrink)

This paper tries to express a critical point of view on the computational turn in philosophy by looking at a specific field of study: philosophy of science. The paper starts by briefly discussing the main contributions that information and communication technologies have given to the rising of computational philosophy of science, and in particular to the cognitive modelling approach. The main question then arises, concerning how computational models can cope with the presence of tacit knowledge in science. Would it be (...) possible to develop new ways of handling this specific type of knowledge, in order to incorporate it in computational models of scientific thinking? Or should tacit knowledge lead us to other approaches in using computer sciences to model scientific cognition? These questions are addressed by making reference to a detailed case study of a recent innovation development in the field of biotechnology. (shrink)

Structural realism is considered by many realists and antirealists alike as the most defensible form of scientific realism. There are now many forms of structural realism and an extensive literature about them. There are interesting connections with debates in metaphysics, philosophy of physics and philosophy of mathematics. This entry is intended to be a comprehensive survey of the field.

My purpose in this chapter is to survey some of the principal approaches to inductive inference in the philosophy of science literature. My first concern will be the general principles that underlie the many accounts of induction in this literature. When these accounts are considered in isolation, as is more commonly the case, it is easy to overlook that virtually all accounts depend on one of very few basic principles and that the proliferation of accounts can be understood as efforts (...) to ameliorate the weaknesses of those few principles. In the earlier sections, I will lay out three inductive principles and the families of accounts of induction they engender. In later sections I will review standard problems in the philosophical literature that have supported some pessimism about induction and suggest that their import has been greatly overrated. In the final sections I will return to the proliferation of accounts of induction that frustrates efforts at a final codification. I will suggest that this proliferation appears troublesome only as long as we expect inductive inference to be subsumed under a single formal theory. If we adopt a material theory of induction in which individual inductions are licensed by particular facts that prevail only in local domains, then the proliferation is expected and not problematic. (shrink)

This is the most comprehensive book ever published on philosophical methodology. A team of thirty-eight of the world's leading philosophers present original essays on various aspects of how philosophy should be and is done. The first part is devoted to broad traditions and approaches to philosophical methodology. The entries in the second part address topics in philosophical methodology, such as intuitions, conceptual analysis, and transcendental arguments. The third part of the book is devoted to essays about the interconnections between philosophy (...) and neighbouring fields, including those of mathematics, psychology, literature and film, and neuroscience. (shrink)

Showcasing original arguments for well-defined positions, as well as clear and concise statements of sophisticated philosophical views, this volume is an ...

Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...) that is, by employing tools from logic and mathematics. The goal of this entry is to give the reader an overview of the formal tools available to epistemologists for the representation of belief. A particular focus will be the relation between formal representations of qualitative belief and formal representations of quantitative degrees of belief. (shrink)