My goal, in this paper, is to critically assess the categorization of “interpretations of probability” as it appears in the literature. In some sources only Carnap’s treatment of probability is understood to be the best example of “logical” probability. This is surprisingly narrow and I will here suggest otherwise. In fact, I believe that certain forms of Baysianism should also be included in the logical camp.

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

Ockham’s razor is the characteristic scientific penchant for simpler, more testable, and more unified theories. Glymour’s early work on confirmation theory eloquently stressed the rhetorical plausibility of Ockham’s razor in scientific arguments. His subsequent, seminal research on causal discovery still concerns methods with a strong bias toward simpler causal models, and it also comes with a story about reliability—the methods are guaranteed to converge to true causal structure in the limit. However, there is a familiar gap between convergent reliability and (...) scientific rhetoric: convergence in the long run is compatible with any conclusion in the short run. For that reason, Carnap suggested that the proper sense of reliability for scientific inference should lie somewhere between short-run reliability and mere convergence in the limit. One natural such concept is straightest possible convergence to the truth, where straightness is explicated in terms of minimizing reversals of opinion and cycles of opinion prior to convergence. We close the gap between scientific rhetoric and scientific reliability by showing that Ockham’s razor is necessary for cycle-optimal convergence to the truth, and that patiently waiting for information to resolve conflicts among simplest hypotheses is necessary for reversal-optimal convergence to the truth. (shrink)

With the ascent of modern epidemiology in the Twentieth Century came a new standard model of prediction in public health and clinical medicine. In this article, we describe the structure of the model. The standard model uses epidemiological measures-most commonly, risk measures-to predict outcomes (prognosis) and effect sizes (treatment) in a patient population that can then be transformed into probabilities for individual patients. In the first step, a risk measure in a study population is generalized or extrapolated to a target (...) population. In the second step, the risk measure is particularized or transformed to yield probabilistic information relevant to a patient from the target population. Hence, we call the approach the Risk Generalization-Particularization (Risk GP) Model. There are serious problems at both stages, especially with the extent to which the required assumptions will hold and the extent to which we have evidence for the assumptions. Given that there are other models of prediction that use different assumptions, we should not inflexibly commit ourselves to one standard model. Instead, model pluralism should be standard in medical prediction. (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)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

‘Bayesian epistemology’ became an epistemological movement in the 20th century, though its two main features can be traced back to the eponymous Reverend Thomas Bayes (c. 1701-61). Those two features are: (1) the introduction of a formal apparatus for inductive logic; (2) the introduction of a pragmatic self-defeat test (as illustrated by Dutch Book Arguments) for epistemic rationality as a way of extending the justification of the laws of deductive logic to include a justification for the laws of inductive logic. (...) The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of conditionalization. (shrink)

Consider a group of people whose preferences satisfy the axioms of one of the current versions of utility theory, such as von Neumann-Morgenstern (1944), Savage (1954), or Bolker-Jeffrey (1965). There are political and economic contexts in which it is of interest to find ways of aggregating these individual preferences into a group preference ranking. The question then arises of whether methods of aggregation exist in which the group’s preferences also satisfy the axioms of the chosen utility theory, and in which (...) at the same time the aggregation process satisfies certain plausible conditions (e.g., the Pareto conditions below). (shrink)

Selectionist evolutionary theory has often been faulted for not making novel predictions that are surprising, risky, and correct. I argue that it in fact exhibits the theoretical virtue of predictive capacity in addition to two other virtues: explanatory unification and model fitting. Two case studies show the predictive capacity of selectionist evolutionary theory: parallel evolutionary change in E. coli, and the origin of eukaryotic cells through endosymbiosis.

Some think that issues to do with scientific method are last century's stale debate; Popper was an advocate of methodology, but Kuhn, Feyerabend, and others are alleged to have brought the debate about its status to an end. The papers in this volume show that issues in methodology are still very much alive. Some of the papers reinvestigate issues in the debate over methodology, while others set out new ways in which the debate has developed in the last decade. The (...) book will be of interest to philosophers and scientists alike in the reassessment it provides of earlier debates about method and current directions of research. (shrink)

outlined. This account is partly inspired by the work of C.S. Peirce. When we want to consider how degree of confirmation varies with changing I show that a large class of quantitative Bayesian measures of con-.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, (...) the Theorem's central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology. (shrink)

Let R(X, B) denote the class of probability functions that are defined on algebra X and that represent rationally permissible degrees of certainty for a person whose total relevant background evidence is B. This paper is concerned with characterizing R(X, B) for the case in whichX is an algebra of propositions involving two properties and B is empty. It proposes necessary conditions for a probability function to be in R(X, B), some of which involve the notion of statistical dependence. The (...) class of probability functions that satisfy these conditions, here denoted PI, includes a class that Carnap once proposed for the same situation. Probability functions in PI violate Carnap's axiom of analogy but, it is argued, that axiom should be rejected. A derivation of Carnap's model by Hesse has limitations that are not present in the derivation of PI given here. Various alternative probability models are considered and rejected. (shrink)

To explain the phenomena in the world of our experience, to answer the question “why?” rather than only the question “what?”, is one of the foremost objectives of all rational inquiry; and especially, scientific research in its various branches strives to go beyond a mere description of its subject matter by providing an explanation of the phenomena it investigates. While there is rather general agreement about this chief objective of science, there exists considerable difference of opinion as to the function (...) and the essential characteristics of scientific explanation. In the present essay, an attempt will be made to shed some light on these issues by means of an elementary survey of the basic pattern of scientific explanation and a subsequent more rigorous analysis of the concept of law and of the logical structure of explanatory arguments. (shrink)

Most handbooks on statistics and the theory of probability leave the reader in a mysterious tangle of mathematical rules for computing apparently arbitrarily chosen numerical functions. At first sight, then, a treatise on the Logical Foundations of Probability raises hopes that it will be a guide to clarity in these matters. These hopes are strengthened if the reader remembers that the author, Professor Rudolph Carnap of the University of Chicago, is noted for his thesis that philosophy is the study of (...) the logic of science. On the other hand, a first glance into this book may discourage a reader who, though familiar with statistics, is not familiar with modern logic and its notation. For this reason particularly I shall try to give an account of this book that will enable the interested student to form some opinion of its usefulness to him. (shrink)

Peter Achinstein gives in his papers [1] and [2] interesting analyses of some problems of inductive logic and of some approaches I have proposed. I shall discuss here some of these problems in order to clarify my present position. My comments will mainly concern the variety of instances, and only briefly the analogy influence, and the inductive methods for a coordinate language.

In 1947 Donald Cary Williams claimed in The Ground of Induction to have solved the Humean problem of induction, by means of an adaptation of reasoning first advanced by Bernoulli in 1713. Later on David Stove defended and improved upon Williams’ argument in The Rational- ity of Induction (1986). We call this proposed solution of induction the ‘Williams-Stove sampling thesis’. There has been no lack of objections raised to the sampling thesis, and it has not been widely accepted. In our (...) opinion, though, none of these objections has the slightest force, and, moreover, the sampling thesis is undoubtedly true. What we will argue in this paper is that one particular objection that has been raised on numerous occasions is misguided. This concerns the randomness of the sample on which the inductive extrapolation is based. (shrink)

Confirmation theorists seek to define a function that will take into account the various factors relevant in determining the degree to which an hypothesis is confirmed by its evidence. Among confirmation theorists, only Rudolf Carnap has constructed a system which purports to consider factors in addition to the number of instances, viz. the variety manifested by the instances and the amount of analogy between the instances. It is the purpose of this paper to examine the problem which these additional factors (...) raise for confirmation theory, and to prove that, despite Carnap's claim, no confirmation function satisfying the requirements he has specified can take account of variety and analogy. This result is first proved for a special case, and then, in a subsequent section, is generalized through the introduction of a theorem (the proof of which is given in Appendix I). In the final section of the paper it is shown that, contrary to a claim which Carnap has made, not even the concept of the "logical width" of a predicate will enable confirmation functions satisfying his requirements to take adequate account of analogies between instances. (shrink)

The aim of this paper is to argue for a revised and precisified version of the infamous Verifiability Criterion for the meaningfulness of declarative sentences. The argument is based on independently plausible premises concerning probabilistic confirmation and meaning as context-change potential, it is shown to be logically valid, and its ramifications for potential applications of the criterion are being discussed. Although the paper is not historical but systematic, the criterion thus vindicated will resemble the original one(s) in some important ways. (...) At the same time, it will also be more modest insofar as meaningfulness will turn out to be relativized linguistically and probabilistically, and different choices of the linguistic and probabilistic parameters may lead to different verdicts on meaningfulness. (shrink)

Susanne K. Langer is best known as a philosopher of culture and student of Ernst Cassirer. In this chapter, however, I argue that this standard picture ignores her contributions to the development of analytic philosophy in the 1920s and 1930s. I reconstruct the reception of Langer’s first book *The Practice of Philosophy*—arguably the first sustained defense of analytic philosophy by an American philosopher—and describe how prominent European philosophers of science such as Moritz Schlick, Rudolf Carnap, and Herbert Feigl viewed her (...) as one of the most important allies in the United States. In the second half of this chapter, I turn to Langer’s best-selling *Philosophy in a New Key* and reconstruct her attempts to broaden the scope of the, by then, rapidly growing U.S. analytic movement. I argue that her book anticipated various developments in analytic philosophy but was largely ignored by her former colleagues. I end the chapter by offering some clues as to why New Key did not incite the same laudatory responses from analytic philosophers as her earlier work. (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...

The maximum entropy principle is widely used to determine non-committal probabilities on a finite domain, subject to a set of constraints, but its application to continuous domains is notoriously problematic. This paper concerns an intermediate case, where the domain is a first-order predicate language. Two strategies have been put forward for applying the maximum entropy principle on such a domain: applying it to finite sublanguages and taking the pointwise limit of the resulting probabilities as the size n of the sublanguage (...) increases; selecting a probability function on the language as a whole whose entropy on finite sublanguages of size n is not dominated by that of any other probability function for sufficiently large n. The entropy-limit conjecture says that, where these two approaches yield determinate probabilities, the two methods yield the same probabilities. If this conjecture is found to be true, it would provide a boost to the project of seeking a single canonical inductive logic—a project which faltered when Carnap's attempts in this direction succeeded only in determining a continuum of inductive methods. The truth of the conjecture would also boost the project of providing a canonical characterisation of normal or default models of first-order theories. Hitherto, the entropy-limit conjecture has been verified for languages which contain only unary predicate symbols and also for the case in which the constraints can be captured by a categorical statement of quantifier complexity. This paper shows that the entropy-limit conjecture also holds for categorical statements of complexity, for various non-categorical constraints, and in certain other general situations. (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)

Richard Pettigrew has recently advanced a justification of the Principle of Indifference on the basis of a principle that he calls “cognitive conservatism,” or “extreme epistemic conservatism.” However, the credences based on the Principle of Indifference, as Pettigrew formulates it, violate another desideratum, namely, that learning from experience be possible. If it is accepted that learning from experience should be possible, this provides grounds for rejecting cognitive conservatism. Another set of criteria considered by Pettigrew, which involves a weighted mean of (...) worst-case and best-case accuracy, affords some learning, but not the sort that one would expect. This raises the question of whether accuracy-based considerations can be adapted to justify credence functions that permit induction. (shrink)

Algorithmic information theory gives an idealized notion of compressibility that is often presented as an objective measure of simplicity. It is suggested at times that Solomonoff prediction, or algorithmic information theory in a predictive setting, can deliver an argument to justify Occam’s razor. This article explicates the relevant argument and, by converting it into a Bayesian framework, reveals why it has no such justificatory force. The supposed simplicity concept is better perceived as a specific inductive assumption, the assumption of effectiveness. (...) It is this assumption that is the characterizing element of Solomonoff prediction and wherein its philosophical interest lies. (shrink)

So-called “traditional epistemology” and “Bayesian epistemology” share a word, but it may often seem that the enterprises hardly share a subject matter. They differ in their central concepts. They differ in their main concerns. They differ in their main theoretical moves. And they often differ in their methodology. However, in the last decade or so, there have been a number of attempts to build bridges between the two epistemologies. Indeed, many would say that there is just one branch of philosophy (...) here—epistemology. There is a common subject matter after all. In this paper, we begin by playing the role of a “bad cop,” emphasizing many apparent points of disconnection, and even conflict, between the approaches to epistemology. We then switch role, playing a “good cop” who insists that the approaches are engaged in common projects after all. We look at various ways in which the gaps between them have been bridged, and we consider the prospects for bridging them further. We conclude that this is an exciting time for epistemology, as the two traditions can learn, and have started learning, from each other. (shrink)

The problem of rational prediction, launched by Wesley Salmon, is without doubt the Achilles heel of the critical method defended by Popper. In this paper, I assess the response given both by Popper and by the popperian Alan Musgrave to this problem. Both responses are inadequate and thus the conclusion of Salmon is reinforced: without appeal to induction, there is no way to make of the practical prediction a rational action. Furthermore, the critical method needs to be vindicated if one (...) pretends that its application is suitable for the preference of a hypothesis. I argue that the nature of this vindication is such that it may be applied also to induction. Thus, to be a popperian is a good reason also to be an inductivist. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

A Bayesian account of independent evidential support is outlined. This account is partly inspired by the work of C. S. Peirce. I show that a large class of quantitative Bayesian measures of confirmation satisfy some basic desiderata suggested by Peirce for adequate accounts of independent evidence. I argue that, by considering further natural constraints on a probabilistic account of independent evidence, all but a very small class of Bayesian measures of confirmation can be ruled out. In closing, another application of (...) my account to the problem of evidential diversity is also discussed. (shrink)

My dissertation explores the ways in which Rudolf Carnap sought to make philosophy scientific by further developing recent interpretive efforts to explain Carnap’s mature philosophical work as a form of engineering. It does this by looking in detail at his philosophical practice in his most sustained mature project, his work on pure and applied inductive logic. I, first, specify the sort of engineering Carnap is engaged in as involving an engineering design problem and then draw out the complications of design (...) problems from current work in history of engineering and technology studies. I then model Carnap’s practice based on those lessons and uncover ways in which Carnap’s technical work in inductive logic takes some of these lessons on board. This shows ways in which Carnap’s philosophical project subtly changes right through his late work on induction, providing an important corrective to interpretations that ignore the work on inductive logic. Specifically, I show that paying attention to the historical details of Carnap’s attempt to apply his work in inductive logic to decision theory and theoretical statistics in the 1950s and 1960s helps us understand how Carnap develops and rearticulates the philosophical point of the practical/theoretical distinction in his late work, offering thus a new interpretation of Carnap’s technical work within the broader context of philosophy of science and analytical philosophy in general. (shrink)

Inductive probability is the logical concept of probability in ordinary language. It is vague but it can be explicated by defining a clear and precise concept that can serve some of the same purposes. This paper presents a general method for doing such an explication and then a particular explication due to Carnap. Common criticisms of Carnap's inductive logic are examined; it is shown that most of them are spurious and the others are not fundamental.

Many papers have been devoted to the semantic turn Carnap took in the late 1930s after Tarski had explained to him his method for defining truth and his work on the establishment of scientific semantics. Commentators have often argued that the major turn in Carnap’s approach to languages had already been taken in the Logical Syntax of Language, but they have usually assumed that Carnap was happy to subsequently follow Tarski and adopt Tarskian semantics. In this paper, it is argued (...) that this assumption needs to be qualified and that Carnap was actually far from following Tarski when he decided to complement his syntactic method with a semantic one. Carnap and Tarski had different goals, divergent programs, and dissenting views on truth and semantics. After exploring several possible methods for the explication of logical concepts such as L-truth and L-implication, Carnap opted for definitions based on concepts he had found in Wittgenstein’s Tractatus and Waismann’s work on a logical interpretation of probability. Carnap’s reasons for taking a semantic turn are to be understood in the context of his principle of tolerance. He first hoped he could use Tarski’s technique to recover in the semantic setting the completeness result he had tried to establish in the Logical Syntax. His eventual adoption of non-Tarskian semantics can be accounted for by his program of a logical analysis of science—including empirical science—and his ambition to elaborate a unified logical framework for deductive, inductive, and modal logic, and for explicating analyticity. (shrink)

In October 2009 I decided to stop doing philosophy. This meant, in particular, stopping work on the book that I was writing on the nature of probability. At that time, I had no intention of making my unfinished draft available to others. However, I recently noticed how many people are reading the lecture notes and articles on my web site. Since this draft book contains some important improvements on those materials, I decided to make it available to anyone who wants (...) to read it. That is what you have in front of you. The account of Laplace’s theory of probability in Chapter 4 is very different to what I said in my seminar lectures, and also very different to any other account I have seen; it is based on a reading of important texts by Laplace that appear not to have been read by other commentators. The discussion of von Mises’ theory in Chapter 7 is also new, though perhaps less revolutionary. And the final chapter is a new attempt to come to grips with the popular, but amorphous, subjective theory of probability. The material in the other chapters has mostly appeared in previous articles of mine but things are sometimes expressed differently here. I would like to say again that this is an incomplete draft of a book, not the book I would have written if I had decided to finish it. It no doubt contains poor expressions, it may contain some errors or inconsistencies, and it doesn’t cover all the theories that I originally intended to discuss. Apart from this preface, I have done no work on the book since October 2009. (shrink)

The conditional probability of h given e is commonly claimed to be equal to the probability that h would have if e were learned. Here I contend that this general claim about conditional probabilities is false. I present a counter-example that involves probabilities of probabilities, a second that involves probabilities of possible future actions, and a third that involves probabilities of indicative conditionals. In addition, I briefly defend these counter-examples against charges that the probabilities they involve are illegitimate.

A careful analysis of Salmon’s Theoretical Realism and van Fraassen’s Constructive Empiricism shows that both share a common origin: the requirement of literal construal of theories inherited by the Standard View. However, despite this common starting point, Salmon and van Fraassen strongly disagree on the existence of unobservable entities. I argue that their different ontological commitment towards the existence of unobservables traces back to their different views on the interpretation of probability via different conceptions of induction. In fact, inferences to (...) statements claiming the existence of unobservable entities are inferences to probabilistic statements, whence the crucial importance of the interpretation of probability. (shrink)

ABSTRACTTime-consciousness has long been a focus of research in phenomenology and phenomenological psychology. We advance and extend this tradition of research by focusing on the character of temporal experience under conditions of mania. Symptom scales and diagnostic criteria for mania are peppered with temporally inflected language: increased rate of speech, racing thoughts, flight-of-ideas, hyperactivity. But what is the underlying structure of temporal experience in manic episodes? We tackle this question using a strategically hybrid approach. We recover and reconstruct three hypotheses (...) regarding manic temporality that were advanced and modeled by two pioneers of clinical phenomenology: Eugène Minkowski and Ludwig Binswanger. We then test, critique, and refine these hypotheses using heterophenomenological methods in an interview-based study of persons with a history of bipolar and a current diagnosis of acute mania. Our conclusions support a central hypothesis due to Minkowski... (shrink)

Testimonial evidence that is particularly helpful to confirmation combines agreement on some content with variation of detail. I examine the phenomenon of “undesigned coincidences” from a probabilistic point of view to explain how varied reports, including those that dovetail in detail, assist confirmation of an hypothesis. The formal analysis uses recent work in probability theory surrounding the concepts of dependence, independence, and varied evidence. I also discuss the connection between these types of report connections and an hypothesis about the reliability (...) of the sources involved. (shrink)

Inductive logic admits a variety of semantics (Haenni et al., 2011, Part 1). This paper develops semantics based on the norms of Bayesian epistemology (Williamson, 2010, Chapter 7). §1 introduces the semantics and then, in §2, the paper explores methods for drawing inferences in the resulting logic and compares the methods of this paper with the methods of Barnett and Paris (2008). §3 then evaluates this Bayesian inductive logic in the light of four traditional critiques of inductive logic, arguing (i) (...) that it is language independent in a key sense, (ii) that it admits connections with the Principle of Indifference but these connections do not lead to paradox, (iii) that it can capture the phenomenon of learning from experience, and (iv) that while the logic advocates scepticism with regard to some universal hypotheses, such scepticism is not problematic from the point of view of scientific theorising. (shrink)

The debates between Bayesian, frequentist, and other methodologies of statistics have tended to focus on conceptual justifications, sociological arguments, or mathematical proofs of their long run properties. Both Bayesian statistics and frequentist (“classical”) statistics have strong cases on these grounds. In this article, we instead approach the debates in the “Statistics Wars” from a largely unexplored angle: simulations of different methodologies’ performance in the short to medium run. We conducted a large number of simulations using a straightforward decision problem based (...) around tossing a coin with unknown bias and then placing bets. In this simulation, we programmed four players, inspired by Bayesian statistics, frequentist statistics, Jon Williamson’s version of Objective Bayesianism, and a player who simply extrapolates from observed frequencies to general frequencies. The last player functions as a benchmark: a statistical methodology should at least outperform a crude form of induction. We focused on the performance of these methodologies in guiding the players towards good decisions. Unlike an earlier simulation study of this type, we found no systematic difference in performance between the Bayesian and frequentist players, provided the Bayesian used a flat prior and the frequentist used a low confidence level. Unlike that study, we were able to use Big Data methods to mitigate problems of random error in the simulation results. The Williamsonian player, who is a novel element of our study, also had no systematic differences in their performance, provided that they use a low confidence level. These players performed similarly even in the very short run, when players were making different decisions. Our study indicates that all three methodologies should be taken seriously by philosophers and practitioners of statistics. However, the frequentist and Williamsonian performed poorly when their confidence levels were high, and the Bayesian was surprisingly harmed by biased priors, providing some unexpected lessons for these methodologies when facing this type of decision problem. (shrink)

This volume recreates the received notion of reflective equilibrium. It reconfigures reflective equilibrium as both a cognitive ideal and a method for approximating this ideal. The ideal of reflective equilibrium is restructured using the concept of discursive strata, which are formed by sentences and differentiated by function. Sentences that perform the same kind of linguistic function constitute a stratum. The book shows how moral discourse can be analyzed into phenomenal, instrumental, and teleological strata, and the ideal of reflective equilibrium reworked (...) in these terms. In addition, the work strengthens the method of reflective equilibrium by harnessing the resources of decision theory and inductive logic. It launches a comparative version of decision theory and employs this framework as a guide to moral theory choice. It also recruits quantitative inductive logic to inform a standard of inductive cogency. When used in tandem with comparative decision theory, this standard can aid in the effort to turn the undesirable condition of reflective disequilibrium into reflective equilibrium. (shrink)

ABSTRACT We consider evolution of knowledge bases caused by a sequence of basic steps of acquisition of a new information, either consistent or inconsistent with the original system. To make this process comply with the Principe of Minimal Change, a special evidence metric is introduced for measuring distance between states of knowledge. Then a novel semantics of knowledge bases is developed suggested by the heuristics of weighted maximally consistent subsets. The latter is efficiently applied to the processes of consistent and (...) inconsistent acquisition of knowledge, belief revision and contraction. (shrink)

In 1959 Carnap published a probability model that was meant to allow forreasoning by analogy involving two independent properties. Maher (2000)derived a generalized version of this model axiomatically and defended themodel''s adequacy. It is thus natural to now consider how the model mightbe extended to the case of more than two properties. A simple extension waspublished by Hess (1964); this paper argues that it is inadequate. Amore sophisticated one was developed jointly by Carnap and Kemeny in theearly 1950s but never (...) published; this paper gives the first published descriptionof Carnap and Kemeny''s model and argues that it too is inadequate. Since noother way of extending the two-property model is currently known, the conclusionof this paper is that a satisfactory extension to multiple properties requires somenew approach. (shrink)