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)

According to Hempel's paradox, evidence (E) that an object is a nonblack nonraven confirms the hypothesis (H) that every raven is black. According to the standard Bayesian solution, E does confirm H but only to a minute degree. This solution relies on the almost never explicitly defended assumption that the probability of H should not be affected by evidence that an object is nonblack. I argue that this assumption is implausible, and I propose a way out for Bayesians. Introduction Hempel's (...) paradox, the standard Bayesian solution, and the disputed assumption Attempts to defend the disputed assumption Attempts to refute the disputed assumption A way out for Bayesians Conclusion. (shrink)

At present, there is a renewed interest in thoseaspects of Rudolf Carnap ''s LogischerAufbau der Welt that cannot just be reduced tothe tradition of logical positivism. There is, however,one of these aspects which seems to have beenneglected by the historical analyses of theAufbau''s background: what may be called aprogram for the mathematization of sense experience,as developed by Carnap in the most difficult partof his work, Chapter IV/A. It is the program of applying settheory and topology to the reconstruction of phenomenal (...) structures,quite independently of any other general philosophical aim.I claim that there are three forerunners of this program:Henri Poincaré''s essayPourquoi l''espace a trois dimensions, Chapter 4of Bertrand Russell ''s Our Knowledge of the ExternalWorld, and Jean Nicod''s La géométriedans le monde sensible. This article provides acomparison of these different instances of theabove-mentioned program. (shrink)

The traditional No-Miracles Argument (TNMA) asserts that the novel predictive success of science would be a miracle, and thus too implausible to believe, if successful theories were not at least approximately true. The TNMA has come under fire in multiple ways, challenging each of its premises and its general argumentative structure. While the TNMA relies on explaining novel predictive success via the truth of the theories, we put forth a deductive version of the No-Miracles argument (DNMA) that avoids inference to (...) the best explanation entirely. Instead, a relatively simple empirical framework and a probabilistic analysis can accomplish the ambitious goals of the TNMA while entirely sidestepping its problems. This close-but-distinct argument has many independent strengths and comparatively few weaknesses. Indeed, objections tailored specifically to the DNMA reveal surprising insights into how exactly NMAs are neither circular nor question-begging, as has been widely speculated. (shrink)

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

(This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with examples such as (...) Hilbert’s programme and Gödel’s incompleteness theorems; social choice theory, with examples such as Condorcet’s paradox and Arrow’s theorem; ‘how possibly’ results, with examples such as Condorcet’s jury theorem and recent work on intersectionality theory; and the application of advanced mathematics in philosophy, with examples such as accuracy-first epistemology. (shrink)

Bayesian confirmation theory offers an explicatum for a pretheoretic concept of confirmation. The “problem of irrelevant conjunction” for this theory is that, according to some people's intuitions, the pretheoretic concept differs from the explicatum with regard to conjunctions involving irrelevant propositions. Previous Bayesian solutions to this problem consist in showing that irrelevant conjuncts reduce the degree of confirmation; they have the drawbacks that (i) they don't hold for all ways of measuring degree of confirmation and (ii) they don't remove the (...) conflict with intuition but merely “soften the impact” (as Fitelson has written). A better solution, which avoids both these drawbacks, is to show that the intuition is wrong. (shrink)

L'idée d'associer probabilité et induction n'est pas propre au xxe siècle, mais elle a reçu un développement systématique lorsque les philosophes néo-positivistes s'en sont emparés. Dès les années 1940, le philosophe Rudolf Carnap s'est proposé de relever le «défi humien» en fondant une théorie de la confirmation par la construction d'une logique probabiliste dite «inductive». Ce projet avait été esquissé à Cambridge dans les années 1920 par l'économiste John M. Keynes. Examiner le programme de Carnap dans sa totalité, le situer (...) dans son contexte historique, suivre son évolution et les influences qu'il a eues, tels sont les buts de cet article. The idea of associating probability and induction is not a theme suitable for the xxth century but it has received a systematic development when the neo-positivist philosophers seized it. Beginning with the 1940's, the philosopher Rudolph Carnap proposed to affront the «Humian challenge» by founding a theory of confirmation through the construction of a probabilistic logic called «inductive». This project had been outlined in Cambridge during the 1920's by the economist John M. Keynes. To examine Carnap's program in its totality, to situate it in its historical context, to follow its evolution and the influences it has had, these are the aims of this article. (shrink)