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)

Przedmowa Problematyka związana z zależnościami przyczynowymi, ich modelowaniem i odkrywa¬niem, po długiej nieobecności w filozofii i metodologii nauk, budzi współcześnie duże zainteresowanie. Wiąże się to przede wszystkim z dynamicznym rozwojem, zwłaszcza od lat 1990., technik obli¬czeniowych. Wypracowane w tym czasie sieci bayesowskie uznaje się za matematyczny język przyczynowości. Pozwalają one na daleko idącą auto¬matyzację wnioskowań, co jest także zachętą do podjęcia prób algorytmiza¬cji odkrywania przyczyn. Na potrzeby badań naukowych, które pozwalają na przeprowadzenie eksperymentu z randomizacją, standardowe metody ustalania zależności przyczynowych (...) opracowano na początku XX wieku. Zupełnie inaczej sprawa przedstawia się w przypadku badań nieeksperymentalnych, gdzie podobne rozwiązania pozostają kwestią przyszłości. Zadaniem tej książki jest podanie warunków, które powinny być spełnione przez te rozwiązania, oraz sformułowanie proceduralnego kryterium zależności przy¬czynowych jako szczegółowej realizacji tych warunków. Pociąga ono waż¬kie konsekwencje dla filozofii i metodologii nauk, które ujawnia – podany w Części II – zarys me-todolo¬gii proceduralnej. W literaturze przedmiotu brakuje w miarę wszechstronnego i systema¬tycznego omówie¬nia najnowszych filozoficznych i metodologicznych dys¬kusji na temat przy¬czynowości, co niech będzie wytłumaczeniem, dlaczego w niektórych punktach obecnej książki szczegółowo referuję trudno dos¬tępne teksty źró¬dłowe. Przymiotnik „proceduralny” używam tu w znaczeniu węższym niż Huw Price (w którego pracach właściwszy byłby termin „kryterialny”) dla podkre¬ślenia – zgodnie z łacińskim źródłosłowem procedo – że dla ustalenia przy¬czyny niezbędne jest podjęcie przez uczonych określonych interakcji z ba¬daną rzeczywistością. Zalążki zamysłu prezentowanego w tej książce przedstawiłem podczas warsztatów filozoficznych „Philosophy and Probability” w roku 2002, zor¬ganizowanych przez Instytut Filozofii Uniwersytetu w Konstancji. Wdzięczny jestem uczestnikom tych warsztatów za uwagi, a przede wszyst¬kim następującym osobom: Luc Bovens, Brandon Fitelson, Alan Hájek, Stephan Hartmann oraz Jon Williamson. Podczas międzynarodowej konferencji „Analytical Pragmatism”, zorgani¬zowanej w Lublinie w roku 2003 przez Wydział Filo¬zofii Katolickiego Uniwersytetu Lubelskiego, odniosłem swoją koncepcję do prac Nancy Cartwright. Szczególnie inspirujący okazał się komentarz Huw Price’a do mojego referatu i przeprowadzona z nim dysku¬sja. Ujęcie koncepcji metodologii proceduralnej na szerszym tle współ-czes¬nego nurtu empirystycznego w filozofii nauki przedstawiłem w roku 2004 podczas konferencji „5th Quadrennial Fellows Conference”, zorgani¬zowanej przez Instytut Filozofii Uniwersytetu Jagiellońskiego oraz Centrum Filozofii Nauki w Pittsburghu. Szczególnie pomocne w dalszych moich pra¬cach były uwagi Jamesa Bogena, Janet Kourany, Jamesa Lennoxa, Johna Nortona, Thomasa Bonka, Jana Woleńskiego i Johna Worralla, za które wyra¬żam swoją wdzięczność. Korpus książki powstał podczas mojego stażu w Centrum Filozofii Nauki w Pittsburghu, który odbyłem jako stypendysta Fundacji na Rzecz Nauki Polskiej w roku akademickim 2004-2005. Uczestniczyłem w tym czasie w życiu naukowym Centrum i w pracach badawczych zespołu z Instytutu Filozofii Uniwersytetu Carnegie-Mellon w Pittsburghu kierowanego przez Clarka Glymoura. Na jego ręce składam podziękowanie za wiele po¬mocnych uwag do moich wy¬stąpień oraz tekstów i za dyskusje przede wszystkim z nim samym i z jego najbliższymi współpracownikami: Peterem Spirtesem oraz Richardem Scheinesem, a także pozostałymi członkami tego zes¬połu, doktorantami i uczestnikami seminarium badawczego „Causality in the Social Sciences”. Za wieloletnie wsparcie, wielopłaszczyznowe inspiracje towarzyszące pi¬saniu tej książki, a także liczne pomocne uwagi do jej wcześniejszych wersji dziękuję przede wszystkim Księdzu Profesorowi Andrzejowi Bronkowi oraz Księdzu Profesorowi Józefowi Herbutowi, współprowadzącemu seminarium doktorskie w Katedrze Metodologii Nauk Katolickiego Uniwersytetu Lubel¬skiego im. Jana Pawła II, jak również pozostałym uczestnikom tego semina¬rium. Dziękuję mojej Żonie, dr Annie Kawalec za wiele wysiłku włożonego w ulepszenie redakcji – językowej i merytorycznej – obecnej książki. Książkę tę można czytać na kilka sposobów. Czytelnikom zainteresowa¬nym przede wszystkim prowadzeniem badań empirycznych polecałbym rozpoczęcie od Rozdziału 2. i kontynuację pozostałych rozdziałów Części I, a następnie Dodatków. Czytelnikom zainteresowanym problemami filozo¬fii i metodologii nauk polecałbym rozpoczęcie lektury książki od Części II i uzupełniającą lekturę Rozdziału 2., a następnie Wprowadzenia i Zakończenia. Czytelnikom mniej zainteresowanym zagadnieniami teoretycznymi pole¬całbym zapoznanie się z fascynującymi dziejami odkrycia przyczyn cholery przez Johna Snowa, które rekonstruuję w Rozdziale 1. W dalszej części nato¬miast polecałbym przejście do Wprowadzenia i Zakończenia, które w mniej specjalistyczny sposób przybliżają proponowane tu rozstrzygnięcia. Tekst książki nie był dotąd publikowany. Wyjątkiem są pewne fragmenty Rozdziału 8. oraz 9., które w zmienionej postaci ukazały się w Rocznikach Filozoficznych (Kawalec 2004). -/- Lublin, luty 2006 r. (shrink)

1 Logic in philosophy The century that was Logic has played an important role in modern philosophy, especially, in alliances with philosophical schools such as the Vienna Circle, neopositivism, or formal language variants of analytical philosophy. The original impact was via the work of Frege, Russell, and other pioneers, backed up by the prestige of research into the foundations of mathematics, which was fast bringing to light those amazing insights that still impress us to-day. The Golden Age of the 1930s (...) deeply affected philosophy, and heartened the minority of philosophers with a formalanalytical bent. As Brand Blanshard writes in Reason and Analysis (1964) – I quote from memory here, to avoid the usual disappointment when re-reading an original text. (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)

Starting from the sixties of the past century theory change has become a main concern of philosophy of science. Two of the best known formal accounts of theory change are the post-Popperian theories of verisimilitude (PPV for short) and the AGM theory of belief change (AGM for short). In this paper, we will investigate the conceptual relations between PPV and AGM and, in particular, we will ask whether the AGM rules for theory change are effective means for approaching the truth, (...) i.e., for achieving the cognitive aim of science pointed out by PPV. First, the key ideas of PPV and AGM and their application to a particular kind of propositional theories - the so called "conjunctive propositions" - will be illustrated. Afterwards, we will prove that, as far as conjunctive propositions are concerned, AGM belief change is an effective tool for approaching the truth. (shrink)

The justification of induction is of central significance for cross-cultural social epistemology. Different ‘epistemological cultures’ do not only differ in their beliefs, but also in their belief-forming methods and evaluation standards. For an objective comparison of different methods and standards, one needs (meta-)induction over past successes. A notorious obstacle to the problem of justifying induction lies in the fact that the success of object-inductive prediction methods (i.e., methods applied at the level of events) can neither be shown to be universally (...) reliable (Hume's insight) nor to be universally optimal. My proposal towards a solution of the problem of induction is meta-induction. The meta-inductivist applies the principle of induction to all competing prediction methods that are accessible to her. By means of mathematical analysis and computer simulations of prediction games I show that there exist meta-inductive prediction strategies whose success is universally optimal among all accessible prediction strategies, modulo a small short-run loss. The proposed justification of meta-induction is mathematically analytical. It implies, however, an a posteriori justification of object-induction based on the experiences in our world. In the final section I draw conclusions about the significance of meta-induction for the social spread of knowledge and the cultural evolution of cognition, and I relate my results to other simulation results which utilize meta-inductive learning mechanisms. (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)

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)

This article argues that a successful answer to Hume's problem of induction can be developed from a sub-genre of philosophy of science known as formal learning theory. One of the central concepts of formal learning theory is logical reliability: roughly, a method is logically reliable when it is assured of eventually settling on the truth for every sequence of data that is possible given what we know. I show that the principle of induction (PI) is necessary and sufficient for logical (...) reliability in what I call simple enumerative induction. This answer to Hume's problem rests on interpreting PI as a normative claim justified by a non-empirical epistemic means-ends argument. In such an argument, a rule of inference is shown by mathematical or logical proof to promote a specified epistemic end. Since the proof concerning PI and logical reliability is not based on inductive reasoning, this argument avoids the circularity that Hume argued was inherent in any attempt to justify PI. (shrink)

Philosophically, one of the most important questions in the enterprise termed confirmation theory is this: Why should one stick to well confirmed theories rather than to any other theories? This paper discusses the answers to this question one gets from absolute and incremental Bayesian confirmation theory. According to absolute confirmation, one should accept ''absolutely well confirmed'' theories, because absolute confirmation takes one to true theories. An examination of two popular measures of incremental confirmation suggests the view that one should stick (...) to incrementally well confirmed theories, because incremental confirmation takes one to (the most) informative (among all) true theories. However, incremental confirmation does not further this goal in general. I close by presenting a necessary and sufficient condition for revealing the confirmational structure in almost every world when presented separating data. (shrink)

Many people believe that there is a Dutch Book argument establishing that the principle of countable additivity is a condition of coherence. De Finetti himself did not, but for reasons that are at first sight perplexing. I show that he rejected countable additivity, and hence the Dutch Book argument for it, because countable additivity conflicted with intuitive principles about the scope of authentic consistency constraints. These he often claimed were logical in nature, but he never attempted to relate this idea (...) to deductive logic and its own concept of consistency. This I do, showing that at one level the definitions of deductive and probabilistic consistency are identical, differing only in the nature of the constraints imposed. In the probabilistic case I believe that R.T. Cox's ‘scale-free’ axioms for subjective probability are the most suitable candidates. 1 Introduction 2 Coherence and Consistency 3 The Infinite Fair Lottery 4 The Puzzle Resolved—But Replaced by Another 5 Countable Additivity, Conglomerability and Dutch Books 6 The Probability Axioms and Cox's Theorem 7 Truth and Probability 8 Conclusion: ‘Logical Omniscience’ CiteULike Connotea Del.icio.us What's this? (shrink)

While there are several arguments on either side, it is far from clear as to whether or not countable additivity is an acceptable axiom of subjective probability. I focus here on de Finetti's central argument against countable additivity and provide a new Dutch book proof of the principle, To argue that if we accept the Dutch book foundations of subjective probability, countable additivity is an unavoidable constraint.

The problem adressed in this paper is “the main epistemic problem concerning science”, viz. “the explication of how we compare and evaluate theories [...] in the light of the available evidence” (van Fraassen 1983, 27).

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.

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)

This essay defends the view that inductive reasoning involves following inductive rules against objections that inductive rules are undesirable because they ignore background knowledge and unnecessary because Bayesianism is not an inductive rule. I propose that inductive rules be understood as sets of functions from data to hypotheses that are intended as solutions to inductive problems. According to this proposal, background knowledge is important in the application of inductive rules and Bayesianism qualifies as an inductive rule. Finally, I consider a (...) Bayesian formulation of inductive skepticism suggested by Lange. I argue that while there is no good Bayesian reason for judging this inductive skeptic irrational, the approach I advocate indicates a straightforward reason not to be an inductive skeptic. (shrink)

Contrary to formal theories of induction, I argue that there are no universal inductive inference schemas. The inductive inferences of science are grounded in matters of fact that hold only in particular domains, so that all inductive inference is local. Some are so localized as to defy familiar characterization. Since inductive inference schemas are underwritten by facts, we can assess and control the inductive risk taken in an induction by investigating the warrant for its underwriting facts. In learning more facts, (...) we extend our inductive reach by supplying more localized inductive inference schemes. Since a material theory no longer separates the factual and schematic parts of an induction, it proves not to be vulnerable to Hume's problem of the justification of induction. (shrink)

A model of inductive inquiry is defined within a first-order context. Intuitively, the model pictures inquiry as a game between Nature and a scientist. To begin the game, a nonlogical vocabulary is agreed upon by the two players along with a partition of a class of structures for that vocabulary. Next, Nature secretly chooses one structure ("the real world") from some cell of the partition. She then presents the scientist with a sequence of atomic facts about the chosen structure. With (...) each new datum the scientist announces a guess about the cell to which the chosen structure belongs. To succeed in his inquiry, the scientist's successive conjectures must be correct all but finitely often, that is, the conjectures must converge in the limit to the correct cell. A special kind of scientist selects his hypotheses on the basis of a belief revision operator. We show that reliance on belief revision allows scientists to solve a wide class of problems. (shrink)

I propose that empirical procedures, like computational procedures, are justified in terms of truth-finding efficiency. I contrast the idea with more standard philosophies of science and illustrate it by deriving Ockham's razor from the aim of minimizing dramatic changes of opinion en route to the truth.

Reasoning from inconclusive evidence, or ‘induction’, is central to science and any applications we make of it. For that reason alone it demands the attention of philosophers of science. This Element explores the prospects of using probability theory to provide an inductive logic, a framework for representing evidential support. Constraints on the ideal evaluation of hypotheses suggest that overall support for a hypothesis is represented by its probability in light of the total evidence, and incremental support, or confirmation, indicated by (...) an increased probability given the evidence than otherwise. This proposal is shown to have the capacity to reconstruct many canons of the scientific method and inductive inference. Along the way, significant objections are discussed, such as the challenge from inductive scepticism and the objection that the probabilistic approach makes evidential support arbitrary. (shrink)

At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would generate a non-distributive lattice of propositions, and from quantum superpositions, which would entail new rules for quantum disjunctions. While the quantum logic program is not as popular as it once was, a crucial question remains unsettled: what is the relationship between the logical structures (...) of classical and quantum mechanics? In this essay we answer this question by showing that the original arguments promoting quantum logic contain serious flaws, and that quantum theory does satisfy the classical distributivity law once the full meaning of quantum propositions is properly taken into account. Moreover, we show that quantum mechanics can generate a distributive lattice of propositions, which, unlike the one of quantum logic, includes statements about expectation values which are of undoubtable physical interest. Lastly, we show that the lattice of statistical propositions in classical mechanics follows the same structure, yielding an analogue non-commutative sublattice of classical propositions. This fact entails that the purported difference between classical and quantum logic stems from a misconstructed parallel between the two theories. (shrink)

Turingin testi, interrogatiivimalli ja tekoäly.

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

Our aim here is to present a result that connects some approaches to justifying countable additivity. This result allows us to better understand the force of a recent argument for countable additivity due to Easwaran. We have two main points. First, Easwaran’s argument in favour of countable additivity should have little persuasive force on those permissive probabilists who have already made their peace with violations of conglomerability. As our result shows, Easwaran’s main premiss – the comparative principle – is strictly (...) stronger than conglomerability. Second, with the connections between the comparative principle and other probabilistic concepts clearly in view, we point out that opponents of countable additivity can still make a case that countable additivity is an arbitrary stopping point between finite and full additivity. (shrink)

Must probabilities be countably additive? On the one hand, arguably, requiring countable additivity is too restrictive. As de Finetti pointed out, there are situations in which it is reasonable to use merely finitely additive probabilities. On the other hand, countable additivity is fruitful. It can be used to prove deep mathematical theorems that do not follow from finite additivity alone. One of the most philosophically important examples of such a result is the Bayesian convergence to the truth theorem, which says (...) that conditional probabilities converge to 1 for true hypotheses and to 0 for false hypotheses. In view of the long-standing debate about countable additivity, it is natural to ask in what circumstances finitely additive theories deliver the same results as the countably additive theory. This paper addresses that question and initiates a systematic study of convergence to the truth in a finitely additive setting. There is also some discussion of how the formal results can be applied to ongoing debates in epistemology and the philosophy 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)

Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general.

Le problème de l’induction (humien) a récemment été abordé par Steel dans son article de 2010. Celui-ci soutient que les théories d’apprentissage formelles permettent de justifier logiquement le principe de l’induction, ce dernier assurant la fiabilité logique des méthodes. Cette proposition a été critiquée par Howson en 2011, ce dernier mettant en doute la possibilité même qu’une méthode puisse être logiquement fiable. Bien que Steel ait offert une réponse à cette critique, il n’y répond pas directement. Dans le présent article, (...) une réponse frontale à celle-ci est offerte en s’inspirant des pratiques de tests d’hypothèses en sciences biologiques. Pour ce faire, une règle de construction des ensembles d’hypothèses est proposée, règle offrant une justification logique au fait qu’une méthode convergera nécessairement vers la vérité. Cet amendement étant cohérent avec l’ensemble de la proposition de Steel, il est ainsi possible d’affirmer que sa thèse est renforcée par cette proposition. (shrink)

This paper has three interdependent aims. The first is to make Reichenbach’s views on induction and probabilities clearer, especially as they pertain to his pragmatic justification of induction. The second aim is to show how his view of pragmatic justification arises out of his commitment to extensional empiricism and moots the possibility of a non-pragmatic justification of induction. Finally, and most importantly, a formal decision-theoretic account of Reichenbach’s pragmatic justification is offered in terms both of the minimax principle and the (...) dominance principle. (shrink)

The thesis of this paper is that we can justify induction deductively relative to one end, and deduction inductively relative to a different end. I will begin by presenting a contemporary variant of Hume ’s argument for the thesis that we cannot justify the principle of induction. Then I will criticize the responses the resulting problem of induction has received by Carnap and Goodman, as well as praise Reichenbach ’s approach. Some of these authors compare induction to deduction. Haack compares (...) deduction to induction, and I will critically discuss her argument for the thesis that we cannot justify the principles of deduction next. In concluding I will defend the thesis that we can justify induction deductively relative to one end, and deduction inductively relative to a different end, and that we can do so in a non-circular way. Along the way I will show how we can understand deductive and inductive logic as normative theories, and I will briefly sketch an argument to the effect that there are only hypothetical, but no categorical imperatives. (shrink)

In this paper a new conception of foundation-oriented epistemology is developed. The major challenge for foundation-oriented justifications consists in the problem of stopping the justificational regress without taking recourse to dogmatic assumptions or circular reasoning. Two alternative accounts that attempt to circumvent this problem, coherentism and externalism, are critically discussed and rejected as unsatisfactory. It is argued that optimality arguments are a new type of foundation-oriented justification that can stop the justificational regress. This is demonstrated on the basis of a (...) novel result in the area of induction: the optimality of meta-induction. In the final section the method of optimality justification is generalized to deductive and abductive inferences. (shrink)

In this paper a theory of finitistic and frequentistic approximations — in short: f-approximations — of probability measures P over a countably infinite outcome space N is developed. The family of subsets of N for which f-approximations converge to a frequency limit forms a pre-Dynkin system $${{D\subseteq\wp(N)}}$$. The limiting probability measure over D can always be extended to a probability measure over $${{\wp(N)}}$$, but this measure is not always σ-additive. We conclude that probability measures can be regarded as idealizations of (...) limiting frequencies if and only if σ-additivity is not assumed as a necessary axiom for probabilities. We prove that σ-additive probability measures can be characterized in terms of so-called canonical and in terms of so-called full f-approximations. We also show that every non-σ-additive probability measure is f-approximable, though neither canonically nor fully f-approximable. Finally, we transfer our results to probability measures on open or closed formulas of first-order languages. (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)

Currently, the most popular views about how to update de se or self-locating beliefs entail the one-third solution to the Sleeping Beauty problem.2 Another widely held view is that an agent‘s credences should be countably additive.3 In what follows, I will argue that there is a deep tension between these two positions. For the assumptions that underlie the one-third solution to the Sleeping Beauty problem entail a more general principle, which I call the Generalized Thirder Principle, and there are situations (...) in which the latter principle and the principle of Countable Additivity cannot be jointly satisfied. The most plausible response to this tension, I argue, is to accept both of these principles, and to maintain that when an agent cannot satisfy them both, she is faced with a rational dilemma. (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)

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)

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.

This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...) highlighting their relationship and allowing a better understanding of how they interact together. (shrink)

It has been common wisdom for centuries that scientific inference cannot be deductive; if it is inference at all, it must be a distinctive kind of inductive inference. According to demonstrative theories of induction, however, important scientific inferences are not inductive in the sense of requiring ampliative inference rules at all. Rather, they are deductive inferences with sufficiently strong premises. General considerations about inferences suffice to show that there is no difference in justification between an inference construed demonstratively or ampliatively. (...) The inductive risk may be shouldered by premises or rules, but it cannot be shirked. Demonstrative theories of induction might, nevertheless, better describe scientific practice. And there may be good methodological reasons for constructing our inferences one way rather than the other. By exploring the limits of these possible advantages, I argue that scientific inference is neither of essence deductive nor of essence inductive. (shrink)

Science depends on judgments of the bearing of evidence on theory. Scientists must judge whether an observation or the result of an experiment supports, disconfirms, or is simply irrelevant to a given hypothesis. Similarly, scientists may judge that, given all the available evidence, a hypothesis ought to be accepted as correct or nearly so, rejected as false, or neither. Occasionally, these evidential judgments can be made on deductive grounds. If an experimental result strictly contradicts a hypothesis, then the truth of (...) the data deductively entails the falsity of the hypothesis. In the great majority of cases, however, the connection between evidence and hypothesis is non-demonstrative, or inductive. In particular, this is so whenever a general hypothesis is inferred to be correct on the basis of the available data, since the truth of the data will not deductively entail the truth of the hypothesis. It always remains possible that the hypothesis is false even though the data are correct. (shrink)

This chapter contains sections titled: Highlights of Past Literature Current Work Future Work.