Decision Theory and Hypothesis Testing

This essay presents a unified account of safety, sensitivity, and severe testing. S’s belief is safe iff, roughly, S could not easily have falsely believed p, and S’s belief is sensitive iff were p false S would not believe p. These two conditions are typically viewed as rivals but, we argue, they instead play symbiotic roles. Safety and sensitivity are both valuable epistemic conditions, and the relevant alternatives framework provides the scaffolding for their mutually supportive roles. The relevant alternatives condition (...) holds that a belief is warranted only if the evidence rules out relevant error possibilities. The safety condition helps categorise relevant from irrelevant possibilities. The sensitivity condition captures ‘ruling out’. Safety, sensitivity, and the relevant alternatives condition are typically presented as conditions on warranted belief or knowledge. But these properties, once generalised, help characterise other epistemic phenomena, including warranted inference, legal verdicts, scientific claims, reaching conclusions, addressing questions, warranted assertion, and the epistemic force of corroborating evidence. We introduce and explain Mayo’s severe testing account of statistical inference. A hypothesis is severely tested to the extent it passes tests that probably would have found errors, were they present. We argue Mayo’s account is fruitfully understood using the resulting relevant alternatives framework. Recasting Mayo’s condition using the conceptual framework of contemporary epistemology helps forge fruitful connections between two research areas—philosophy of statistics and the analysis of knowledge—not currently in sufficient dialogue. The resulting union benefits both research areas. (shrink)

The replication crisis has prompted many to call for statistical reform within the psychological sciences. Here we examine issues within Frequentist statistics that may have led to the replication crisis, and we examine the alternative—Bayesian statistics—that many have suggested as a replacement. The Frequentist approach and the Bayesian approach offer radically different perspectives on evidence and inference with the Frequentist approach prioritising error control and the Bayesian approach offering a formal method for quantifying the relative strength of evidence for hypotheses. (...) We suggest that rather than mere statistical reform, what is needed is a better understanding of the different modes of statistical inference and a better understanding of how statistical inference relates to scientific inference. (shrink)

In this work, we explore the epistemic import of the value-ladenness of Neyman-Pearson’s Theory of Testing Hypotheses by reconstructing and extending Daniel Steel’s argument for the legitimate influence of pragmatic values on scientific inference. We focus on how to properly understand N-P’s pragmatic value-ladenness and the epistemic reliability of N-P. We develop an account of the twofold influence of pragmatic values on N-P’s epistemic reliability and replicability. We refer to these two distinguished aspects as “direct” and “indirect”. We discuss the (...) replicability of experiments in terms of the indirect aspect and the replicability of outcomes in terms of the direct aspect. We argue that the influence of pragmatic values is beneficial to N-P’s epistemic reliability and replicability indirectly. We show that while the direct influence of pragmatic values can be beneficial, its negative effects on reliability and replicability are also unavoidable in some cases, with the direct and indirect aspects possibly being incongruent. (shrink)

Due to the innovative possibilities of digital technologies, the issue of increasing automation is once again on the agenda – and not only in the industry, but also in other branches and sectors of contemporary societies. Although public and scientific discussions about automation seem to raise relevant questions of the “old” debate, such as the replacement of human labor by introducing new technologies, the authors focus here on the new contextual quality of these questions. The debate should rethink the relationship (...) between technology and work with regard to quantitative and qualitative changes in work. In this article, our example will be the introduction of automation in industry, which has been reflected in the widely recognized study by Frey and Osborne in 2013. They estimated the expected impacts of future computerization on US labor market outcomes as very high, specifically regarding the number of jobs at risk. Surprisingly, this study was the starting point of an intensive international debate on the impact of technologies on the future of work and the role of technological change in working environments. Thus, according to the authors, “old” questions remain important, but they should be reinterpreted for “new” societal demands and expectations of future models of work. (shrink)

How we can reliably draw inferences from data, evidence and/or experience has been and continues to be a pressing question in everyday life, the sciences, politics and a number of branches in philosophy (traditional epistemology, social epistemology, formal epistemology, logic and philosophy of the sciences). In a world in which we can now longer fully rely on our experiences, interlocutors, measurement instruments, data collection and storage systems and even news outlets to draw reliable inferences, the issue becomes even more pressing. (...) While we were working on this question using a formal epistemology approach Landes and Osimani (2020); De Pretis et al. (2019); Osimani and Landes (2020); Osimani (2020), we realised that the width of current active interests in the notion of reliability was much broader than we initially thought. Given the breadth of approaches and angles present in philosophy (even in this journal Schubert 2012; Avigad 2021; Claveau and Grenier 2019; Kummerfeld and Danks 2014; Landes 2021; Trpin et al. 2021; Schippers 2014; Schindler 2011; Kelly et al. 2016; Mayo-Wilson 2014; Olsson and Schubert 2007; Pittard 2017), we thought that it would be beneficial to provide a forum for an open exchange of ideas, in which philosophers working in different paradigms could come together. Our call for expression of interest received a great variety of promised manuscripts, the variety is reflected in the published papers. They range from fields far away from our own interests such as quantum probabilities de Ronde et al. (2021), evolvable software systems Primiero et al. (2021), to topics closer to our own research in the philosophy of medicine Lalumera et al. (2020), psychology Dutilh et al. (2021), traditional epistemology Dunn (2021); Tolly (2021) to finally close shared interests in formal epistemology Romero and Sprenger (2021) even within our own department Merdes et al. (2021). Our job is now to reliably inform you about all the contributions in the papers in this special issue. Unfortunately, that task is beyond our capabilities. What we can and instead do is to summarise the contributed papers to inform your reliable inference to read them all in great detail. (shrink)

The enduring replication crisis in many scientific disciplines casts doubt on the ability of science to estimate effect sizes accurately, and in a wider sense, to self-correct its findings and to produce reliable knowledge. We investigate the merits of a particular countermeasure—replacing null hypothesis significance testing with Bayesian inference—in the context of the meta-analytic aggregation of effect sizes. In particular, we elaborate on the advantages of this Bayesian reform proposal under conditions of publication bias and other methodological imperfections that are (...) typical of experimental research in the behavioral sciences. Moving to Bayesian statistics would not solve the replication crisis single-handedly. However, the move would eliminate important sources of effect size overestimation for the conditions we study. (shrink)

Some experiments are risky in that they cannot repeatedly produce certain phenomenon at will for study because the scientific knowledge of the process generating the uncertain phenomenon is poorly understood or may directly contradict with existing scientific knowledge. These experiments may have great impact not just to the scientific community but to mankind in general. Banning them from study may incur societies a great opportunity cost but accepting them runs the risk that scientists are doing junk science. How to make (...) an informed decision to accept/reject such study scientifically for the mainstream scientific community is of great importance to mankind. Here, we propose a statistical methodology to handle the situation. Specifically, we consider the likelihood of not observing the phenomenon after n trails so that it is statistically significant to have nil result. Consequently, we reject the hypothesis that there is some probability that we observe the phenomenon. (shrink)

Bayesian confirmation theory is a leading theory to decide the confirmation/refutation of a hypothesis based on probability calculus. While it may be much discussed in philosophy of science, is it actually practiced in terms of hypothesis testing by scientists? Since the assignment of some of the probabilities in the theory is open to debate and the risk of making the wrong decision is unknown, many scientists do not use the theory in hypothesis testing. Instead, they use alternative statistical tests that (...) can measure the risk or the reliability in decision making, circumventing some of the theoretical problems in practice. Therefore, the theory is not very popular in hypothesis testing among scientists at present. However, there are some proponents of Bayesian hypothesis testing, and software packages are made available to accelerate utilization by scientists. Time will tell whether Bayesian confirmation theory can become both a leading theory and a widely practiced method. In addition, this theory can be used to model the belief of scientists when testing hypotheses. (shrink)

A prominent type of scientific realism holds that some important parts of our best current scientific theories are at least approximately true. According to such realists, radically distinct alternatives to these theories or theory-parts are unlikely to be approximately true. Thus one might be tempted to argue, as the prominent anti-realist Kyle Stanford recently did, that realists of this kind have little or no reason to encourage scientists to attempt to identify and develop theoretical alternatives that are radically distinct from (...) currently accepted theories in the relevant respects. In other words, it may seem that realists should recommend that scientists be relatively conservative in their theoretical endeavors. This paper aims to show that this argument is mistaken. While realists should indeed be less optimistic of finding radically distinct alternatives to replace current theories, realists also have greater reasons to value the outcomes of such searches. Interestingly, this holds both for successful and failed attempts to identify and develop such alternatives. (shrink)

Tässä luvussa tarkastelemme hypoteesien testaamista ja kokeellista kausaalista järkeilyä tieteenfilosofisesta näkökulmasta. Arvioimme kokeellisen menetelmän mahdollisuuksia ja rajoituksia yhteiskuntatieteellisen tutkimuksen kontekstissa, jossa luonnontieteille ominaisia yleispäteviä teorioita harvoin on saatavilla ja jossa suoraviivaisiin kausaaliväitteisiin suhtaudutaan usein epäillen. Tämä luku ei siis ole menetelmäopas, joka kädestä pitäen opastaisi, kuinka yhteiskuntatieteellisiä kokeita tulisi rakentaa, vaan katsaus niihin perustaviin metodologisiin kysymyksiin ja periaatteisiin, joihin varsinaiset menetelmät nojaavat.

The paper examines the claim that significance testing violates the Principle of Total Evidence. I argue that p-values violate PTE for two-sided tests but satisfy PTE for one-sided tests invoking a sufficient test statistic independent of the preferred theory of evidence. While the focus of the paper is to evaluate a particular claim about the relationship of significance testing and PTE, I clarify the reading of this methodological principle along the way.

This research aims to identify the use of decision support systems as an entry point for operations of re-engineering in the Palestinian universities in Gaza Strip. The researchers used the method of questionnaire to collect data, and the researchers used a sample stratified random way, were (350) questionnaire distributed on the research sample and (312) questionnaire were collected back (89.1%). The study results showed that the most important ones are: there exists statistically significant impact at the level of significance (α (...) ≤ 0.05) for physical requirements, human requirements. technical requirements and regulatory requirements. The results showed also, the presence of statistically significant differences between the averages of the study sample estimates on the use of decision support systems as an entry point for operations of re-engineering in the Palestinian universities in Gaza Strip due to the variable sex in favor of males requirements. Furthermore, the results showed the existence of differences to the variable name of the university and each area of study for the benefit of the Islamic University then Al-Azhar University and then Al-Aqsa University. The study also concluded a series of recommendations including: encourage Palestinian universities in Gaza Strip, which are planning to re-engine Information Systems to start implementing the programs in the radical change as soon as possible. The need for the Palestinian universities in Gaza Strip, to develop the infrastructure for information technology in general, and decision support systems, in particular, when doing re-engineering operations. And the need for a separate unit of decision support systems and organizational structure to allow information to flow seamlessly between colleges and various departments and divisions. And investment of available information in building the capacities of integration techniques, in order to enable them to continue with the re-engineering of Information Systems. (shrink)

“Dutch Book” arguments and references to gambling theorems are typical in the debate between Bayesians and scientists committed to “classical” statistical methods. These arguments have rarely convinced non-Bayesian scientists to abandon certain conventional practices, partially because many scientists feel that gambling theorems have little relevance to their research activities. In other words, scientists “don’t bet.” This article examines one attempt, by Schervish, Seidenfeld, and Kadane, to progress beyond such apparent stalemates by connecting “Dutch Book”–type mathematical results with principles actually endorsed (...) by practicing experimentalists. (shrink)

In a recent paper in this journal, Carter and Peterson raise two distinctly epistemological puzzles that arise for anyone aspiring to defend the precautionary principle. The first puzzle trades on an application of epistemic contextualism to the precautionary principle; the second puzzle concerns the compatibility of the precautionary principle with the de minimis rule. In this note, I argue that neither puzzle should worry defenders of the precautionary principle. The first puzzle can be shown to be an instance of the (...) familiar but conceptually harmless challenge of adjudicating between relevant interests to reach assessments of threats when applying the precautionary principle. The second puzzle can be shown to rely on a subtle but crucial misrepresentation of the relevant probabilities at play when applying the precautionary principle. (shrink)

Exploratory inquiry has difficulty attracting research funding because funding agencies have little sense of how to detect good science in exploratory contexts. After documenting and explaining the focus on hypothesis testing among a variety of institutions responsible for distinguishing between good and bad science, I analyze the NIH grant review process. I argue that a good explanation for the focus on hypothesis testing—at least at the level of science funding agencies—is the fact that hypothesis-driven research is relatively easy to appraise. (...) I then explore one method by which we might gauge the epistemic merits of different styles of inquiry. (shrink)

Theory choice can be approached in at least four ways. One of these calls for the application of decision theory, and this article endorses this approach. But applying standard forms of decision theory imposes an overly demanding standard of numeric information, supposedly satisfied by point-valued utility and probability functions. To ameliorate this difficulty, a version of decision theory that requires merely comparative utilities and plausibilities is proposed. After a brief summary of this alternative, the article illustrates how comparative decision theory (...) affords a rational reconstruction of decisions made by exemplary scientists in two cases of theory choice: Buffon’s law and the luminiferous ether. It also offers a rational reconstruction of two cases of theory diagnosis: Mendeleev’s anomalies and the Pioneer anomaly. (shrink)

Recent epistemology has introduced a new criterion of adequacy for analyses of knowledge: such an analysis, to be adequate, must be compatible with the common view that knowledge is better than true belief. One account which is widely thought to fail this test is reliabilism, according to which, roughly, knowledge is true belief formed by reliable process. Reliabilism fails, so the argument goes, because of the "swamping problem". In brief, provided a belief is true, we do not care whether or (...) not it was formed by a reliable process. The value of reliability is "swamped" by the value of truth: truth combined with reliability is no better than truth alone. This paper approaches these issues from the perspective of decision theory. It argues that the "swamping effect" involves a sort of information-sensitivity that is well modelled decision-theoretically. It then employs this modelling to investigate a strategy, proposed by Goldman and Olsson, for saving reliabilism from the swamp, the so-called "conditional probability solution". It concludes that the strategy is only partially successful. (shrink)

Beliefs come in different strengths. What are the norms that govern these strengths of belief? Let an agent's belief function at a particular time be the function that assigns, to each of the propositions about which she has an opinion, the strength of her belief in that proposition at that time. Traditionally, philosophers have claimed that an agent's belief function at any time ought to be a probability function (Probabilism), and that she ought to update her belief function upon obtaining (...) new evidence by conditionalizing on that evidence (Conditionalization). Until recently, the central arguments for these claims have been pragmatic. But these putative justifications fail to identify what is epistemically irrational about violating Probabilism or Conditionalization. A new approach, which I will call epistemic utility theory, attempts to remedy this. It treats beliefs as epistemic acts; and it appeals to the notion of an epistemic utility function, which measures of how epistemically valuable a particular belief function is for a particular way the world might be. It then formulates fundamental epistemic norms that are analogous to the fundamental practical norms that underlie decision theory. I survey the results obtained so far in this young research project, and present a sustained critique of certain assumptions that have been made by a number of philosophers working in this area. (shrink)

Bayesian decision theory is here construed as explicating a particular concept of rational choice and Bayesian probability is taken to be the concept of probability used in that theory. Bayesian probability is usually identified with the agent’s degrees of belief but that interpretation makes Bayesian decision theory a poor explication of the relevant concept of rational choice. A satisfactory conception of Bayesian decision theory is obtained by taking Bayesian probability to be an explicatum for inductive probability given the agent’s evidence.

Rayleigh and Ramsay discovered the inert gas argon in the atmospheric air in 1895 using a carefully designed sequence of experiments guided by an informal statistical analysis of the resulting data. The primary objective of this article is to revisit this remarkable historical episode in order to make a case that the error‐statistical perspective can be used to bring out and systematize (not to reconstruct) these scientists' resourceful ways and strategies for detecting and eliminating error, as well as dealing with (...) Duhemian ambiguities and underdetermination problems as they arose in the context of their local research settings. *Received December 2009; revised January 2010. †To contact the author, please write to: Department of Economics, 3016 Pamplin Hall, Virginia Tech, Blacksburg, VA 24061; e‐mail: [email protected] (shrink)

The issues of double-counting, use-constructing, and selection effects have long been the subject of debate in the philosophical as well as statistical literature. I have argued that it is the severity, stringency, or probativeness of the test—or lack of it—that should determine if a double-use of data is admissible. Hitchcock and Sober ([2004]) question whether this ‘severity criterion' can perform its intended job. I argue that their criticisms stem from a flawed interpretation of the severity criterion. Taking their criticism as (...) a springboard, I elucidate some of the central examples that have long been controversial, and clarify how the severity criterion is properly applied to them. Severity and Use-Constructing: Four Points (and Some Clarificatory Notes) 1.1 Point 1: Getting beyond ‘all or nothing’ standpoints 1.2 Point 2: The rationale for prohibiting double-counting is the requirement that tests be severe 1.3 Point 3: Evaluate severity of a test T by its associated construction rule R 1.4 Point 4: The ease of passing vs. ease of erroneous passing: Statistical vs. ‘Definitional’ probability The False Dilemma: Hitchcock and Sober 2.1 Marsha measures her desk reliably 2.2 A false dilemma Canonical Errors of Inference 3.1 How construction rules may alter the error-probing performance of tests 3.2 Rules for accounting for anomalies 3.3 Hunting for statistically significant differences Concluding Remarks. (shrink)

We argue for a naturalistic account for appraising scientific methods that carries non-trivial normative force. We develop our approach by comparison with Laudan’s (American Philosophical Quarterly 24:19–31, 1987, Philosophy of Science 57:20–33, 1990) “normative naturalism” based on correlating means (various scientific methods) with ends (e.g., reliability). We argue that such a meta-methodology based on means–ends correlations is unreliable and cannot achieve its normative goals. We suggest another approach for meta-methodology based on a conglomeration of tools and strategies (from statistical modeling, (...) experimental design, and related fields) that affords forward looking procedures for learning from error and for controlling error. The resulting “error statistical” appraisal is empirical—methods are appraised by examining their capacities to control error. At the same time, this account is normative, in that the strategies that pass muster are claims about how actually to proceed in given contexts to reach reliable inferences from limited data. (shrink)

How should the concept of evidence be understood? And how does the concept of evidence apply to the controversy about creationism as well as to work in evolutionary biology about natural selection and common ancestry? In this rich and wide-ranging book, Elliott Sober investigates general questions about probability and evidence and shows how the answers he develops to those questions apply to the specifics of evolutionary biology. Drawing on a set of fascinating examples, he analyzes whether claims about intelligent design (...) are untestable; whether they are discredited by the fact that many adaptations are imperfect; how evidence bears on whether present species trace back to common ancestors; how hypotheses about natural selection can be tested, and many other issues. His book will interest all readers who want to understand philosophical questions about evidence and evolution, as they arise both in Darwin's work and in contemporary biological research. (shrink)

I consider the error-statistical account as both a theory of evidence and as a theory of inference. I seek to show how inferences regarding the truth of hypotheses can be upheld by avoiding a certain kind of alternative hypothesis problem. In addition to the testing of assumptions behind the experimental model, I discuss the role of judgments of implausibility. A benefit of my analysis is that it reveals a continuity in the application of error-statistical assessment to low-level empirical hypotheses and (...) highly general theoretical principles. This last point is illustrated with a brief sketch of the issues involved in the parametric framework analysis of tests of physical theories such as General Relativity and of fundamental physical principles such as the Einstein Equivalence Principle. (shrink)

According to Bayesian epistemology, the epistemically rational agent updates her beliefs by conditionalization: that is, her posterior subjective probability after taking account of evidence X, pnew, is to be set equal to her prior conditional probability pold(·|X). Bayesians can be challenged to provide a justification for their claim that conditionalization is recommended by rationality—whence the normative force of the injunction to conditionalize? There are several existing justifications for conditionalization, but none directly addresses the idea that conditionalization will be epistemically rational (...) if and only if it can reasonably be expected to lead to epistemically good outcomes. We apply the approach of cognitive decision theory to provide a justification for conditionalization using precisely that idea. We assign epistemic utility functions to epistemically rational agents; an agent’s epistemic utility is to depend both upon the actual state of the world and on the agent’s credence distribution over possible states. We prove that, under independently motivated conditions, conditionalization is the unique updating rule that maximizes expected epistemic utility. (shrink)

A conceptual analysis of falsificationism is performed, in which the central falsificationist thesis is divided into several components. Furthermore, an empirical study of falsification in science is reported, based on the 70 scientific contributions that were published as articles in Nature in 2000. Only one of these articles conformed to the falsificationist recipe for successful science, namely the falsification of a hypothesis that is more accessible to falsification than to verification. It is argued that falsificationism relies on an incorrect view (...) of the nature of scientific inquiry and that it is, therefore, not a tenable research methodology. (shrink)

Despite the widespread use of key concepts of the Neyman–Pearson (N–P) statistical paradigm—type I and II errors, significance levels, power, confidence levels—they have been the subject of philosophical controversy and debate for over 60 years. Both current and long-standing problems of N–P tests stem from unclarity and confusion, even among N–P adherents, as to how a test's (pre-data) error probabilities are to be used for (post-data) inductive inference as opposed to inductive behavior. We argue that the relevance of error probabilities (...) is to ensure that only statistical hypotheses that have passed severe or probative tests are inferred from the data. The severity criterion supplies a meta-statistical principle for evaluating proposed statistical inferences, avoiding classic fallacies from tests that are overly sensitive, as well as those not sensitive enough to particular errors and discrepancies. Introduction and overview 1.1 Behavioristic and inferential rationales for Neyman–Pearson (N–P) tests 1.2 Severity rationale: induction as severe testing 1.3 Severity as a meta-statistical concept: three required restrictions on the N–P paradigm Error statistical tests from the severity perspective 2.1 N–P test T(): type I, II error probabilities and power 2.2 Specifying test T() using p-values Neyman's post-data use of power 3.1 Neyman: does failure to reject H warrant confirming H? Severe testing as a basic concept for an adequate post-data inference 4.1 The severity interpretation of acceptance (SIA) for test T() 4.2 The fallacy of acceptance (i.e., an insignificant difference): Ms Rosy 4.3 Severity and power Fallacy of rejection: statistical vs. substantive significance 5.1 Taking a rejection of H0 as evidence for a substantive claim or theory 5.2 A statistically significant difference from H0 may fail to indicate a substantively important magnitude 5.3 Principle for the severity interpretation of a rejection (SIR) 5.4 Comparing significant results with different sample sizes in T(): large n problem 5.5 General testing rules for T(), using the severe testing concept The severe testing concept and confidence intervals 6.1 Dualities between one and two-sided intervals and tests 6.2 Avoiding shortcomings of confidence intervals Beyond the N–P paradigm: pure significance, and misspecification tests Concluding comments: have we shown severity to be a basic concept in a N–P philosophy of induction? (shrink)

Three experiments were used to investigate individuals' hypothesis-testing process as a function of moral perceived utilities , which in turn depend on perceived responsibility and fear of guilt. Moral perceived utilities are related to individuals' moral standards and specifically to people's attempt to face up to their own responsibilities, and to avoid feeling guilty of irresponsibility. The results showed that responsibility and fear of guilt in testing hypotheses involved a process defined as prudential mode , which entails focusing on and (...) confirming the worst hypothesis , and then reiterating the testing process. In particular, the results showed that responsible and guilt-fearing individuals: (1) tended to search prudentially for examples confirming the worst hypothesis and to search for counter-examples falsifying the positive hypothesis; (2) focused on the worst alternative, and tended to confirm it; (3) prudentially kept up the testing process, even if faced with initial positive evidence. Our discussion of the results emphasises how people are largely pragmatic in their hypothesis testing, using efficient cognitive strategies that focus on error minimisation rather than on truth detection. In a context of responsibility and guilt, the errors are linked to people's failure to face up to their own responsibilities, and are thus moral errors. (shrink)

En este trabajo se plantea, en primer lugar, la conveniencia de distinguir en el proceso de la contrastación empirica de hipótesis y teorías entre observación cientifíca y percepción y, en segundo lugar, se muestra como el munda procesado a través de la percepción se erige en base o soporte empírico del conocimiento científico. Una de las consecuencias del trabajo es que Ia tesis de “la carga teórica" de Ia observación ha sido mal planteada, al dar par sentado que esa carga (...) teórica afecta tambien al procesamiento perceptivo de los outputs proporeionados al científico por el instrumental de observación.This paper first suggests that, in analyses of the empirical testing of hypotheses and theories, scientific observation should be distinguished from perception; and goes on to say that the world, as processed by perception, is the basis or empirical foundation of scientific knowledge. This thesis that observation is “theory-laden” has been flawed by its being articulated as applying not only to scientific observation but also to the perceptional processing of the output provided to the scientists by observational instruments. (shrink)

According to a traditional view, scientific laws and theories constitute algorithmic compressions of empirical data sets collected from observations and measurements. This article defends the thesis that, to the contrary, empirical data sets are algorithmically incompressible. The reason is that individual data points are determined partly by perturbations, or causal factors that cannot be reduced to any pattern. If empirical data sets are incompressible, then they exhibit maximal algorithmic complexity, maximal entropy and zero redundancy. They are therefore maximally efficient carriers (...) of information about the world. Since, on algorithmic information theory, a string is algorithmically random just if it is incompressible, the thesis entails that empirical data sets consist of algorithmically random strings of digits. Rather than constituting compressions of empirical data, scientific laws and theories pick out patterns that data sets exhibit with a certain noise. (shrink)

A model of inductive inquiry is defined within the context of first‐order logic. The model conceives of 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 countable structures for that vocabulary. Next, Nature secretly chooses one structure from some cell of the partition. She then presents the scientist with a sequence of 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 or her 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. Different kinds of scientists can be investigated within this framework. At opposite ends of the spectrum are dumb scientists that rely on the strategy of “induction by enumeration,” and smart scientists that rely on an operator of belief revision. We report some results about the scope and limits of these two inductive strategies. (shrink)

In seeking general accounts of evidence, confirmation, or inference, philosophers have looked to logical relationships between evidence and hypotheses. Such logics of evidential relationship, whether hypothetico-deductive, Bayesian, or instantiationist fail to capture or be relevant to scientific practice. They require information that scientists do not generally have (e.g., an exhaustive set of hypotheses), while lacking slots within which to include considerations to which scientists regularly appeal (e.g., error probabilities). Building on my co-symposiasts contributions, I suggest some directions in which a (...) new and more adequate philosophy of evidence can move. (shrink)

This paper analyzes Deborah Mayo's recent criticism of use-novelty requirement. She claims that her severity criterion captures actual scientific practice better than use-novelty, and that use-novelty is not a necessary condition for severity. Even though certain cases in which evidence used for the construction of the hypothesis can test the hypothesis severely, I do not think that her severity criterion fits better with our intuition about good tests than use-novelty. I argue for this by showing a parallelism in terms of (...) severity between the confidence interval case and what she calls 'gellerization'. To account for the difference between these cases, we need to take into account certain additional considerations like a systematic neglect of relevant alternatives. (shrink)

That some propositions are testable, while others are not, was a fundamental idea in the philosophical program known as logical empiricism. That program is now widely thought to be defunct. Quine’s (1953) “Two Dogmas of Empiricism” and Hempel’s (1950) “Problems and Changes in the Empiricist Criterion of Meaning” are among its most notable epitaphs. Yet, as we know from Mark Twain’s comment on an obituary that he once had the pleasure of reading about himself, the report of a death can (...) be an exaggeration. The research program that began in Vienna and Berlin continues, even though many of the specific formulations that came out of those circles are flawed and need to be replaced. (shrink)

Several leading topics outstanding after John Earman's Bayes or Bust? are investigated further, with emphasis on the relevance of Bayesian explication in epistemology of science, despite certain limitations. (1) Dutch Book arguments are reformulated so that their independence from utility and preference in epistemic contexts is evident. (2) The Bayesian analysis of the Quine-Duhem problem is pursued; the phenomenon of a "protective belt" of auxiliary statements around reasonably successful theories is explicated. (3) The Bayesian approach to understanding the superiority of (...) variety of evidence is pursued; a recent challenge (by Wayne) is converted into a positive result on behalf of the Bayesian analysis, potentially with far-reaching consequences. (4) The condition for applying the merger-of-opinion results and the thesis of underdetermination of theories are compared, revealing significant limitations in applicability of the former. (5) Implications concerning "diachronic Dutch Book" arguments and "non-Bayesian shifts" are drawn, highlighting the incompleteness, but not incorrectness, of Bayesian analysis. (shrink)

1. Introduction. The papers by Hellman and Mayo offer up a rich menu of problems and proposed solutions, so there is much here for a friendly critic to fasten on. In order to bring a modicum of focus to my commentary, I shall limit my remarks to the Duhem problem and its radiations in epistemology and methodology. Both Mayo and Hellman claim to have solutions to that hoary old problem and they tout these solutions as key indicators of the explanatory (...) power of their respective technical epistemologies, whether Bayesian or Neyman/Pearsonian. Like Mayo, I shall be arguing that the Bayesian treatment of Duhem's problem is no solution at all; that, indeed, it fails to grapple with the core challenges posed by the purported ambiguities of falsification. My response to Mayo's more detailed, and I think more right-headed, treatment of the Duhem problem will be more complex. While I believe that she is moving in the right direction in many respects, I think that she fails to see one key dimension of the Duhemian conundrum. Indeed, she risks solving not Duhem's problem but quite a different one. I shall gently try to encourage her to steer her way back towards the central task. (shrink)

It is sometimes held that facts confirm a hypothesis only if they were not used in the construction of that hypothesis. This requirement of "use novelty" introduces a historical aspect into the assessment of evidence claims. I examine a methodological principle invoked by physicists in the experimental search for the top quark that bears a striking resemblance to this view. However, this principle is better understood, both historically and philosophically, in terms of the need to conduct a severe test than (...) in terms of use novelty. Nevertheless, a historical factor remains in the assessment of some evidence claims. (shrink)

This article explores whether theory-ladenness makes empirical testing an inse cure foundation for objectivity. Specifically, this article uses path diagrams as visual heuristics to assist in (1) developing a parsimonious representation of the traditional empiricist view of empirical testing, (2) showing how the "New Image" view ostensibly threatens the objectivity of science, (3) proposing a unified, realist theory of empirical testing, (4) developing a representation of the unified theory, (5) exploring several potential threats to objectivity, (6) discussing the proposed theory's (...) implications for social science, and (7) adumbrating three foundational premises for scientific realism. (shrink)