The quantitative problem of old evidence is the problem of how to measure the degree to which e confirms h for agent A at time t when A regards e as justified at t. Existing attempts to solve this problem have applied the e-difference approach, which compares A's probability for h at t with what probability A would assign h if A did not regard e as justified at t. The quantitative problem has been widely regarded as unsolvable primarily on (...) the grounds that the e-difference approach suffers from intractable problems. Various philosophers have proposed that 'Bayesianism' should be rejected as a research strategy in confirmation theory in part because of the unsolvability of this problem. I develop a version of the e-difference approach which overcomes these problems and possesses various advantages (but also certain limitations). I develop an alternative 'theistic' approach which handles many cases that my development of the e-difference approach does not handle. I conclude with an assessment of the significance of the quantitative problem for Bayesianism and argue that this problem is misunderstood in so far as it is regarded as unsolvable, and in so far as it is regarded as a problem only for Bayesians. (shrink)

This paper is a sequel to my 'Theological Misinterpretations of Current Physical Cosmology' (Foundations of Physics [1996], 26 (4); revised in Philo [1998], 1 (1)). There I argued that the Big Bang models of (classical) general relativity theory, as well as the original 1948 versions of the steady state cosmology, are each logically incompatible with the time-honored theological doctrine that perpetual divine creation ('creatio continuans') is required in each of these two theorized worlds. Furthermore, I challenged the perennial theological doctrine (...) that there must be a divine creative cause (as distinct from a transformative one) for the very existence of the world, a ratio essendi. This doctrine is the theistic reply to the question: 'Why is there something, rather than just nothing?' I begin my present paper by arguing against the response by the contemporary Oxford theist Richard Swinburne and by Leibniz to what is, in effect, my counter-question: 'But why should there be just nothing, rather than something?' Their response takes the form of claiming that the a priori probability of there being just nothing, vis-à-vis the existence of alternative states, is maximal, because the non-existence of the world is conceptually the simplest. On the basis of an analysis of the role of simplicity in scientific explanations, I show that this response is multiply flawed, and thus provides no basis for their three contentions that (i) if there is a world at all, then its 'normal', natural, spontaneous state is one of utter nothingness or total non-existence, so that (ii) the very existence of matter, energy and living beings constitutes a deviation from the allegedly 'normal', spontaneous state of 'nothingness', and (iii) that deviation must thus have a suitably potent (external) divine cause. Related defects turn out to vitiate the medieval Kalam Argument for the existence of God, as espoused by William Craig. Next I argue against the contention by such theists as Richard Swinburne and Philip L. Quinn that (i) the specific content of the scientifically most fundamental laws of nature, including the constants they contain, requires supra-scientific explanation, and (ii) a satisfactory explanation is provided by the hypothesis that the God of theism willed them to be exactly what they are. Furthermore, I contend that the theistic teleological gloss on the 'Anthropic Principle' is incoherent and explanatorily unavailing. Finally, I offer an array of considerations against Swinburne's attempt to show, via Bayes's theorem, that the existence of God is more probable than not. (shrink)

According to influential accounts of scientific method, such as critical rationalism, scientific knowledge grows by repeatedly testing our best hypotheses. But despite the popularity of hypothesis tests in statistical inference and science in general, their philosophical foundations remain shaky. In particular, the interpretation of non-significant results—those that do not reject the tested hypothesis—poses a major philosophical challenge. To what extent do they corroborate the tested hypothesis, or provide a reason to accept it? Popper sought for measures of corroboration that could (...) adequately answer this question. According to Popper, corroboration is different from probability-raising, and grounded in the predictive success and testability of a hypothesis. As such, corroboration becomes an indicator of the scientific value of a hypothesis and guides our practical preferences over hypotheses that have been subjected to severe tests. This article proves two impossibility results for corroboration measures based on statistical relevance. The generality of these results shows that Popper’s qualitative characterization of corroboration must be misguided. I explore what a more promising and scientifically useful concept of corroboration could look like. (shrink)

Résumé L’article évoque les bases de la méthode expérimentale en général et son adaptation à l’étude des phénomènes économiques tout en rendant compte des réflexions philosophiques récentes sur la nature des expériences en laboratoire. Il recense par ailleurs les principales procédures expérimentales qui caractérisent la bonne pratique des économistes – dont certaines témoignent d’une grande ingéniosité – en pointant en parallèle ce qui la sépare de celle plus ancienne des psychologues. La question des incitations financières y fait l’objet d’une attention (...) toute particulière. L’article souligne les immenses progrès réalisés en quelques décennies comme le caractère très professionnel de la démarche expérimentale, sans pour autant occulter les désaccords qui persistent entre certains expérimentalistes et l’existence de quelques questions « ouvertes » d’importance. A cet égard, l’article tente de faire le point sur l’un des questionnements méthodologiques qui, bien que central dans un argumentaire de défense contre la critique courante du caractère « artificiel » des expériences, n’est vraiment abordé de manière sérieuse que depuis peu : le problème de la « validité externe » des résultats expérimentaux, i.e. leur capacité à être généralisés en dehors du laboratoire. (shrink)

Kerr coined the term ‘HARKing’ to refer to the practice of ‘hypothesizing after the results are known’. This questionable research practice has received increased attention in recent years because it is thought to have contributed to low replication rates in science. The present article discusses the concept of HARKing from a philosophical standpoint and then undertakes a critical review of Kerr’s twelve potential costs of HARKing. It is argued that these potential costs are either misconceived, misattributed to HARKing, lacking evidence, (...) or that they do not take into account pre- and post-publication peer review and public availability to research materials and data. It is concluded that it is premature to conclude that HARKing has led to low replication rates. (shrink)

“What data will show the truth?” is a fundamental question emerging early in any empirical investigation. From a statistical perspective, experimental design is the appropriate tool to address this question by ensuring control of the error rates of planned data analyses and of the ensuing decisions. From an epistemological standpoint, planned data analyses describe in mathematical and algorithmic terms a pre-specified mapping of observations into decisions. The value of exploratory data analyses is often less clear, resulting in confusion about what (...) characteristics of design and analysis are necessary for decision making and what may be useful to inspire new questions. This point is addressed here by illustrating the Popper-Miller theorem in plain terms and using a graphical support. Popper and Miller proved that probability estimates cannot generate hypotheses on behalf of investigators. Consistently with Popper-Miller, we show that probability estimation can only reduce uncertainty about the truth of a merely possible hypothesis. This fact clearly identifies exploratory analysis as one of the tools supporting a dynamic process of hypothesis generation and refinement which cannot be purely analytic. A clear understanding of these facts will enable stakeholders, mathematical modellers and data analysts to better engage on a level playing field when designing experiments and when interpreting the results of planned and exploratory data analyses. (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)