This paper develops a statistical approach to the problem of primitive representation. Representation of the kind commonly attributed to litmus paper, fuel gauges and tree rings occurs when, so to speak, there is a sufficiently good correlation between two variables. The fundamental distinction between misrepresentation and non-representation is explained in terms of the notion of an informationally useful correlation. The paper further argues that the statistical approach satisfactorily resolves well known puzzles such as Fodor's disjunction problem.

Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random phenomena are interpreted as classical probabilities, and this interpretation of equally likely chance outcomes is applied to statistical inference using urn models. These are used to address Bayesian criticisms of frequentist methods. Recent descriptions of p-values, confidence intervals, and power are viewed through the lens of classical probability (...) based on a single random sample from the population. (shrink)

In this paper we consider the problem of how to measure the strength of statistical evidence from the perspective of evidence amalgamation operations. We begin with a fundamental measurement amalgamation principle : for any measurement, the inputs and outputs of an amalgamation procedure must be on the same scale, and this scale must have a meaningful interpretation vis a vis the object of measurement. Using the p value as a candidate evidence measure, we examine various commonly used approaches to amalgamation (...) of evidence across similar studies, including standard forms of meta-analysis. We show that none of these methods satisfies MAP. Thus an underlying measurement problem remains. We argue that a successful approach to evidence amalgamation necessitates a solution to the problem of evidence measurement, and we suggest some lines of reasoning that might guide further work towards this end. (shrink)

This paper will critically assess Popper’s evolutionary philosophy. There exists a rich literature on the topic with which we have many reservations. We believe that Popper’s evolutionary philosophy should be assessed in light of the intriguing theoretical insights offered, during the last 10 years or so, by the philosophy of biology, evolutionary biology and molecular biology. We will argue that, when analysed in this manner, Popper’s ideas concerning the nature of selection, Lamarckism and the theoretical limits of neo-Darwinism can be (...) appreciated in their full biological and philosophical value. (shrink)

The propensity nature of evolutionary fitness has long been appreciated and is nowadays amply discussed. The discussion has, however, on occasion followed long standing conflations in the philosophy of probability literature between propensities, probabilities, and frequencies. In this paper, I apply a more recent conception of propensities in modelling practice to some of the key issues, regarding the mathematical representation of fitness and how it may be regarded as explanatory. The ensuing complex nexus of fitness emphasises the distinction between biological (...) propensities and the probability distributions over offspring numbers that they give rise to; and how critical it is to distinguish the possession conditions of the underlying dispositional properties from those of their probabilistic manifestations. (shrink)

This paper considers a key point of contention between classical and Bayesian statistics that is brought to the fore when examining so-called ‘persistent experimenters’—the issue of stopping rules, or more accurately, outcome spaces, and their influence on statistical analysis. First, a working definition of classical and Bayesian statistical tests is given, which makes clear that (1) once an experimental outcome is recorded, other possible outcomes matter only for classical inference, and (2) full outcome spaces are nevertheless relevant to both the (...) classical and Bayesian approaches, when it comes to planning/choosing a test. The latter point is shown to have important repercussions. Here we argue that it undermines what Bayesians may admit to be a compelling argument against their approach—the Bayesian indifference to persistent experimenters and their optional stopping rules. We acknowledge the prima facie appeal of the pro-classical ‘optional stopping intuition’, even for those who ordinarily have Bayesian sympathies. The final section of the paper, however, provides three error theories that may assist a Bayesian in explaining away the apparent anomaly in their reasoning. (shrink)

The likelihood principle (LP) is a core issue in disagreements between Bayesian and frequentist statistical theories. Yet statements of the LP are often ambiguous, while arguments for why a Bayesian must accept it rely upon unexamined implicit premises. I distinguish two propositions associated with the LP, which I label LP1 and LP2. I maintain that there is a compelling Bayesian argument for LP1, based upon strict conditionalization, standard Bayesian decision theory, and a proposition I call the practical relevance principle. In (...) contrast, I argue that there is no similarly compelling argument for or against LP2. I suggest that these conclusions lead to a restrictedly pluralistic view of Bayesian confirmation measures. (shrink)

Amalgamating evidence of different kinds for the same hypothesis into an overall confirmation is analogous, I argue, to amalgamating individuals’ preferences into a group preference. The latter faces well-known impossibility theorems, most famously “Arrow’s Theorem”. Once the analogy between amalgamating evidence and amalgamating preferences is tight, it is obvious that amalgamating evidence might face a theorem similar to Arrow’s. I prove that this is so, and end by discussing the plausibility of the axioms required for the theorem.

Error statistics is an important methodological view in philosophy of statistics and philosophy of science that can be applied to scientific experiments such as clinical trials. In this paper, I raise two potential issues for ES when it comes to guiding, and explaining early stopping of randomized controlled trials : ES provides limited guidance in cases of early unfavorable trends due to the possibility of trend reversal; ES is silent on how to prospectively control error rates in experiments requiring multiple (...) interim analyses. The method of conditional power, together with a rationing principle for RCTs, can assist ES in addressing such issues. (shrink)

This paper develops a probabilistic reconstruction of the No Miracles Argument in the debate between scientific realists and anti-realists. The goal of the paper is to clarify and to sharpen the NMA by means of a probabilistic formalization. In particular, we demonstrate that the persuasive force of the NMA depends on the particular disciplinary context where it is applied, and the stability of theories in that discipline. Assessments and critiques of "the" NMA, without reference to a particular context, are misleading (...) and should be relinquished. This result has repercussions for recent anti-realist arguments, such as the claim that the NMA commits the base rate fallacy. It also helps to explain the persistent disagreement between realists and anti-realists. (shrink)

Scientific and statistical inferences build heavily on explicit, parametric models, and often with good reasons. However, the limited scope of parametric models and the increasing complexity of the studied systems in modern science raise the risk of model misspecification. Therefore, I examine alternative, data-based inference techniques, such as bootstrap resampling. I argue that their neglect in the philosophical literature is unjustified: they suit some contexts of inquiry much better and use a more direct approach to scientific inference. Moreover, they make (...) more parsimonious assumptions and often replace theoretical understanding and knowledge about mechanisms by careful experimental design. Thus, it is worthwhile to study in detail how nonparametric models serve as inferential engines in science. (shrink)

Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis for Bayesian (...) reasoning with idealized models in science. (shrink)

This article calls into question the charge that frequentist testing is susceptible to the base-rate fallacy. It is argued that the apparent similarity between examples like the Harvard Medical School test and frequentist testing is highly misleading. A closer scrutiny reveals that such examples have none of the basic features of a proper frequentist test, such as legitimate data, hypotheses, test statistics, and sampling distributions. Indeed, the relevant error probabilities are replaced with the false positive/negative rates that constitute deductive calculations (...) based on known probabilities among events. As a result, the ampliative dimension of frequentist induction—learning from data about the underlying data-generating mechanism—is missing. *Received August 2009; revised January 2010. †To contact the author, please write to: Department of Economics, Virginia Tech, Blacksburg, VA 24061; e-mail: [email protected]. (shrink)

The main objective of the paper is to propose a frequentist interpretation of probability in the context of model-based induction, anchored on the Strong Law of Large Numbers (SLLN) and justifiable on empirical grounds. It is argued that the prevailing views in philosophy of science concerning induction and the frequentist interpretation of probability are unduly influenced by enumerative induction, and the von Mises rendering, both of which are at odds with frequentist model-based induction that dominates current practice. The differences between (...) the two perspectives are brought out with a view to defend the model-based frequentist interpretation of probability against certain well-known charges, including [i] the circularity of its definition, [ii] its inability to assign ‘single event’ probabilities, and [iii] its reliance on ‘random samples’. It is argued that charges [i]–[ii] stem from misidentifying the frequentist ‘long-run’ with the von Mises collective. In contrast, the defining characteristic of the long-run metaphor associated with model-based induction is neither its temporal nor its physical dimension, but its repeatability (in principle); an attribute that renders it operational in practice. It is also argued that the notion of a statistical model can easily accommodate non-IID samples, rendering charge [iii] simply misinformed. (shrink)

Historical sciences like evolutionary biology reconstruct past events by using the traces that the past has bequeathed to the present. Markov chain theory entails that the passage of time reduces the amount of information that the present provides about the past. Here we use a Moran process framework to show that some evolutionary processes destroy information faster than others. Our results connect with Darwin’s principle that adaptive similarities provide scant evidence of common ancestry whereas neutral and deleterious similarities do better. (...) We also describe how the branching in phylogenetic trees affects the information that the present supplies about the past. (shrink)

Richard Boyd and Nicholas Sturgeon develop distinctive naturalistic arguments for scientific realism and moral realism. Each defends a realist position by an inference to the best explanation. In this paper, I suggest that these arguments for realism should be reformulated, with the law of likelihood replacing inference to the best explanation. The resulting arguments for realism do not work.

This paper is a sympathetic critique of the argument that Reichenbach develops in Chap. 2 of Experience and Prediction for the thesis that sense experience justifies belief in the existence of an external world. After discussing his attack on the positivist theory of meaning, I describe the probability ideas that Reichenbach presents. I argue that Reichenbach begins with an argument grounded in the Law of Likelihood but that he then endorses a different argument that involves prior probabilities. I try to (...) show how this second step in Reichenbach's approach can be strengthened by using ideas that have been developed recently for understanding causation in terms of the idea of intervention. (shrink)

“Absence of evidence isn’t evidence of absence” is a slogan that is popular among scientists and nonscientists alike. This article assesses its truth by using a probabilistic tool, the Law of Likelihood. Qualitative questions (“Is E evidence about H ?”) and quantitative questions (“How much evidence does E provide about H ?”) are both considered. The article discusses the example of fossil intermediates. If finding a fossil that is phenotypically intermediate between two extant species provides evidence that those species have (...) a common ancestor, does failing to find such a fossil constitute evidence that there was no common ancestor? Or should the failure merely be chalked up to the imperfection of the fossil record? The transitivity of the evidence relation in simple causal chains provides a broader context, which leads to discussion of the fine-tuning argument, the anthropic principle, and observation selection effects. (shrink)

To evaluate Hume's thesis that causal claims are always empirical, I consider three kinds of causal statement: ?e1 caused e2 ?, ?e1 promoted e2 ?, and ?e1 would promote e2 ?. Restricting my attention to cases in which ?e1 occurred? and ?e2 occurred? are both empirical, I argue that Hume was right about the first two, but wrong about the third. Standard causal models of natural selection that have this third form are a priori mathematical truths. Some are obvious, others (...) less so. Empirical work on natural selection takes the form of defending causal claims of the first two types. I provide biological examples that illustrate differences among these three kinds of causal claim. (shrink)

Carl Hempel argued that probabilistic hypotheses are limited in what they can explain. He contended that a hypothesis cannot explain why E is true if the hypothesis says that E has a probability less than 0.5. Wesley Salmon and Richard Jeffrey argued to the contrary, contending that P can explain why E is true even when P says that E’s probability is very low. This debate concerned noncontrastive explananda. Here, a view of contrastive causal explanation is described and defended. It (...) provides a new limit on what probabilistic hypotheses can explain; the limitation is that P cannot explain why E is true rather than A if P assign E a probability that is less than or equal to the probability that P assigns to A. The view entails that a true deterministic theory and a true probabilistic theory that apply to the same explanandum partition are such that the deterministic theory explains all the true contrastive propositions constructable from that partition, whereas the probabilistic theory often fails to do so. (shrink)

I discuss two versions of the doomsday argument. According to ``Gott's Line'',the fact that the human race has existed for 200,000 years licences the predictionthat it will last between 5100 and 7.8 million more years. According to ``Leslie'sWedge'', the fact that I currently exist is evidence that increases the plausibilityof the hypothesis that the human race will come to an end sooner rather than later.Both arguments rest on substantive assumptions about the sampling process thatunderlies our observations. These sampling assumptions have (...) testable consequences,and so the sampling assumptions themselves must be regarded as empirical claims.The result of testing some of these consequences is that both doomsday argumentsare empirically disconfirmed. (shrink)

Es wird begründet, daß die Konstruktion des Kartenparadoxons von Kerridge auf einer fehlerhaften Betrachtungsweise beruht. Eine genauere Analyse zeigt, daß das Kerridge-Argument mit dem Hackingschen Likelihood-Stützungsargument im Einklang steht.

Humans come prepared to recognize two fundamental features of our surroundings: animate objects and agents. This recognition begins early in ontogeny and pervades our ecological and social space. This cognitive capacity reveals an important adaptation and sets the conditions for pervasive shared experiences. One feature of our species and our evolved cephalic substrates is that we are prepared to recognize self-propelled action in others. Our cultural evolution is knotted to an expanding sense of shared experiences.

The replication crisis has caused researchers to distinguish between exact replications, which duplicate all aspects of a study that could potentially affect the results, and direct replications, which duplicate only those aspects of the study that are thought to be theoretically essential to reproduce the original effect. The replication crisis has also prompted researchers to think more carefully about the possibility of making Type I errors when rejecting null hypotheses. In this context, the present article considers the utility of two (...) types of Type I error probability: the Neyman–Pearson long run Type I error rate and the Fisherian sample-specific Type I error probability. It is argued that the Neyman–Pearson Type I error rate is inapplicable in social science because it refers to a long run of exact replications, and social science deals with irreversible units that make exact replications impossible. Instead, the Fisherian sample-specific Type I error probability is recommended as a more meaningful way to conceptualize false positive results in social science because it can be applied to each sample-specific decision about rejecting the same substantive null hypothesis in a series of direct replications. It is concluded that the replication crisis may be partly due to researchers’ unrealistic expectations about replicability based on their consideration of the Neyman–Pearson Type I error rate across a long run of exact replications. (shrink)

: Philosophical naturalism is ambiguous between conjoining philosophy with science or with nature understood scientifically. Reconciliation of this ambiguity is necessary but rarely attempted. Feminist science studies often endorse the former naturalism but criticize the second. Karen Barad's agential realism, however, constructively reconciles both senses. Barad then challenges traditional metaphysical naturalisms as not adequately accountable to science. She also contributes distinctively to feminist reinterpretations of objectivity as agential responsibility, and of agency as embodied, worldly, and intra-active.

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)

The p value is the probability under the null hypothesis of obtaining an experimental result that is at least as extreme as the one that we have actually obtained. That probability plays a crucial role in frequentist statistical inferences. But if we take the word ‘extreme’ to mean ‘improbable’, then we can show that this type of inference can be very problematic. In this paper, I argue that it is a mistake to make such an interpretation. Under minimal assumptions about (...) the alternative hypothesis, I explain why ‘extreme’ means ‘outside the most precise predicted range of experimental outcomes for a given upper bound probability of error’. Doing so, I rebut recent formulations of recurrent criticisms against the frequentist approach in statistics and underscore the importance of random variables. (shrink)

This paper deals with meta-statistical questions concerning frequentist statistics. In Sections 2 to 4 I analyse the dispute between Fisher and Neyman on the so called logic of statistical inference, a polemic that has been concomitant of the development of mathematical statistics. My conclusion is that, whenever mathematical statistics makes it possible to draw inferences, it only uses deductive reasoning. Therefore I reject Fisher's inductive approach to the statistical estimation theory and adhere to Neyman's deductive one. On the other hand, (...) I assert that Neyman-Pearson's testing theory, as well as Fisher's tests of significance, properly belong to decision theory, not to logic, neither deductive nor inductive. I then also disagree with Costantini's view of Fisher's testing model as a theory of hypothetico-deductive inferences.In Section 5 I disapprove Hacking1's evidentialists criticisms of the Neyman-Pearson's theory of statistics (NPT), as well as Hacking2's interpretation of NPT as a theory of probable inference. In both cases Hacking misses the point. I conclude, by claiming that Mayo's conception of the Neyman-Pearson's testing theory, as a model of learning from experience, does not purport any advantages over Neyman's behavioristic model. (shrink)

Conventional discussion of research methodology contrast two approaches, the quantitative and the qualitative, presented as collectively exhaustive. But if qualitative is taken as the understanding of lifeworlds, the two approaches between them cover only a tiny fraction of research methodologies; and the quantitative, taken as the routine application to controlled experiments of frequentist statistics by way of the Null Hypothesis Significance Testing Procedure, is seriously flawed. It is contrary to the advice both of Fisher and of Neyman and Pearson, the (...) two sources from which it is drawn. (shrink)

This article sketches a theory of objective probability focusing on nomic probability, which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the statistical syllogism. It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of induction. The theory of induction (...) is not of the familiar Bayesian variety, but consists of a precise version of the traditional Nicod Principle and its statistical analogues. (shrink)

Philosophers of science have often favoured reductive approaches to how-possibly explanation. This article identifies three alternative conceptions making how-possibly explanation an interesting phenomenon in its own right. The first variety approaches “how possibly X?” by showing that X is not epistemically impossible. This can sometimes be achieved by removing misunderstandings concerning the implications of one’s current belief system but involves characteristically a modification of this belief system so that acceptance of X does not result in contradiction. The second variety offers (...) a potential how-explanation of X. It is usually followed by a range of further potential how-explanations of the same phenomenon. In recent literature the factual claims implied by the second variety have been downplayed whereas the heuristic role of mapping the space of conceptual possibilities has been emphasized. I will focus especially on this truth-bracketing sense of potentiality when looking closer at the second variety in the paper. The third variety has attracted less interest. It presents a partial how-explanation of X. Typically it aims to establish the existence of a mechanism by which X could be and was generated. The third conception stands out as the natural alternative for the advocate of ontic how-possibly explanations. This article transfers Salmon’s view that explanation-concepts can be broadly divided into epistemic, modal, and ontic to the context of how-possibly explanations. Moreover, it is argued that each of the three above-mentioned varieties of how-possibly explanation occurs in science. To recognize this may be especially relevant for philosophers. We are often misled by the promises of various why-explanation accounts, and seem to have forgotten nearly everything about the diversity of how-possibly explanations. (shrink)

What sort of evidence can confer the strongest support to a hypothesis? A natural answer is that the evidence entails the hypothesis. Roush (Tracking Truth: Knowledge, Evidence, and Science, Clarendon Press, Oxford, 2005) claims that the likelihood ratio measure of degree of incremental support can deliver this intuitively natural result, and regards it as unifying “[the] account of induction and deduction in the only way that makes sense” (p. 163). In this paper, we highlight a difficulty in the treatment of (...) this case, and question the great significance that is attached to this measure and its alleged capacity to accommodate the logicality requirement. We contrast the likelihood ratio measure with other measures (such as the Kemeny–Oppenheim measure and the difference measure), and argue that problems still emerge in light of tensions with plausible requirements for confirmation measures more generally. (shrink)

The history of statistics is filled with many controversies, in which the prime focus has been the difference in the “interpretation of probability” between Fre- quentist and Bayesian theories. Many philosophical arguments have been elabo- rated to examine the problems of both theories based on this dichotomized view of statistics, including the well-known stopping-rule problem and the catch-all hy- pothesis problem. However, there are also several “hybrid” approaches in theory, practice, and philosophical analysis. This poses many fundamental questions. This paper (...) reviews three cases and argues that the interpretation problem of probabil- ity is insufficient to begin a philosophical analysis of the current issues in the field of statistics. A novel viewpoint is proposed to examine the relationship between the stopping-rule problem and the catch-all hypothesis problem. (shrink)

A complete calculus of inductive inference captures the totality of facts about inductive support within some domain of propositions as relations or theorems within the calculus. It is demonstrated that there can be no complete, non-trivial calculus of inductive inference.

In 1958, to refute the argument known as the theoretician's dilemma, Hempel suggested that theoretical terms might be logically indispensable for inductive systematization of observational statements. This thesis, in some form or another, has later been supported by Scheffler, Lehrer, and Tuomela, and opposed by Bohnert, Hooker, Stegmüller, and Cornman. In this paper, a critical survey of this discussion is given. Several different putative definitions of the crucial notion inductive systematization achieved by a theory are discussed by reference to the (...) properties of inductive inference. The consequences of the following differences between deductive and inductive inference are emphasized: the lack of simple transitivity properties (even in a modified sense) of inductive inference, and the failure of the inductive analogue of the converse of The Deduction Theorem. The main conclusions are: (i) Hempel's original thesis may very well be right but his argument for it is unsatisfactory, (ii) theoretical terms can be logically indispensable for a non-Hempelian kind of inductive systematization, relative to both Craigian and Ramseyan elimination, (iii) Lehrer's attempt to prove the indispensability of theoretical terms for inductive-probabilistic systematization is, as a modification of Hempelian kind of inductive-deterministic systematization, unsatisfactory, and (iv) there does not seem to be much hope of escaping the conclusion (ii), if it is true, by extending the Craigian replacement programme along the lines suggested by Cornman. (shrink)