Our Vision and our Mission: Bulishit,Assertion and Belief

Given ht as the hypothesis of theism, hm as the hypothesis of materialism, and e as the evidence of a complex life-bearing universe, Richard Swinburne presents these arguments in The Existence of God: (1) that this ordered universe is a priori improbable, given the stringent requirements for life and the Second Law of Thermodynamics; (2) that this universe's structure is evidence for theism, and that theism therefore explains this universe; Swinburne argues that because P(e|ht) > P(e|hm), it follows that P(ht|e)>P(hm|e); and (3) a theistic explanation for the universe is more probable because it is simpler; therefore it is more likely that God exists than not. As I have addressed (3) in a prior paper, this paper will address the Bayesian argument that Swinburne offers in (2), i.e. that P(e|ht)>P(e). In the paper I draw a number of conclusions, most pertinently, that Hacking's Total Probability Rule (TPR) for cases of mutually exclusive hypotheses [ht vs hm] and evidence e entails that ht can only be confirmed if P(e|～ht) is low. I also conclude that if we follow the TPR for Swinburne's argument, we achieve the result that theism is at best slightly improbable, or equiprobable with materialism.     

Is Theism a Simple,and hence Probable,Explanation for the Universe?

Abstract

Richard Swinburne, in his The Existence of God (2004), presents a cosmological argument in defence of theism (Swinburne 1991: 119, 135). God, Swinburne argues, is more likely to bring about an ordered universe than other states (ibid.: 144, 299). To defend this view, Swinburne presents the following arguments: (1) That this ordered universe is a priori improbable (2004: 49, 150, 1991: 304 et seq.), given the stringent requirements for life (cf. also Leslie 2000: 12), and the Second Law of Thermodynamics (Giancoli 1990: 396); (2) That it seems as if this ordered universe can be explained by theism; (3) A theistic explanation for the universe is more probable because it is a simple explanation. To this end, Swinburne makes use of Bayes’ Theorem. Symbolically, this claim can be represented as (e) for the evidence of the existence of a complex universe, and (h) for a hypothesis. Swinburne’s argument is that theism has a higher prior probability, P(h_theism) > P(h_materialism), since theism is simpler than materialism. He concludes that P(e|h_theism) > P(e|h_materialism). In this paper I will address only this argument (3) above, and defend the view that it is false: theism is not simpler than materialism, nor it is more probably true. I conclude that theism is less probable than materialism, expressed by P(h_theism) < P(h_materialism) : 2/N(2n+1) < 1/n, where N is the number of possible universes and n the number of entities in existence.     

Cronbach’s α, Revelle’s β, and Mcdonald’s ω<Subscript><Emphasis Type="Italic">H</Emphasis></Subscript>: their relations with each other and two alternative conceptualizations of reliability

We make theoretical comparisons among five coefficients—Cronbach’s α, Revelle’s β, McDonald’s ω_h, and two alternative conceptualizations of reliability. Though many end users and psychometricians alike may not distinguish among these five coefficients, we demonstrate formally their nonequivalence. Specifically, whereas there are conditions under which α, β, and ω_h are equivalent to each other and to one of the two conceptualizations of reliability considered here, we show that equality with this conceptualization of reliability and between α and ω_h holds only under a highly restrictive set of conditions and that the conditions under which β equals ω_h are only somewhat more general. The nonequivalence of α, β, and ω_h suggests that important information about the psychometric properties of a scale may be missing when scale developers and users only report α as is almost always the casePreparation of this article was supported by the Patricia M Nielsen Research Chair of the Family Institute at Northwestern UniversityWe thank Lewis R. Goldberg, Win Hill, Dan McAdams, Tony Z. Tang and especially Roderick P. McDonald for their comments on earlier drafts of portions of this articleThis revised article was published online in August 2005 with the PDF paginated correctly.     

Epistemic and Dialectical Models of Begging the Question

This paper addresses the problem posed by the current split between the two opposed hypotheses in the growing literature on the fallacy of begging the question the epistemic hypothesis, based on knowledge and belief, and the dialectical one, based on formal dialogue systems. In the first section, the nature of split is explained, and it is shown how each hypothesis has developed. To get the beginning reader up to speed in the literature, a number of key problematic examples are analyzed illustrating how both approaches can be applied. Useful tools are brought to bear on them, including the automated argument diagramming system Araucaria, and profiles of dialogue used to represent circular argumentation in a dialogue tableau format. These tools are used to both to model circular reasoning and to provide the contextual evidence needed to properly determine whether the circular reasoning in a given case is better judged fallacious or not. A number of technical problems that have impeded the development of both hypotheses are studied. One central problem is the distinction between argument and explanation. It is concluded that the best way to move forward and solve these problems is to reformulate the two hypotheses in such a way that they might be able to co-exist. On this basis, a unified methodology is proposed that allows each hypothesis to move forward as a legitimate avenue for research using the same tools.     

The psychological side of Hempel’s paradox of confirmation

People often test hypotheses about two variables (X andY), each with two levels (e.g.,X1 andX2). When testing “IfX1, thenY1,” observing the conjunction ofX1 andY1 is overwhelmingly perceived as more supportive than observing the conjunction ofX2 andY2, although both observations support the hypothesis. Normatively, theX2&Y2 observation provides stronger support than theX1&Y1 observation if the former is rarer. Because participants in laboratory settings typically test hypotheses they are unfamiliar with, previous research has not examined whether participants are sensitive to the rarity of observations. The experiment reported here showed that participants were sensitive to rarity, even judging a rareX2&Y2 observation more supportive than a commonX1&Y1 observation under certain conditions. Furthermore, participants’ default strategy of judgingX1&Y1 observations more informative might be generally adaptive because hypotheses usually regard rare events.     

Is There A Logic Of Confirmation Transfer?

This article begins by exploring a lost topic in the philosophy of science:the properties of the relations evidence confirming h confirmsh' and, more generally, evidence confirming each ofh₁, h₂, ..., h_m confirms at least one of h₁, h₂,ldots;, h_n'.The Bayesian understanding of confirmation as positive evidential relevanceis employed throughout. The resulting formal system is, to say the least, oddlybehaved. Some aspects of this odd behaviour the system has in common withsome of the non-classical logics developed in the twentieth century. Oneaspect – its ``parasitism' on classical logic – it does not, and it is this featurethat makes the system an interesting focus for discussion of questions in thephilosophy of logic. We gain some purchase on an answer to a recently prominentquestion, namely, what is a logical system? More exactly, we ask whether satisfaction of formal constraints is sufficient for a relation to be considered a (logical) consequence relation. The question whether confirmation transfer yields a logical system is answered in the negative, despite confirmation transfer having the standard properties of a consequence relation, on the grounds that validity of sequents in the system is not determined by the meanings of the connectives that occur in formulas. Developing the system in a different direction, we find it bears on the project of ``proof-theoretic semantics': conferring meaning on connectives by means of introduction (and possibly elimination) rules is not an autonomous activity, rather it presupposes a prior, non-formal,notion of consequence. Some historical ramifications are alsoaddressed briefly.     

Is the conjunction fallacy tied to probabilistic confirmation?

Crupi et al. (2008) offer a confirmation-theoretic, Bayesian account of the conjunction fallacy—an error in reasoning that occurs when subjects judge that Pr(h ₁ & h ₂|e) > Pr(h ₁|e). They introduce three formal conditions that are satisfied by classical conjunction fallacy cases, and they show that these same conditions imply that h ₁ & h ₂ is confirmed by e to a greater extent than is h ₁ alone. Consequently, they suggest that people are tracking this confirmation relation when they commit conjunction fallacies. I offer three experiments testing the merits of Crupi et al.’s account specifically and confirmation-theoretic accounts of the conjunction fallacy more generally. The results of Experiment 1 show that, although Crupi et al.’s conditions do seem to be causally linked to the conjunction fallacy, they are not necessary for it; there exist cases that do not meet their three conditions in which subjects still tend to commit the fallacy. The results of Experiments 2 and 3 show that Crupi et al.’s conditions, and those offered by other confirmation-theoretic accounts of the fallacy, are not sufficient for the fallacy either; there exist cases that meet all three of CFT’s conditions in which subjects do not tend to commit the fallacy. Additionally, these latter experiments show that such confirmation-theoretic conditions are at best only weakly causally relevant to the presence of the conjunction fallacy. Given these findings, CFT’s account specifically, and any general confirmation-theoretic account more broadly, falls short of offering a satisfying explanation of the presence of the conjunction fallacy.     

Defeating Dr. Evil with Self-Locating Belief

Dr. Evil learns that a duplicate of Dr. Evil has been created. Upon learning this, how seriously should he take the hypothesis that he himself is that duplicate? I answer: very seriously. I defend a principle of indifference for self‐locating belief which entails that after Dr. Evil learns that a duplicate has been created, he ought to have exactly the same degree of belief that he is Dr. Evil as that he is the duplicate. More generally, the principle shows that there is a sharp distinction between ordinary skeptical hypotheses, and self‐locating skeptical hypotheses.     

Discovery as correction

In recent years, there have been some attempts to defend the legitimacy of a non-inductive generative logic of discovery whose strategy is to analyze a variety of constraints on the actual generation of explanatory hypotheses. These proposed new theories, however, are only weakly generative (relying on sophisticated processes of elimination) rather than strongly generative (embodying processes of correction).This paper develops a strongly generative theory which holds that we can come to know something new only as a variant of what we already know — and that the novelty of this variant is not thereby eliminated nor beyond our powers of characterization, a double requirement that is vital for resolving the Meno paradox. In this light, the discovery of a new hypothesis is taken as the correction of an antecedent hypothesis in response to the discrepancies between the predictions generated by that antecedent hypothesis and the desired result (e.g. the actual data to be explained). This process comprises two parallel operations: the first, which demonstrates the positive role of the facts in generating new explanations, involves a mapping between multiple hypotheses and sets of predictions generated from those hypotheses, for the purpose of taking the actual data as a determinable variant of neighboring sets of predictions. This mapping permits the facts to indicate how corrective adjustments in the working hypothesis should be made; the second operation, which demonstrates the positive role of explanations in generating new facts, involves a mapping between differently construed versions of the actual data and the conceptualizations derived from those perceptual versions, for the purpose of taking the working hypothesis as a determinable variant of these neighboring conceptualizations. This mapping permits a given hypothesis to generate predictions increasingly closer to the actual facts.The proposed theory provides the basis for a reformed conception of justification. Because hypotheses are meaningful only as variants of neighboring hypotheses, and because such variation is corrective, their justification in the reformed sense will incorporate not only their justification in the traditional sense, but their generation as well.     

Understanding the language of reasoning: Cognitive,linguistic, and developmental influences

Certain linguistic structures imply speakers' beliefs about their utterances. Factuals imply that the speaker's hypothesis matches observed data; counterfactuals suggest that hypotheses and observations differ, and uncertainty implies that unclear observations make many hypotheses tenable. We examined how age(11-and 16-year-olds and college students) and syntactic structure (subordinating conjunctions, cognitive verbs, and verb modifications) affect the ability to specify the hypothetical and observational referents of expressions of factual, counterfactual, and uncertainty beliefs. There was considerable linguistic growth during adolescence. College students outperformed the younger students. Age differences were most pronounced on judging the hypothetical referents of counterfactuals and uncertainty structures. The two precollege groups often misinterpreted counterfactuals and uncertainty structures because they equated hypotheses with observations. They seldom understood that uncertainty meant that more than one hypothesis could account for observations. Verb modifications were easier to interpret than cognitive verbs, and subordinating conjunctions were hardest. Factuals were easier than counterfactuals and uncertainty structures.     

Positive and Negative Hypothesis Testing by Cooperative Groups

In a rule induction problem positive hypothesis tests select evidence that the tester expects to be an example of the correct rule if the hypothesis is correct, whereas negative hypothesis tests select evidence that the tester expects to be a nonexample if the hypothesis is correct. Previous research indicates the general effectiveness of a positive test strategy for individuals, but there has been very little research with cooperative groups. We extend the analysis of Klayman and Ha (Psychological Review, 1987) of ambiguous verification or conclusive falsification of five possible types of hypotheses by positive and negative tests by emphasizing the importance of further examples following hypothesis tests. In two experiments four-person cooperative groups solved rule induction problems by proposing a hypothesis and selecting evidence to test the hypothesis on each of four arrays on each trial. In different conditions the groups were instructed to use different combinations of positive and negative tests on the four arrays. Positive tests were more likely to lead to further examples than negative tests, and the proportion of correct hypotheses corresponded to the proportion of positive tests, in both experiments. We suggest that positive tests are more effective than negative hypothesis tests in generating further evidence, and thus in inducing the correct rule, in experimental rule induction tasks with a criterion of certainty imposed by the researcher.     

Regression tests for several samples

In many situations it is desirable or necessary to administer a set of tests to several different groups, and to ask if the results obtained in the different groups may be regarded as being essentially the same in some sense. In the case of two variables (one dependent and one independent) one may, for instance, ask if the errors of estimate and the regression lines may be regarded as being the same for the populations from which the different groups are drawn. For this case, the present article considers tests for three hypotheses regarding the populations from which the different groups are drawn: (a)H _A, the hypothesis that all standard errors of estimate are equal; (b)H _B, the hypothesis that all regression lines are parallel, (assumingH _A); and (c)H _C, the hypothesis that the regression lines are identical, (assumingH _B). Test criteria for these three hypotheses and their sampling theory for large samples are presented. The results are extended to the case of several independent variables. An illustrative problem is presented for two groups, two independent and one dependent variable.     

Comparing dependent robust correlations

Let r₁ and r₂ be two dependent estimates of Pearson's correlation. There is a substantial literature on testing H₀ : ρ₁ = ρ₂, the hypothesis that the population correlation coefficients are equal. However, it is well known that Pearson's correlation is not robust. Even a single outlier can have a substantial impact on Pearson's correlation, resulting in a misleading understanding about the strength of the association among the bulk of the points. A way of mitigating this concern is to use a correlation coefficient that guards against outliers, many of which have been proposed. But apparently there are no results on how to compare dependent robust correlation coefficients when there is heteroscedasicity. Extant results suggest that a basic percentile bootstrap will perform reasonably well. This paper reports simulation results indicating the extent to which this is true when using Spearman's rho, a Winsorized correlation or a skipped correlation.     

Probabilistic Inferences Under Emotional Stress: How Arousal Affects Decision Processes

Many models of decision making neglect emotional states that could affect individuals' cognitive processes. The present work explores the effect of emotional stress on people's cognitive processes when making probabilistic inferences. Two contrasting hypotheses are tested against one another: the uncertainty‐reduction and attention‐narrowing hypotheses of how emotional stress affects decision making. In the experimental study, emotional stress was induced through the use of highly aversive pictures immediately before each decision. Emotional state was assessed by both subjective (state anxiety, arousal, and pleasantness ratings) and objective (skin conductance) measures. The results show that emotional stress impacts decision making; in particular, emotionally aroused participants seem to have focused on the most important information and selected simpler decision strategies relative to participants in a control condition. The results are in line with the attention‐narrowing hypothesis and suggest that emotional stress can impact decision making through limited predecisional information search and the selection of simpler decision strategies. Copyright © 2015 John Wiley & Sons, Ltd.     

A mixture model for distributions of correlation coefficients

An old problem in personnel psychology is to characterize distributions of test validity correlation coefficients. The proposed model views histograms of correlation coefficients as observations from a mixture distribution which, for a fixed sample sizen, is a conditional mixture distributionh(r|n) = _{j j} h(r; _j ,n), whereR is the correlation coefficient, _j are population correlation coefficients and _j are the mixing weights. The associated marginal distribution ofR is regarded as the parent distribution underlying histograms of empirical correlation coefficients. Maximum likelihood estimates of the parameters _j and _j can be obtained with an EM algorithm solution and tests for the number of componentst are achieved after the (one-component) density ofR is replaced with a tractable modeling densityh(r; _j ,n). Two illustrative examples are provided.     

Do Conditional Hypotheses Target Rare Events?

When testing hypotheses, rare or unexpected observations are normatively more informative than common observations, and recent studies have shown that participants' behavior reflects this principle. Research has also shown that, when asked to test conditional hypotheses (“If X, then Y”) that are abstract or unfamiliar, participants overwhelmingly consider a supporting observation mentioned in the hypothesis (X&Y) to be more informative than a supporting observation not mentioned (XY). These two empirical findings would mesh well if conditional hypotheses tend to be phrased in terms of rare, rather than common, events. Six experiments are reported indicating that people do have a tendency—often a very strong one—to phrase conditional hypotheses in terms of rare events. Thus, observations mentioned in conditional hypotheses might generally be considered highly informative because they usually are highly informative.     

Goodness of fit of trend curves and significance of trend differences

Experimental studies of the successive changes (frequently represented by curves describing laws of learning and other similar functional relationships) in a criterion variable accompanying experimental variations in a given treatment, and experimental comparisons of such changes for different populations or for different treatments, constitute a large and important class of psychological experiments. In most such experiments, no attempt has been made to analyze or to make allowance for errors of sampling or of observation. In many others, the techniques of error analysis that have been employed have been inefficient, inexact, or inappropriate. This paper suggests tests, using the methods of analysis of variance, of certain hypotheses concerning trends and trend differences in sample means obtained in experiments of this general type. For means of successive independent samples, tests are provided of the hypotheses: (H ₁) that there is no trend, or that the trend is a horizontal straight line, (H ₃) that there is a linear trend, (H ₅) that the trend is as described by a line not derived from the observed means, and (H ₇) that the trend is as described by a line fitted to the observed means. Tests are also provided of similar hypotheses (H ₂,H ₄,H ₆, andH ₈, respectively) for means of successive measurements of the same sample. Finally, tests are provided of the null hypotheses that there is no difference in trend in two series of means: (H ₉) when each mean in each series is based on an independent sample, (H ₁₀) when each pair of corresponding means is based on an independent sample, (H ₁₁) when each series of means is based on an independent sample, and (H ₁₂) when both series are based on a single sample.     

Simultaneous testing of McNemar's problem for several populations

McNemar's problem concerns the hypothesis of equal probabilities for the unlike pairs of correlated binary variables. We consider four different extensions to this problem, each for testing simultaneous equality of proportions of unlike pairs inc independent populations of correlated binary variables, but each under different assumptions and/or additional hypotheses. For each extension both the likelihood ratio test and the goodness-of-fit chi-square test are given. Whenc=1, all cases reduce to McNemar's problem. Forc ≥ 2, however, the tests are quite different, depending on exactly how the hypothesis and alternatives of McNemar are extended. An example illustrates how widely the results may differ, depending on which extended framework is appropriate.     

A meta‐analysis of the relationship between socioeconomic status and executive function performance among children

The relationship between childhood socioeconomic status (SES) and executive function (EF) has recently attracted attention within psychology, following reports of substantial SES disparities in children's EF. Adding to the importance of this relationship, EF has been proposed as a mediator of socioeconomic disparities in lifelong achievement and health. However, evidence about the relationship between childhood SES and EF is mixed, and there has been no systematic attempt to evaluate this relationship across studies. This meta‐analysis systematically reviewed the literature for studies in which samples of children varying in SES were evaluated on EF, including studies with and without primary hypotheses about SES. The analysis included 8760 children between the ages of 2 and 18 gathered from 25 independent samples. Analyses showed a small but statistically significant correlation between SES and EF across all studies (r_random = .16, 95% CI [.12, .21]) without correcting for attenuation owing to range restriction or measurement unreliability. Substantial heterogeneity was observed among studies, and a number of factors, including the amount of SES variability in the sample and the number of EF measures used, emerged as moderators. Using only the 15 studies with meaningful SES variability in the sample, the average correlation between SES and EF was small‐to‐medium in size (r_random = .22, 95% CI [.17, .27]). Using only the six studies with multiple measures of EF, the relationship was medium in size (r_random = .28, 95% CI [.18, .37]). In sum, this meta‐analysis supports the presence of SES disparities in EF and suggests that they are between small and medium in size, depending on the methods used to measure them.     

A quasi-nonmetric method for multidimensional scaling VIA an extended euclidean model

An Extended Two-Way Euclidean Multidimensional Scaling (MDS) model which assumes both common and specific dimensions is described and contrasted with the standard (Two-Way) MDS model. In this Extended Two-Way Euclidean model then stimuli (or other objects) are assumed to be characterized by coordinates onR common dimensions. In addition each stimulus is assumed to have a dimension (or dimensions) specific to it alone. The overall distance between objecti and objectj then is defined as the square root of the ordinary squared Euclidean distance plus terms denoting the specificity of each object. The specificity,s _j , can be thought of as the sum of squares of coordinates on those dimensions specific to objecti, all of which have nonzero coordinatesonly for objecti. (In practice, we may think of there being just one such specific dimension for each object, as this situation is mathematically indistinguishable from the case in which there are more than one.)We further assume that _ij =F(d _ij ) +e _ij where _ij is the proximity value (e.g., similarity or dissimilarity) of objectsi andj,d _ij is the extended Euclidean distance defined above, whilee _ij is an error term assumed i.i.d.N(0, ²).F is assumed either a linear function (in the metric case) or a monotone spline of specified form (in the quasi-nonmetric case). A numerical procedure alternating a modified Newton-Raphson algorithm with an algorithm for fitting an optimal monotone spline (or linear function) is used to secure maximum likelihood estimates of the paramstatistics) can be used to test hypotheses about the number of common dimensions, and/or the existence of specific (in addition toR common) dimensions.This approach is illustrated with applications to both artificial data and real data on judged similarity of nations.