Why Friedman's non-monotonic reasoning defies Hempel's covering law model

In this paper we will show that Hempel's covering law model can't deal very well with explanations that are based on incomplete knowledge. In particular the symmetry thesis, which is an important aspect of the covering law model, turns out to be problematic for these explanations. We will discuss an example of an electric circuit, which clearly indicates that the symmetry of explanation and prediction does not always hold. It will be argued that an alternative logic for causal explanation is needed. And we will investigate to what extent non-monotonic epistemic logic can provide such an alternative logical framework. Finally we will show that our non-monotonic logical analysis of explanation is not only suitable for simple cases such as the electric circuit, but that it also sheds new light on more controversial causal explanations such as Milton Friedman's explanation of the business cycle.We gratefully acknowledge the helpful suggestions and critical comments of Johan van Benthem, Bert Hamminga, Kevin Hoover, Theo Kuipers, and Rick Looyen.     

Situational logic and covering law explanations in history

Donagan has argued (a) that the covering law model of explanation does not apply in certain cases in historical explanations; (b) that situational logic explanations do apply, and (c) that situational logic explanations are fundamentally different from covering law explanations. It is argued that (b) is false as Donagan construes situational logic explanations. Once situational logic explanations are correctly construed they are similar to Hempel's rational explanations in covering law forms — hence (c) is false if situational logic explanations are correctly interpreted. Finally it is argued that one major reason Donagan gives for (a) is mistaken.     

The power law and Weber's law in fixed-interval postreinforcement pausing: A scalar timing model

Some quantitative properties of the postreinforcement pause under fixed-interval schedules were simulated by a computer model embodying two processes, either of which could initiate responding in an interval. The first was a scalar timing system similar to that hypothesized to underlie behaviour on other tasks. The second was a process that initiated responding without regard to elapsed time in the interval. The model produced simulated pauses with a mean that varied as a power function of the interval value, and a standard deviation that appeared to grow as a linear function of the mean. Both these features were found in real data. The model also predicted several other features of pausing and responding under fixed-interval schedules and was also consistent with the results produced under some temporal differentiation contingencies. The model thus illustrated that behaviour that conformed to the power law could nevertheless be reconciled with scalar timing theory, if an additional non-timing process could also initiate responding.     

The scope of formal explanation

The existence of multiple modes of explanation means that a crucial step in the process of generating explanations has to be selecting a particular mode. The present article identifies the key conceptual, as well as some pragmatic and epistemological, considerations that license the use of the formal mode of explanation, and thus that enter into the process of selecting and generating a formal explanation. Formal explanations explain the presence of certain properties in an instance of a kind by reference to the kind of thing it is (e.g. That has four legs because it is a dog). As such, this mode of explanation is intrinsically tied to kind representations and is applicable domain-generally. Although it is possible for formal explanation to apply domain-generally, for any given kind it is selective in its application, in that it can explain some, but not all, properties of the instances of a kind. It also appears that different types of properties can receive formal explanations across different domains. This article provides a sketch of a theory of the selectivity of formal explanation that results from the manner in which kinds of different types are distinguished. The present discussion also suggests how the mechanisms underlying formal explanations may contribute to the illusion of explanatory depth Keil (Trends in Cognitive Sciences, 7, 368–373,2003), the operation of the inherence heuristic Cimpian & Salomon (Behavioral and Brain Sciences, 37, 461–480, 2014a; Behavioral and Brain Sciences, 37, 506–527,2014b), and psychological essentialism (Gelman, 2003).     

A memory-based model of Hick's law

We propose and evaluate a memory-based model of Hick’s law, the approximately linear increase in choice reaction time with the logarithm of set size (the number of stimulus–response alternatives). According to the model, Hick’s law reflects a combination of associative interference during retrieval from declarative memory and occasional savings for stimulus–response repetitions due to non-retrieval. Fits to existing data sets show that the model accounts for the basic set-size effect, changes in the set-size effect with practice, and stimulus–response-repetition effects that challenge the information-theoretic view of Hick’s law. We derive the model’s prediction of an interaction between set size, stimulus fan (the number of responses associated with a particular stimulus), and stimulus–response transition, which is subsequently tested and confirmed in two experiments. Collectively, the results support the core structure of the model and its explanation of Hick’s law in terms of basic memory effects.     

Covariational influences on goal-based explanation: an integrative model

Covariational and goal-based approaches to social attribution have been treated as competitive or incommensurable. This article integrates key aspects of each approach. Four studies examined preferences for motivating factors (or goals) and enabling factors (or preconditions) as explanations of intentional actions. The studies manipulated (Studies 1-3) and measured (Study 4) the perceived covariation of these goal-based causes with target actions. Causes that covaried with actions were preferred explanations, in contrast with the goal-based view that motivating factors are generally preferred to enabling factors. Combining goal-based beliefs and covariational reasoning resolves problems faced by each individual approach and generates a novel explanatory typology that combines strengths of goal-based and covariational typologies.     

The Bayesian explanation of transmission failure

Even if our justified beliefs are closed under known entailment, there may still be instances of transmission failure. Transmission failure occurs when P entails Q, but a subject cannot acquire a justified belief that Q by deducing it from P. Paradigm cases of transmission failure involve inferences from mundane beliefs (e.g., that the wall in front of you is red) to the denials of skeptical hypotheses relative to those beliefs (e.g., that the wall in front of you is not white and lit by red lights). According to the Bayesian explanation, transmission failure occurs when (i) the subject’s belief that P is based on E, and (ii) P(Q|E) < P(Q). But there are compelling cases of transmission failure where P(Q|E) > P(Q). No modifications of the Bayesian explanation are capable of accommodating such cases, so the explanation must be rejected as inadequate. Alternative explanations employing simple subjunctive conditionals are fully capable of capturing all of the paradigm cases, as well as those missed by the Bayesian explanation.     

The non-epistemic explanation of religious belief

Conclusion The preceding two sections have considered, respectively, the discreditation of psychological belief, and of propositional belief, which begins with the claim that a belief possessed by some person is non-epistemically explicable and ends with the claim that that person is unreasonable or that that belief is (probably) false. Obviously, only certain strategies of discreditation were discussed, and those only partially. But if the examples of discrediting strategies were representative, and the remarks made about them were correct, what, if anything, follows?It seems clear that the sheer fact that a person's belief is non-epistemically explicable entails very little if anything about the person's reasonability in holding it or the probable falsehood of the belief in question. Nor does the fact that a basic belief is held without reason or grounds seem to speak against the rationality of its believer - not at least with respect to the sort of propositions we called structural. It does not follow that one cannot rationally assess competing structural beliefs - that is another, and given the present argument an entirely open, question. It does seem correct that the more restrictive axioms of the ethics of properly held basic beliefs are ill-suited to deal responsibly with the acceptance of structural propositions. And at least some religious propositions - God exists among them - seem to me to be of that sort. Of course, that raises the question of what, exactly, a structural proposition is - which, again, is another topic.If the argument of this essay is correct, the shift from considering whether some particular (and perhaps idiosyncratic) person is reasonable in accepting some proposition, in cases where this is an interesting and debateable matter, to whether (on the whole) this proposition is one that can be accepted without rendering oneself unreasonable, seems to be an issue usually not capable of rational resolution without engaging in some sort of direct assessment of the proposition believed, and the strategy of trying to escape this by considering whether a person's acceptance of that proposition can be non-epistemically explained seems, on the whole, not a profitable enterprise. Further, often, at least, it can be countered in one or another of the ways we considered in the preceding two sections. So I am inclined to view the attempt to settle interesting debates about whether a person is reasonable in accepting a proposition by arguing that his acceptance is non-epistemically explicable as, on the whole, a failure.If anything, things are worse, so far as I can see, for attempts to argue from the fact that a person's belief is non-epistemically explicable to the conclusion that it is probably false. For, again, this argument has force only if the fact that this person's acceptance of it is non-epistemically explicable is not idiosyncratic, and this is establishable, often at least, only by appealing to the results of a direct assessment of the proposition believed (or by offering a judgment on this matter without benefit of any assessment, which of course is worthless). Nor, of course, is the nonepistemic explicability of a person's belief that P sufficient to discredit the person, let alone P, and the sorts of properties that are often alleged to accompany non-epistemically explicable beliefs seem either in fact not to accompany them, or to accompany only a basically irrelevant and uninteresting sub-set of them, or not to be such as to make falsehood of the propositions whose belief they accompany probable.A final comment These remarks, at best, scratch the surface of a difficult and complex topic. It is a topic on which, so far as I am aware, not a great deal has been written. My hope is that what I have said here may stimulate sufficient interest in the topic for others to provide a further exploration of the issues that I have here only been able to highlight.     

A person-environment analysis of job stress: a contingency model explanation

The contingency model of leadership was applied in a field study of job stress. Fifty-one university administrators completed a series of questionnaires that assessed their leadership style, degree of situational control within their work setting, perceived job stress, physical health, and psychological well-being. Multivariate analyses of variance (MANOVAs) showed that administrators whose leadership style and level of situational control were "in match" reported significantly less job stress, fewer health problems, and fewer days missed from work than administrators who were "out of match." The results are discussed as supporting the person-environment fit model of job stress.     

Functional explanation and the function of explanation

Teleological explanations (TEs) account for the existence or properties of an entity in terms of a function: we have hearts because they pump blood, and telephones for communication. While many teleological explanations seem appropriate, others are clearly not warranted--for example, that rain exists for plants to grow. Five experiments explore the theoretical commitments that underlie teleological explanations. With the analysis of [Wright, L. (1976). Teleological Explanations. Berkeley, CA: University of California Press] from philosophy as a point of departure, we examine in Experiment 1 whether teleological explanations are interpreted causally, and confirm that TEs are only accepted when the function invoked in the explanation played a causal role in bringing about what is being explained. However, we also find that playing a causal role is not sufficient for all participants to accept TEs. Experiment 2 shows that this is not because participants fail to appreciate the causal structure of the scenarios used as stimuli. In Experiments 3-5 we show that the additional requirement for TE acceptance is that the process by which the function played a causal role must be general in the sense of conforming to a predictable pattern. These findings motivate a proposal, Explanation for Export, which suggests that a psychological function of explanation is to highlight information likely to subserve future prediction and intervention. We relate our proposal to normative accounts of explanation from philosophy of science, as well as to claims from psychology and artificial intelligence.     

The inference to the best explanation

In a situation in which several explanations compete, is the one that is better qua explanation also the one we should regard as the more likely to be true? Realists usually answer in the affirmative. They then go on to argue that since realism provides the best explanation for the success of science, realism can be inferred to. Nonrealists, on the other hand, answer the above question in the negative, thereby renouncing the inference to realism. In this paper I separate the two issues. In the first section it is argued that a rationale can be provided for the inference to the best explanation; in the second, that this rationale cannot justify an inference to realism. The defence of the inference rests on the claim that our standards of explanatory power are subject to critical examination, which, in turn, should be informed by empirical considerations. By means of a comparison of the realist's explanation for the success of science with that of conventionalism and instrumentalism it is then shown that realism does not offer a superior explanation and should not, therefore, be inferred to.