Circular definitions,circular explanations,and infinite regresses

This paper discusses some of the ways in which circular definitions and circular explanations entail or fail to entail infinite regresses. And since not all infinite regresses are vicious, a few criteria of viciousness are examined in order to determine when the entailment of a regress refutes a circular definition or a circular explanation.I would like to thank Professors Robert Tully, Howard Sobel, and Derek Allen for their constructive comments.     

Undecidability and intuitionistic incompleteness

Let S be a deductive system such that S-derivability (s) is arithmetic and sound with respect to structures of class K. From simple conditions on K and s, it follows constructively that the K-completeness of s implies MP(S), a form of Markov's Principle. If s is undecidable then MP(S) is independent of first-order Heyting arithmetic. Also, if s is undecidable and the S proof relation is decidable, then MP(S) is independent of second-order Heyting arithmetic, HAS. Lastly, when s is many-one complete, MP(S) implies the usual Markov's Principle MP.An immediate corollary is that the Tarski, Beth and Kripke weak completeness theorems for the negative fragment of intuitionistic predicate logic are unobtainable in HAS. Second, each of these: weak completeness for classical predicate logic, weak completeness for the negative fragment of intuitionistic predicate logic and strong completeness for sentential logic implics MP. Beth and Kripke completeness for intuitionistic predicate or sentential logic also entail MP.These results give extensions of the theorem of Gödel and Kreisel (in [4]) that completeness for pure intuitionistic predicate logic requires MP. The assumptions of Gödel and Kreisel's original proof included the Axiom of Dependent Choice and Herbrand's Theorem, no use of which is explicit in the present article.     

Beyond the relational principle of reinforcement

Behavior under baseline conditions in which the contingency is absent can shed some light on the individual's performance under a schedule, but is insufficient as a basis for prediction of performance. This insufficiency of the baseline data runs counter to a recent formalization of the relational principle of reinforcement (Donahoe, 1977). A more satisfactory predictive model must incorporate not only the baseline level of the instrumental response and that of the contingent response, but also the schedule requirements, the character of each response in relation to the other, and the behavior required in simply switching from each to the other.     

GOD'S ACTION IN THE REAL WORLD1

Abstract. The scientific and theological enterprises are regarded as interacting and mutually illuminating approaches to reality. The theological consequences of the transformation of the scientific worldview through twentieth-century physics and cosmology are considered with respect to notions of God's transcendence, time, continuous creation, determinism, and multiple universes. The theological implications of the worldview of biology are similarly assessed with respect to certain features of biological evolution: its continuity, its open-endedness, its mechanism, and the role of "chance" and law. The model of human agency for the agency of God in the hierarchy of natural systems is examined. The article concludes with some reflections on a science-informed understanding of God's relation to the world as transcendent, incarnate, and immanent.     

Word Order Variation is Partially Constrained by Syntactic Complexity

Previous work suggests that when speakers linearize syntactic structures, they place longer and more complex dependents further away from the head word to which they belong than shorter and simpler dependents, and that they do so with increasing rigidity the longer expressions get, for example, longer objects tend to be placed further away from their verb, and with less variation. Current theories of sentence processing furthermore make competing predictions on whether longer expressions are preferentially placed as early or as late as possible. Here we test these predictions using hierarchical distributional regression models that allow estimates of word order and word order variation at the level of individual dependencies in corpora from 71 languages, while controlling for confounding effects from the type of dependency (e.g., subject vs. object), and the type of clause (main vs. subordinate) involved as well as from trends that are characteristic of individual languages, language families, and language contact areas. Our results show the expected correlations of length with position and variation only for two out of six dependency types (obliques and nominal modifiers) and no difference between clause types. These findings challenge received theories of across-the-board effects of complexity on word order and word order variation and call for theoretical models that relativize effects to specific kinds of syntactic structures and dependencies.     

Priming productive study strategies with preparatory quizzes in an engineering course

One approach to encourage productive study strategies is to incorporate preparatory quizzes (or pre‐quizzes) in which students are required to submit answers to questions before the underlying material is covered in class. In the present study, students took an introductory mechanical engineering class that either included pre‐quizzes (treatment group) or did not (control group). Students in the treatment group visited the online textbook more often and earlier in advance of deadlines, indicating better management of their study time—behaviors that have been shown to be productive study strategies. They also performed better in the course, indicating that techniques intended to prime productive study strategies can pay off. Finally, measures of productive learning strategies correlated with measures of course performance for both groups. These findings support the pretesting principle, which holds that students study more effectively and learn better when they take practice tests before a lesson.     

On the evaluation of one-sided evidence

We examine predictions and judgments of confidence based on one-sided evidence. Some subjects saw arguments for only one side of a legal dispute while other subjects (called ‘jurors’) saw arguments for both sides. Subjects predicted the number of jurors who favored the plaintiff in each case. Subjects who saw only one side made predictions that were biased in favor of that side. Furthermore, they were more confident but generally less accurate than subjects who saw both sides. The results indicate that people do not compensate sufficiently for missing information even when it is painfully obvious that the information available to them is incomplete. A simple manipulation that required subjects to evaluate the relative strength of the opponent's side greatly reduced the tendency to underweigh missing evidence.     

The effects of statistical training on choice heuristics in choice under uncertainty

Kahneman and Tversky (1984) proposed that decision makers perceive choice uncertainty in two ways: (1) as a distribution of possible outcomes or (2) as a single uncertain outcome. Using statistical training as a factor that influences these perceptions, and thus the type of decision approach individuals use, we found that individuals with different levels of experience displayed differences in the decisions they made and in the choice heuristics used to make those decisions. Statistically naive individuals were more likely to prefer loss-minimizing alternatives, use a more non-compensatory heuristic, and spend more time on loss-related information than their statistically experienced counterparts. When a distributional cue, indicating the distributional nature of choice outcomes, was presented to both experience groups, the naive group was found to use a decision approach similar to the experienced group and to make similar decisions. The results are discussed in terms of the need to include factors that alter individuals' approaches to uncertainty in future behavioral models of uncertain choice.     

Confidence and Uncertainty in Judgmental Forecasting: Differential Effects of Scenario Presentation

Multiple scenario analysis is used by many organizations for long-term planning, in part because the development of more than one scenario of the future is thought to prevent overconfidence in any one specific forecast. The present study attempts to clarify some of the questions concerning the cognitive effects of scenario presentation by distinguishing between confidence and subjective uncertainty. It examined the impact of different types of scenario information on confidence ratings, credible intervals, and features of forecast series. Subjects (N=186) read either one, two, or no scenario(s) describing potential changes in the level of a stimulus variable, then made forecasts of that variable over the next fifty years. Reading any type of scenario information increased confidence in forecasts; there was no reduction in confidence due to presentation of multiple conflicting scenarios, compared to presentation of only one scenario. Differences in number and in type of scenarios presented did, however, affect subjective uncertainty.     

Blind justice: Fairness to groups and the do-no-harm principle

People are reluctant to harm some people in order to help others, even when the harm is less than the forgone help (the harm resulting from not acting). The present studies use hypothetical scenarios to argue that these judgments go against what the subjects themselves would take to be the best overall outcome. When the outcomes in question are income gains and losses for two groups of farmers, subjects judge the harm they would not impose through their action to be smaller than the harm they would impose through inaction. Some subjects refuse to reduce cure rates for one group of AIDS patients in order to increase cure rates more for another group, even when group membership was unknowable to anyone, so that, from each patient's point of view, the change would increase the probability of cure. Likewise, they resisted a vaccine that reduced overall mortality in one group but increased deaths from side effects in another group, even when, again, group membership was unknowable. Some people apply a do-no-harm principle to groups without apparent understanding of how such a principle might be justified in terms of its consequences. The capacity for such judgments makes them vulnerable to learning principles that have no justification at all.