More Triviality

This paper uses the framework of Popper and Miller's work on axiom systems for conditional probabilities to explore Adams' thesis concerning the probabilities of conditionals. It is shown that even very weak axiom systems have only a very restricted set of models satisfying a natural generalisation of Adams' thesis, thereby casting severe doubt on the possibility of developing a non-Boolean semantics for conditionals consistent with it.     

Partitions and Conditionals

The literature on conditionals is rife with alternate formulations of the abstract semantics of conditional logic. Each formulation has its own advantages in terms of applications and generalizations; nevertheless, they are for the most part equivalent, in the sense that they underwrite the same range of logical systems. The purpose of the present note is to bring under this umbrella the partition semantics introduced by Brian Skyrms in (Skyrms, 1984).     

Preferences for and against stimuli paired with food.

Pigeons were presented with a concurrent-chains schedule in which terminal-link entries were assigned to two response keys on a percentage basis. The terminal links were fixed delays that sometimes ended with food and sometimes did not. In most conditions, 80% of the terminal links were assigned to one key, but a smaller percentage of the terminal links ended with food for this key, so the number of food reinforcers delivered by the two alternatives was equal. When the same terminal-link stimuli (orange houselights) were used for both alternatives, the pigeons showed a preference for whichever alternative delivered more frequent terminal links. When different terminal-link stimuli (green vs. red houselights) were used for the two alternatives, the pigeons showed a preference for whichever alternative delivered fewer terminal links when terminal-link durations were long, and no systematic preferences when terminal-link durations were short. This pattern of results was consistent with the predictions of Grace's (1994) contextual choice model. Preference for the alternative that delivered more frequent terminal links was usually stronger in the first few sessions of a condition than at the end of a condition, suggesting that the conditioned reinforcing effect of the additional terminal-link presentation was, in part, transitory.     

Negotiating the Boundaries of Science and Religion: The Case of Henry Margenau

The life of Henry Margenau (1901–1997) offers a case study in the complexity of the science-religion relation. As a physicist-philosopher at Yale University, he pursued a public program of "amalgamating religion with science." He drew upon his authority as a physicist and a tradition of philosophical idealism to advocate a "reciprocity" between the two spheres. He argued that a "new modesty" and "metaphysical attitude" among scientists created new opportunities for collaboration. At the same time, his view of faith and his sense of the religiousness of science created troubling ambiguities. In the end, Margenau embodied the ambivalent relation between science and religion while revealing the limits of renegotiating the boundaries.     

Reinforcement probability and ordinal position of response in fixed-interval schedules

Four rats pressed levers and received food pellets under fixed-interval reinforcement schedules of 20, 60, and 180 seconds. The number of responses in each interval was recorded. From these data, the probability of reinforcement was determined as a function of response count. These functions were generally increasing. This finding is consistent with previous suggestions that increasing response rates within fixed intervals may be a function of response count in addition to or instead of elapsed or remaining time.     

Avoidance based on shock intensity reduction with no change in shock probability

Rats were trained on a free-operant avoidance procedure in which shock intensity was controlled by interresponse time. Shocks were random at a density of about 10 shocks per minute. Shock probability was response independent. As long as interresponse times remained less than the limit in effect, any shocks received were at the lower of two intensities (0.75 mA). Whenever interresponse times exceeded the limit, any shocks received were at the higher intensity (1.6 mA). The initial limit of 15 seconds was decreased in 3-second steps to either 6 or 3 seconds. All animals lever pressed to avoid higher intensity shock. As the interresponse time limit was reduced, the response rate during the lower intensity shock and the proportion of brief interresponse times increased. Substantial warmup effects were evident, particularly at the shorter interresponse-time limits. Shock intensity reduction without change in shock probability was effective in the acquisition and maintenance of avoidance responding, as well as in differentiation of interresponse times. This research suggests limitations on the generality of a safety signal interpretation of avoidance conditioning.     

Assessing the Predictive Accuracy of hMLH1 and hMSH2 Mutation Probability Models

Hereditary nonpolyposis colorectal cancer (HNPCC) is characterized by a susceptibility to colorectal and extra-colonic cancers. Several guidelines exist for the identification of families suspected of having HNPCC, however these guidelines lack adequate sensitivity and specificity. In an attempt to improve accuracy for the detection of individuals with HNPCC, the Wijnen pre-test probability model (1998) and Myriad Genetics Laboratory prevalence table (2004) were developed. Here we evaluate the Wijnen model and Myriad table at predicting the presence of a mutation in individuals undergoing genetic testing for HNPCC. Forty-nine patients who had undergone genetic testing for germline mutations in hMLH1 and/or hMSH2 were part of our analysis. Our results revealed that the revised Bethesda guidelines performed with the highest sensitivity for germline mutations (94.4%), however the specificity was low (12.9%). Using a 10.0% mutation probability threshold, the Wijnen model and Myriad table had sensitivities of 55.6 and 60.0%, respectively and specificities of 54.8 and 23.8%, respectively. The Wijnen model and Myriad table were poor predictors of mutation prevalence, which is shown by the areas underneath their corresponding receiver operator characteristic curves (0.616 and 0.400, respectively). The results of this study demonsrate that neither the Wijnen model nor the Myriad table are sensitive or specific enough to be used as the only indication when to offer genetic testing for HNPCC.     

Freedom,foreknowledge, and betting

Certain kinds of prediction, foreknowledge, and future-oriented action appear to require settled future truths. But open futurists think that the future is metaphysically unsettled: if it is open whether p is true, then it cannot currently be settled that p is true. So, open futurists—and libertarians who adopt the position—face the objection that their view makes rational action and deliberation impossible. I defuse the epistemic concern: open futurism does not entail obviously counterintuitive epistemic consequences or prevent rational action.     

Run length, visit duration, and reinforcers per visit in concurrent performance

The contingencies in each alternative of concurrent procedures consist of reinforcement for staying and reinforcement for switching. For the stay contingency, behavior directed at one alternative earns and obtains reinforcers. For the switch contingency, behavior directed at one alternative earns reinforcers but behavior directed at the other alternative obtains them. In Experiment 1, responses on the main lever, in S1, incremented stay and switch schedules and obtained a stay reinforcer when it became available. Responses on the switch lever changed S1 to S2 and obtained switch reinforcers when available. In S2, neither responses on the main lever nor on the switch lever were reinforced, but a switch response changed S2 to S1. Run lengths and visit durations were a function of the ratio of the scheduled probabilities of reinforcement (staying/switching). From run lengths and visit durations, traditional concurrent performance was synthesized, and that synthesized performance was consistent with the generalized matching law. Experiment 2 replicated and extended this analysis to concurrent variable-interval schedules. The synthesized results challenge any theory of matching that requires a comparison among the alternatives.     

Human symbolic matching-to-sample performance: Effects of reinforcer and sample-stimulus probabilities

Four experiments, each with 6 human subjects, varied the distribution of reinforcers for correct responses and the probability of sample-stimulus presentation in symbolic matching-to-sample procedures. Experiment 1 held the sample-stimulus probability constant and varied the ratio of reinforcers obtained for correct responses on the two alternatives across conditions. There was a positive relation between measures of response bias and the ratio of reinforcers. Experiment 2 held the ratio of reinforcers constant and varied the sample-stimulus probability across conditions. Unlike previous studies that used pigeons as subjects, there was a negative relation between bias and the ratio of sample-stimulus presentations. In Experiment 3, the sample-stimulus probability and the reinforcer ratio covaried across conditions. Response bias did not vary systematically across conditions. In Experiments 1 to 3, correct responses were reinforced intermittently. Experiment 4 used the same procedure as Experiment 3, but all correct responses now produced some scheduled consequence. There was a positive relation between response bias and the ratio of reinforcers. The results suggest that human performance in these tasks was controlled by both the relative frequency of reinforced responses and the relative frequency of nonreinforced responses.