Online research in philosophy

We explore the ability to distinguish random from non-random events. Randomness is defined in terms of radioactive decay whereas non-randomness is quantified by excess repetitions (“repeat”) or alternations (“switch”) between successive bits. In the first four experiments no mention was made of randomness, probability, or related concepts in task instructions. We found superior performance in distinguishing random stimuli from repeat stimuli compared to switch stimuli. The last three experiments explicitly evoked the concept of randomness, thus allowing comparison of perceptual and (...) conceptual performance. The ability to identify random events from switch distracters was inferior to the ability to discriminate random from switch stimuli. In contrast, for repeat stimuli the concept of randomness appears to roughly coincide with perceptual discriminability. Finally, the ability to identify or produce stimuli as random did not co-vary with the ability to discriminate random from non-random stimuli. (shrink)

Jeffrey (1983) proposed a generalization of conditioning as a means of updating probability distributions when new evidence drives no event to certainty. His rule requires the stability of certain conditional probabilities through time. We tested this assumption (“invariance”) from the psychological point of view. In Experiment 1 participants offered probability estimates for events in Jeffrey’s candlelight example. Two further scenarios were investigated in Experiment 2, one in which invariance seems justified, the other in which it does not. Results were in (...) rough conformity to Jeffrey (1983)’s principle. (shrink)

In standard treatments of probability, Pr (A|B) is defined as the ratio of Pr (A∩B) to Pr (B), provided that Pr (B) > 0. This account of conditional probability suggests a psychological question, namely, whether estimates of Pr (A|B) arise in the mind via implicit calculation of Pr (A ∩ B)/Pr (B). We tested this hypothesis (Experiment 1) by presenting brief visual scenes composed of forms, and collecting estimates of relevant probabilities. Direct estimates of conditional probability were not well predicted (...) by Pr (A ∩ B)/Pr (B). Direct estimates were also closer to the objective probabilities defined by the stimuli, compared to estimates computed from the foregoing ratio. The hypothesis that Pr (A|B) arises from the ratio Pr (A ∩ B)/[Pr (A ∩ B) + Pr (A ∩ B)] fared better (Experiment 2). In a third experiment, the same hypotheses were evaluated in the context of subjective estimates of the chance of future events. (shrink)