Meta-Critical Thinking, Paradox, and the Plethora of Probabilities

Abstract

There is as much lack of clarity concerning what “critical thinking” involves, even among those charged with teaching it, as there is consensus that we need more emphasis on it in both academia and society. There is an apparent need to think critically about critical thinking, an exercise that might be called meta-critical thinking. It involves emphasizing a practice in terms of which “critical thinking” is helpfully carried out and clarifying one or more of the concepts in terms of which “critical thinking” is usually defined. The practice is distinction making and the concept that of evidence. Science advances by constructing models that explain real-world processes. Once multiple potential models have been distinguished, there remains the task of identifying which models match the real-world process better than others. Since statistical inference has in large part to do with showing how data provide support, i.e., furnish evidence, that the model/hypothesis is more or less likely while still uncertain, we turn to it to help make the concept more precise and thereby useful. In fact, two of the leading methodological paradigms—Bayesian and likelihood—can be taken to provide answers to the questions of the extent to which as well as how data provide evidence for conclusions. Examining these answers in some detail is a highly promising way to make progress. We do so by way of the analysis of three well-known statistical paradoxes—the Lottery, the Old Evidence, and Humphreys’—and the identification of distinctions on the basis of which their plausible resolutions depend. These distinctions, among others between belief and evidence and different concepts of probability, in turn have more general applications. They are applied here to two highly contested public policy issues—the efficacy of COVID vaccinations and the fossil fuel cause of climate change. Our aim is to provide some tools, they might be called “healthy habits of mind,” with which to assess statistical arguments, in particular with respect to the nature and extent of the evidence they furnish, and to illustrate their use in well-defined ways.