The authors of the letter use “induction” to mean what I call a probabilism. Here probability is used to quantify degrees of belief, confirmation, plausibility

The authors of the letter use “induction” to mean what I call a probabilism. Here probability is used to quantify degrees of belief, confirmation, plausibility support–whether absolute or comparative. This is rooted in the old idea of confirmation by enumerative induction. Conclusions of statistical tests go strictly beyond their premises, and it does not follow that we cannot assess the warrant of the inference without using a probabilism. They are qualified by the error probing capacities of the tools. A claim is severely tested when it is subjected to and passes a test that probably would have found it flawed if it is. The notion isn’t limited to formal testing, but holds as well for estimation, prediction, exploration and problem solving. You don’t have evidence for a claim if little if anything has been done to probe and rule out how it may be flawed. That is the minimal principle for evidence. Popper spoke similarly of corroboration only he was unable to cash it out. He wasn’t sufficiently well versed in statistics, and anyway, he wanted to distinguish corroboration from induction, as the latter was being used at the time. The same impetus led Neyman to speak of inference as an act (of inferring). I explain all this in my recent book, Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (Mayo 2018,CUP. As I say there, “In my view an account of what is warranted and unwarranted to infer – a normative epistemology – is not a matter of using probability to assign rational beliefs, but to control and assess how well probed claims are.” (p. 54)