The gap and the error arguments for values in science: structure and mutual relationship

The underdetermination or ‘gap’ argument (GA), and the inductive risk or ‘error’ argument (EA), are the two main arguments used to defend the influence of non-epistemic values on scientific reasoning. However, they are often presented in a superficial or imprecise way, and their mutual relationship is not clear. This article analyses their respective structures in detail, as well as their relationship with each other. The GA considers the logical structure of non-deductive inference (and of relative observation), and claims that (value-laden) background assumptions are needed to constitute (relative) observations and for those observations to confirm a hypothesis. It does not explicitly consider the consequences of these (value-laden) choices: rather, values are considered given and preexisting, so to speak. It is not normative: it claims that non-epistemic values are necessary to determine background assumptions in the sense that they are inevitable. By contrast, the EA considers the decision-theoretical problem of accepting or not a hypothesis, according to a (value-laden) required degree of confirmation. It is explicitly concerned with the consequences of these choices. It is normative: it claims that scientists should (in the sense of a moral obligation) take into account the non-epistemic consequences of their choices. By substituting the condition for hypothesis acceptance of the EA in the Bayesian account of the GA, one can provide a determinate limit when confirmation can be seen as sufficient to justify acceptance, thereby making the EA appear as a special case of the GA.