*3.1. Likelihood*

Probabilistic approaches in cognitive science, and beyond, span a large spectrum (see Table 1, upper part, for a first impression thereof). At one end of this spectrum are Bayesian approaches like Friston's free-energy predictive coding approach [18]. This approach claims to have high explanatory power, but in fact, hardly goes beyond data accommodation, hardly produces falsifiable predictions, and suffers from computational intractability (see, e.g., [19–23]). In my view, it therefore qualifies as what Chomsky called an "analogic guess", that is, it "creates the illusion of a rigorous scientific theory with very broad scope" [24] (p. 32).

Most Bayesian models in cognitive science, however, take a stance that, in my view, is more appropriate and adequate. Instead of considering the likelihood principle as a strong explanatory principle, they rather consider it as a powerful modeling principle by which free-to-choose probabilities can be assigned to free-to-choose things in order to perform sophisticated data fitting and data extrapolation. This may not always be easy to do, but it means that there is no fundamental obstacle for the inclusion of local aspects like the effects of contrast polarity. Pinna and Conti wrote "[If] we do not consider the contrast polarity as a constraint or as a prior, Bayes' inference cannot easily explain these conditions" [2] (p. 12 of 32)—indeed, but why would we? Therefore, they knowingly ignored the above flexibility and applied likelihood as if it is fundamentally blind to contrast polarity. Thereby, they missed the mark in their assessment of likelihood approaches.
