Is the Probabilistic No-Miracle Argument Inferentially Fallacious?

The probabilistic no-miracle argument (NMA) for scientific realism has faced significant criticism from Colin Howson’s base-rate fallacy objection, which claims the argument violates Bayesian reasoning principles. This paper argues that such criticisms are premature. Through systematic mathematical analysis, I show that, for theories with high predictive precision, NMA would be inferentially fallacious only if opponents assume prior probabilities of approximate truth that are either “miraculously low” or “super miraculously low.” These assumptions are implausible, question-begging against realism, and unsupported by standard anti-realist arguments. The burden of proof thus shifts to critics to justify these extraordinary claims about prior probabilities.