Clinger, argues that we trust mathematics because it has demonstrated extraordinary success within empirical science. However, this argument does not provide an independent justification for mathematics, because modern science itself relies on mathematical and logical structures to formulate hypotheses, construct models, interpret data, and evaluate predictions.
The problem is not simply a logical circularity in the formal sense, but an epistemological circularity: the method used to confirm the reliability of mathematics already presupposes the mathematical and logical tools whose reliability is being evaluated.
The empirical success of science demonstrates that certain mathematical structures are extremely effective for representing aspects of the physical world, but it does not, by itself, demonstrate that mathematical axioms are true, that mathematical objects exist, or that mathematics possesses necessary validity independent of experience.
Therefore, Clinger’s argument may justify a pragmatic trust in mathematics — that is, the belief that mathematics is an extraordinarily effective tool — but it does not provide an ultimate epistemological