Not exactly sure what the circularity problem is and how naturalism could encounter it?
closed as unclear what you're asking by Keelan, James Kingsbery, Swami Vishwananda, Nick R, virmaior Dec 28 '15 at 5:30
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Have a look at Explaining Quine's dismissal of the circularity problem in naturalistic epistemology, which problem was characterized as follows by Ronald Giere in his Philosophy of Science Naturalized:
The general idea behind the circle argument is that the use of scientific methods to investigate scientific methods must be circular, beg the question, or lead to a regress. A more explicit version of the argument might go something like this: One of the things any study of science must investigate is the methods (criteria, canons, etc.) scientists use in evaluating evidence. To pursue such an investigation scientifically requires using data about scientific practice to reach conclusions about scientific methods. Thus, any empirical investigation aimed at discovering the criteria that scientists use for evaluating evidence would necessarily presuppose at least some of the criteria it was supposedly setting out to discover. So not all the methods of science could be discovered by scientific investigation. At least some must be discoverable by other means.”