The "A Priori Method" of belief fixation is based on the idea that the human mind (or brain) has direct access the a body of knowledge prior to experience. Thus, if you want to know the Truth all you have to do is think real hard about it and you instantly ascertain "know" the Truth. As Peirce suggests, there are two problems here: 1.) There is very little agreement among philosophers in terms of a list of universally accepted a priori empirical truths. 2.) When we introspect our consciousness, we are actually looking in at relative culturally-based truths that are usually based on authority.
However, Peirce is not as hostile to the A Priori Method as one might think. In his other writings, he acknowledges that when faced with an enormously complex question (like the structure of DNA) humans have an uncanny ability to guess the right answer and that hypotheses often originate as feelings. In fact, Crick and Watson literally guessed the double-helical structure of DNA out of thin air! In fact many scientific theories "emerge" out of dream states. What's important here is that Peirce differentiates between the process of generating theories (intuition or feeling) and the process of determining whether those intuitions are, in fact, True or False. Peirce insists that although we often guess right, we still cannot rely solely on authority or a priori intuition. Truth, Peirce argues, has experimental consequences. That is, if a theory is True it should enable you to either predict or control that phenomena. Although many a priori theories generate highly plausible, psychologically pleasing explanations, Truth is ultimately "Pragmatic." As William James later observed Truth must ultimately exhibit "cash value." Just because the double helical structure of DNA originated a priori, it was not "True" until it's "cash value" was established in the laboratory. And of course, today the "cash value" of their discovery continue to roll in, as illustrated by genetic testing and genetic therapy.
Another point worth mentioning here is that Peirce did not believe that scientific theories could ever be finally verified in the laboratory. Why? Because of David Hume's "problem of induction," which observes that, eventually, future experiments (observations) almost always falsify previous previous observations. Therefore Peirce argued that all theories are, therefore, fallible and subject to future revision. So when we say that "DNA has a double helical structure," we're really saying that Crick and Watson's theory has not been falsified. In my next blog, I'll sketch in Peirce's Scientific Theory of the Fixation of Belief.