The purpose of inquiry is to move from doubt to belief.  Belief is a mental state in which there is no doubt.  A belief may cease to be held and lead back to discomfort in the (former) believer, so the best kind of belief is the settled and stable kind.  Inquiry itself is the struggle to attain belief.

    There are many methods used to attain belief and some are better than others.

1.  The method of tenacity.  Keep repeating it, ignore all other things that might disturb the belief.
        This method can't hold in practice - we will inevitably know that other people think differently and their beliefs are just as good.  This acknowledgement shakes one's beliefs and leads back to doubt.

2.  The method of authority.  The state keeps correct doctrines and reiterates them for you.  It prevents contrary doctrines from being expressed primarily by killing off or otherwise persecuting those who differ.
        This is mentally superior to the method of tenacity - it works better.  But even this can't work because at least some people will realize that other people in other places believe differently, or at least people in other times have believed differently (and may do so in the future).  People will then begin to realize that what they believe now (or what they are forced to claim they believe) is nothing more than belief induced by the accident of the way they were taught and the society in which they live.

3.  A priori rationalism - Pretends to certainty by "agreement with reason."  For Peirce, all this claim means is that the person who appeals to "reason" is saying that a belief agrees with what that person was inclined to believe at the outset.
        This is basically a matter of taste, not of reason.

4.  Empirical Science - all the other methods are good for fixing a belief,b ut they can't prevent them becoming un-fixed.  They are not self-corrective.  The method of empirical science is self-corrective.
        It is self-corrective in the sense that though it unsettles beliefs at first by exposing them to criticism, over the long run it brings us closer to beliefs.  The notion in this method is that there is a reality outside ourselves - there are real things independent of us and those things affect our senses according to regular laws of nature.  Even though our sensations are all different (note, for example, that no two people ever look at any given thing from exactly the same perspective), the laws of perception are the same and can lead to a True conclusion.

    The method of science works because it is verifiable empirically.  We can test the claims that are made.  How can you test a claim that can't be verified or falsified?

    You can't define Truth as Satisfaction because then anything that satisfies is true.  There has to be a way to distinguish warranted and unwarranted satisfaction.

    Peirce insisted that he was a Realist - that the activity of thought is going on and is directed toward and approximating an objective world independent of us.  At the same time, he also reconized that there is nothing directly present in perception except ideas, and so the data of experience and the process of reasoning leads to interpretation that gives us a conclusion.

    We should be prepared to test and re-test our conclusions, and be ready to shed them if they are no longer satisfactory on the method of science.