1. Is Peirce a dualist? - I think he is trying hard not to be, but he still has some lingering bits that make me wonder if he's fully cut the cord. I suspect that at this stage of his career he would say that beliefs and thoughts are real. Later, in his career, he comes to believe that only "generals" are "real", and that's a whole different can of worms. His work on what we might broadly call "psychology" is probably the weakest part of his work.
2. What about quantum physics and the "observer" problem? I'm not sure this intersects with Peirce's work. I suspect Peirce wouldn't like quantum indeterminacy, but he might be fine with it so long as we held the emphasis on how that doesn't really affect interaction with macro objects.
3. Why does Peirce privileged Reason? (weak post-modernism) In the Fixation of Belief, Peirce is pretty honest that the only thing the scientific method has going for it is that it leads to stable beliefs. If you don't care whether or not your beliefs pan out when tested, there are some good reasons to prefer other methods of fixating beliefs. One of my favorite things about that paper is Peirce's honestly that the other methods for fixating beliefs have things in their favor.
4. Why constrain the 'solution space'? (strong post-modernism) Well, Peirce actually thinks there will not be a solution to almost all questions we might think to ask. The question isn't really how to constrain the solution space though, the question is what gets to count as a solution. You can't solve problems that don't exist, so if we are asking questions about things that are not real, we will never find an answer. There might be perfectly good reasons to pretend there are answers to poorly formed questions - to facilitate social cohesion in various ways, to avoid getting killed by fanatics, etc., etc. - but that's a totally different problem. The assertion that some belief is "true" is an assertion about what would happen if we systematically started examining the consequences of that belief. If you want to talk about some other properties a belief might have, that's fine, just don't pretend you are talking about whether or not it is true. And we may "examine the consequences" of a belief using the full scope of examination methods. There are no preconceived restrictions. "Our senses" is meant in the most generous sense, not a narrow one, and merely acknowledges that we cannot examine anything except via the methods by which humans are capable of examining things.
Does that help?
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Eric P. Charles, Ph.D.
Department of Justice - Personnel Psychologist
American University - Adjunct Instructor