Peirce is Descartes plus wiki's

“...all the things which can fall under human knowledge are interconnected in the same way...”

First thing to point out is that D warns that his third rule above “suppos[es] some order even among objects that have no natural order of precedence”—though (presumably) we ought to suppose such order as we follow that rule. Fine. But the question has to be asked: if there is no natural order, then what guides us in our supposing of an order of thought? This is much like the earlier blog where I wondered about the coherence of a standard we are supposed to apply—first we have to evaluate the standard itself to see whether we ought to apply it, much as a carpenter examines his/her tools, or a football analyst decides what should have happened in the Super Bowl before considering what to make of what actually did happen.

The more I think about D’s rationalism the more I am impressed by the importance of a fully functional and autonomous reason—a central rational faculty. I guess I didn’t realize how meta it is.

“...there can be nothing too remote to be reached in the end or too well hidden to be discovered.”

Peirce is optimistic this same way about the progress of inquiry, yet he builds his idea around a ‘community’ of inquirers. I’m not sure the two are all that far apart—Peirce is Descartes, plus wiki’s, more or less.

Suppose the probable is false

“...considering how many diverse opinions learned men may maintain on a single question—even though it is impossible for more than one to be true—I held as well-nigh false everything that was merely probable.”

This is so familiar to readers of D, but it remains absolutely stunning, in my opinion: why suppose everything that’s merely probable as false, until shown otherwise? Sure, if the goal of the theory of knowledge is to accumulate true things, then there ought to be a presumption against truth until some particular proposition has paid its way and been established. But D is such a method-based thinker—the book is called a discourse on method, after all—the focus should be on the soundness of the method. One could just be agnostic about truths (in the ordinary way we are agnostic about many things we don’t have definitive evidence for or against in our everyday lives) and then be strict about the application of the method (again, like the way in our ordinary lives we might insist on reading the paper or watching the news to get the story on some unbelievable event, rather than simply trusting hearsay). True, this is an appeal to authority rather than the application of a method, but the authority is established in virtue of the reporter having a method.

This is what bothered Peirce, for instance—it seems fake to suppose that everything is false, while it seems more genuine to suppose proof to consist of a gradual, methodical testing of claims to truth. Besides, D himself clearly advocates such a method-based approach in the book; why not carry it all the way through?

All I can think is that D is thinking about the problem like a geometer, whose proof might begin with the assumption of the falsehood of the premise. If a contradiction can be derived from that assumption, then the falsehood of the premise must itself be false, implying that the premise is true.