In response to your request for ideas about how we might better understand Peirce's remark, here is a reference.
In the second essay of the 1903 Harvard Lectures, entitled "On Phenomenology," Peirce articulates three faculties necessary for the proper development of the science of phenomenology. The first is "that rare faculty, the faculty of seeing what stares one in the face, just as it presents itself, unreplaced by any interpretation, unsophisticated by any allowance for this or supposed modifying circumstance" (Essential Peirce, vol. 2, p. 147). The second faculty "is a resolute discrimination which fastens itself like a bulldog upon the particular faeature that we are studying, follows it wherever it may lurk, and detects it beneath all its disguises." The third faculty "is the generalizing power of the mathematician who produces the abstract formula that comprehends the very essence of the feature under examination purified from all admixture of extraneous and irrelevant accompaniments."
In the fifth memoir of L75, Peirce talks about two arts. How do these two arts match up with the three faculties he mentions in "On Phenomenology?" My suggestion is that the first faculty is the art that Hegel, Aristotle and Kant failed properly to employ, because they did not go back to the phenomena themselves. Instead, they viewed the phenomena from the perspective of the conceptions that were current in their own day. The third faculty is the second special art. It is the method of abstraction that is employed by the mathematician, and it is central to the theorematic method in math. He has a number of extensive discussions of this method, including the discussion in "On Phenomenology."
Chair, Department of Philosophy
Northern Arizona University
Flagstaff, AZ 86011
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