Robert, Your summary of the issues is very good, and I strongly agree with the need for examples. In a search for examples, I went back to _Photometric Researches_, which I believe is essential for understanding the development of Peirce's philosophy. It's not an accident that it was published in 1878, the same year in which "How to make our ideas clear" was published in the _Scientific American_. The title of Chapter 1 is "The sensation of light." See http://jfsowa.com/peirce/PRexcerpts.pdf . On page 2, he wrote "Light considered purely as something in the external world may be called _noumenal light_. Light considered as an appearance, and as a function of the sensation, such that it is measured by the convention just mentioned, may be termed _phenomenal light_. Photometry generally concerns phenomenal light..." Just reading a few pages (my PRexperts, for example) is enough to show how deeply Peirce's phaneroscopy is grounded in his scientific and engineering research. It's also important to compare that research with R602, which was written after his 1903 classification of the sciences. See http://jfsowa.com/peirce/r602.htm : p 12> But preliminary to normative science, which is essentially classificatory,  stop to take that well in, I beg you, gentle reader, there should be a nomological science, which shall make out all the different indecomposable elements which enter into everything that is conceivably possible, discriminates them with care, and shows how they can be varied and combined. This science I hesitate to call phenomenology after Hegal, for fear of marring his peculiar conception of it; and therefore, though I think it is essentially the same thing under a somewhat different aspect, I will name phaneroscopy. p 13> It is the science of the different elementary constituents of all ideas. Its material [m13] is, of course, universal experience,  experience I mean of the fanciful and the abstract, as well as of the concrete and real. Yet to suppose that in such experience the elements were to be found already separate would be to suppose the unimaginable and selfcontradictory. They must be separated by a process of thought that cannot be summoned up Hegel-wise on demand. They must be picked out of the fragments that necessary reasonings scatter; and therefore it is that phaneroscopic research requires a previous study of mathematics. Observation from p, 12: normative science is essentially _classificatory_. That implies that logic as semeiotic is a classification of the ways that formal logic is applied to practice. The reasoning methods of logic as semeiotic are derived from mathematical logic. Many people who talk about Peirce's semeiotic ignore the fact that the reasoning methods are based on mathematical logic. Observation from p, 13 of R602 and pp. 10 and 11 of PRexcerpts: Phaneroscopic research requires a previous study of mathematics. The kind of mathematics depends on the application, and there is no limit on the amount and depth of mathematics that may be needed. John
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