Robert and Jon, I was browsing through and deleting some old email, and I came across the points quoted below. I also remember that Jon claimed that Peirce's word 'classificatory' for normative science made it sound trivial. But there are only three kinds of science: (1) mathematical, (2) classificatory. and (3) some combination of #1 and #2 in various proportions. Physics, after Galileo and Newton, became highly mathematical, but it has always depended on classification for its choice of hypotheses. Chemistry began as the classificatory science of alchemy, but it became more and more mathematical as it used physics to interpret and develop its study of the phenomena. And biology was almost purely classificatory until the late 20th century. As for phaneroscopy, Peirce derived his semeiotic by applying mathematics to the analysis of experiences in the phaneron. (See R602, Photometric Researches, and the sections of CP vol. 1 which the editors labeled 'Phenomenology'.) Pure mathematics (which includes mathematical logic) is the only science that is purely mathematical. But mathematics in practice depends on the classificatory sciences for the choice of various hypotheses to study. As for phaneroscopy, Peirce derived his semeiotic by applying mathematics to the analysis of experiences in the phaneron. (See R602, Photometric Researches, and the sections of CP vol. 1, which the editors labeled 'Phenomenology'.) That is why I used the term "formal semeiotic" for the methods Peirce used to derive his categories. And I agree that mathematical category theory is a powerful method for analyzing the structure. I believe that it makes a strong case for the label "formal". The next step after deriving formal semeiotic is to use it to classify the open-ended variety of phenomena labeled aesthetics, ethics, and rhetoric -- essentially every book on those subjects from Aristotle to the present. All the work on government and legal matters combines ethics and rhetoric with some logic (mostly limited to Aristotle's version). All that work is classificatory, and it's by no means trivial. John --------------- RM> Thank you very much John for these texts I did not ... I could have known the R602 since I had access to microfilmed manuscripts, but at the time, I was mainly interested in sign classifications and I did not think that this ms could contain such assertions . I particularly remember this sentence: "Phaneroscopic research requires a previous study of mathematics. The type of mathematics depends on the application, and there is no limit on the amount and depth of mathematics that may be needed" that I have had the opportunity to show to all those who will tell me that it does not have the ability to access the elementary definitions of category theory ... "Scientific research is a fighting sport".--------------------------JFS> 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 _Popular Science Monthly_. (Peirce met the editor of that magazine when they were both in Sicily, observing the solar eclipse.) 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 his 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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