John, List: I agree that it is important always to keep in mind that mathematics is preliminary to phenomenology/phaneroscopy, which in turn is preliminary to the normative sciences including logic as semeiotic. However, Peirce summarizes the relationship between logic as semeiotic and formal/mathematical logic by stating, "The one studies the science of drawing conclusions, the other the science which draws necessary conclusions" (CP 4.239, 1902). He then immediately adds the following.
CSP: But, indeed, the difference between the two sciences is far more than that between two points of view. Mathematics is purely hypothetical: it produces nothing but conditional propositions. Logic, on the contrary, is categorical in its assertions. True, it is not merely, or even mainly, a mere discovery of what really is, like metaphysics. It is a normative science. It thus has a strongly mathematical character, at least in its methodeutic division; for here it analyzes the problem of how, with given means, a required end is to be pursued. (CP 4.240) Logic as semeiotic--especially its third branch, methodeutic--"has a strongly mathematical character" such that, much like phenomenology/phaneroscopy, it "depend[s] upon the Conditional or Hypothetical Science of *Pure Mathematics*" (CP 5.40, EP 2:144, 1903). But as Peirce goes on to say, the same is true of *every *positive science. CSP: This is, at most, to say that it has to call in the aid of mathematics; that it has a mathematical branch. But so much may be said of every science. There is a mathematical logic, just as there is a mathematical optics and a mathematical economics. Mathematical logic is formal logic. Formal logic, however developed, is mathematics. Formal logic, however, is by no means the whole of logic, or even its principal part. It is hardly to be reckoned as a part of logic proper. (CP 4.240) Formal/mathematical logic is not the "principal part" of logic as semeiotic; in fact, "It is hardly to be reckoned as a part of logic proper." Hence logic as semeiotic is much more than merely "a classification of the ways that formal logic is applied to practice." With that in mind, how exactly does all this bear on the current discussion in progress about the definitions and relations of the destinate/effective/explicit interpretants and immediate/dynamical/final interpretants? Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt P.S. One correction, "How to Make Our Ideas Clear" and the other five "Illustrations of the Logic of Science" articles originally appeared in *Popular Science Monthly*, not *Scientific American*. On Wed, May 20, 2020 at 2:58 PM John F. Sowa <[email protected]> wrote: > 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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