The philosopher Charles Sanders Peirce (1839–1914) did considerable work over a period of years on the classification of sciences (including mathematics).
Peirce himself was well grounded and produced work in many research fields, including logic, mathematics, statistics, philosophy, spectroscopy, gravimetry, geodesy, chemistry, and experimental psychology.
Noting Peirce's "important" contribution, Denmark's Birger Hjørland commented: "There is not today (2005), to my knowledge, any organized research program about the classification of the sciences in any discipline or in any country".
In a letter to J. H. Kehler, printed in The New Elements of Mathematics v.3, p. 207 and dated 1911,[25] Peirce wrote: I have now sketched my doctrine of Logical Critic, skipping a good deal.
One which may be called Analytic examines the nature of thought, not psychologically but simply to define what it is to doubt, to believe, to learn, etc., and then to base critic on these definitions is my real method, though in this letter I have taken the third branch of logic, Methodeutic, which shows how to conduct an inquiry.
This is what the greater part of my life has been devoted to, though I base it upon Critic.There in 1911 Peirce does not mention the 1906 division into logics of icons, indices and symbols.
[28] On the question of the relationship between Stechiology and the Analytic that seems to have replaced it, note that, in Draft D of Memoir 15 in his 1902 Carnegie Institute application, Peirce said that stechiology[check spelling], also called grammatica speculativa, amounts to an Erkenntnisslehre, a theory of cognition, provided that that theory is stripped of matter irrelevant and inadmissible in philosophical logic, irrelevant matter such as all truths (for example, the association of ideas) established by psychologists, insofar as the special science of psychology depends on logic, not vice versa.