John, List I totally agree with you. This can be seen very clearly in Tommi Vehkavaara's compilation of the classifications of sciences from 1902 to 1911. We can see that the Mathematics at level (AI) are divided in:
(AIa) *Mathematics of Logic (e.g.*,* formal logic
in contemporary sense)*
(AIb) Mathematics of Discrete Series
(AIc) Mathematics of Continua and Pseudo-continua
and the level (AII) is divided as follows
:
(AII) Cenoscopy -Philosophia prima- positive
science (which rests upon familiar, general experience) Special sciences -
positive sciences (based on special experiences, discover new phenomena)
(AIIa)
Phenomenology(1902-3,1906,1911) -Phaneroscopy (1904-)
(AIIb) Normative Sciences the
Normative Sciences are divided in:
(AIIbi) Esthetics
(Axiagastics, 1905
(AIIbii) Ethics -
Anthetics/Practics (1906)
(AIIbiii)*Logic- Science
of general laws of Signs -Formal Semiotic(Semeiotic)- theory of
(self)-controlled thought*
Moreover, in my article on the "Podium" in section 3, I pointed out that
this confusion was at the origin of the elimination of mathematics in the
secondary literature on Peirce, mainly that concerning semiotics (I quote
Houser, Belluci and Pietarinen, and De Tienne). In fact, by using the logic
of the level (AIIbiii) in which Mathematical Logic is implemented from the
level (AIa) on which it depends, one can ignore the level (AIb) of Discrete
Mathematics in which the mathematical structures that operate on
Phenomenology (Phaneroscopy) are located, thus creating an "illusion of
mathematical structures" despite the loss of the constitutive relations. It
is a more or less conscious avoidance strategy, depending on the case.
Robert Marty
Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy
fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>*
Le mer. 7 juil. 2021 à 05:35, John F. Sowa <s...@bestweb.net> a écrit :
> Robert and Gary F,
>
> The issue you're debating is caused by the ambiguity in Peirce's use of
> the word 'logic'. In his 1903 classification of the sciences, the word
> 'logic' appears in two places: mathematics of logic is the first of three
> branches of mathematics. But logic proper is a branch of normative science.
>
> The logic that is used to derive the categories and hypoicons is th logic
> of mathematics, AKA mathematical logic, AKA formal logic. The logic that
> scientists use to evaluate the truth of their hypotheses is normative
> logic, which is misleadingly called logic proper.
>
> See the comments and quotations below.
>
> John
>
> ----------------------------------------
>
> The categories and hypoicons, the foundation for semeiotic, are
> derived from the phaneron by applying the three branches of pure
> mathematics: formal logic; discrete mathematics (arithmetic, graphs,
> and discrete sets); and continuous mathematics (geometry, topology,
> and uncountable sets).
>
> We must also distinguish the term *formal logic*, which occurs 119 times
> in CP, from* logic proper*, which occurs just 7 times in CP. DeMorgan
> coined the term formal logic, and Peirce adopted it for every logic
> notation developed by himself or others. Note its importance:
>
> CSP: The little that I have contributed to pragmatism (or, for that
> matter, to any other department of philosophy), has been entirely the
> fruit of this outgrowth from formal logic, and is worth much more than
> the small sum total of the rest of my work, as time will show.
> (CP 5.469, R318, 1907)
>
> CSP: My trichotomy is plainly of the family stock of Hegel’s three
> stages of thought, — an idea that goes back to Kant, and I know not
> how much further. But the arbitrariness of Hegel’s procedure, utterly
> unavoidable at the time he lived, — and presumably, in less degree,
> unavoidable now, or at any future date, — is in great measure avoided
> by my taking care never to miss the solid support of mathematically
> exact formal logic beneath my feet.... (EP 2:428, R318, 1907
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