> On Jan 7, 2024, at 9:10 AM, robert marty <robert.mart...@gmail.com> wrote: > > It's clear, then, that the composition of the two determinations gives rise > to the triadic relation for Peirce. That's why I've underlined "therefore." > Consequently, the formalization is simplified considerably, without any loss > of information, by : > > O à S à I > > The arrows represent determinations, and this diagram reads: > > O determines S, which determines I > > Referring to the Peircean conception of a determination: > > We thus learn that the Object determines (i.e. renders definitely to be such > as it will be) the Sign in a particular manner. (CP 8.361, 1908) > > We can see that O determines I by transitivity. Peirce verified this in MS > 611 (Nov. 1908). > > This diagram has the considerable advantage of being equivalent to the > mathematical object below: > > Schematic representation of a category with objects X, Y, Z and morphisms f, > g, g ∘ f. > <https://upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Commutative_diagram_for_morphism.svg/200px-Commutative_diagram_for_morphism.svg.png> > (click) > > It's an algebraic category, the simplest there is (non-trivial). This one is > the archetypal example of a category on the >
Robert: You may want to check your mathematical conclusions. While I understand that the following details are highly technical in nature, it is important that mathematics NOT be treated as merely a symbolic metaphor when an inquiry into the meaning of symbols is under the microscope. The sequence O—> S —> I. as three alphabets symbols and two arrows. The schematic diagram referenced by the “click," (which is, by the way, only a partial representation of a mathematical category,) has three arrows and repeats the function labels and even composes the two functions. In addition, the identity arrows necessary to define a mathematical category are missing. These notational constraints are essential for the additional property of closure, which is far beyond the simple property of transitivity illustrated by the simple sequence of three alphabetic symbols and two arrows. Cheers Jerry
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