Sung, Just for starters, A is a "sign" at the top of your account and an "object" at the bottom.
Jon On 2/4/2015 6:00 PM, Sungchul Ji wrote:
Jon, My understanding is that the 'commutative triangle' is the simplest category. The Peircean sign defined below (reproduced from http://www.iupui.edu/~arisbe/rsources/76DEFS/76defs.HTM) to me is a commutative triangle and a mathematical category: *"30 - 1905 - SS. pp. 192-193 - Letter to Lady Welby (Draft) presumably July 1905 .* A "sign" is anything, A, which, (1) in addition to other characters of its own, (2) stands in a dyadic relation Þ, to a purely active correlate, B, (3) and is also in a triadic relation to B for a purely passive correlate, C, this triadic relation being such as to determine C to be in a dyadic relation, µ, to B, the relation µ corresponding in a recognized way to the relation Þ." Which can be diagrammed as: Þ µ A -------> B -------> C | ^ | | |_____________________| h Figure 3. The Peircean sign as a mathematical triad. A = object; B = sign or representamen; C = interpretant, with the commutative condition satisfied, i.e., Þ x µ = h, where Þ = sign production; µ= sign interpretation, and h = information flow. If figure is right, information flow is possible only because the sign is a mathematical category. Hence Figure 1 can be viewed as the definition of information, just as it is a definition of the sign. Let me know if you disagree. All the best. Sung
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