(Sorry if the figure gets distorted.) Clark quoted Sowa as having said that
"There are other developments, such as DNA and Heisenberg's (100314-1) uncertainty principle in quantum mechanics, which are much closer to themes that Peirce had discussed. Those could be considered support for his positions, but I'd put category theory into an area that is compatible with Peirce's views, but not directly supportive of anything he said in particular." I wonder if Sowa read the following quote of Peirce (http://www.iupui.edu/~arisbe/rsources/76DEFS/76defs.HTM), which clearly indicates to me that the Peircean sign is a mathematical category which I often represent as: f g Object ------ > Sign -------> Interpretent | ^ | | |__________________________________| h where the three structure-preserving mappings, f, g and h corresponds to the relations Þ, µ the following quote from Peirce. with the third mapping missing (as far as I can tell): Peirce wrote: "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." With all the best. Sung __________________________________________________ Sungchul Ji, Ph.D. Associate Professor of Pharmacology and Toxicology Department of Pharmacology and Toxicology Ernest Mario School of Pharmacy Rutgers University Piscataway, N.J. 08855 732-445-4701 www.conformon.net > >> On Oct 3, 2014, at 12:20 PM, Benjamin Udell <bud...@nyc.rr.com> wrote: >> >> On 10/3/2014 2:04 PM, Sungchul Ji wrote: >> >>> Ben, Jeff, Jon, lists, >>> >>> 1) Can we say that there can be many triads, depending one how one >>> defines them, but the Peircean triad is special and identical with a >>> mathematical category ? > > Category theory is one of those things Iâve always wanted to learn and > never have had time. I canât say much about it. However I did have this > in my notes. Itâs from *way* back on May 1st, 2006 here on Peirce-L. > Itâs from John Sowa whom I suspect most of us are familiar with. This is > him replying on connections between category theory and Peirce. > > I would say that the description of category theory by > Irving A. is a reasonable explanation of the subject. > > But category theory wasn't invented until about 40 years > after Peirce died. Therefore, he wasn't aware of it. > > On the other hand, I don't think that there's much point in > arguing "whether it can be connected to any part of the work > of Peirce in any significant way?" He probably would have > approved of it, but so what? > > There are other developments, such as DNA and Heisenberg's > uncertainty principle in quantum mechanics, which are much > closer to themes that Peirce had discussed. Those could be > considered support for his positions, but I'd put category > theory into an area that is compatible with Peirce's views, > but not directly supportive of anything he said in particular. > >
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