Helmut, List: Peirce's three universal categories (1ns/2ns/3ns) are discovered in the primal positive science of phaneroscopy (quality/reaction/mediation) and diagrammatized in the hypothetical science of mathematics (monadic/dyadic/triadic relations).
I do not know whether anyone has posted a mathematical proof of Peirce's reduction thesis on the Internet. Robert Burch wrote an entire book to present his ( https://books.google.com/books/about/A_Peircean_Reduction_Thesis.html?id=MK-EAAAAIAAJ) and provides a very brief summary in his SEP entry about Peirce ( https://plato.stanford.edu/entries/peirce/#red), while Sergiy Koshkin purports to demonstrate it even more rigorously in a recent paper ( https://muse.jhu.edu/pub/3/article/886447). Personally, I find Peirce's own diagrammatic demonstration to be simple and persuasive enough--relations of any adicity can be built up of triads, but triads cannot be built up of monads or dyads despite involving them (EP 2:364, 1905). [image: image.png] I likewise noticed that the Commens website (http://www.commens.org/) was down for a while, so I was using the 12/31/23 Internet Archive version ( https://web.archive.org/web/20231231054741/http://www.commens.org/), but it came back up a couple of days ago. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Thu, Feb 15, 2024 at 1:37 PM Helmut Raulien <[email protected]> wrote: > Supplement: Ok, I can access Commens Dictionary again! > John, List, > The answer to "why", "because" always needs two premisses, with itself > being the third. So a thirdness is the answer to "why". Firstness can just > say "I". Secondness is a second following a first, and so can say "I am". > Obviously, just by having a first for predecessor, not because of something > (An observer can say, that it can say "I am", because of that, but the > secondness, subjectively, cannot say so, as it doesn´t have the ability of > inference. It only has the propositional ability to say "I am"). Thirdness > can say "I am, because", because a cause (an argument) needs two > sequentally related ancestors to be one. I really think, that the Peircean > categories basicly, like this, rely on the sheer numbers one, two, three. > BTW, I have two questions: > > -Can I see anywhere in the internet the mathematical proof, that a triad > is irreducible, but a four-ad is reducible? > > -I donot have access anymore to the Commens Dictionary. Is something wrong > with my computer, or with the website? > > Best, helmut >
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