Helmut, Thanks for mentioning the word 'because'. That's another way to explain the 3-way connection that answers a why-question, In general, every instance of thirdness that relates (A B C) can be explained by a sentence of the form "A is related to B because C." But some linguistic transformations may be needed to transform the answer sentence into the syntactic form of a because-sentence, Some transformations may sound awkward, but they would be intelligible answers.
For your question: The simplest way to show that a four-way connection can be reduced to two three-way connections is to draw a diagram. To avoid going to my drawing tools, I'll just explain how you can draw the diagram with a pencil and paper First draw a large dot that is connected to A, B, C, and D. Then translate that four-way connection to two three way connections. Start by drawing two dots: Then connect the one on the left to A and B, and the one on the right to C and D. You now have two two-way connections. Now draw a line that connects both of the dots. As a result, the left dot has three connections: A, B, and the dot on the right. And the dot on the right also has three connections: C, D, and the dot on the left. You can repeat this procedure for reducing a dot that connects A, B, C, D, and E to a middle dot that has three connections: the first to the A, B pair, the second to the C, D pair, and the third to E. For 6, the dot in the middle will connect to three pairs, A,B, C,D, E,F, For 7 and 8, the dot in the middle will have four connections. Use the procedure for A,B,C,D to split a 4-way connection to two 3-way connections. Then keep going for as many connections as you need. John From: "Helmut Raulien" <h.raul...@gmx.de> 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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