Supplement: The laws of duality say, that duality can be achieved by replacing all "or"s with "and"s, and/or vice versa. Therefore, an Entitative Graph and an Existential Graph, which look alike, are dual to each other.
Duality can also be achieved by negating all variables plus the whole formula.
Now, if you first exchange "or"s and "and"s, and then do the said negation thing, you have the dual of the dual, so the same formula you have started with.
Jon, List,
Thank you, Jon, it works! You wrote:
"CSP: Any entitative graph may be converted into the equivalent existential graph [or vice-versa] by, first, enclosing each spot separately and secondly enclosing the whole graph. (R 485:1)".
Example:
EG: (A(B(C))) means: "Not (A and not (B and not C)))".
To transform into Entitative Graph I put each variable into extra brackets: ((A)((B)((C)))), put extra brackets around all: (((A)((B)((C))))), delete all double
brackets: (A)((B)C). This Entitative Graph means: "Not A or not (not B or C)". It shows the same Venn-Diagram, so is the same formula.
Transforming back also works: (A)((B)C), enclose each variable: ((A))(((B))(C)), enclose all: (((A))(((B))(C))), delete double negations (double brackets whereever they are on both sides of something, save the external ones): (A(B(C))).
So, if you have a formula containing "not"s and "and"s, but you are rather the "or"-type, you can change it into a formula containing only "not"s and "or"s. Or vice versa.
Best,
Helmut
Helmut, List:
HR: somewhere, I forgot where, I have read, that Existential Graphs are Entitative Graphs turned inside out.
Peirce himself is the one who said that existential graphs "are merely entitative graphs turned inside out" (R 280:21; c. 1905). There was a thread on this same topic last summer, and as I noted back then, he provided the following simple instructions.
CSP: Any entitative graph may be converted into the equivalent existential graph [or vice-versa] by, first, enclosing each spot separately and secondly enclosing the whole graph. (R 485:1)
The "fundamental symbol" in both systems is juxtaposition, which by convention asserts conjunction in existential graphs vs. inclusive disjunction (or alternation) in entitative graphs. In other words, when multiple propositions appear unenclosed on a sheet, the claim in existential graphs is that all of them are true (a copulative proposition), whereas the claim in entitative graphs is that at least one of them is true (a hypothetical proposition). Hence the relation represented by a pair of existential graph-instances on the same sheet is that of coexistence, while the relation represented by a pair of entitative graph-instances on the same sheet is that of conditional necessity--if not one, then the other.
Cuts indicate negation in both systems, and are necessary in order to express hypothetical propositions in existential graphs and copulative propositions in entitative graphs. However, the scroll in existential graphs properly emphasizes that sequence is a more basic concept than negation, as Peirce discusses at some length in "The Bed-Rock Beneath Pragmaticism" (R 300; 1908); a cut is really a scroll with an inner close that is blackened and then reduced to infinitesimal size (CP 4.454-456; 1903 and CP 4.564n; c. 1906). Finally, a line of identity denotes an existentially quantified subject in existential graphs ("something") and a universally quantified subject in entitative graphs ("anything").
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
On Thu, Jan 30, 2020 at 11:22 AM Helmut Raulien <[email protected]> wrote:
Supplement: With alternation of the backround of Venn diagrams in the case of Entitative Graphs / Laws of Form I meant, that this alternation takes place between graphs with no variable written into the unmarked space. That would be: (C) : Black background. (B(C)): White background. (A(B(C))): Black background. With EGs, I guess you never write a variable into the blank sheet, and in this case the background always is black.List,somewhere, I forgot where, I have read, that Existential Graphs are Entitative Graphs turned inside out. In the attachment I have tried to see whether this is so or not, by visualizing some graphs with Venn diagrams. I have found that for two variables in cuts inside each other (page 1 of the attachment), but not for three of them (page 2).It is also said (Wikipedia), that Entitative and Existential Graphs are dual with each other. I have not checked that yet. I first thought I had, thinking that dual Venn-Diagrams are like one being a negative photo-copy of the other. But that is not so. I dont know, whether duality is visible at all by comparing Venn-Diagrams. Duality means, that between two compared truth-tables "true" and "false" outcome values are replaced with each other.Another thing is, that, while this is not the case with EGs, in Entitative Graphs the background of the Venn-Diagram alternates between black and white with additional cuts inside each other.Entitative Graphs are isomorphic with Laws of Form, so this alternating background should not be, I guess, as in Laws of Form, it should be "unmarked space", isnt it? So nothing should happen with it, should it?But maybe, I have made mistakes? I was assuming, that a cut means "not" to its inside, and that elements besides each other are connected with "or" in Entitative Graphs, but with "and" in EGs.Best regards,Helmut
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