Jon AS, Gary F, Helmut, and Jerry LRC, To illustrate the issues in this thread, see the attached EntG.png which shows an entitative graph (Fig. 1) and a chemical graph (Fig. 2).
CSP, CP 3.469: The proposition "John gives John to John" corresponds in its constitution, as Figs. 1 and 2 show, precisely to ammonia. But beyond this point, the analogy ceases to be striking. In fact, the analogy with the ruling theory of chemical compounds quite breaks down. Yet I cannot resist the temptation to pursue it. After all, any analogy, however fanciful, which serves to focus attention upon matters which might otherwise escape observation is valuable.
GR
entitative graphs and existential graphs... seem at first glance to be something of mirror images of each other, especially as I've read that the alpha part of existential graphs is dual to entitative graphs in the sense of an "involution operation" ...
HR
perhaps entitative graphs are the inversion of existential graphs and vice versa, like, turned inside out.
JAS, quoting CSP:
As a matter of fact, "Existential Graphs, which are merely entitative graphs turned inside out ..." (R 280:21; c. 1904-1905)
The term 'inside out' is a fanciful analogy that can focus attention, but more detail is necessary to specify a precise transformation.
In mathematics and logic, the words 'dual' and 'duality' cover several different kinds of transformations. They all transform one structure to another and back again. But there are many variations. For an overview, see https://en.wikipedia.org/wiki/Duality_(mathematics) In CP 3.469, Peirce said that Fig. 1 states the proposition "John gives John to John." But that reading is derived more directly from the corresponding existential graph (EG). In this case, the EG can be derived from the entitative graph (EntG) by erasing the three ovals. But that operation, by itself, is not sufficient to convert an arbitrary entitative graph (EntG) to an equivalent EG. See the attached EntGEG.png for a copy of the transformation rules from p. 136 of Don Roberts' book. The rules for "P and Q" and "P or Q" are exact inverses. But the rules for "All F is G" and "Some F is G" are not exact inverses. To show how these rules are applied, consider Fig. 1. In that EntG, there are three ovals that contain the monad 'John'. That monad corresponds to F in the rule for transforming "All F is G". The oval that contains the triad 'gives' corresponds to G. If you apply that rule to each of the three ovals that contain the monad 'John', each one implies an additional oval around the oval that contains the triad 'gives'. That would create a double negation around 'gives'. Then the inference rule for erasing a double negation would produce the EG for the sentence "John gives John to John." Technically speaking, one could say that the extra inference step means that EntGs and EGs are not exact duals. But according to the looser criteria summarized in the Wikipedia article, EntGs and EGs could be called duals. GR
I have also very recently read in an encyclopedia article that Spencer-Brown's primary algebra as presented in Laws of Form is isomorphic to entitative graphs, while earlier I'd only read of its similarities to existential graphs.
Short answer: It's not isomorphic to either one, but there are some similarities. For the details, see "The Mathematics of CSP" by Louis Kaufman: http://homepages.math.uic.edu/~kauffman/CHK.pdf HR
in Wikipedia they write, that entitative graphs are "dual" to alpha-existential graphs
Wikipedia cites Kauffman's article, which is more detailed and more accurate. Note what Kaufman wrote at the top of p. 23:
LHK: we have exhibited a version of the Logical Garnet that intermediates between Peirce’s Existential Graphs and the dual approach of Laws of Form... The diagrammatic investigations of Peirce, Venn, Carroll, Nicod and Spencer-Brown are all ways of finding geometry in logic, but in Zellweger’s Logical Garnet classical three-dimensional geometry appears, and this is an indication that one should think again on the relationship of logic and mathematics.
JLRC
In light of subsequent developments in graph theory, these assertions of CSP are not consistent with the notion of organic chemistry as the bedrock of pragmatic representations of matter.
That's true. As the quotation in CP 3.469 says, "the analogy with the ruling theory of chemical compounds quite breaks down." Peirce wrote that in 1896, and many more breaks have been found since then. JLRC
This basic semantic and grammatical difference ... casts a very dark shadow over the meaning and truth content of many many CSP texts.
Note quite. What it shows is that no version of ordinary language or logic can accurately represent the details of quantum mechanics. But the calculations based on mathematical theories have made excellent predictions about the outcome of various experiments. What that means: Science requires two-levels of definitions. (1) An application of logic to specify the axioms and definitions of the many theories of mathematics; and (2) an application of some of those theories to analyze and make predictions about the phenomena of physics and chemistry. This two-level combination was developed and applied thousands of years ago. Euclid's version is the best documented. Whenever possible, Euclid used Aristotle's version of logic, but he had to add much more fill in the gaps. Peirce did a lot to clarify those gaps and show where more R & D was necessary. That is a sign of strength, not weakness. John
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