Gary R., List: GR: They seem at first glance to me 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" (which I understand to be that if the dual of A is B, then the dual of B is A). Is that correct?
Yes, as I included in one of the manuscript quotes, "Any entitative graph may be converted into the equivalent existential graph by, first, enclosing each spot separately and secondly enclosing the whole graph" (R 485:1). The same two steps likewise convert an Existential Graph into the equivalent Entitative Graph. GR: What is not yet clear to me is exactly why Peirce ceased work on his entitative graphs and decided to develop his existential graphs ... why did Peirce just stop at the sentential part of entitative graphs while going on to develop his existential graphs as isomorphic to first-order and modal logic? Once again, Don Roberts addressed these questions in *The Existential Graphs of Charles S. Peirce* (1973). DDR: Peirce was not long satisfied with the system of entitative graphs. In fact, while he was reading the proof sheets of the *Monist *article in which the system appeared, a second system suggested itself to him.* *Ms 500; Ms Am 806*; Ms 498; Ms 280; Ms 513; and the letter to Woods begun October 4, 1913, Ms L 477. (p. 27) DDR: Why did Peirce say that EG is 'far preferable' to the entitative system? Because he thought that EG was simpler (Ms L 477) and much easier to use (Ms 513), and that the system of entitative graphs was unnatural in some of its basic conventions (Ms 484). The most unnatural feature of the system is its interpretation of the juxtaposition of two propositions as alternation. For since the writing down of a proposition asserts it, the writing down of two propositions naturally suggests asserting them both (as in EG) ... Finally, the greater simplicity of expression in EG shows up in connection with relative propositions. (p. 29) Although it is an arbitrary convention whether to treat multiple propositions on the same sheet as a disjunction (conditional) or a conjunction (copulative), the latter is more *natural*; in a sense, more *iconic*. Recognizing this, Peirce had already effectively abandoned Entitative Graphs by the time they first appeared in print, and that is why he only further developed Existential Graphs thereafter. GR: I have also very recently read in an encyclopedia article that Spencer-Brown's primary algebra as presented in Laws of Form is isomophic to entitative graphs, while earlier I'd only read of its similarities to existential graphs. Some online searching confirmed this. As nicely summarized in a paper <https://pdfs.semanticscholar.org/d610/64f3eeac228df980a5a084cc6f34578ab548.pdf> on "Boundary Logic and Alpha Existential Graphs" by William Bricken, "Spencer Brown's *Laws of Form* (LoF) presents a version of diagrammatic logic that maps to Peirce's Entitative Graphs [CP 3.456-552], the dual interpretation of Existential Graphs." Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Thu, Jun 27, 2019 at 5:36 PM Gary Richmond <[email protected]> wrote: > Jon, list, > > Thanks for further clarifying the difference between entitative graphs and > existential graphs. They seem at first glance to me 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" (which I understand to be that if the dual of A is > B, then the dual of B is A). Is that correct? > . > What is not yet clear to me is exactly why Peirce ceased work on his > entitative graphs and decided to develop his existential graphs (not that I > have a great deal of facility with either graph type, actually none > whatsoever with entitative graphs). Or, another way of asking this > question--sure to show my ignorance of graphical logic--why did Peirce just > stop at the sentential part of entitative graphs while going on to develop > his existential graphs as isomorphic to first-order and modal logic? > > I have also very recently read in an encyclopedia article that > Spencer-Brown's primary algebra as presented in *Laws of Form* is > isomophic to entitative graphs, while earlier I'd only read of its > similarities to existential graphs. Perhaps Mary Libertin can put some > light on this matter. > > Now, given my ignorance of graphical logic generally, answers to these > questions may prove more valuable to others on the list than to me. But the > topic seems intrinsically of interest to those with facility in graphical > logics. I certainly hope to learn a bit more myself. > > Best, > > Gary > > *Gary Richmond* > *Philosophy and Critical Thinking* > *Communication Studies* > *LaGuardia College of the City University of New York* > >>
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