Helmut, List: Indeed, that passage by Peirce in R 490 is challenging to untangle. I had to read and reread it several times myself when I first studied it a few months ago, and then again yesterday while drafting my previous post.
Both graphs are existential, not entitative. The only difference between them is the addition of the line of identity connecting the two instances of "man," which indicates that they are referring to the *same *man. For any propositions X and Y, all three expressions--"if X then Y," "not-(X and not-Y)," and "not-X or Y"--are equivalent translations in classical logic because it is strictly confined to reasoning about prolonged determinate states of things where there are *only *symmetrical relations between the signified propositions. Again, what is missing is the *unsymmetrical *relation of consequence between the antecedent and consequent, such that the latter *follows *from the former. On the other hand, in intuitionistic logic the three expressions are *not *equivalent. Specifically, "not-(X and not-Y)" and "not-X or Y" can be inferred from "if X then Y," but not vice-versa. Accordingly, in Arnold Oostra's intuitionistic existential graphs the continuous scroll for a conditional proposition, with its inner loop connected to its outer loop at one point, is distinguished from detached/nested cuts or shaded/unshaded areas for a conjunctive or disjunctive proposition. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Sun, Dec 27, 2020 at 10:33 AM Helmut Raulien <h.raul...@gmx.de> wrote: > Jon, List, > > Thank you! I need examples. This one is tricky, I have to read it some > more times, as now I don´t see the asymmetry. And I don´t understand > > "Nevertheless, these are different propositions that signify different > states of things, which is reflected by their different existential graphs > (see attached from R 490:22). > > , because one of them, the one with the "or" should be an entitive graph, > due to the "or", or not? But as I said, I must read it again and again, > maybe I will understand, what about classical logic is not sufficient. > > Best, Helmut >
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