John, List, All: JFS: Thank you for emphasizing the fact that Peirce's only comments in favor of the scroll came before June 1911.
Indeed, his "only" comments in favor of the scroll are in numerous passages from his extensive writings about EGs between late 1896 and June 1911. Nevertheless, as far as I know--please provide a citation if I am mistaken--there is no passage whatsoever in his entire vast corpus where he *repudiates *those favorable comments, nor his underlying analysis of inference. As I keep pointing out, omission is not rejection. JFS: In Peirce's writings after that date, the scroll is "equivalent" to a nest of two negations. Actually, he never uses the word "scroll" in any of those writings, and he states that a figure showing nested ovals "is equivalent to" one showing a scroll (without calling it that) exactly once. It is in a draft manuscript for a lecture that would have introduced EGs to an audience not previously familiar with them, where it occurs in the context of explaining why shading is a much better alternative to thin lines for distinguishing oddly and evenly enclosed areas. Again, as far as I know--please provide a citation if I am mistaken--there is no passage whatsoever in his entire vast corpus where he *repudiates *the philosophical basis for taking consequence (scroll) as a primitive, such that negation (cut/oval) is derived from it. Moreover, even in June and December 1911, he remains consistently adamant about his primary objective in developing and promoting EGs. CSP: I wish to draw your attention, in the most emphatic way possible, to the purpose this Syntax is intended to subserve; since anybody who did not pay attention to that statement would be all but sure, not merely to mistake the intention of this syntax, but to think that intention as CONTRARY to what it really is as well he could. Namely he would suppose the object was to reach the conclusion from given premisses with the utmost facility and speed, while the real purpose is to dissect the reasoning into the greatest possible number of distinct steps and so to force attention to every requisite of the reasoning. The *supposed* purpose would be of little consequence, and it is the business of the mathematicians to furnish inventions to attain it; but the real purpose is to supply a real and crying need, although logicians are so stupid as not to recognize it and to put obstacles in the way of meeting it. (RL 231, NEM 3:168, 1911 Jun 22) CSP: The ultimate purpose of contriving this diagrammatic syntax, is to enable one with facility to divide any *necessary*, or *mathematical*, reasoning into its ultimate logical steps. (RL 376, R 500:3, 1911 Dec 6) As I discussed previously ( https://list.iupui.edu/sympa/arc/peirce-l/2021-02/msg00019.html), Shafiei's example of *ex falso quodlibet* conclusively demonstrates the vast superiority of scrolls over cuts/ovals for fulfilling the real and ultimate purpose of EGs, even when employed in accordance with classical logic. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Mon, Feb 8, 2021 at 9:21 AM John F. Sowa <[email protected]> wrote: > Jon AS, > > Thank you for emphasizing the fact that Peirce's only comments in favor of > the scroll came before June 1911. > > In Peirce's writings after that date, the scroll is "equivalent" to a nest > of two negations. In mathematics and logic, equivalence means freely > interchangeable in all contexts without any change in meaning. > > Other people may choose to use a scroll for any purpose they please, but > their choices have no effect on the logic or on anything Peirce wrote. > > John >
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