List, All: I have been further pondering these remarks by Peirce near the end of R 669.
CSP: It now only remains to formulate those general permissions to modify what has already been scribed which express the logicality of those several forms of elementary deductive inference, out of which all other deductions can be built up. There are but two of these general illative permissions; but before stating them there is one other thing that has to be said. Namely, it is to be imagined that every graph-instance anywhere on the sheet can be freely moved about upon the sheet; and since a scroll both of whose closes are empty asserts nothing, it is to be imagined that there is an abundant store of empty scrolls on a part of the sheet that is out of sight, whence one of them can be brought into view whenever desired. What is here said ought to be reckoned as a permission, but it is not an illative permission, i.e. a permission authorizing a species of inference. (R 669:21-22[19-20], LF 1:583, 1911) Again, erasure/insertion and iteration/deiteration are the only *illative* permissions--i.e., the only rules of *inference*. The double-cut rule, which becomes "scrolling" in intuitionistic/synechistic EGs, is a permission of a different sort--it merely brings something "into view" that was previously "out of sight" but taken for granted in accordance with Peirce's insight that "every proposition [is] a conditional proposition at bottom" (CP 3.440, 1896). As he puts it in RL 231, "The third permission amounts to declaring that to say that if anything whatever is true, P is true is precisely as much as to say that P is true, and *vice versa*" (NEM 3:181, 1911). In other words, "a and [image: image.png] represent the same state of things, without either being more analytical than the other" (NEM 3:349, 1903). Hence every EG is effectively within the inner close of a scroll with an empty outer close, regardless of whether it is explicitly scribed that way. Moreover, in intuitionistic/synechistic EGs, inclusive disjunction is expressed by a scroll with multiple inner closes, raising the question of whether and how this sign can be introduced on the blank sheet. My suggested solution is a minor modification of the scroll as the third primitive--adding a second inner close that is small and blackened, which does not change the interpretation since "either A or falsity" is equivalent to "A," and "A implies either B or falsity" is equivalent to "A implies B." As with ovals in classical EGs, having a single symbol that can signify disjunction (empty outer close and graph in each inner close), implication (antecedent in outer close and disjunctive consequents in inner closes), and negation (graph in outer close and one blackened inner close) complies with Peirce's principle that "if one sign can be expressed as a complication or special determination of another, we are bound so to express it in logical analysis" (R 482:12, 1896-7). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt >
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