List, All: For the benefit of those on the cc: line who are not List members, here is a link to my entire post to which John Sowa was replying.
https://list.iupui.edu/sympa/arc/peirce-l/2021-01/msg00002.html In addition, here are links to an earlier exchange between us, in which I provided several relevant excerpts from a 2016 paper by Bellucci and Pietarinen ( https://www.cambridge.org/core/journals/review-of-symbolic-logic/article/existential-graphs-as-an-instrument-of-logical-analysis-part-i-alpha/9C4689940BDC5B17F739C34A87C2B77F ). https://list.iupui.edu/sympa/arc/peirce-l/2020-12/msg00086.html https://list.iupui.edu/sympa/arc/peirce-l/2020-12/msg00095.html As they rightly observe, "Taking the idea of negation as primary is philosophically inaccurate ... . Negation is not a primitive idea; rather, it is a conception derived from that of implication. Therefore, the sign of negation ought to be considered as a complication or determination of a more primitive sign, the scroll" (pp. 220-221). I sincerely hope that Parts II and III on Beta and Gamma are still forthcoming from them, and I would welcome any feedback from them and/or others on what follows. JFS: I realized that Peirce's insight on 2 June 1911 was that the adjective 'illative' is irrelevant and misleading for all three permissions (rules of inference). This is obviously false. Peirce does state in R 669 that although the double cut rule "ought to be reckoned as a permission," it nevertheless "is not an illative permission, i.e. a permission authorizing a species of inference." However, he then goes on to present deletion/insertion as the "First Illative Permission" and iteration/deiteration as the "Second Illative Permission." In other words, only these two permissions are rules of *inference*, such that together they "will suffice to enable any valid deduction to be performed." JFS: I believe that R669 is the *last* MS in which he wrote the words 'illative' or 'illation'. I have not read all his extant MSS, but I very strongly doubt that he would continue using a word he had rejected. Omission is not rejection. I am not aware of any textual evidence that Peirce ever explicitly *rejects *the words "illation" and "illative," let alone the associated concept. JFS: Any comment about modal issues in 1913 should be evaluated in terms of the Delta graphs, for which we don't have any MSS. I agree, with one major exception--there is an important modal aspect to shading since it corresponds to a universe of possibility rather than actuality. In fact, Peirce ultimately considers Beta EGs plus shading to be the Gamma part (CP 4.576-581, 1906) as a welcome simplification of the "nonsensical tinctures" that he later regrets introducing in "Prolegomena" (RL 477, 1913). That is why a new Delta part would be necessary to include and extend the additional modal considerations that he had explored previously in the Gamma part of 1903. JFS: In R670, negation is a primitive. The scroll is nothing but a way of drawing a nest of two negations without raising the pen. I agree, and I continue to acknowledge that the same is true in RL 231, RL 378, and RL 376. However, I disagree strongly about Peirce's *reason *for taking this approach. In my view, he deliberately *simplifies *his presentation of EGs for the uninitiated, accepting the tradeoff of making it *less analytical* by not explaining how shading for negation is derived from the scroll for consequence. The latter is the true third primitive in addition to the blank sheet for coexistence and the heavy line for identity. CSP: We have seen that there are three relations which subsist between the parts of graphs. The first is the relation expressed by the scroll. This is the most important of all, since this is the relation of premiss and conclusion; that is, if it be true that if A is true B is true, then should A occur as a premiss we have a right to conclude B. The second relation is that expressed by writing two graphs side by side AB, that is to say, the relation of coexistence, and the third is the relation of individual identity expressed by the heavy line. (R 466:18-19, 1903) I am not aware of any textual evidence that Peirce ever explicitly *rejects *this analysis. JFS: Oostra's choice of the scroll as a marker for intuitionistic rules has no similarity to Peirce's use for any version of EGs. On the contrary, Peirce on multiple occasions uses the scroll to derive the cut for negation from a consequence with falsity as its consequent (CP 4.402, 1903; CP 4.454-456, 1903; CP 4.564n, c. 1906; R 669:18-20[16-18], 1911). This is precisely how negation is defined in intuitionistic logic. Moreover, he calls it an "error" and an "inaccuracy" to analyze "if A then B," which is represented by a scroll, as strictly equivalent to "not-(A and not-B)," which is represented by nested cuts (R 300:48-49[47-48], 1908). The latter can be inferred from the former in intuitionistic logic, but not the other way around. I find it quite remarkable that merely distinguishing a scroll from nested cuts is all that it takes to adapt EGs for intuitionistic logic. It is directly parallel to omitting "Peirce's law" (a misnomer) from his axiomatization of classical logic in the groundbreaking paper, "On the Algebra of Logic: A Contribution to the Philosophy of Notation" (CP 3.359-403, 1885). Peirce thus comes tantalizingly close to inventing that system well before Brouwer and Heyting, albeit with very different philosophical motivations. As I recently suggested in another thread ( https://list.iupui.edu/sympa/arc/peirce-l/2021-01/msg00011.html), had he only gone a step or two farther, we might instead refer to it today as *synechistic *logic. JFS: The 1911 EGs are Peirce's last and best version. I agree, but only for the *practical *purpose of explaining and using EGs in accordance with classical logic. For the *scientific *purpose of exploring and understanding the theoretical underpinnings of EGs and/or extending their applicability to non-classical systems, Peirce's earlier writings about them are indispensable--including the Lowell Lectures and accompanying Syllabus as "The better exposition of 1903" (RL 376), R 490 (1906), RS 30 (c. 1906), and R 669 as the immediate predecessor of R 670 and RL 231. JFS: All earlier versions, their primitives, their rules of inference, and their semantics (endoporeutic) can be defined in terms of the 1911 version. I strongly disagree. In particular, the unsymmetrical relation of consequence *cannot *be properly defined in terms of the symmetrical relation of negation. "Now an unsymmetrical relation can never be expressed as a complex or special case of a symmetrical relation" (R 482:12, 1896-7). "The first relation of logic, that of antecedent and consequent, is unsymmetrical. Now an unsymmetrical relation cannot result from any combination of symmetrical relations alone" (NEM 3:821, 1905). It requires "a real movement of thought in the mind" that is completely absent from "a state of things that should consist in there not being an A without a B. For in such a state of things there would be no change at all" (R 300:49[48], 1908). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Thu, Jan 21, 2021 at 9:42 PM John F. Sowa <s...@bestweb.net> wrote: > Jon AS, List, > > For anyone who is not familiar with Peirce's 1911 EGs, see my introduction > to EGs, which is based on the 1911 version. The first 10 slides are > sufficient for an overview. The remaining slides show features of the 1911 > EGs that make a major advance over the logics of the 20th century: > http://jfsowa.com/talks/egintro.pdf > > The following comment shows why Peirce rejected R669 and replaced it with > R670 and L231: > > JAS> Peirce had a very good reason for not writing a third rule at the end > of R 669, and it was not because "he suddenly realized" something at that > moment in time and "abruptly" abandoned his previous train of thought. It > was simply because he had already stated the third rule a few paragraphs > earlier, and had explicitly pointed out that it is not an illative > permission; i.e., it is not a rule of inference. > > After reading that comment, I realized that Peirce's insight on 2 June > 1911 was that the adjective 'illative' is irrelevant and misleading for all > three permissions (rules of inference). The rules depend only on > negation. They do not depend on a "sign of illation", such as a scroll or > other symbol for if-then. > > In L231, Peirce called all three rules permissions (without the adjective > 'illative'). I believe that R669 is the *last* MS in which he wrote the > words 'illative' or 'illation'. I have not read all his extant MSS, but I > very strongly doubt that he would > continue using a word he had rejected. > > See slides 11 and 12 of egintro.pdf for an explanation in terms of the > 20th c logics. For the details about Peirce's five MSS that document his > development of the 1911 EGs and his rejection R669, see the attached file > eg1911x,pdf. > JAS> The final sentences [of R669] note the inadequacy of automated > reasoning to apply "the two illative permissions," since they require "a > living intelligence" (R 669:23-24[21-22], LoF 1:584). > > No. Modern theorem provers can use Peirce's rules (and other rules > derived from them) quite efficiently. For an overview of the issues, see > the slides in http://jfsowa.com/talks/ppe.pdf . For more detail, slide2 > of ppe.pdf has a link to a 76-page article in the Journal of Applied Logics, > > JAS> Unlike "Prolegomena" (CP 4.569), none of these manuscripts includes a > "4th Permission" expressing "the strange rule" that Peirce deemed to be > inconsistent with "the reality of some possibilities" as affirmed by his > pragmatism (CP 4.580-581, 1906), such that he was ultimately "sceptical as > to the universal validity of" it (RL 477:33[13], 1913). > > That gets into his modal logic, which he intended to replace with Delta > graphs. Any comment about modal issues in 1913 should be evaluated in > terms of the Delta graphs, for which we don't have any MSS. > > JAS> deriving negation from... a scroll with a blackened inner close... is > more analytical because it preserves the fundamental asymmetry of reasoning > and can thus be easily adapted for intuitionistic/triadic logic without > excluded middle, which "is universally true" (R 339:515[344r]). > > No. In R670, negation is a primitive. The scroll is nothing but a way of > drawing a nest of two negations without raising the pen. Since negation is > a primitive in R670, it would be absurd to derive negation from a nest of > two negations plus a pseudograph. > > In structure, motivation, and applications, intuitionistic and 3-valued > logic are totally different from each other and from any version of > Peirce's EGs. Oostra's choice of the scroll as a marker for intuitionistic > rules has no similarity to Peirce's use for any version of EGs. There is > much more to say about these issues, and I'll write another note about them. > > John
_ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
