John, List, All: Thanks for the opportunity to summarize and contrast our positions on these matters one more (hopefully last) time. Perhaps Francesco will have something to add.
JFS: But that does not explain why Peirce began R669 with the 1906 version of EGs and five days later switched to a new version for R670. As I have pointed out before, it is not a new *version*. It is merely a new *description*, deliberately simplified for the uninitiated. JFS: Two concepts with different names and verbal definitions are equivalent if they produce the same interpretations and responses at the two gates. As I have pointed out before, the scroll is vastly superior to cuts/ovals for analyzing the process of reasoning into its most basic and irreducible elements, which was Peirce's explicit purpose in inventing EG. Mohammed Shafiei's example of *ex falso quodlibet* demonstrates this conclusively. JFS: In MM_AVP.png (attached below), the only effect of the 1911 EGs is to replace the word "define" by "it is true that". As I have pointed out before, your "translation" in that image is incorrect. In the 1911 descriptions, a shaded area replaces a cut, which is a scroll with a blackened inner close shrunk to infinitesimal size. JFS: The conditional and any symbol that represents it remain just as iconic, and all proof procedures remain valid. As I have pointed out before, this is true only for *classical* logic. Moreover, nested cuts/ovals lack the continuity of the scroll that iconically represents the continuity between antecedent and consequent. JFS: But the 1911 EGs support a richer, more general set of logico-philosophical ideas that go beyond the 1906 ideas. As I have pointed out before, the 1911 description is "philosophically inaccurate" (Bellucci and Pietarinen). Among other things, it completely obscures Peirce's remarkably prescient anticipations of what we now know as intuitionistic logic. JFS: The shaded ovals for 1911 negations can be generalized to shaded regions in three dimensions or even 3D plus time. As I have pointed out before, the scroll can likewise be generalized to three dimensions or even 3D plus time. It only requires maintaining one point of intersection between its inner and outer closes. JFS: The words represent predicates or rhemes. As I have pointed out before, the words are names that describe general concepts. Along with the lines of identity that designate indefinite objects within the universe of discourse, they are *subjects *of the proposition being represented (not predicates) because they require collateral experience in order to be understood. JFS: The conditional is defined by two negations and a conjunction. As I have pointed out before, Peirce explicitly denies that a consequence is properly analyzed as a composite of two negations. The latter is static, leaving out the "real movement of thought in the mind" from antecedent to consequent. JFS: Based on your study of linguistics and related issues, what is your opinion about the following paragraph? As I have pointed out before, Peirce's classification of the sciences precludes grounding anything in logic on linguistics. Like psychology and every other special science, linguistics depends on logic for its principles, not the other way around. JFS: In this paragraph, Peirce ... fabricated a dubious explanation for the derivation in Figures 24 to 27 (copy attached in R699figs.png). As I have pointed out before, it is neither the first time nor the last time that Peirce says something similar. He does so many years earlier (CP 3.488, 1897), a few years earlier (RS 30:20-21[Copy T:14-15], c. 1906), and a few months later (RL 376, R 500:12, 1911 Dec 6). JFS: If he had reviewed this paragraph (on or about 3 June 1911), he would not have been satisfied. As I have pointed out before, it is inappropriate to ascribe such judgments to Peirce without explicit textual evidence. He never *repudiates *that paragraph, nor his derivation of negation from the implication of falsity/absurdity. JFS: L378 (Sept. 1911) and L376 (Dec. 1911) confirm the fact that R670 and L231 are a total rejection of R669 and the 1906 version of EGs on which it is based. As I have pointed out before, the only thing that Peirce rejects in those letters is his *description *of EG in "Prolegomena to an Apology for Pragmaticism." The 1911 *version *is still the 1906 *version*, but with more iconic shading in place of cuts or tinctures and the simplification of skipping the derivation of negation from the implication of falsity/absurdity. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Wed, Mar 10, 2021 at 8:40 PM John F. Sowa <[email protected]> wrote: > > Dear Francesco, Jon, and Dan. > > I put Dan Everett on the list because he is a linguist who recommended a > 600-page book on negation and is writing a book about Peirce. I'd like to > hear his comments about a paragraph in R669. > > FB> I must say that in the dispute I agree completely with Jon A. > Schmidt. He has supported his points with abundant textual evidence and > with several convincing exegetical arguments. > > If we were discussing Peirce's writings prior to 3 June 1911, I would > agree with you. But that does not explain why Peirce began R669 with the > 1906 version of EGs and five days later switched to a new version for R670. > > FB> What we dispute is whether [Peirce's] 1911 presentations of the > logical graphs show that he retracted one of his most stable > logico-philosophical ideas. > > Peirce's criterion for significant ideas: "The elements of every concept > enter into logical thought at the gate of perception and make their exit at > the gate of purposive action; and whatever cannot show its passports at > both those two gates is to be arrested as unauthorized by reason" (CP > 5.212). > > Note that this criterion says nothing about the words used to define or > explain the concept. Two concepts with different names and verbal > definitions are equivalent if they produce the same interpretations and > responses at the two gates. > > FB> What [Peirce] claimed is that implication ("If A then B") mirrors > inference; inference ("A, ergo B") is a transitive, anti-symmetrical > relation, and the only truth-functional operator that is also > anti-symmetrical and transitive is implication. > > On that issue, it's irrelevant whether the conditional is primitive or > defined. In MM_AVP.png (attached below), the only effect of the 1911 EGs > is to replace the word "define" by "it is true that". The conditional and > any symbol that represents it remain just as iconic, and all proof > procedures remain valid. > > But the 1911 EGs support a richer, more general set of > logico-philosophical ideas that go beyond the 1906 ideas. The shaded ovals > for 1911 negations can be generalized to shaded regions in three dimensions > or even 3D plus time. But the 1906 recto/verso semantics is limited to > 2D. On that issue, note what Peirce wrote in L231: "an algebraist like > Boole plainly thought in algebraic symbols; and so did I, until, at great > pains, I learned to think in diagrams, which is a much superior method. I > am convinced there is a far better one, capable of wonders; but the great > cost of the apparatus forbids my learning it. It consists in thinking in > stereoscopic moving pictures. Of course one might substitute the real > objects moving in solid space; and that might not be so very unreasonably > costly." (NEM 3:191) > > For evidence that Peirce's significant ideas are not affected by the > transition from R669 to R670, I recommend Ahti's 2011 article, "Existential > Graphs: What a Diagrammatic Logic of Cognition Might Look Like", History > and Philosophy of Logic, 32:3, 265-281. That article discusses a wide > range of philosophical ideas, including the quotation from NEM 3:191. But > it doesn't mention the idea of deriving negation from implication. On the > contrary, see page 14: "given two nested cuts, implication is ability to > continue a passage from the area of an outer cut area to the area of the > inner cut." > > FB quoting Frege> "By means of negation the hypothetical mode can thus be > reduced to conjunction and conjunction to the hypothetical mode. Looked at > from a logical standpoint both appear equally primitive. But since the > hypothetical mode is more closely connected with drawing inferences, it is > best to give it pride of place, and see it as the primitive form, reducing > conjunction to it." (Frege, Posthumous Writings, 1979, p. 200) > > But Frege assumed *both* negation and implication as primitives, and he > defined conjunction in terms of them. That is contrary to Peirce who > assumed that conjunction was so fundamental that he didn't assign a symbol > to it. Conjunction is implicit when two or more EGs are scribed in the > same area. > > Although Peirce never mentioned Frege, he did criticize Russell, who > adopted Frege's primitives for his Principles of Mathematics: "true in the > main and throughout, however, he betrays insufficient reflection on the > fundamental conceptions of the subject, with the primary difficulty... his > not having begun with a thorough examination of the elements". (Houghton > Library, Series I, no. 12. Notes Preparatory to a Criticism of Bertrand > Russell's Principles of Mathematics, 5 February 1912) > > That comment shows no sympathy for Frege's primitives. The tone is > milder, but the comments are consistent with the sharp criticisms in L378 > and L376 (copy below). > > I also recommend another article by Ahti: "Two papers on existential > graphs by Charles Peirce", Synthese, July 2014. The two "papers" actually > consist of some MSS that Ahti grouped in two chapters. > > Chapter 1, "Recent Developments of Existential Graphs and their > Consequences for Logic (MS 498, 499, 470, S-36, 1906)". In R498 and R499, > Peirce discussed a variety of ideas, which do not conflict with any version > of EGs. In R470, he presented the 1906 EGs with recto/verso semantics for > the cut. But he presented the conditional as a nest of two cuts. He did > not define a single cut in terms of a double cut plus a pseudograph. > > Chapter 2, "Assurance Through Reasoning (MS 669 & MS 670, 1911)." For this > "paper", Ahti placed R670 first, and treated it as an introduction to the > more detailed R669. He did not comment on any discrepancies between them. > > But on page 27 of R670, Peirce states "There are but three peculiar signs > that the Syntax of Existential Graphs absolutely requires. The first of > these is a sign of identity." On p. 28, "This way of asserting > identity... [furnishes] the second general sign required by the syntax of > existential graphs. This is the "Spot of Teridentity". On p. 29, "the > third indispensable peculiar sign of the Syntax of Existential Graphs... is > one that shall deny a Graph-instance, or scribed assertion... But that > Conditional Proposition just written may be expressed by the aid of a sign > of Negation in the form, 'That the Antecedent is true and the Consequent > not true, is not true'. On p. 31, "It is a help to shade the > oddly-enclosed areas and omit the lines that represent the cuts, as in Fig. > 11 [just shading], which is equivalent to Fig. 10 [drawn as a scroll with > no shading]." > > Peirce added two non-peculiar signs to the three peculiar signs: > "according to this syntax any single word is an assertion" (p. 27) which > may have zero or more pegs for attaching lines. Conjunction is another > non-peculiar sign, which is represented by drawing two or more EGs in the > same area. > > Altogether, the R670 syntax has five signs: peculiar (existence, > teridentity, and negation) and non-peculiar (words and conjunction). The > words represent predicates or rhemes. The conditional is defined by two > negations and a conjunction. > > These definitions, which preserve all the logical ideas, also preserve > philosophical ideas that are violated by the 1906 semantics. For > observation (phaneroscopy), the only logical operators that can be observed > are existence, conjunction and negation: any sensation is a sign that > something exists; any observation of a difference is a sign of a > conjunction (A and B) and a sign of negation (A is not B). From those three > operaters all others can be derived. > > Since Francesco and Jon claim that the following paragraph is significant, > I'd like to ask for Dan's opinion: Based on your study of linguistics and > related issues, what is your opinion about the following paragraph? Would > you consider it a convincing argument for adopting the conditional as > primitive and negation as derivative? > > From R669, p. 43: "The Cut came to be thought of because of the immense > frequency of occasions on which it was necessary to express the assertion > "If X be true, then every assertion is true". It was forced upon the > logician’s attention that a certain development of reasoning was possible > before, or as if before, the concept of falsity had ever been framed, or > any recognition of such a thing as a false assertion had ever taken place. > Probably every human being passes through such a grade of intellectual > life, which may be called the state of paradisiacal logic, when reasoning > takes place but when the idea of falsity, whether in assertion or in > inference, has never been recognized. But it will soon be recognized that > not every assertion is true; and that once recognized, as soon as one > notices that if a certain thing were true, every assertion would be true, > one at once rejects the antecedent that lead to that absurd consequence. > Now that conditional > proposition "If A is true, every proposition is true", is represented, in > the model of Fig. 24, "If A is true, C is true" by blackening the entire > inner close, as if there were no room, in reason, for any additional > consequence. This gives Fig. 25: "If > A be true whatever can be asserted is true", which is as much as to say > that "A is not true and the inner close being cut very small", we get, > first Fig. 26 and finally Fig. 27, in which the idea of flat falsity is > first matured." (R669, p. 43) > > My opinion: this paragraph is embarrassingly bad. For years, Peirce > derided the typical reasoning of metaphysicians who start with a conclusion > they claim is infallible and generate evidence that makes it seem > plausible. In this paragraph, Peirce is doing the same thing. He > fabricated a dubious explanation for the derivation in Figures 24 to 27 > (copy attached in R699figs.png). > > But Peirce knew he was fallible. If he had reviewed this paragraph (on or > about 3 June 1911), he would not have been satisfied. Five days later, he > wrote R670. On June 22, he began writing the more polished L231. > > In summary, the 1911 version discards a huge amount of irrelevant verbiage > (see the quotations below), But it's sufficiently general to go beyond two > dimensions (see http://jfsowa.com/talks/ppe.pdf ). That generalization > supports a wide rage of new logico-philosophical ideas without discarding > any significant ideas from the earlier versions. > > John > ____________________________________________________________________ > > L378 (Sept. 1911) and L376 (Dec. 1911) confirm the fact that R670 and L231 > are a total rejection of R669 and the 1906 version of EGs on which it is > based. In L378, Peirce wrote: "I use a diagrammatic syntax, which I > described very badly and at an intolerable length in the Monist of October > 1906." In L376, he was more explicit about the 1906 version: "For > although the system itself is marked by extreme simplicity, the description > fills 55 pages, and defines over a hundred technical terms applying to it. > The necessity for these was chiefly due to the lines called cuts which > simply appear in the present description as the boundaries of shadings, or > shaded parts of the sheet." >
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