John, List, All: Thanks for sharing the first part of your draft article.
JFS: As a result, they [Peirce and Frege] made a mistake in drawing a sharp distinction between logic as a theory and logic as a calculus. The fact that you happen to disagree with them does not entail that they "made a mistake," only that they had a different opinion. For Peirce, this "sharp distinction" is a fundamental aspect of his architectonic classification of the sciences. He situates "logic as a calculus" within mathematics (formal logic) as "the science which draws necessary conclusions," and he situates "logic as a theory" within the normative sciences (logic as semeiotic) as "the science of drawing conclusions" (CP 4.239-240, 1902). JFS: One of his [Peirce's] rare misconception was the claim that a system designed to be “as analytic as possible” could not be just as useful for calculation. Peirce's actual claim was that his *primary purpose* when developing both algebraic and graphical systems of logic was "not at all the construction of a calculus to aid the drawing of inferences," but rather "that the system devised for the investigation of logic should be as analytical as possible, breaking up inferences into the greatest possible number of steps, and exhibiting them under the most general categories possible" (CP 4.373, 1902). As a result, "in the construction of no algebra [nor EG] was the idea of making a calculus which would turn out conclusions by a regular routine other than a very secondary purpose" (CP 4.581, 1906). JFS: For the 1911 version of EGs, Peirce chose three logical primitives: existence, conjunction, and negation. These primitives, even without any derived rules, are far more efficient than Frege’s choice. Indeed, treating negation as if it were the third logical primitive results in a more efficient calculus for classical logic, as well as a simpler introduction of EG for the previously uninitiated such as the National Academy of Sciences (R 670, June 1911), J. H. Kehler (RL 231, June 1911), A. Robert (RL 378, September 1911), A. D. Risteen (RL 376, December 1911), and F. A. Woods (RL 477, October-November 1913). Nevertheless, Peirce recognized and affirmed repeatedly in his writings over the preceding decades that it is "philosophically inaccurate" (Bellucci and Pietarinen). From a strictly theoretical standpoint, the unsymmetrical relation of implication is the third logical primitive, and negation is a derived rule of inference where absurdity/falsity is the consequent. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Wed, Feb 17, 2021 at 11:55 PM John F. Sowa <s...@bestweb.net> wrote: > Peirce's Monist article of 1906 is a goldmine of ideas. Like a gold mine, > it has many nuggets of gold embedded in tons of rock and debris. It's > important to distinguish the gold from the dross. > > An unfinished draft of "Existential Graphs as a Calculus" is attached. > See below for the abstract. > > There are many other nuggets of gold that Peirce himself extracted in > later writings, and I'll write more about them later. > > John > ______________________________________________ > > Existential Graphs as a Calculus > > Abstract. Peirce and Frege were pioneers in the development of modern > logic. Frege (1879) deserves credit for the first publication of classical > first-order logic (FOL). But Peirce (1885) developed the algebraic > notation for first-order and higher-order logic. With a change of symbols > by Peano (1895), and some additions by Whitehead and Russell (1910), > Peirce’s algebraic notation became the foundation for the mainstream logics > of the 20th century (Putnam 1982). But as pioneers, Peirce and Frege > emphasized the theoretical issues. Neither of them could have foreseen the > wide range of applications of logic in the century that followed. As a > result, they made a mistake in drawing a sharp distinction between logic as > a theory and logic as a calculus. With derived rules of inference, there > is no conflict. A good version of logic can have a small theoretical core > and an open-ended variety of extensions that support efficient calculation. > > 1. Peirce’s misconception about a calculus > 2. Frege’s misconception about a calculus > 3. Using EGs as a calculus > 4. Choice of logical primitives >
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