Jerry, List: JLRC: The classical logic of mathematical reasoning (symbolized by five signs - negation, conjunction, disjunction, material conditional, and bi-conditional.
Actually, Peirce points out that only two signs are needed as primitives, with the others being derived from them. CSP: Out of the conceptions of non-relative deductive logic, such as consequence, coexistence or composition, aggregation, incompossibility, negation, etc., it is only necessary to select two, and almost any two at that, to have the material needed for defining the others. What ones are to be selected is a question the decision of which transcends the function of this branch of logic. (CP 2.379, 1902) For example, in the Alpha part of Existential Graphs for propositional logic, the simplest approach is to select the two primitives as juxtaposition for conjunction (coexistence) and shading for negation* such that disjunction is then defined as multiple unshaded areas within a shaded area, material conditional (consequence) as one unshaded area within a shaded area (scroll), and bi-conditional as juxtaposed scrolls with the antecedent and consequent reversed. The Beta part for first-order predicate logic adds one more primitive, the line of identity for existential quantification such that universal quantification is then defined as a line of identity whose outermost part is within a shaded area. *As I have discussed on the List many times before, although this choice is practically more efficient and easier to explain, Peirce suggests on several occasions that it is philosophically more accurate to select the scroll for material implication as the second primitive such that negation is then defined as a scroll with a blackened inner close shrunk to infinitesimal size, signifying that *every *proposition is true if the antecedent is true (CP 4.454-456, 1903; CP 4.564n, c. 1906; R 300:[47-51], 1908; R 669:[16-18], 1911). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Thu, Jan 11, 2024 at 12:52 PM Jerry LR Chandler < jerry_lr_chand...@icloud.com> wrote: > On Jan 11, 2024, at 11:28 AM, Edwina Taborsky <edwina.tabor...@gmail.com> > wrote: > > But you already know this > > Edwinia: > > If I understood the meaning of the “triadic relations”, I would not waste > my time attempting to frame precise questions and intensely analyzing the > grammatical structures of your and other responses. > > Mathematical reasoning is grounded in set theory - the relation between > *ordered > pair*s. > > The classical logic of mathematical reasoning (symbolized by five signs - > negation, conjunction, disjunction, material conditional, and > bi-conditional. > > These signs are often interpreted in terms of the Aristotelian > syllogisms. Which in turn, are related to sentences and sentence > grammars. For a discussion of Peircian *“tokens and types” *from a > categorical perspective, see the recent text by Ursula Skadowski, Logic - > Language - Ontology. 2022. > > Or, asserted in similar terms, is the meaning of a triadic relation > constrained to multi-valued logics? > > My interpretation of the posts by the John / Jon / Robert posts is that > the classical logic for deduction preserves the truths of propositions of > molecular sentences. (Note, it was not necessary to invoke either Robert > Rosen’s writings on the philosophy of science or thermodynamics or entropy > or dogmas or…. Just seeking a scientifically useful meaning for my > research. > > Cheers > Jerry >
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