List: Jon, John: Obviously, both of you are struggling with what I am seeking to communicate. Perhaps the following paragraph will open your minds, your cognitive capabilities for understanding, to navigating a semantic “symbol space” more like a biological organism (the sonar system of a bat) than a machine (an oil tanker with massive momentum). I think that cognitive triadic relations are “real” - mens re. I continue to struggle with how CSP navigated the symbolic channels of the quantitative chemical notational system into a theory of logic. This is not merely a question of semantics or classical symbolic logic.
According to some, Schelling had a powerful influence on CSP. "Was Schelling’s “Identitatssystem” a contributing factor to organizing the trichotomies?” is a rhetorical question worthy of significant perusal . Cheers Jerry Research Professor (Retired) Krasnow Institute for Advanced Study George Mason University From: Daniel Whistler. Symbolic Language ‘Symbol’ is one of the most polysemic words in theoretical discourse. Its connotations can be logico-mathematical, Lacanian, Peircean, anthropo- logical, liturgical, or romantic—and more often than not the symbol plays on a mixture of more than one of these discursive frameworks. What is more, the symbol takes on divergent, often opposed forms depending on the conno- tations one has in mind: the slippage and deferral constitutive of the Lacanian symbolic realm stand opposed to the unity of meaning and being in ‘the romantic symbol’. Nevertheless, the following is not a Begriffsgeschichte of the symbol, but a study of its fate in the hands of F. W. J. Schelling alone. What matters is not how we understand the term ‘symbol’ today, but how Schelling did: the contexts on which he drew and the conversations into which he entered when forming his theory of the symbol. In what follows, therefore, I will be almost entirely concerned with ‘the romantic symbol’ which emerged in German aesthetics and philosophy at the turn of the nineteenth century— even if one of my aims in what follows is to problematize the very existence of one, monolithic ‘romantic’ symbol. Part I of this book is devoted to the context in which Schelling’s construc- tion of symbolic language takes place. The present chapter considers theories of the symbol written during the Goethezeit, prior to Schelling’s own. I initially consider them historically, then from a synchronic viewpoint, examining in particular the essential properties of a symbol and the typical ways in which it was interpreted. As always, it is the interplay between ‘the romantic symbol’ and the Schellingian symbol in which I am interested: to what extent is Schelling to be positioned unproblematically in a genealogy of ‘the romantic symbol’ and to what extent does his theory in fact react against such an interpretation of the symbol? > On Jan 11, 2024, at 6:16 PM, John F Sowa <s...@bestweb.net> wrote: > > Jon, Jerry, List, > > We had discussed this issue many times before. R 669 was an attempt by > Peirce to relate all the versions of EGs he had written, published, and toyed > with. The result (R 669) was a hodge-podge that had many ad hoc > constructions that Peirce was unable to justify by any convincing proof. He > knew that it was bad. > > In R 670, he began to sketch out a new version, and a few weeks later he > produced his clearest, most precise, and most elegant foundation for EGs. > And he confirmed that version as his final choice in his last major letter in > 2013. > > Peirce's three primitives are conjunction (AND), negation (NOT), and the > existential quantifier (line of identity). These three primitives with > Peirce's 1911 rules of inference are so general and powerful, that they unify > and simplify Gerhard Gentzen's two systems -- clause form and natural > deduction. > > As a result an unsolved research problem about the relationship between the > two systems (stated in the 1970s) was finally solved by a simple proof when > translated to Peirce's 1911 notation and rules of inference. That is > conclusive evidence beyond any shadow of a doubt that Peirce's 1911 system is > one of his most brilliant achievements. > > I'll send another note with all the references. > > John > > > From: "Jon Alan Schmidt" <jonalanschm...@gmail.com> > Sent: 1/11/24 6:13 PM > To: Peirce-L <peirce-l@list.iupui.edu> > Subject: Re: [PEIRCE-L] Categorizations of triadic Relationships (Was Re: > Graphical Representations of the Sign by Peirce) > > 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 > > <http://www.linkedin.com/in/JonAlanSchmidt>www.LinkedIn.com/in/JonAlanSchmidt > <http://www.linkedin.com/in/JonAlanSchmidt> / twitter.com/JonAlanSchmidt > <http://twitter.com/JonAlanSchmidt> > On Thu, Jan 11, 2024 at 12:52 PM Jerry LR Chandler > <jerry_lr_chand...@icloud.com <mailto:jerry_lr_chand...@icloud.com>> wrote: >> On Jan 11, 2024, at 11:28 AM, Edwina Taborsky <edwina.tabor...@gmail.com >> <mailto: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 pairs. > > 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 > _ _ _ _ _ _ _ _ _ _ > ARISBE: THE PEIRCE GATEWAY is now at > https://cspeirce.com and, just as well, at > https://www.cspeirce.com . It'll take a while to repair / update all the > links! > ► 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 UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in > the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . > ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and > co-managed by him and Ben Udell.
_ _ _ _ _ _ _ _ _ _ ARISBE: THE PEIRCE GATEWAY is now at https://cspeirce.com and, just as well, at https://www.cspeirce.com . It'll take a while to repair / update all the links! ► 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 UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
