Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
Jon: On review, this comment is of possible interest to a purist! > On Feb 27, 2024, at 12:26 PM, Jon Alan Schmidt > wrote: > > JAS: Every explicitly scribed EG is a replica (instance), a sinsign (token) > of a peculiar kind that embodies a legisign (type). > > JLRC: Frankly, I fail to find a connection between this stance regarding the > existential graphs and the prior development of the metaphysics of substance > of 1868. This reading of token and type is novel. > > Peirce does not introduce the terminology of qualisign/sinsign/legisign and > tone/token/type until 1903 and 1906, respectively, so I am puzzled by your > reference to something from nearly four decades earlier. In any case, there > is nothing novel about this reading, it is a well-known aspect of his > speculative grammar within the normative science of logic as semeiotic. The 1868 notions from metaphysics remain foundational today. History has not not changed these foundational arguments and the organization of these semes and semantics. 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.
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
Jon, List, I don't have time to respond right now. But there are two points that are true for every version of modal logic from Aristotle to the Scholastics to Peirce and to the latest and greatest versions of today: 1. For every version of modal logic, there is some reason WHY certain worlds (or contexts within a world) are possible or necessary or not. 2. The postulates or whatever statements are asserted about that world add that additional information. There is more to say, but those two statements are true. Peirce said a great deal more in many ways about many kinds of possibilities in his many years of MSS, publications, reports, etc. There is no need for him to use the word 'modal' in those discussions. That is implicit. In fact, every branch of science and engineering is about possible interpretations (science) and possible designs (engineering). Every thought about what to do when you or Peirce or anybody else gets up in the morning is a thought about the possible world before you or them. CP has 1072 occurrences of the word 'possible'. Every such sentence is a sentence in modal logic. Any version of modal logic that is adequate for supporting ordinary English must be able to represent all of them. That was the goal for the IKL logic. I believe that was the goal for Peirce's Delta graphs: support the logic necessary for pragmaticism. That implies every version of science, including all the practical sciences -- and daily life. A proof of pragmaticism was the primary goal of Peirce's final decade, and everything he wrote must be evaluated according to its utility in supporting it. John _ _ _ _ _ _ _ _ _ _ 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.
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
John, List: JFS: The first is that all modern versions of modal logic after C. I. Lewis (including those based on post-1970 methods) are consistent with or variations of one or more of the versions specified by Lewis. Indeed, Lewis specified *S1*-*S5* in 1932, of which only *S4* and *S5* are normal modal logics that include distributive axiom K, which is named for Kripke. Feys specified *T* in 1937 by subtracting axiom 4 from *S4*, and Von Wright specified *M* in 1951, which was later proved to be equivalent to *T*. Lemmon offered simplified specifications for *S1*-*S5 *and *T* in 1957, along with a new system *S0.5* that matches *T* except that instead of all theorems being necessarily true, only tautologies are necessarily true. *B* is named for Brouwer and is an alternative to *S4* since both contain *T* and are contained in *S5*, but neither contains the other. Pollock specified *P* (my suggested name) in 1967, which matches *S0.5* and *T* except that iterated modalities are prohibited. JFS: But the papers of Delta graphs can represent more information about each world, including the reasons why it happens to be possible, actual, necessary, or impossible. ... The specifications about papers in L376 would allow a tree structure of papers. Again, the only purpose that Peirce states in R L436 for needing to add a Delta part to EGs is "in order to deal with modals," which he consistently defines elsewhere as propositions involving possibility or necessity/certainty. There is no evidence in the 19 extant pages of R L436 (or elsewhere) that he expects Delta EGs to address other kinds of modality, incorporate any kind of metalanguage, or involve "a tree structure." Peirce also does not say nor imply in R L436 that the "many papers" are unique to Delta. In fact, as described there, they are equally applicable to Alpha, Beta, and Gamma. We know this because he discusses in some earlier writings the idea that an individual page represents only a *portion *of the much larger sheet of assertion or phemic sheet, namely, the part that "is before the common attention" of the utterer and interpreter at any given time. CSP: Two parties are, in our make-believe, feigned to be concerned in the scribing of graphs; the one called the Graphist, the other the interpreter. Namely, although the sheet that is actually employed may be quite small, we make believe that the so-called sheet of assertion is only a particular region, or area, of an immense surface; namely, the former is that part of the latter that falls within the field of view of the interpreter. Upon the great surface the Graphist alone has the power to scribe any graph; while he scribes what he sees fit. The interpreter, for his part, has the power, with more or less effort, to move the graph-instances about as he pleases, so long as he keeps them separate from one another, so that no two shall touch. In particular, he can move such ones as he likes and as many as he likes into his field of view, the sheet of assertion; or he can move them away. We further conceive that this feigned sensible state of things is the icon or emblem of a mental state of things. Namely, the immense surface with the graphs scribed upon it is the image of the interpreter’s experience, while the sheet of assertion, his field of view is the image of his field of attention. His experience is forced upon him, while he attends to what he pleases, if he puts forth sufficient effort. (R 280, c. 1905) CSP: Moreover, the Phemic Sheet iconizes the Universe of Discourse, since it more immediately represents a field of Thought, or Mental Experience, which is itself directed to the Universe of Discourse, and considered as a sign, denotes that Universe. Moreover, it [is because it must be understood] *as *being directed to that Universe, that it is iconized by the Phemic Sheet. So, on the principle that logicians call "the *Nota notae*" that the sign of anything, X, is itself a sign of the very same X, the Phemic Sheet, in representing the field of attention, represents the general object of that attention, the Universe of Discourse. This being the case, the continuity of the Phemic Sheet in those places, where, nothing being scribed, no *particular *attention is paid, is the most appropriate Icon possible of the continuity of the Universe of Discourse--where it only receives *general *attention as that Universe--that is to say of the continuity in experiential appearance of the Universe, relatively to any objects represented as belonging to it. (CP 4.561n, 1908) In the complete absence of any exact quotations from Peirce spelling out what (if anything) he had in mind for Delta EGs *beyond *dealing with modals, any proposed candidate going farther than that can only be offered as a hypothesis, not treated as a definitive specification. I am still wondering exactly how yours would represent the five modal propositions that he wrote in his Logic Notebook, if not exactly as he scribed their
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
Jon, There are several points that must be considered. The first is that all modern versions of modal logic after C. I. Lewis (including those based on post-1970 methods) are consistent with or variations of one or more of the versions specified by Lewis). That includes the versions of modal logic supported by the IKL logic of 2006. Further qualifiers such as wishing, hoping, fearing, specified in Holy Scriptures. . . may be ADDED to the specifications that determine possibility, actuality, or necessity. Second, Lewis was inspired by Peirce's 1903 specifications, and no one knows how many other MSS Lewis may have read. But Lewis adopted the much more readable basic operators, represented by □ and ◇. For readability, they correspond to the words 'necessary' and 'possible' in English or their equivalents in other languages. Third, all of Peirce's 1903 combinations can be represented by combinations of those two symbols and negation. But the papers of Delta graphs can represent more information about each world, including the reasons why it happens to be possible, actual, necessary, or impossible. That is also true of the worlds specified by Hintikka, Dunn, IKL, and others. The specifications of those worlds can also add further information beyond just those two operators plus negation. Fourth, more issues of modality related to Peirce and modern variations were discussed at a workshop in Bogota hosted by invitation of Zalamea. Some of the presentations were published in the Journal of Applied Logics 5:5, 2018. http://www.collegepublications.co.uk/downloads/ifcolog00025.pdf . Others in the Journal Zalamea edited, Cuadernos de Sistemática Peirceana 8, 2016. https://ucaldas.academia.edu/CuadernosSistem%C3%A1ticaPeirceana . (Although this version is dated 2016, it was delayed by late submissions and editing until 2019.) Fifth, Risteen's background was significant. He was a former student of Peirce's at Johns Hopkins, and he was a paid assistant to Peirce for definitions in the Century Dictionary from S to Z. His most important contribution (at least for Delta graphs) was his note about Cayley's mathematical trees for the dictionary entry and in the discussions with Peirce in December 1911. It would have been wonderful to have a YouTube of their discussions on 3 Dec. 1911. The specifications about papers in L376 would allow a tree structure of papers. Risteen's knowledge of mathematical trees is a likely reason why Peirce had invited him to visit in December and why he was writing that letter to him shortly after the visit. And note the very strange coincidence that occurred shortly after Peirce began the letter L376: Juliette had washed and scrubbed the floor in December after a visitor had left. There were papers on the floor. Peirce slipped on the floor in an unusual fall that caused the kind of injury that occurs in a twisting motion. And the injury took six months to heal. Scientists, engineers, and crime investigators do not believe in strange coincidences that involve two or more unusual causes. They search for a hidden connection. John From: "Jon Alan Schmidt" List: As I continue contemplating my updated candidate for Delta EGs (see earlier posts below), I am finding that, in conjunction with the laws and facts semantics (LFS) developed by Dunn and Goble, it is very helpful for explicating the effects of adding various modal axioms to classical logic. For example, the distribution axiom K = □(p → q) → (□p → □q) that is included in all so-called "normal" modal logics is illustrated by the fact that if p → q is on every sheet for a possible state of things (PST) and p is also on every PST sheet, then q is likewise on every PST sheet or can be derived on any PST sheet where it is initially missing. As I have mentioned before, other axioms assign different properties of the binary alternativeness/accessibility relation (AR) between the actual state of things (AST) and any PSTs, as well as the latter and their higher-order PSTs when there are iterated modalities. - Serial, axiom D = □p → ◇p, or ◇⊤; every law-graph on the AST sheet is a fact-graph on at least one PST sheet, and any graph that can be derived from the blank on the AST sheet can also be derived from the blank on at least one PST sheet. - Reflexive, axiom T = □p → p, or p → ◇p; every law-graph on the AST sheet is also a fact-graph on the AST sheet, and every fact-graph on the AST sheet is a fact-graph on at least one PST sheet. - Symmetric, axiom B = ◇□p → p, or p → □◇p; every law-graph on any PST sheet is a fact-graph on the AST sheet, and every fact-graph on the AST sheet is a fact-graph on at least one second-order PST sheet for every first-order PST sheet. - Transitive, axiom 4 = □p → □□p, or ◇◇p → ◇p; every law-graph on the AST sheet is a law-graph on every PST sheet, and every fact-graph on a second-order
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
List: As I continue contemplating my updated candidate for Delta EGs (see earlier posts below), I am finding that, in conjunction with the laws and facts semantics (LFS) developed by Dunn and Goble, it is very helpful for explicating the effects of adding various modal axioms to classical logic. For example, the distribution axiom K = □(*p* → *q*) → (□*p* → □*q*) that is included in all so-called "normal" modal logics is illustrated by the fact that if *p* → *q* is on every sheet for a possible state of things (PST) and *p* is also on every PST sheet, then *q* is likewise on every PST sheet or can be derived on any PST sheet where it is initially missing. As I have mentioned before, other axioms assign different properties of the binary alternativeness/accessibility relation (AR) between the actual state of things (AST) and any PSTs, as well as the latter and their higher-order PSTs when there are iterated modalities. - Serial, axiom D = □*p* → ◇*p*, or ◇⊤; every law-graph on the AST sheet is a fact-graph on at least one PST sheet, and any graph that can be derived from the blank on the AST sheet can also be derived from the blank on at least one PST sheet. - Reflexive, axiom T = □*p* → *p*, or *p* → ◇*p*; every law-graph on the AST sheet is also a fact-graph on the AST sheet, and every fact-graph on the AST sheet is a fact-graph on at least one PST sheet. - Symmetric, axiom B = ◇□*p* → *p*, or *p* → □◇*p*; every law-graph on any PST sheet is a fact-graph on the AST sheet, and every fact-graph on the AST sheet is a fact-graph on at least one second-order PST sheet for every first-order PST sheet. - Transitive, axiom 4 = □*p* → □□*p*, or ◇◇*p* → ◇*p*; every law-graph on the AST sheet is a law-graph on every PST sheet, and every fact-graph on a second-order PST sheet is a fact-graph on at least one first-order PST sheet. - Euclidean, axiom 5 = ◇□*p* → □*p*, or ◇*p* → □◇*p*; every law-graph on a PST sheet is a law-graph on the AST sheet, and every fact-graph on a PST sheet is a fact-graph on at least one second-order PST sheet for every first-order PST sheet. LFS effectively stipulates that the AR is serial because every law-graph on the AST sheet is a fact-graph on *every* PST sheet--its basic principle is that possibility is *defined* as consistency with the laws of the AST--and any classical tautology can be derived from the blank on *every *sheet. The AR properties and their corresponding axioms are then combined in different ways for different formal systems--serial for *D* (deontic logic), reflexive for *T* (or *P* with no iterated modalities), reflexive and symmetric for *B*, reflexive and transitive for *S4*, or reflexive and euclidean for *S5*. Any relation that is reflexive is also serial, while any relation that is reflexive and euclidean is also symmetric and transitive, and therefore an equivalence. As a result, in *S5*, every law-graph on the AST sheet is likewise a law-graph on every PST sheet, every second-order PST sheet, and vice-versa--i.e., every PST of any order has the very same laws as the AST. On the other hand, in *S4*, every law-graph on the AST sheet is likewise a law-graph on every PST sheet and every second-order PST sheet, but there might be *additional* law-graphs on those PST sheets--the set of relevant laws never *shrinks *when going to a higher-order PST, but it can *grow*. Applied to temporal logic, this is reminiscent of Peirce's hyperbolic cosmology in accordance with synechism. CSP: At present, the course of events is approximately determined by law. In the past that approximation was less perfect; in the future it will be more perfect. The tendency to obey laws has always been and always will be growing. We look back toward a point in the infinitely distant past when there was no law but mere indeterminacy; we look forward to a point in the infinitely distant future when there will be no indeterminacy or chance but a complete reign of law. But at any assignable date in the past, however early, there was already some tendency toward uniformity; and at any assignable date in the future there will be some slight aberrancy from law. (CP 1.409, EP 1:277, 1887-8) CSP: The state of things in the infinite past is chaos, tohu bohu, the nothingness of which consists in the total absence of regularity. The state of things in the infinite future is death, the nothingness of which consists in the complete triumph of law and absence of all spontaneity. Between these, we have on *our* side a state of things in which there is some absolute spontaneity counter to all law, and some degree of conformity to law, which is constantly on the increase owing to the growth of *habit*. (CP 8.317, 1891) In other words, the universe is constantly proceeding from a PST with only facts (no laws) toward a PST with only laws (no facts), while the AST always has *both* facts and laws. Regards, Jon On Thu, Feb 29, 2024 at 12:50 PM Jon
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
John, Some observations: For any theory of any kind with any logic of any kind, axioms are always stated in an if-then form. The if-part (shaded) states the condition, and the then part states the conclusion. Even definitions are stated as if-then statements in EGs. For example: "If x=y and y=z, then x=z." "Every triangle has three sides" is equivalent to "If x is a triangle, x has three sides." In that example, the proposition (pheme) about equality is an axiom, since it must be true of every possible world. But the pheme about triangles is a postulate that is true in geometry, but it might not be a postulate in some other possible world. The distinction between axioms and postulates is one that Peirce adopted from Euclid, but modern logicians use the word 'axiom' for the starting assumptions of any theory. They rarely use the word 'postulate. After re-reading Don Roberts' chapter on Gamma graphs (which I hadn't read for years), I realize that there is no conflict between that chapter and his writings about Delta graphs in L376. And L376 is completely consistent with the IKL logic of 2006. But IKL has some features that go beyond L376. Anything stated in Delta graphs may be mapped to IKL, but some IKL statements cannot be mapped to Delta graphs. Furthermore, what Peirce wrote about Delta graphs in L376 is consistent with his 1903 version of modal logic in every possible world. But the "papers" of L376 allow the "postulates" in the margins to state additional information about the nested graphs. For example that the nested graphs, may be wished, hoped, feared, imagined, or occurring at some time in the past, present, future in the real word or in heaven, hell, Wonderland, or the Looking Glass. Wonderland, for example, would be a possible world that could not be actualized -- as Peirce said in CP 8.192, stated below. John From: "Jon Alan Schmidt" List: I need to amend my previous post explaining my updated candidate for Delta EGs to "deal with modals" (see underline/strikethrough below). It still combines the graphs scribed in R 339:[340r] for representing the actual state of things (AST) with the "many papers" concept in R L376 for representing different possible states of things (PST) and the "red pencil" improvement in R 514 for distinguishing PST sheets with shaded margins from the AST sheet that lacks this feature. However, it is not the case that a PST sheet has its law-graphs in its shaded margin and its fact-graphs in its unshaded area; in fact, there is no requirement for any particular graphs to be in the margin of a PST sheet--the implied antecedent, from which all the EGs in the unshaded area follow necessarily, is "this PST is actualized." Instead, just like the AST, law-graphs on a PST are those where the outermost portion of the outermost line of compossibility (LoC) is in a shaded area, and fact-graphs are those with no LoCs. Moreover, every graph on the AST with at least one LoC is reproduced on PST sheets, except with its outermost LoC removed. If that LoC is shaded, then the graph without it appears on every PST sheet; and if that LoC is unshaded, then the graph without it appears on at least one PST sheet. With these corrections and clarifications, Delta EGs can still be used to implement any of the standard formal systems of modal logic, with iterated modalities requiring another set of PST sheets for every first-order PST sheet that includes any graphs with LoCs. However, according to Peirce, pragmaticism considers the only real possibilities to be facts in PSTs that are directly alternative/accessible to the AST. CSP: That a possibility which should never be actualized, (in the sense of having a bearing upon conduct that might conceivably be contemplated,) would be a nullity is a form of stating the principle of pragmaticism. One obvious consequence is that the potential, or really possible, must always refer to the actual. The possible is what can become actual. A possibility which could not be actualized would be absurd, of course. (R 288:[134-135], 1905) This suggests dispensing with iterated modalities, such that letters on the AST sheet are never attached to more than one LoC, no LoCs appear on any PST sheets, and no second-order PST sheets are needed. An additional benefit is that the graphs on PST sheets could then be scribed more informatively by using lines of identity and attached names as in Beta, instead of just letters as in Alpha, as long as there is a way to match up the AST letters with the PST graphs. Peirce further states that pragmaticism requires every law-proposition for the AST to be a subjunctive conditional whose antecedent is a real possibility; formally, □(p → q) ∧ ◇p. CSP: But what the answer to the pragmatist's self-question [how could law ever reasonably affect human conduct?] does require is that the law should be a truth
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
List: I need to amend my previous post explaining my updated candidate for Delta EGs to "deal with modals" (see underline/strikethrough below). It still combines the graphs scribed in R 339:[340r] for representing the actual state of things (AST) with the "many papers" concept in R L376 for representing different possible states of things (PST) and the "red pencil" improvement in R 514 for distinguishing PST sheets with shaded margins from the AST sheet that lacks this feature. However, it is *not *the case that a PST sheet has its law-graphs in its shaded margin and its fact-graphs in its unshaded area; in fact, there is no requirement for any particular graphs to be in the margin of a PST sheet--the implied antecedent, from which all the EGs in the unshaded area follow necessarily, is "this PST is actualized." Instead, just like the AST, law-graphs on a PST are those where the outermost portion of the outermost line of compossibility (LoC) is in a shaded area, and fact-graphs are those with no LoCs. Moreover, every graph on the AST with at least one LoC is reproduced on PST sheets, except with its outermost LoC removed. If that LoC is shaded, then the graph without it appears on every PST sheet; and if that LoC is unshaded, then the graph without it appears on at least one PST sheet. With these corrections and clarifications, Delta EGs can still be used to implement any of the standard formal systems of modal logic, with iterated modalities requiring another set of PST sheets for every first-order PST sheet that includes any graphs with LoCs. However, according to Peirce, pragmaticism considers the only *real* possibilities to be facts in PSTs that are *directly* alternative/accessible to the AST. CSP: That a possibility which *should* never be actualized, (in the sense of having a bearing upon conduct that might conceivably be contemplated,) would be a nullity is a form of stating the principle of pragmaticism. One obvious consequence is that the potential, or really possible, must always *refer* to the actual. The possible is what *can become actual*. A possibility which could not be actualized would be absurd, of course. (R 288:[134-135], 1905) This suggests dispensing with iterated modalities, such that letters on the AST sheet are never attached to more than one LoC, no LoCs appear on any PST sheets, and no second-order PST sheets are needed. An additional benefit is that the graphs on PST sheets could then be scribed more informatively by using lines of identity and attached names as in Beta, instead of just letters as in Alpha, as long as there is a way to match up the AST letters with the PST graphs. Peirce further states that pragmaticism requires every law-proposition for the AST to be a *subjunctive* conditional whose antecedent is a real possibility; formally, □(*p* → *q*) ∧ ◇*p*. CSP: But what the answer to the pragmatist's self-question [how could law ever reasonably affect human conduct?] does require is that the law should be a truth expressible as a conditional proposition whose antecedent and consequent express experiences *in a future tense*, and further, that, as long as the law retains the character of a law, there should be possible occasions in an indefinite future when events of the kind described in the antecedent may come to pass. Such, then, *ought* to be our conception of law, whether it has been so or not. (CP 8.192, 1905) The upshot is that, other than the tautologies of classical logic, every law-proposition for the AST is a *strict* implication, □(*p* → *q*); its antecedent, *p*, is a fact-proposition in at least one PST; and the corresponding *material* implication, *p* → *q*, is a fact-proposition in *every* PST.* Peirce himself anticipates this by suggesting that a strict implication is logically equivalent to a multitude of material implications. CSP: An ordinary Philonian conditional proposition [strict implication], having a range of possibility and asserting that "If *A* is true, *B* is true,'' that is, that in every possible state of things in which *A* is true, *B* is likewise true, may be regarded as a simultaneous assertion of a multitude of propositions each asserting that if [there is] a single state of things in which *A* is true, *B* is true [in that state of things], each therefore being a *consequentia de inesse* [material implication]. (NEM 4:278, c. 1895) The specific formal system that is implemented with these restrictions is one first suggested by William T. Parry in 1953 and fully specified by John L. Pollock in 1967 (https://www.jstor.org/stable/2270778). It includes modal axioms K and T, as well as all the theorems of standard systems *S1*- *S5*, *T*, and *B* that have no iterated modalities, which they have in common--as Pollock notes, these constitute "the core of theorems that everyone accepts" (p. 363). Again, the only *absolute* necessities are the tautologies of classical logic; all other law-propositions for the AST are
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
Jon, List > On Feb 23, 2024, at 5:22 PM, John F Sowa wrote: > > > JLRC> First, the question of modern modal symbolic logic is remote from > probability theory and even remoter from the Peircian notion of “qualisign, > sinsign, legisign” > > That is true of Peirce's modal logic of 1903, which was the mainstream of > modal logic for most of the 20th C and which is still taught in introductory > courses. But Peirce became very interested in probability theory, as shown > in his writings in the Logic Notebook. The that-operator from 1898 and the > "papers" of June and December 1911 can support the kind of metalanguage that > is widely used today for computational and theoretical methods for either or > both possibilities and probabilities. > I respectably disagree with breadth and depth of this justification of the meanings to be associated with the sign-generating terms, qualisign, sin-sign and legisign. These three terms all refer to the metaphysics of Being paper of 1868, don’t they? The concept of a sign is intrinsically singular, yet any real object in the world offers many many necessary and possible signs. Thus, the need for a concept of “sin-sign” as a singular entity. Corresponding to this need is an exact name for the object under inquiry, that is, a legisign. The quali-sign determines the attributes of the sin-sign and the name for the legisign, does it not? My point is that these three terms point to the metaphysical nature of the “Being" of the subject of a sentence that specifies an existent object. These terms are necessarily deterministic in form and character in order to specify the identity of the object. Please note that this interpretation of the semiology of the CSP’s semantics also addresses the distinction between the copulative grammar of sentences from the pseudo-first order logic of modern probability theories, discrete or continuous. The fact that the “computational and theoretical methods” used today are based on probability theories lacks relevancy to the situational logic developed by CSP. The terms of the trichotomy were defined by CSP to ascribe meaning to the metaphysical “being” of objects with precision, not to merely describe a convenient possibility for engineering purposes. 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.
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
List: The sole reason that Peirce expresses in R L376 (1911 Dec 6) for needing to add a Delta part to EGs is "in order to deal with modals," which he explicitly and repeatedly defines elsewhere as propositions involving possibility or necessity. As I spell out in detail in my forthcoming paper, "Peirce and Modal Logic: Delta Existential Graphs and Pragmaticism," the five modal EGs scribed in R 339:[340r] (1909 Jan 7) can serve as a basis for implementing various formal systems of modal logic. The sheet represents the actual state of things (AST), heavy lines of compossibility (LoCs) represent possible states of things (PSTs), letters attached to LoCs denote atomic non-modal propositions that would be true or false in those PSTs, and new transformation rules for LoCs correspond to various modal axioms for reasoning *about *those PSTs. A new wrinkle occurred to me yesterday, thanks to my exchanges with John Sowa. Each PST has its own separate sheet, and together, the AST sheet and all the PST sheets--potentially, an infinite number of them--comprise the "many papers" that Peirce mentions in R L376. In accordance with the Dunn/Goble semantics using Hintikka's model sets as described in my other forthcoming paper, "Laws and Facts Semantics for Modal Logic," the AST and every PST has both *laws *and *facts*, with the binary alternativeness/accessibility relation (AR) defined as requiring every law-proposition for the AST to be a fact-proposition in every PST. On the AST sheet, law-graphs have oddly enclosed LoCs and fact-graphs have no LoCs. Each PST sheet has a red line just inside its edges as proposed in R 514 (1909)--or rather, as I suggested yesterday, a shaded margin with its law-graphs, the remaining unshaded area with its fact-graphs, and (mostly) the usual transformation rules for reasoning *within* that PST. Each modal axiom assigns a specific property to the AR, which in the Dunn/Goble semantics dictates containment relations between the different sets of law-propositions and fact-propositions. For example, Peirce's erasure/insertion rule for broken cuts in Gamma EGs implements axiom T, making the AR *reflexive*--every law-graph on the AST sheet or any PST sheet is also a fact-graph on that same sheet. This is consistent with the usual permission for iterating graphs from the shaded margin of a PST sheet to its unshaded area, so for formal systems where the AR is *not *reflexive--such as deontic logic, where possibility and necessity are replaced with permission and obligation--this specific transformation is prohibited on PST sheets. Another example is axiom 4, which makes the AR *transitive*--every law-graph on the AST sheet is also a law-graph on every PST sheet, so every graph with an oddly enclosed LoC on the AST sheet is reproduced without that LoC in the shaded margin of every PST sheet. With this specification, Peirce's five modal propositions in R 339:[340r] are represented on PST sheets as follows. 1. ◇*p* = *p* is on at least one PST sheet. 2. ¬◇¬*p* = □*p* = *p* is on every PST sheet. 3. ◇*p* ∧ ◇*q* = *p* is on at least one PST sheet, and *q* is on at least one PST sheet. 4. ◇(*p* ∧ *q*) = *p* and *q* are together on at least one PST sheet. 5. ◇*p* ∧ ◇*q* ∧ ¬◇(*p* ∧ *q*) = *p* is on at least one PST sheet, and *q* is on at least one PST sheet, but *p* and *q* are not together on any PST sheet. It gets more complicated for iterated modalities, where a non-modal proposition (such as *p* or *q*) is within the scope of more than one modal operator (such as ◇ for possibility or □ for necessity). The letter would then be attached to more than one LoC on the AST sheet and at least one LoC on each PST sheet, which would have its own set of multiple PST sheets--potentially, an infinite number of them--and so on. Peirce scribed several Gamma EGs with iterated modalities while preparing for the 1903 Lowell Lectures (R S-1:[74], LF 2/2:398), but there are reasons to suspect that he ultimately would have dispensed with them in accordance with pragmaticism. That is a subject for another post. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt > _ _ _ _ _ _ _ _ _ _ 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.
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
John, List: I had an epiphany of sorts while I was initially drafting this reply. For now, I will just respond to a few specific points, but in a later post, I intend to propose a way forward for Delta EGs that could be truly collaborative instead of competitive--both/and, not either/or. JFS: Since the content of L376 is very different from his sources and from his own writings before and after, that provides very little guidance. That's why nobody was able to interpret L376 to determine what Peirce wrote and how he intended to use what he was specifying. The content of R L376 is perfectly consistent with Peirce's other writings about EGs. The only reason why nobody has been able to determine definitively what he had in mind for Delta is because the manuscript breaks off before he gets around to distinguishing it from the other parts by explaining how it deals with modals. JFS: The second way of interpreting Peirce is to look backwards from the developments in logic in the century or more after Peirce and interpreting what he wrote in comparison to ALL developments in the same or similar subjects. The words 'metalanguage' and 'metalogic' were coined by Tarski and Carnap a few decades after Peirce died. This is not so much an alternative interpretation of Peirce as a recognition of his prescience with respect to subsequent developments in logic. His 1898 example indeed anticipates metalanguage and metalogic, "assert[ing] something about a proposition without asserting the proposition itself" (RLT 151). However, I still see nothing in R 514 nor in R L376 about *modal *applications of these concepts, only their *classical *application to a conditional proposition--it does not assert the antecedent itself, only that *if *it is true, then the consequent is *also *true. From that standpoint, ordinary Alpha EGs are metalogical because they often assert propositions about propositions. JFS: But the that-operator in RLT (1898) can support the methods they used for metalanguage. It is logically identical to writing postulates in the margin of a paper in R514 (June 1911) and to the "papers" of a phemic sheet in L376 (December 1911). The that-operator in RLT is *not* "logically identical to" the "red pencil" improvement in R 514, nor the "many papers" remark in R L376. In fact, Peirce's very next example in RLT is "That you are a good girl is false," leading directly to the convention that enclosing a proposition within "a lightly drawn oval," such that it "is merely fenced off from the field of assertion without any assertion being explicitly made concerning it," is "an elliptical [no pun intended?] way of saying that it is false" (RLT 151-152). What Peirce describes in R 514 is converting the entire sheet into nested cuts, thus asserting a conditional proposition. The margin is the outer close (antecedent), where "whatever is scribed is merely asserted to be possible," such as mathematical postulates. The area within the red line is the inner close (consequent), where whatever is scribed follows necessarily from what is in the margin, such as mathematical theorems. What Peirce describes in R L376 is treating the "many papers" as different portions of the phemic sheet to which the utterer and interpreter give their "common attention" at different times, where "some of those pieces relate to one subject and part to another." In other words, each individual page represents a different subuniverse of discourse within the overall universe of discourse. However, what occurred to me today is that the latter two approaches are compatible *with each other*. Again, I expect to say a lot more about this in the near future. JFS: What he [Peirce] wrote about modals in 1903 represents his views about modals in 1903. But 1903 was the end of the line for earlier projects, especially lexicography (Century & Baldwin dictionaries) and Minute Logic (rejection). Peirce still limits modal propositions to those asserting possibility or necessity several years later, not long before he writes the letter to Risteen. CSP: Now assertions differ in *modality*,--a term which must be explained at once. It refers to the different relations there may be between the *affirmation *of the state of things asserted and the *denial *of it, these different relations distinguishing three different "modes" of assertion [including "the mode of actuality," i.e., being "without modality"]. If a man says "It may rain tomorrow," his assertion is in "the mode of possibility," because it may be true that possibly it will rain tomorrow and, at the same time, be true that possibly it will not rain tomorrow. Any assertion is said to be made in the mode of possibility if, and only if, it is conceivable that the affirmation and the denial of that which it so asserts should be both at once true. ... On the other hand, an assertion is said to be made in "the mode of necessity," if, and only if, the affirmation and the denial of that which is so
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
Jon, Jerry, List, My interpretation of L376 depends on two ways of interpreting Peirce's L376. The first way is the one followed by most scholars: Comparing the content to an MS to everything written by Peirce and his sources prior to the date of the MS and to everything written later by him. Since the content of L376 is very different from his sources and from his own writings before and after, that provides very little guidance. That's why nobody was able to interpret L376 to determine what Peirce wrote and how he intended to use what he was specifying. JFS> The single most important innovation of Delta graphs is an operator for metalanguage or metalogic. JAS> That is not what Peirce says about Delta EGs in the letter to Risteen. He simply states, "I shall now have to add a Delta part in order to deal with modals..." That is true. The second way of interpreting Peirce is to look backwards from the developments in logic in the century or more after Peirce and interpreting what he wrote in comparison to ALL developments in the same or similar subjects. The words 'metalanguage' and 'metalogic' were coined by Tarski and Carnap a few decades after Peirce died. But the that-operator in RLT (1898) can support the methods they used for metalanguage. It is logically identical to writing postulates in the margin of a paper in R514 (June 1911) and to the "papers" of a phemic sheet in L376 (December 1911). It is also identical to methods used by Hintikka and others from the 1970s and later. It's not possible to interpret what Peirce intended in L376 with just the vocabulary he used. It's likely that he would have coined more terminology if he had been able to finish that MS. But his accident and the six months of morphine by the "quack" who treated him prevented him from finishing it and explaining his intentions and applications in detail. JLRC> First, the question of modern modal symbolic logic is remote from probability theory and even remoter from the Peircian notion of “qualisign, sinsign, legisign” That is true of Peirce's modal logic of 1903, which was the mainstream of modal logic for most of the 20th C and which is still taught in introductory courses. But Peirce became very interested in probability theory, as shown in his writings in the Logic Notebook. The that-operator from 1898 and the "papers" of June and December 1911 can support the kind of metalanguage that is widely used today for computational and theoretical methods for either or both possibilities and probabilities. JLRC> Is not the distinction between logic of syntax and the logic of semantics? Is not the semantic gap in the meanings of signs was probably a constitutive factor in the categorization of signs, would you agree? I agree that those distinctions are important. But any operators for metalanguage, including Peirce's three versions, can be and are used to represent, reason about, and compute with representations for syntax and/or semantics of any notation of any kind. See the many references in https://jfsowa.com/ikl . That text, by me, is very short. I wrote it as a guide to a wide range of documents from the 1980 to 2010. I haven't added anything since then because the amount of publication is huge. But it is still a useful guide to 30 years of developments, many of which take advantage of various methods of metalanguage. And Peirce's three notations for metalanguage are logically equivalent to methods that have been reinvented in several versions since the 1970s. The second way is to look backwards from the developments in logic in the century or more after Peirce and interpreting what he wrote in comparison to ALL developments in the same or similar subjects. From the perspective of the late 20th and 21st C, the specifications in RLT (1898), R514 (June 1911), and L376 (December 1911) define the that-operator of IKL. That operator specifies 20th and 21st C operations for metalanguage and metalogic. That single operator, when added to first-order logic, supports a very powerful version of logic. JAS> in the letter to Risteen. He simply states, "I shall now have to add a Delta part in order to deal with modals," and we do not have to guess at what he means by "modals" since he provides a straightforward definition elsewhere. "A modal proposition takes account of a whole range of possibility. According as it asserts something to be true or false throughout the whole range of possibility, it is necessary or impossible. According as it asserts something to be true or false within the range of possibility (not expressly including or excluding the existent state of things), it is possible or contingent" (CP 2.323, EP 2:283, 1903). What he wrote about modals in 1903 represents his views about modals in 1903. But 1903 was the end of the line for earlier projects, especially lexicography (Century & Baldwin dictionaries) and Minute Logic
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
Jerry, List: JLRC: First, the question of modern modal symbolic logic is remote from probability theory and even remoter from the Peircian notion of “qualisign, sinsign, legisign” Peirce developed Existential Graphs (EGs) as a diagrammatic notation for formal systems of deductive logic. As such, within his architectonic classification of the sciences, it falls under the hypothetical science of mathematics, not the normative science of logic as semeiotic. That is why EGs can be utilized in the primal positive science of phaneroscopy. The chief advantage of EGs over algebraic notations for modern symbolic logic is their iconicity. Every explicitly scribed EG is a replica (instance), a sinsign (token) of a peculiar kind that embodies a legisign (type). JLRC: Is not the distinction between logic of syntax and the logic of semantics? Could you please elaborate on exactly what you have in mind by "logic of syntax" vs. "logic of semantics"? For EGs vs. algebraic notations implementing formal systems of deductive logic (modal or otherwise), the syntax is obviously very different, but the semantics is the same. More generally, it seems to me that both syntax and semantics would have to do with interpretants--for a proposition, syntax corresponds to its overall interpretant by signifying its pure/continuous predicate, while semantics perhaps corresponds to the interpretants of the individual names/rhemes/semes that denote its subjects. JLRC: The semantic gap in the meanings of signs was probably a constitutive factor in the categorization of signs, would you agree? Could you please elaborate on exactly what you have in mind by "the semantic gap in the meanings of signs"? For Peirce, "meaning" is roughly synonymous with "interpretant," but he also classifies signs on the basis of their objects and relations. JLRC: What particular texts of CSP were you referring to when you listed five modal phrases? I am referring to a specific page in Peirce's Logic Notebook (R 339:[340r], LF 1:624, 1909 Jan 7) where he provides five EGs with their direct translations into modal propositions. Here again is the image that I included in my post last night. [image: image.png] In my post earlier today, I restated these five modal propositions using modern standard notation--(1) ◇*p*, (2) ¬◇¬*p* = □*p*, (3) ◇*p* ∧ ◇*q*, (4) ◇(*p* ∧ *q*), and (5) ◇*p* ∧ ◇*q* ∧ ¬◇(*p* ∧ *q*); again, in each case, *p* and *q* are atomic non-modal propositions. JLRC: Do either of you feel that your interpretations of "delta graphs" bridge the yawning gaps between semiotics and semiology? I doubt it since that is not the purpose of EGs. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Fri, Feb 23, 2024 at 2:08 PM Jerry LR Chandler < jerry_lr_chand...@icloud.com> wrote: > Jon, John, List: > > Thanks to both of you for pushing the discourse toward the potential > modern interpretations of CSP’s thoughts (semes?). > > I only have time for a couple of feedbacks, although your texts motivated > deeper deliberations. > > 1. First, the question of modern modal symbolic logic is remote from > probability theory and even remoter from the Peircian notion of “qualisign, > sinsign, legisign” > > Is not the distinction between logic of syntax and the logic of > semantics? The semantic gap in the meanings of signs was probably a > constitutive factor in the categorization of signs, would you agree? > > 2. Jon: What particular texts of CSP were you referring to when you listed > five modal phrases? I am more than a little skeptical that this is both > sound and complete interpretations of CSP’s texts but I am open to > persuasion! You might look at my online paper, An Introduction to > Chemical Information Theory, where I search for a Peircian approach from a > Natural science perspective. > > 3. Do either of you feel that your interpretations of "delta graphs" > bridge the yawning gaps between semiotics and semiology? > > 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.
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
Jon, John, List: Thanks to both of you for pushing the discourse toward the potential modern interpretations of CSP’s thoughts (semes?). I only have time for a couple of feedbacks, although your texts motivated deeper deliberations. 1. First, the question of modern modal symbolic logic is remote from probability theory and even remoter from the Peircian notion of “qualisign, sinsign, legisign” Is not the distinction between logic of syntax and the logic of semantics? The semantic gap in the meanings of signs was probably a constitutive factor in the categorization of signs, would you agree? 2. Jon: What particular texts of CSP were you referring to when you listed five modal phrases? I am more than a little skeptical that this is both sound and complete interpretations of CSP’s texts but I am open to persuasion! You might look at my online paper, An Introduction to Chemical Information Theory, where I search for a Peircian approach from a Natural science perspective. 3. Do either of you feel that your interpretations of "delta graphs" bridge the yawning gaps between semiotics and semiology? Cheers Jerry > On Feb 23, 2024, at 12:21 PM, Jon Alan Schmidt > wrote: > > John, List: > > I fully agree with your comment last week that "Peirce List is a > collaboration, not a competition," and I hope that you will receive this > response in that spirit. My questions are genuinely intended to help me (and > others) better understand your position, and I would appreciate direct > answers. > > JFS: The single most important innovation of Delta graphs is an operator for > metalangage or metalogic. > > That is not what Peirce says about Delta EGs in the letter to Risteen. He > simply states, "I shall now have to add a Delta part in order to deal with > modals," and we do not have to guess at what he means by "modals" since he > provides a straightforward definition elsewhere. "A modal proposition takes > account of a whole range of possibility. According as it asserts something to > be true or false throughout the whole range of possibility, it is necessary > or impossible. According as it asserts something to be true or false within > the range of possibility (not expressly including or excluding the existent > state of things), it is possible or contingent" (CP 2.323, EP 2:283, 1903). > Hence, the 1898 example--"That you are a good girl is much to be wished"--is > not what Peirce considered to be a modal proposition; only something like > "That you are a good girl is possible" would qualify. > > Where exactly do you see anything about "an operator for metalanguage or > metalogic" in the letter to Risteen? Again, what does Peirce say in that text > that would not be fully applicable to Alpha, Beta, and Gamma EGs as he had > described them previously? Please provide exact quotations. > > JFS: Although Peirce never developed it further (as far as I know), the > option of attaching a line of identity to an oval is exactly the same > operation as taking a sheet of paper, drawing a line around the nested text > (You are a good girl), and stating postulates in the margin (as in R514 and > L376). > > It is not the same operation at all since "--is much to be wished" is not a > postulate from which "you are a good girl" follows necessarily. As I > explained before, Peirce's "red pencil" operation in R 514 effectively turns > each individual sheet of paper on which EGs are scribed into a conditional > proposition. Its physical edges and the red line drawn just inside them are > cuts, the latter nested within the former, so that the margin is the outer > close (antecedent) and the area within the red line is the inner close > (consequent). Any propositions in the margin (postulates) are "merely > asserted to be possible," and if they are all true, then all the propositions > within the red line (theorems) are also true. There is no "line of identity" > connecting the red line to the postulates in the margin. > > Where exactly do you see anything about "stating postulates in the margin" in > R L376? Please provide exact quotations. > > JFS: As for the five EGs from 1909, quoted below, none of them express modal > logic. All five of them can be translated to statements in first-order logic: > > Those translations are incorrect. It is unambiguous from Peirce's own > handwritten translations that the EGs scribed on that Logic Notebook page are > not Beta graphs with heavy lines for indefinite individuals attached to > lowercase letters for general concepts being attributed to them. Instead, the > heavy lines are for "circumstances," and they are attached to lowercase > letters for propositions (as in Alpha) that would be true in them. There is > an analogy between quantifying predicates over subjects in first-order > predicate logic and quantifying propositions over possible states of things > in propositional modal logic--in Peirce's words, "The
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
John, List: I fully agree with your comment last week that "Peirce List is a collaboration, not a competition," and I hope that you will receive this response in that spirit. My questions are genuinely intended to help me (and others) better understand your position, and I would appreciate direct answers. JFS: The single most important innovation of Delta graphs is an operator for metalangage or metalogic. That is *not* what Peirce says about Delta EGs in the letter to Risteen. He simply states, "I shall now have to add a *Delta *part in order to deal with modals," and we do not have to guess at what he means by "modals" since he provides a straightforward definition elsewhere. "A modal proposition takes account of a whole range of possibility. According as it asserts something to be true or false throughout the whole range of possibility, it is *necessary *or *impossible*. According as it asserts something to be true or false within the range of possibility (not expressly including or excluding the existent state of things), it is *possible *or *contingent*" (CP 2.323, EP 2:283, 1903). Hence, the 1898 example--"That you are a good girl is much to be wished"--is *not *what Peirce considered to be a modal proposition; only something like "That you are a good girl is possible" would qualify. Where exactly do you see anything about "an operator for metalanguage or metalogic" in the letter to Risteen? Again, what does Peirce say in that text that would *not *be fully applicable to Alpha, Beta, and Gamma EGs as he had described them previously? Please provide exact quotations. JFS: Although Peirce never developed it further (as far as I know), the option of attaching a line of identity to an oval is exactly the same operation as taking a sheet of paper, drawing a line around the nested text (You are a good girl), and stating postulates in the margin (as in R514 and L376). It is *not *the same operation at all since "--is much to be wished" is not a postulate from which "you are a good girl" follows necessarily. As I explained before, Peirce's "red pencil" operation in R 514 effectively turns each individual sheet of paper on which EGs are scribed into a *conditional *proposition. Its physical edges and the red line drawn just inside them are cuts, the latter nested within the former, so that the margin is the outer close (antecedent) and the area within the red line is the inner close (consequent). Any propositions in the margin (postulates) are "merely asserted to be possible," and if they are all true, then all the propositions within the red line (theorems) are also true. There is no "line of identity" connecting the red line to the postulates in the margin. Where exactly do you see anything about "stating postulates in the margin" in R L376? Please provide exact quotations. JFS: As for the five EGs from 1909, quoted below, none of them express modal logic. All five of them can be translated to statements in first-order logic: Those translations are incorrect. It is unambiguous from Peirce's own handwritten translations that the EGs scribed on that Logic Notebook page are not Beta graphs with heavy lines for indefinite individuals attached to lowercase letters for general concepts being attributed to them. Instead, the heavy lines are for "circumstances," and they are attached to lowercase letters for propositions (as in Alpha) that would be true in them. There is an *analogy *between quantifying predicates over subjects in first-order predicate logic and quantifying propositions over possible states of things in propositional modal logic--in Peirce's words, "The distinction between the Indefinite, the Singular, and the General ls obviously only another application of the distinction between the Possible, the Actual, and the Necessary, for which the Germans have invented the convenient name *Modality*" (NEM 3:814, 1905)--but they still require different formal systems. In modern standard notation, Peirce's five modal propositions are (1) ◇*p*, (2) ¬◇¬*p* = □*p*, (3) ◇*p* ∧ ◇*q*, (4) ◇(*p* ∧ *q*), and (5) ◇*p* ∧ ◇*q* ∧ ¬◇(*p* ∧ *q*); in each case, *p* and *q* are atomic non-modal propositions. How would you represent them in your candidate for Delta EGs? For example, would ◇*p* simply be *p* inside an oval with a heavy line attached to the verb phrase "--is possible," and would □*p* simply be *p* inside an oval with a heavy line attached to the verb phrase "--is necessary"? If so, then that seems much more cumbersome--much less iconic--than my candidate for Delta EGs. Instead of formulating new graphical transformation rules, would you just stipulate the usual modal axioms--for example, "necessary" may always be changed to "possible" (D), "actual" (T), or "necessarily necessary" (4)? Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Thu, Feb 22, 2024 at 10:18 PM
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
Jon, The single most important innovation of Delta graphs is an operator for metalangage or metalogic. Just that one operator, when added to ordinary first-order logic, makes it possible to define a wide range of modal logics and logics for probability. In fact, Peirce's modal logic of 1903 and his tinctured modal logic of 1906 (as well as may other kinds of modalities and probabilities) can all be defined in terms of Delta graphs (which I assume to be first-order EGs with the operator summarized below). The reason why I make that claim is that I was on the committee of 9 logicians and computer scientists that defined the IKL logic of 2006. And as exercises, we showed how to define all those options by extending FOL with just one operator, which is equivalent to what Peirce defined in RLT (1898), in R514 (June 1911), and in L376 (Dec. 1911). See below. Peirce introduced an operator for metalanguage in RLT (1898). The example he used was the sentence "That you are a good girl is much to be wished." The notation he adopted was a plain white oval with a line of identity attached to the oval. Inside the oval was the sentence "You are a good girl". The line of identity attached to the oval may be read "There exists a proposition p, which is stated by the nested graph for 'You are a good girl'."Outside the oval, he attached the verb phrase "--is much to be wished" to the same line of identity. Although Peirce never developed it further (as far as I know), the option of attaching a line of identity to an oval is exactly the same operation as taking a sheet of paper, drawing a line around the nested text (You are a good girl), and stating postulates in the margin (as in R514 and L376). That is identical the IKL extension to the base logic (called Common Logic). See the cited references about IKL. In IKL, the operator for stating postulates outside the nested statements is named 'that' -- which happens to be the first word in Peirce's example of 1898. When the nine of us defined the IKL logic, I was the only person who had read RLT, but I was not the first person who suggested the word 'that' for the operator. (As they say, great minds run in the same rut.) But as an exercise, we showed that first-order logic plus the that-operator can be used to define all the operators that Peirce defined for his 1903 version of modal logic. So if you like Peirce's 1903 version of modal logic, you can have it. Just use the 'that' operator of 1898 or the Delta papers of 1911 to define the 1903 modal graphs. In short, adopting the Delta graphs of 1911 does not reject the modal logic of 1903, because every option of 1903 can be defined in terms of Delta graphs. As for the five EGs from 1909, quoted below, none of them express modal logic. All five of them can be translated to statements in first-order logic: There exists x such that p(x). If there exists x, then p(x). There exist x and y, such that p(x) and q(y). There exists x, such that p(x) and q(x). There exist x and y, such that p(x) and q(y) and x is not equal to y. John From: "Jon Alan Schmidt" John, List: I sincerely appreciate this clarification of your thought process underlying your conjecture that "The primary subject of L376 is Delta graphs." I am not yet persuaded, but I now intend to review the entire letter carefully in light of your proposed interpretation. Again, on my current reading, what it says about "The Conventions" and "The Phemic Sheet" is not "a version of logic that is different from any that Peirce had previously specified," it is just another description of EGs in general--applicable to Alpha, Beta, Gamma, and (presumably) Delta. Are there specific statements in the text that you view as incompatible with the first three parts? I have a different hypothesis regarding what Peirce might have had in mind for "a Delta part [of EGs] in order to deal with modals," which I have discussed on the List in the past. In fact, I already wrote a paper of my own about it, which will be published sometime this spring. Its title is "Peirce and Modal Logic: Delta Existential Graphs and Pragmaticism," and here is the abstract. Although modern modal logic came about largely after Peirce's death, he anticipated some of its key aspects, including strict implication and possible worlds semantics. He developed the Gamma part of Existential Graphs with broken cuts signifying possible falsity, but later identified the need for a Delta part without ever spelling out exactly what he had in mind. An entry in his personal Logic Notebook is a plausible candidate, with heavy lines representing possible states of things where propositions denoted by attached letters would be true, rather than individual subjects to which predicates denoted by attached names are attributed as in the Beta part. New transformation rules implement various commonly
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
John, List: I sincerely appreciate this clarification of your thought process underlying your conjecture that "The primary subject of L376 is Delta graphs." I am not yet persuaded, but I now intend to review the entire letter carefully in light of your proposed interpretation. Again, on my current reading, what it says about "The Conventions" and "The Phemic Sheet" is *not *"a version of logic that is different from any that Peirce had previously specified," it is just another description of EGs *in general*--applicable to Alpha, Beta, Gamma, and (presumably) Delta. Are there specific statements in the text that you view as incompatible with the first three parts? I have a different hypothesis regarding what Peirce might have had in mind for "a *Delta* part [of EGs] in order to deal with modals," which I have discussed on the List in the past. In fact, I already wrote a paper of my own about it, which will be published sometime this spring. Its title is "Peirce and Modal Logic: Delta Existential Graphs and Pragmaticism," and here is the abstract. Although modern modal logic came about largely after Peirce's death, he anticipated some of its key aspects, including strict implication and possible worlds semantics. He developed the Gamma part of Existential Graphs with broken cuts signifying possible falsity, but later identified the need for a Delta part without ever spelling out exactly what he had in mind. An entry in his personal Logic Notebook is a plausible candidate, with heavy lines representing possible states of things where propositions denoted by attached letters would be true, rather than individual subjects to which predicates denoted by attached names are attributed as in the Beta part. New transformation rules implement various commonly employed formal systems of modal logic, which are readily interpreted by defining a possible world as one in which all the relevant laws for the actual world are facts, each world being partially but accurately and adequately described by a closed and consistent model set of propositions. In accordance with pragmaticism, the relevant laws for the actual world are represented as strict implications with real possibilities as their antecedents and conditional necessities as their consequents, corresponding to material implications in every possible world. Here is an image of the relevant Logic Notebook entry (R 339:[340r], LF 1:624, 1909 Jan 7). [image: image.png] One limitation of using Gamma EGs with broken cuts for modal logic, identified by Jay Zeman in his dissertation ( https://isidore.co/calibre/get/pdf/4481), is that the ordinary transformation rules implement the unusual Ł-modal system of Łukasiewicz; I wrote about this in a previous paper (https://rdcu.be/cQoIz). Zeman proposed various restrictions on iteration/deiteration to implement *S4 *and stronger formal systems, but weaker systems do not seem to be feasible, especially since insertion/erasure as applied to broken cuts themselves directly corresponds to axiom T (□*p* → *p*, or *p* → ◇*p*). By contrast, my candidate for Delta EGs can implement most of the common systems with different combinations of permissions, each pertaining to the heavy "lines of compossibility" (LOCs) and corresponding to one of the well-known modal axioms (K, D, T, 4, 5) that are added to classical propositional logic. As you no doubt recognize, the semantics summarized in the penultimate sentence of my abstract above is the same one that you discuss in your 2003 and 2006 papers, and I explicitly reference the former--it is what first brought J. Michael Dunn's very interesting approach to my attention, for which I am grateful. I wrote a separate paper with a more extensive formalization of it, entitled "Laws and Facts Semantics for Modal Logic," likewise referencing your 2003 paper; it is currently under review, with an initial decision expected soon. Here is that abstract. Dunn and Goble proposed a simplified semantics for modal logic in which a possible world is defined as one where all the relevant laws for the designated world, usually taken to be the actual world, are facts. When formalized with Hintikka's closed and consistent model sets serving as partial but accurate and adequate descriptions of these worlds, different properties of the alternativeness (or accessibility) relation then correspond to different containment relations among the sets of propositions representing the relevant laws and facts. This approach can be helpfully illustrated by Venn diagrams and is arguably more intuitive than the standard one in which the binary relation between worlds is primitive and arbitrary. As I see it, Hintikka's model sets directly correspond to any number of individual EGs that could be explicitly scribed on the phemic sheet--in Alpha, Beta, Gamma, or Delta--without ever exhausting the continuum of true propositions about the universe of discourse. As he says, "In all non-trivial cases, we have to do with an
[PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
hich was also published in 2006. For a list of references to IKL and the IKRIS project that sponsored the development of IKL, see https://jfsowa.com/ikl . Then. look at Five Questions on Epistemic Logic, https://jfsowa.com/pubs/5qelogic.pdf . That article, which was published in 2010, discusses how a logic such as IKL or Peirce's delta graphs could represent various issues in modal logic with an emphasis on epistemic logic -- that is also a consideration for my recent article about phaneroscopy. There is much more that could be said, and I plan to write it in the article on Delta graphs. And by the way, I wonder how you would explain the three questions I asked: Why did Juliette wash and scrub the floor in Deceber? Why were there papers on the floor? Why did Peirce slip on them in a very complex way? John ---- From: "Jon Alan Schmidt" Sent: 2/21/24 1:25 PM To: Peirce-L Subject: Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic) John, List: JFS: The entire letter L376 is about Delta graphs and applications of Delta graphs. This conjecture is quite a leap, considering that--as you acknowledged--Peirce mentions Delta exactly once in that entire 19-page letter, which he left unfinished unless additional pages somehow disappeared from the manuscript folder at Harvard's Houghton Library decades ago. Again, here is that lone sentence. CSP: The better exposition of 1903 divided the system into three parts, distinguished as the Alpha, the Beta, and the Gamma, parts; a division I shall here adhere to, although I shall now have to add a Delta part in order to deal with modals. In the remaining text that we currently have, Peirce never gets around to discussing any of the individual parts of EGs and their differences, despite stating plainly that he was going to maintain them as "the better exposition" of the system as a whole. He also says nothing whatsoever about dealing with modals, which is his only stated purpose for adding a Delta part to the other three. JFS: As Peirce wrote, the phemic sheet of a Delta graph contains multiple "papers", each of which represents one possibility specified by "postulates" that govern the remaining content of the sheet. That is not what Peirce wrote in his letter to Risteen. Again, here is the exact quotation. CSP: I provide my system with a phemic sheet, which is a surface upon which the utterer and interpreter will, by force of a voluntary and actually contracted habit, recognize that whatever is scribed upon it and is interpretable as an assertion is to be recognized as an assertion, although it may refer to a mere idea as its subject. If “snows” is scribed upon the Phemic Sheet, it asserts that in the universe to which a special understanding between utterer and interpreter has made the special part of the phemic sheet on which it is scribed to relate, it sometime does snow. For they two may conceive that the “phemic sheet” embraces many papers, so that one part of it is before the common attention at one time and another part at another, and that actual conventions between them equivalent to scribed graphs make some of those pieces relate to one subject and part to another. Again, there is no mention here of Delta, nor of modals. In fact, there is no mention here of any of the different parts of EGs, because Peirce is describing the phemic sheet as employed in every part. He also does not say that the different "papers" correspond to different possibilities, he says that they correspond to different subjects--different universes of discourse--to which the utterer and interpreter together pay attention at different times. So I ask again, how exactly would the use of multiple "papers" and/or the "red pencil" operation of R 514 facilitate implementing formal systems of modal logic with EGs? Which specific one, "invented in 2006," do you have in mind? JFS: Meanwhile, there are some questions to ponder: Any answers to such questions about the details of Peirce's unfortunate accident are pure speculation. It seems to me that if it had happened while he was "laying out a diagram of papers" for a new version of EGs, then he likely would have said so somewhere. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Tue, Feb 20, 2024 at 9:18 PM John F Sowa wrote: Jon, The entire letter L376 is about Delta graphs and applications of Delta graphs. Since Peirce began the letter to Risteen shortly after his visit, he was assuming that Risteen knew a great deal about the material they had discussed. Therefore, he plunged into examples without much of an intro. As Peirce wrote, the phemic sheet of a Delta graph contains multiple "papers
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
John, List: JFS: The entire letter L376 is about Delta graphs and applications of Delta graphs. This conjecture is quite a leap, considering that--as you acknowledged--Peirce mentions Delta *exactly once* in that entire 19-page letter, which he left unfinished unless additional pages somehow disappeared from the manuscript folder at Harvard's Houghton Library decades ago. Again, here is that lone sentence. CSP: The better exposition of 1903 divided the system into three parts, distinguished as the Alpha, the Beta, and the Gamma, parts; a division I shall here adhere to, although I shall now have to add a *Delta *part in order to deal with modals. In the remaining text that we currently have, Peirce never gets around to discussing *any *of the individual parts of EGs and their differences, despite stating plainly that he was going to maintain them as "the better exposition" of the system as a whole. He also says nothing whatsoever about dealing with modals, which is his only stated purpose for adding a Delta part to the other three. JFS: As Peirce wrote, the phemic sheet of a Delta graph contains multiple "papers", each of which represents one possibility specified by "postulates" that govern the remaining content of the sheet. That is *not *what Peirce wrote in his letter to Risteen. Again, here is the exact quotation. CSP: I provide my system with a *phemic sheet*, which is a surface upon which the utterer and interpreter will, by force of a voluntary and actually contracted habit, recognize that whatever is scribed upon it and is interpretable as an assertion is to be recognized as an assertion, although it may refer to a mere idea as its subject. If “snows” is scribed upon the Phemic Sheet, it asserts that in the universe to which a special understanding between utterer and interpreter has made the special part of the phemic sheet on which it is scribed to relate, it *sometime *does snow. For they two may conceive that the “phemic sheet” embraces many papers, so that one part of it is before the common attention at one time and another part at another, and that actual conventions between them equivalent to scribed graphs make some of those pieces relate to one subject and part to another. Again, there is no mention here of Delta, nor of modals. In fact, there is no mention here of *any *of the different parts of EGs, because Peirce is describing the phemic sheet as employed in *every *part. He also does not say that the different "papers" correspond to different *possibilities*, he says that they correspond to different *subjects*--different universes of discourse--to which the utterer and interpreter together pay attention at different times. So I ask again, how exactly would the use of multiple "papers" and/or the "red pencil" operation of R 514 facilitate implementing formal systems of modal logic with EGs? Which specific one, "invented in 2006," do you have in mind? JFS: Meanwhile, there are some questions to ponder: Any answers to such questions about the details of Peirce's unfortunate accident are pure speculation. It seems to me that if it had happened while he was "laying out a diagram of papers" for a new version of EGs, then he likely would have said so somewhere. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Tue, Feb 20, 2024 at 9:18 PM John F Sowa wrote: > Jon, > > The entire letter L376 is about Delta graphs and applications of Delta > graphs. Since Peirce began the letter to Risteen shortly after his visit, > he was assuming that Risteen knew a great deal about the material they had > discussed. Therefore, he plunged into examples without much of an intro. > > As Peirce wrote, the phemic sheet of a Delta graph contains multiple > "papers", each of which represents one possibility specified by > "postulates" that govern the remaining content of the sheet. There are > many ways of partitioning a sheet of paper to distinguish the postulates > from the content they govern. The excerpt from R514 is one method, and it > happens to fill an entire sheet of paper. He may have thought of some > other notation for partitioning the paper, but the logical result would be > equivalent. > > There is much more to say, and I'll send the full preview later this week. > > Meanwhile, there are some questions to ponder: Why did Juliette scrub and > polish the floor in December? Spring cleaning is rarely done in December. > Why was there some paper on the floor? Why did Peirce slip n it? Didn't > he see it? Why was his accident so serious? If he had been walking in a > straight line, he might have fallen on his rear. That might have been > painful, but it wouldn't cause a serious injury that took 6 months to heal. > Such a serious accident might have occurred if Peirce had been walking > fast while turning or twisting. But why would he be doing
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
Jon, The entire letter L376 is about Delta graphs and applications of Delta graphs. Since Peirce began the letter to Risteen shortly after his visit, he was assuming that Risteen knew a great deal about the material they had discussed. Therefore, he plunged into examples without much of an intro. As Peirce wrote, the phemic sheet of a Delta graph contains multiple "papers", each of which represents one possibility specified by "postulates" that govern the remaining content of the sheet. There are many ways of partitioning a sheet of paper to distinguish the postulates from the content they govern. The excerpt from R514 is one method, and it happens to fill an entire sheet of paper. He may have thought of some other notation for partitioning the paper, but the logical result would be equivalent. There is much more to say, and I'll send the full preview later this week. Meanwhile, there are some questions to ponder: Why did Juliette scrub and polish the floor in December? Spring cleaning is rarely done in December. Why was there some paper on the floor? Why did Peirce slip n it? Didn't he see it? Why was his accident so serious? If he had been walking in a straight line, he might have fallen on his rear. That might have been painful, but it wouldn't cause a serious injury that took 6 months to heal. Such a serious accident might have occurred if Peirce had been walking fast while turning or twisting. But why would he be doing that? Possible answer: Charles had asked Juliette to wash the floor because he wanted to build a diagram with multiple papers. He was laying out a diagram of papers with a large example of what he was writing about. As he turned to lay our another layer, he turned and slipped. John From: "Jon Alan Schmidt" Sent: 2/20/24 2:00 PM To: Peirce-L Subject: Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic) John, List: Here is an exact quotation of what Peirce actually says in R L376 (letter to Risteen) about the phemic sheet consisting of multiple "papers." CSP: I provide my system with a phemic sheet, which is a surface upon which the utterer and interpreter will, by force of a voluntary and actually contracted habit, recognize that whatever is scribed upon it and is interpretable as an assertion is to be recognized as an assertion, although it may refer to a mere idea as its subject. If “snows” is scribed upon the Phemic Sheet, it asserts that in the universe to which a special understanding between utterer and interpreter has made the special part of the phemic sheet on which it is scribed to relate, it sometime does snow. For they two may conceive that the “phemic sheet” embraces many papers, so that one part of it is before the common attention at one time and another part at another, and that actual conventions between them equivalent to scribed graphs make some of those pieces relate to one subject and part to another. There is no mention of Delta, nor anything that would "deal with modals," which again is Peirce's only stated purpose for adding a Delta part to EGs. Instead, the different papers correspond to different subjects that attract "the common attention" of the utterer and interpreter at different times--i.e., different universes of discourse; not different times, aspects, or modalities of the same universe of discourse. There is also nothing about the new "red pencil" operation that Peirce describes in R 514 (as quoted below), and based on his specific example in that text--postulates in geometry--it likewise does not "deal with modals." Instead, it treats the edges of the sheet and the red line drawn a short distance inside them as two cuts, the latter nested within the former, such that what is being represented overall is a conditional--if the propositions in the margin (outer close) are true, then the graphs within the red line (inner close) are also true. In other words, the universe of discourse is made more explicit instead of being entirely taken for granted, and it might be strictly hypothetical--"merely asserted to be possible." In summary, it remains unclear to me what the content of your new article has to do with Delta graphs. How would the use of multiple "papers" and/or the "red pencil" operation facilitate implementing formal systems of modal logic with EGs? Which specific one, "invented in 2006," do you have in mind? Regards, Jon On Mon, Feb 19, 2024 at 10:30 PM John F Sowa wrote: Jon, That's true: JAS> I am admittedly curious about the content of your new article. As you know, there is only one place in Peirce's entire vast corpus of writings where he mentions Delta. But note the following excerpt from R514, which also contains a rough draft of the EGs in L231: "Since my paper of 19
Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
tterer and an interpreter may use Delta graphs in an > investigation. Further hints may be found in several manuscripts he wrote > in the previous six months. As another hint, the intended recipient of the > letter was Allan Risteen. When that letter is combined with information > about Risteen’s expertise and Peirce’s work on a proof of pragmaticism, it > suggests that the phemic sheet of a Delta graph consists of multiple > “papers”, each of which represents a different time, aspect, or modality of > some universe of discourse. Although Peirce did not specify the details of > Delta graphs, a combination of features mentioned in several 1911 > manuscripts would satisfy the hints about Delta graphs. The result would be > similar or perhaps equivalent to a logic for modality that was invented in > 2006. > > John > > -- > *From*: "Jon Alan Schmidt" > *Sent*: 2/18/24 8:08 PM > *To*: Peirce-L > *Subject*: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in > Logic) > > John, List: > > JFS: I am now writing the article on Delta Graphs. That is an example > where Peirce was on solid ground with his deep understanding of logic and > mathematics. Next week, I'll send the abstract and preview of the new > article, which shows how Peirce anticipated a version of logic that was > developed in the 21st century (2006 to be exact). ( > https://list.iupui.edu/sympa/arc/peirce-l/2024-02/msg00038.html) > > > JFS: I'm moving on to the the article on Delta graphs. I'll send a note > with a preview of that article later this week. ( > https://list.iupui.edu/sympa/arc/peirce-l/2024-02/msg00104.html) > > > I am admittedly curious about the content of your new article. As you > know, there is only one place in Peirce's entire vast corpus of writings > where he mentions Delta. > > CSP: In this ["Prolegomena to an Apology for Pragmaticism," CP 4.530-572, > 1906] I made an attempt to make the syntax [of Existential Graphs] cover > Modals; but it has not satisfied me. The description was, on the whole, as > bad as it well could be, in great contrast to the one Dr. Carus rejected > [in 1897]. 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. The better exposition of 1903 > divided the system into three parts, distinguished as the Alpha, the Beta, > and the Gamma, parts; a division I shall here adhere to, although I shall > now have to add a *Delta *part in order to deal with modals. (R L376, R > 500:2-3, 1911 Dec 6) > > > For EGs as described in "the better exposition of 1903," modal logic is > implemented with *broken *cuts in Gamma. However, by the time Peirce > wrote this letter to Allan Douglas Risteen, he had abandoned cuts in > general, having replaced them with more iconic shading for negation. > Consequently, he needed a new way to "deal with modals," and this is the > sole purpose that he states for adding a Delta part. > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Structural Engineer, Synechist Philosopher, Lutheran Christian > <http://www.LinkedIn.com/in/JonAlanSchmidt> > www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt > _ _ _ _ _ _ _ _ _ _ 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.
RE: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
Jon, That's true: JAS> I am admittedly curious about the content of your new article. As you know, there is only one place in Peirce's entire vast corpus of writings where he mentions Delta. But note the following excerpt from R514, which also contains a rough draft of the EGs in L231: "Since my paper of 1906, I have improved the [EG] system slightly (at least), and the manner of exposition of it greatly, by first stating the force of the different signs without going into their deeper significance in the Since my paper of 1906, I have improved the [EG] system slightly (at least), and the manner of exposition of it greatly, by first stating the force of the different signs without going into their deeper significance in the least... One of my possibly slight improvements, is that I begin by drawing (preferably with a red pencil), a line all round my sheet at a little distance from the edge; and in the margin outside the red line, whatever is scribed is merely asserted to be possible. Thus, if the subject were geometry, I could write in that margin the postulates, and any pertinent problems stated in the form of postulates such as, that "if on a plane, there be circle with a ray cutting it, and two be marked [end of R514] That operation is the way L376 represents multiple parts of the phemic sheet. And it is a way of saying the conditions for the nested graph to be possible. That doesn't say much more. But that operation when combined with a notation for first-order logic is a method for representing modality in various logics in the late 20th and early 21st C. There are also other hints that suggest ways of extending FOL. They don't prove that Peirce intended exactly the same kinds of applications. But it shows that his ways of thinking could lead in promising directions. Following is the abstract of the article I'm writing. Abstract. In December 1911, Peirce wrote an intriguing claim about existential graphs: “I shall now have to add a Delta part in order to deal with modals.” Although his unfinished draft does not specify the details, it explains how an utterer and an interpreter may use Delta graphs in an investigation. Further hints may be found in several manuscripts he wrote in the previous six months. As another hint, the intended recipient of the letter was Allan Risteen. When that letter is combined with information about Risteen’s expertise and Peirce’s work on a proof of pragmaticism, it suggests that the phemic sheet of a Delta graph consists of multiple “papers”, each of which represents a different time, aspect, or modality of some universe of discourse. Although Peirce did not specify the details of Delta graphs, a combination of features mentioned in several 1911 manuscripts would satisfy the hints about Delta graphs. The result would be similar or perhaps equivalent to a logic for modality that was invented in 2006. John From: "Jon Alan Schmidt" Sent: 2/18/24 8:08 PM To: Peirce-L Subject: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic) John, List: JFS: I am now writing the article on Delta Graphs. That is an example where Peirce was on solid ground with his deep understanding of logic and mathematics. Next week, I'll send the abstract and preview of the new article, which shows how Peirce anticipated a version of logic that was developed in the 21st century (2006 to be exact). (https://list.iupui.edu/sympa/arc/peirce-l/2024-02/msg00038.html) JFS: I'm moving on to the the article on Delta graphs. I'll send a note with a preview of that article later this week. (https://list.iupui.edu/sympa/arc/peirce-l/2024-02/msg00104.html) I am admittedly curious about the content of your new article. As you know, there is only one place in Peirce's entire vast corpus of writings where he mentions Delta. CSP: In this ["Prolegomena to an Apology for Pragmaticism," CP 4.530-572, 1906] I made an attempt to make the syntax [of Existential Graphs] cover Modals; but it has not satisfied me. The description was, on the whole, as bad as it well could be, in great contrast to the one Dr. Carus rejected [in 1897]. 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. The better exposition of 1903 divided the system into three parts, distinguished as the Alpha, the Beta, and the Gamma, parts; a division I shall here adhere to, although I shall now have to add a Delta part in order to deal with modals. (R L376, R 500:2-3, 1911 Dec 6) For EGs as described in "the better exposition of 1903," modal logic is implemented with broken cuts in Gamma. However, b
[PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
John, List: JFS: I am now writing the article on Delta Graphs. That is an example where Peirce was on solid ground with his deep understanding of logic and mathematics. Next week, I'll send the abstract and preview of the new article, which shows how Peirce anticipated a version of logic that was developed in the 21st century (2006 to be exact). ( https://list.iupui.edu/sympa/arc/peirce-l/2024-02/msg00038.html) JFS: I'm moving on to the the article on Delta graphs. I'll send a note with a preview of that article later this week. ( https://list.iupui.edu/sympa/arc/peirce-l/2024-02/msg00104.html) I am admittedly curious about the content of your new article. As you know, there is only one place in Peirce's entire vast corpus of writings where he mentions Delta. CSP: In this ["Prolegomena to an Apology for Pragmaticism," CP 4.530-572, 1906] I made an attempt to make the syntax [of Existential Graphs] cover Modals; but it has not satisfied me. The description was, on the whole, as bad as it well could be, in great contrast to the one Dr. Carus rejected [in 1897]. 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. The better exposition of 1903 divided the system into three parts, distinguished as the Alpha, the Beta, and the Gamma, parts; a division I shall here adhere to, although I shall now have to add a *Delta *part in order to deal with modals. (R L376, R 500:2-3, 1911 Dec 6) For EGs as described in "the better exposition of 1903," modal logic is implemented with *broken *cuts in Gamma. However, by the time Peirce wrote this letter to Allan Douglas Risteen, he had abandoned cuts in general, having replaced them with more iconic shading for negation. Consequently, he needed a new way to "deal with modals," and this is the sole purpose that he states for adding a Delta part. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt _ _ _ _ _ _ _ _ _ _ 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.
