> On Aug 26, 2023, at 6:12 PM, John F Sowa <[email protected]> wrote: > > Doug F, et al., > > I'm writing an article about Peirce's phaneroscopy and diagrammatic > reasoning, which has strong implications for ontology, reasoning methods, and > their implications for the latest issues in generative artificial > intelligence. See below for excerpts from that article and some links for > further information. > > John > > PS: I just did a cut & paste below, but the diagrams did not get copied. > I'll include a PDF later. But the text explains the issues, and the > citations have more explanations and diagrams. > ___________________________________ > From a Science Egg to a Science of Diagrams > > John F. Sowa > Draft of 26 August 2023 > > Abstract. In the last decade of his life, Peirce developed phaneroscopy and > existential graphs as the basis for a proof of pragmaticism. To publish the > proof, he wrote a series of articles for the Monist. The first two began > with phaneroscopy. But in 1906, he added a version of tinctured existential > graphs to the third article, An Apology for Pragmaticism. In 1908, he began a > fourth article, which he never finished. One reason he stopped may be his > remark in 1909: “Phaneroscopy, still in the condition of a science-egg, > hardly any details of it being as yet distinguishable.” Other reasons involve > issues about the graphs, which he resolved in 1911. Although Peirce did not > complete the proof, his writings inspired aspects of Lady Welby’s significs, > Wittgenstein’s language games, and patterns of diagrams in every branch of > science and engineering. Today, Peirce’s theories of phaneroscopy and > diagrammatic reasoning clarify critical issues in cognitive science. Among > them are the methods of reasoning in linguistics, neuroscience and artificial > intelligence. > 1. Developments from 1903 to 1913 > > For Peirce, 1902 brought an end to two major projects: Baldwin’s dictionary > was finished, and funding for his Minute Logic was rejected. But three > events in 1903 led him to rethink every aspect of his life’s work: his > Harvard lectures in the spring, his Lowell lectures in the fall, and his > correspondence with Victoria Welby. As a guide to the new developments, the > tree in Figure 1 shows his classification of the sciences and dependencies > among them. Branches show the classification, and dotted lines show the > dependencies. Sciences to the right of each dotted line depend on sciences to > the left. Pure mathematics stands alone, and all other sciences and > engineering depend on mathematics (CP 1.180ff, 1903). > . . . [deleted] > In summary, phaneroscopy depends on mathematics, which includes existential > graphs as a formal logic. But as a diagrammatic logic, EGs can be used in > two ways. For phaneroscopy, the option of changing shape is important. > Nodes of a graph may be moved to match the shape of the image they represent. > For logic, however, changing the shape does not change the meaning. Since the > same notation can serve both purposes, EGs support Peirce’s prediction that > phaneroscopy “surely will in the future become a strong and beneficient > science” (R645, 1909). > 2. The Role of Diagrams in Phaneroscopy > > For the third Monist article, Prolegomena to an Apology for Pragmaticism, > Peirce chose a title that echoes Kant’s Prolegomena. In it, he addressed > Kant’s three “transcendental questions”: How is pure mathematics possible? > How is pure natural science possible? How is metaphysics in general > possible? The dotted lines in Figure 1 suggested the answer shown in Figure > 2: diagrams, such as EGs, are mathematical structures that relate > phaneroscopy, metaphysics, and the natural sciences to methods for thinking, > talking, and acting in and on the world. > > > > Figure 2: Diagrams relate thought and language to the world > The first sentence sets the stage: “Come on, my Reader, and let us construct > a diagram to illustrate the general course of thought; I mean a System of > diagrammatization by means of which any course of thought can be represented > with exactitude” (CP 4:530). Figure 2 shows an important step beyond Tarski’s > model theory. Instead of a one-step mapping from the world to language, the > diagram splits the mapping in two distinct steps. > Phaneroscopy maps some aspect of the world to a diagram, which is “an icon of > a set of rationally related objects” (R293, NEM 4:316). It serves as a > Tarski-style model for determining the denotation of languages, formal or > informal. But when a continuous world is mapped to a discrete diagram, an > enormous amount of detail is lost. Although the right side can be a precise > map from a graph to a formal logic, it may be an approximate mapping from an > informal diagram to the informal languages that people speak. In his career > as a scientist, engineer, linguist, lexicographer, and philosopher, Peirce > understood the complexity of both sides. > . . . [deleted] > An appropriate logic should facilitate a proof of pragmaticism. Peirce stated > the requirements in his Prolegomena: “a System of diagrammatization by means > of which any course of thought can be represented with exactitude.” Then > “operations upon diagrams, whether external or imaginary, take the place of > the experiments upon real things that one performs in chemical and physical > research.” The system has four aspects: (1) diagrams in EGs or other > notations; (2) grammars for mapping languages to and from diagrams; (3) > critic for evaluating the denotation {true,false} of diagrams in terms of a > formal logic; and (4) perception and action for relating the world to the > diagram. The arrows in the hexagon of Figure 4 indicate the flow of any > course of thought. > > See https:\\jfsowa.com\talks\eswc.pdf for some of the diagrams > > Figure 4: The flow of thought in an intelligent system > The hexagon in Figure 4 shows details implicit in Figure 2. The upper three > corners and the starburst of phemes represent intelligent processing. The > lower three corners correspond to the drawing by Uexküll in Figure 3. The > arrow from mental experience to and from action supports routine habits or > emergency responses. Behavior that requires complex reasoning may involve > all the nodes and arrows. > As Peirce insisted, a diagram of information flow, such as Figure 4, is not a > psychological theory. It may represent data that controls a robot or the > thought of an alien being in a distant galaxy. But the word exactitude for > representing “any course of thought” poses a challenge. As Figure 2 shows, > the mapping between the world and a diagram can only be approximate, and the > mapping between a diagram and a language can only be exact for notations that > are designed to represent those diagrams. Approximations must be recognized > and accommodated. > With his constant questioning, Peirce’s ideas kept evolving. In 1907, he had > stated the basis for his proof: “the Graphs break to pieces all the really > serious barriers, not only to the logical analysis of thought but also to the > digestion of a different lesson by rendering literally visible before one’s > very eyes the operation of thinking in actu” (CP 4.6, R298). 1909, he > expressed his concerns about phaneroscopy “still in the condition of a > science-egg” (R645). But in In the next two years, he addressed those issues > and generalized existential graphs to accommodate them. > 3. Relating Images to Diagrams > > Since the semes and phemes that flow along the arrows of Figure 4 may contain > uninterpreted percepts and images, ordinary existential graphs cannot > represent them. In the letter L231, in which Peirce specified his most > general notation for EGs, he mentioned his hopes of > representingn“stereoscopic moving images.” To accommodate them, Sowa (2016, > 2018) proposed generalized existential graphs (GEGs). Figure 5 shows Euclid’s > Proposition 1 stated in three kinds of GEGs: “On a given finite straight > line, to draw an equilateral triangle.” > . . . [deleted]. > For details, see Sowa (2018) Reasoning with diagrams and images, Journal of > Applied Logics 5:5, 987-1059. > http://www.collegepublications.co.uk/downloads/ifcolog00025.pdf > 4. Significs > > . . . [deleted] > During the following decade, correspondence between Peirce and Welby strongly > influenced both. In 1903, Peirce had adopted Kant’s abstract phenomenology. > But in 1904, he coined the new word phaneroscopy, which he discussed in terms > that were closer to Welby’s emphasis on observation and mental experience. > In his letters to her, Peirce added examples that clarified the motivation > and explained the details of his abstract analysis. His classification of > the sciences in 1903 (Figure 1) illustrates the differences, Peirce had > sharply distinguished mathematics, phaneroscopy, and the normative sciences. > With her emphasis on examples, Welby showed how practical issues affected the > details of each case. As a result of their correspondence, Peirce revised > and generalized the foundation of his logic, semeiotic, and pragmatism. > . . . [deleted] > Welby shared Peirce”s broad view of meaning and communication. In What is > Meaning (1903), she wrote “There is, strictly speaking, no such thing as the > Sense of a word, but only the sense in which it is used — the circumstances, > state of mind, reference, ‘universe of discourse’ belonging to it”. In the > Encyclopedia Britannica (1911), she emphasized the “importance of acquiring a > clear and orderly use of the terms of what we vaguely call Meaning; and also > of the active modes, by gesture, signal or otherwise, of conveying intention, > desire, impression and rational or emotional thought.” > Whitehead and Wittgenstein would agree, but Frege, Russell, and their > followers would strongly disagree. Among linguists, the founder of > transformational grammar, Zellig Harris, wrote “We understand what other > people say through empathy — imagining ourselves to be in the situation they > were in, including imaging wanting to say what they wanted to say.” But his > star pupil, Noam Chomsky, would claim that empathy is outside the subject > matter of linguistics. > 5. Language Games > > Peirce and Wittgenstein made a major transition from their early philosophy > to their later, and both in the same direction. One critic said that > Wittgenstein began as a logician and ended as a lexicographer. Ironically, > that remark, which was intended in a derogatory sense, is true in a higher > sense: they both discovered the flexibility and expressive power of natural > languages. For Peirce, the transition was marked by the 16,000 definitions he > wrote or edited for the Century Dictionary. For Wittgenstein, it was his > second published book, Wörterbuch für Kindern, which he wrote when he was > teaching elementary school in Austrian mountain villages. He learned that > children do not think or speak along the lines of his first book, the > Tractatus Logico-Philosophicus (TLP). > . . . [deleted] > 6. Diagrams As the Language of Thought > > Peirce’s writings on logic, semeiotic, and diagrammatic reasoning, which had > been neglected for most of the 20th century, are now at the forefront of > research in the 21st. The psychologist Johnson-Laird (2002), who had written > extensively about mental models, said that Peirce’s existential graphs and > rules of inference are a good candidate for a neural theory of reasoning: > Peirce’s existential graphs are remarkable. They establish the feasibility > of a diagrammatic system of reasoning equivalent to the first-order predicate > calculus. They anticipate the theory of mental models in many respects, > including their iconic and symbolic components, their eschewal of variables, > and their fundamental operations of insertion and deletion. Much is known > about the psychology of reasoning... But we still lack a comprehensive > account of how individuals represent multiply-quantified assertions, and so > the graphs may provide a guide to the future development of psychological > theories. > . . . [deleted] > These observations imply that cognition involves an open-ended variety of > interacting processes. Frege’s rejection of psychologism and “mental > pictures” reinforced the behaviorism of the early 20th century. But the > latest work in neuroscience uses “folk psychology” and introspection to > interpret data from brain scans (Dehaene 2014). The neuroscientist Antonio > Damasio (2010) summarized the issues: > The distinctive feature of brains such as the one we own is their uncanny > ability to create maps... But when brains make maps, they are also creating > images, the main currency of our minds. Ultimately consciousness allows us > to experience maps as images, to manipulate those images, and to apply > reasoning to them. > The maps and images form mental models of the real world or of the imaginary > worlds in our hopes, fears, plans, and desires. They provide a “model > theoretic” semantics for language that uses perception and action for testing > models against reality. Like Tarski’s models, they define the criteria for > truth, but they are flexible, dynamic, and situated in the daily drama of > life. > 7. Diagrammatic Reasoning > > Everybody thinks in diagrams — from children who draw diagrams of what they > see to the most advanced scientists and engineers who draw what they think. > Ancient peoples saw diagrams in the sky, and ancient monuments are based on > those celestial diagrams. They correspond to the mathematical “patterns of > plausible inference” identified by Pólya (1954). The role of diagrammatic > reasoning is one of Peirce’s most brilliant insights, and the generalized EGs > in his late writings include much more than an alternative to predicate > calculus. > All necessary reasoning without exception is diagrammatic. That is, we > construct an icon of our hypothetical state of things and proceed to observe > it. This observation leads us to suspect that something is true, which we > may or may not be able to formulate with precision, and we proceed to inquire > whether it is true or not. For this purpose it is necessary to form a plan > of investigation, and this is the most difficult part of the whole operation. > We not only have to select the features of the diagram which it will be > pertinent to pay attention to, but it is also of great importance to return > again and again to certain features. (EP 2:212) > . . . [deleted] > Computer systems can communicate with people by traslating their internal > represenations to and from notations that people can read and understand. > But as Zelling Harris said, computers cannot understand what people say until > they have sufficient empathy to imagine themselves to be in the situations > the humans are in, including imaging wanting to say what the humans want to > say. > > > _ _ _ _ _ _ _ _ _ _ > ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > . > ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to [email protected] > 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.
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