[CG] Diagrams as defined by C. S. Peirce

Alex, Thank you for demonstrating that LLMs can answer some questions and summarize some parts of an article (Excerpts234.pdf) without the slightest understanding of what they are doing. LLMs can extract verbal information from a Q/A session about details, But they may fail to understand why the author made those statements. Anybody who reads only those LLM summaries (see below) will have ZERO understanding of how, why, and what Peirce and I were trying to say. The following question shows that you were misled by the LLMs to misinterpret that article. Alex> I still think that your diagram is a kind of math object. Is that correct? That depends on what you mean by a math object. Since mathematics can represent a continuous infinity of possible structures, everything that can be observed, analyzed, or represented is a math object. Since every possible pattern of any kind can be represented by mathematics (possibly an infinite and/or a very dense finite approximation), calling something a math object means nothing. But Peirce's definitions start with raw experience from the senses (external perception and internal proprioception from bodily processes). That is what Peirce called the phaneron -- mental experience prior to any processing of any kind. Then he analyzed it the way people do. The first stage of processing (what Peirce called phaneroscopy) selects aspects or parts of the phaneron that the mind (or whatever you want to call the neural processes that analyze and interpret experience) considers important or significant for some reason. Those parts are still raw and unprocessed input that retains all the complexity of the phaneron -- and they contain as much detail as human perception can receive, store, and process. Those parts are also attached to links (relations) that add further information, which happens to be in a discrete graph-like form. The results of that early processing are HYBRID GRAPHS, which Peirce called hypoicons. (The Greek prefix hypo- is a synonym for the Latin prefix sub-) The discrete links form a conventional style of diagram. But the parts they link are unprocessed, continuous chunks with all the detail of the fragments of the original imagery. Further processing can analyze the fragments step-by-step into (a) discrete names, symbols and (b) finer and smaller hypoicons. Eventually, all the continuous material is replaced by discrete names, symbols, and relational links. Then and only then can the result be represented by a completely discrete existential graph (EG). Finally, that discrete EG can be mapped to a discrete language, formal or informal, which can be processed by LLMs. However, that graph might not have a simple mapping to a sentence in any natural language. Just look at the musical examples in Figure 7 of Excerpt234.pdf. On the left is a diagram of one bar of music in the usual musical notation. On the right is a conceptual graph (CG) which describes every note in the diagram on the left. Then look at Figure 8, which takes just one small excerpt of the CG in Figure 7, which represents a single note of the bar of music on the left. Then look at the mapping of that one note to a CG and an EG in Figure 8. Then look at the mapping of that CG or EG to an English sentence or a formula in predicate calculus. Any musician who plays music or any listener who enjoys listening to music, would almost never analyze music as expressed on the left of Figure 7 into Figure 8 or into the formula in predicate calculus. The only exception would be what I just did: do the analysis in order to show that the mapping to predicate calculus is NEVER what people do when they play or enjoy music. Conclusion: Most of what people do in their daily lives is like music: it cannot be mapped to words or be processed by LLMs without a distortion and misunderstanding of its meaning. If you don't believe that claim, I can point you to an overwhelming amount of research in cognitive science that supports it many, many times over. Informal analogy: The discrete residue may be adequate for some purposes. But the continuous info is lost. Sometimes the continuous bath water that was thrown away may have taken the baby with it. John ---------------------------------------- From: "Alex Shkotin" <alex.shkotin(a)gmail.com> John and Colleagues, Just as a Saturday addition, have a look at this dialogue [1] with my favorite Claude 2 [2]. After I have uploaded the pdf to it. Alex [1] Here is a Markdown version of our dialog: # Dialog on Graphs Described in Text Excerpts **Human**: what type of graphs are described in this text? **Assistant**: Based on the excerpts provided, the text describes several types of graphs: - Existential graphs (EGs) - These are a type of logical graph developed by Charles Sanders Peirce. They use nested graphs to represent logical assertions and rules of inference. - Generalized existential graphs (GEGs) - These are an extension of EGs that can include additional notations such as images/diagrams within the graph areas. - Conceptual graphs (CGs) - These are a type of semantic graph developed by John Sowa for representing natural language meanings. They use a bipartite structure with concept nodes and relation nodes. - Diagrams - The text discusses various kinds of diagrams, such as musical diagrams, geometrical diagrams, etc. Diagrams are considered a type of iconic sign that represents relations between objects. - Phemic sheets - These are diagrammatic representations of mental experience derived from perception and action on the world. They were proposed by Peirce as a way to iconically represent a "universe of discourse." - Delta graphs - These were a proposed extension of Peirce's existential graphs, intended to support additional features like higher-order logic, probability, and virtual reality representations. They could potentially be represented using generalized existential graphs. So in summary, the key graph types discussed are existential graphs, conceptual graphs, various diagrams, and proposed extensions like generalized existential graphs and delta graphs. The graphs aim to bridge logical formalisms with perceptual and mental models. **Human**: what type of diagrams are described in this text? **Assistant**: Based on the excerpts, the main types of diagrams described are: - Existential graphs (EGs) - Logical diagrams developed by Peirce to represent propositions and inferences. - Generalized existential graphs (GEGs) - Extension of EGs that can incorporate images, diagrams, and additional notation. - Conceptual graphs (CGs) - Semantic networks that represent concepts as nodes and relations between them. - Musical diagrams - Used to represent notes, melodies, tones, durations, etc. More iconic for musicians. - Geometric diagrams - Such as those used in Euclid's proofs. Include shapes like points, lines, and triangles. - Phemic sheets - Diagrammatic representations of mental experience and "universes of discourse." - Delta graphs - A proposed extension of Peirce's EGs to handle more complex representations. - Iconic diagrams - Diagrams that directly resemble the objects or relations they represent. - Symbolic diagrams - More abstract diagrams relying on symbols rather than direct resemblance. The key point is that diagrams act as an intermediate bridge between visual perception and formal logical languages. Different types of diagrams have different tradeoffs in terms of visual resemblance versus symbolic efficiency. **Human**: What is a Delta graph? **Assistant**: Based on the excerpts provided, a Delta graph is a proposed extension to Charles Sanders Peirce's existential graphs (EGs) that Peirce started specifying in 1911. Some key points about Delta graphs: - They were intended to extend EGs to support additional representational capabilities, such as higher-order logic, probability, modality, and virtual reality. - Peirce's specification of Delta graphs was incomplete, but he envisioned them being able to represent things like "stereoscopic moving images." - The capabilities Peirce wanted Delta graphs to have could potentially be represented using an extension of EGs called generalized existential graphs (GEGs). - GEGs allow embedding diagrams, images, and notations within the graph areas. This provides a bridge between visual perception and symbolic logic. - Delta graphs were meant to push EGs beyond just first-order logic and enable representation of Peirce's ideas like tychism (evolution according to chance) and synechism (continuity). - To fully achieve Peirce's vision would require extending graphs to multiple dimensions and incorporating more advanced mathematics. - Although Delta graphs were never fully realized, they point toward enhancing the expressiveness and reasoning capability of diagrammatic logics. So in essence, Delta graphs were proposed by Peirce as a way to build on EGs to create a more versatile diagrammatic reasoning system, but the details were never fully fleshed out before his death. The ideas behind them influenced later extensions like GEGs. **Human**: give Markdown version of this dialog. **Assistant**: Here is a Markdown version of our dialog: (See above) [2] https://claude.ai/chat/bbfc2686-649e-4654-b47c-217dae51299e пт, 17 нояб. 2023 г. в 22:19, John F Sowa <sowa(a)bestweb.net>et>: Alex, The diagrams you are thinking about are limited to what can be translated to a formal linear notation. But I am talking about the general theory of diagrams by C. S. Peirce, which is immensely richer. Those diagrams can INCLUDE full multidimensional images as parts at any arbitrarily refined precision. They can also include as parts any mathematical structures of any kind in any number of dimensions. They can subsume as parts anything and everything that can be included in any digital device or any analog device that can simulate continuity at any resolution. Please read the attached Excerpt234.pdf from Sections 2, 3, and 4 of the article I'm writing. To answer your questions, they can represent EVERYTHING you are asking for in your list below. Please read those excerpts. Then we can begin to discuss the issues in terms of the rich foundation that Peirce was developing. He died before he completed all the work, but he outlined the methods. And I have added some features along the lines that he had suggested. John