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 DiagramsJohn F. Sowa
Draft of 26 August 2023Abstract. 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 1913For 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 PhaneroscopyFor 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 DiagramsSince 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 GamesPeirce 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 ThoughtPeirce’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 ReasoningEverybody 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.
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