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Peirce's Existential Graphs  Readings and Links
This site contains readings and links on the existential graphs,
including his work on the logic of relations (relatives, as he called
them) of Charles Sanders Peirce (18391914). As far as I have read
them, I have written some short comments on the articles and books. Of
course these comments are flavoured by my very personal and
mathematical view on existential graphs (and sometimes much too
short), but nonetheless, I hope they can help you select the right
readings for you. Moreover, I hope that none of my critical comments
will offend any of the authors.
I intend to make this list in the long run, of course as complete as
possible. So If you know more stuff which should be put on this list,
please let me know.
Last, not least: Do not hesitate to inform me about misspellings etc. I
do know that my english is far from perfect. And if you find
any dead links or other problems, please let me know, too.
2005/11/21:
I have created a `small' (1.8 MB) gif with an animated
proof (a moving picture of thought, as Peirce would say)
of Leibniz' splendid theorem, carried out with Peirce's
Alpha graphs. You can find it here:
Leibniz' Praeclarum Theorema
Changes on this website:
 2007/1/01:
 Congratulations to Frederik Stjernfelt that his
thesis "Diagrammatology: An Investigation on the
Borderlines of Phenomenology, Ontology, and Semiotics"
has been published by Springer!
 2007/01/28:
 I am pleased to be invited for a special issue on Peircean
Diagrammatic Logic for Semiotica, Elsevier, which will be published in
2008. My contribution is about ligatures in existential graphs. It can
be found on this site at on my publication list. Moreover, I added
another paper on my own on constants and functions in existential graphs.
 I have two broken links to former sites with scans of Peirce's
original manuscripts. If anybody can help me finding the pics which
had been on these sites (see below), pleas let me know.
 I added some remarks to the book of Hammer.
 2006/09/12: I uploaded a new version of my own treatise. At the moment,
I am very busy and do not have enough time to maintain this site carefully.
I hope this will change next year (2007). Nonetheless, I want to draw
your attention to three recent papers which had been published in the
proceedings of ICCS 2006:
 Joachim Hereth Correia and Reinhard Pöschel finally found a
proof of Peirce's Reduction Thesis in a much more general setting
than that of Herzberger or Burch. Their proof is far from being
trivial and needs much more sophisticated arguments than Herzberger
or Burch need. It is a really great result.
 Frederik Stjernfelt investigates in "Two Iconicity Notions in Peirce's
Diagrammatology", as the title says, the iconicity in Peirce's graphs
to an great extent.
 Last and least :), I published a paper about interesting prooftheoretic
results in Peirces calculus for Alpha graphs.
All papers offer insights into Peirce graphs which has so far not been
unfolded.
 2004/08/23
 2004/06/20
Books  exclusively on Existential Graphs

Markus Arnold: Einführung in die kontextuelle Relationenlogik.
Diploma Thesis, Darmstadt 2001 (Advisor: Rudolf Wille)
This german thesis is based on
Burch's book and
Wille's paper on the algebra of relations.
I think if you want to get a copy of this thesis, you should contact Rudolf Wille.

Robert W. Burch: A Peircean Reduction Thesis: The Foundations of Topological Logic.
Texas Tech University Press, 1991.
This book is a detailed and precise elaboration of the socalled Peircean Algebraic Logic (PAL).
PAL is very closely related to Peirces logic of relatives. I consider the book rather technical
and hard to read, but it provides detailed insights into the nature of existential graphs,
particularly in the roles of the socalled teridentity and hypostatic abstraction.
The main focus of the book is to provide a proof for Peirce's thesis that triadic realtions
are neccessary and suffiecient for constructing all relations.
It is not appropriate for beginners on existential graphs; you should already be familiar
with the graphs if you read the book.

Frithjof Dau:
Mathematical Logic with Diagrams  Based on the Existential Graphs of Peirce.
As the author of this website, it is not very surprising that I am writing on
a treatise about existential graphs on my own ... This treatise is still in
preparation. I dare to supply a preliminary version of it which
contains the core of my work. As the title says, I focus on a mathematical
elaboration of Peirce's Alpha and Beta graphs. Nonetheless, the treatise
contains a chapter about my understanding why Peirce considers his EGs to be
the luckiest find of his career, some general considerations about the
formalization of diagrams, and a chapter with some remarks to the books of
Roberts, Shin and Zeman.
Update: 12. September 2006 I uploaded a new version of the treatise.
The content is finished, it will only be subject of further proofreading.
If you find any mistakes, flaws, misprints etc, please let me know.
compressed pdffile (3.2 MB)
uncompressed pdffile (4.5 MB)

Kenneth Laine Ketner: Elements of Logic: An Introduction to Peirce's Existential Graphs.
Texas Tech University Press, Lubbock, Texas, 1990.
So far, I don't know this one ...

D. D. Roberts:
The Existential Graphs of Charles S. Peirce.
Mouton, The Hague, Paris, 1973.
Probadly the most popular secondary literature on existential graphs.
This book offers a comprehensive description of the whole system of existential graphs.
Particularly, the gamma part of existential graphs is described to a large extent
(far more than the broken cuts, which is the main focus of most papers or books
which deal with gamma). Obviously, Roberts worked through many, many manusscripts of
Peirce, and he justifies his elaboration with a lot of quotations.
From a mathematical point of view, this book is unfortunately insufficient.
Roberts does not provide any (technical or mathematical) definitions, and he
relies solely on the graphical representations of graphs. Nonetheless, this
is definetely a outstanding work.
Together with the books of Shin and
and Zeman, this is a "standard reading".
More detailed critics can be found here.

SunJoo Shin:
The Iconic Logic of Peirce's Graphs.
Bradford Book, Massachusetts, 2002.
I enthusiastically read this book within two days. It is an elaboration of Peirce's alpha and betagraphs,
including improved translations ("readings") to propositional and first order logic.
I liked most the philosophical backgrounds this book offers.
Similar to the book of Roberts,
this treatise lacks mathematical preciseness. Particularly, some of the
rules Shin provides are not sound (but these flaws can easily be fixed),
and the translation of beta graphs to first oder logic contains a flaw
as well (I discussed this with Shin, and she agreed, thus I dare to express
this critics).
Nonetheless, in all other aspects I enjoyed the book very much. It is very good read and can
really recommend it.
Together with the books of Roberts and
and Zeman, this is a "standard reading".
More detailed critics can be found here.

John Stewart :
Theorem Proving Using Existential Graphs
Master thesis (advisor: Robert Levinson), 1996.
A computer science approach for an automatic theorem prover on the basis of existential
graphs. As far as I know, this is the only work using existential graphs for theorem
proving. The underlying structures are abstractions of the diagrams and do not incorporate
any diagrammatic or graphical features of existential graphs. Thus, those who are
interested especially in problems concerning diagrammatic representations will
hardly benefit from this thesis. Moreover, this thesis does not touch any philosophical
questions on existential graphs.
On the other hand: For those who are intested in deduction procedures, this
is of course a good choice.
My impression is that this thesis sometimes mixes up syntax and semantics. So,
in my view, although written by a computer scientist, this thesis lacks sometimes
mathematical preciseness.
As far as I know, this thesis is not published.
I think if you want to get a copy of this thesis, you should contact Robert Levinson.

Frederik Stjernfelt:
Diagrammatology: An Investigation on the
Borderlines of Phenomenology, Ontology, and Semiotics
Synthese Library , Vol. 336. SpringerVerlag, HeidelbergBerlin, 2007.
507 p., Hardcover ISBN: 9781402056512 139,95 Euro
So far, I did not read this book, so I provide a summary from Springers site:
Diagrammatology investigates the role of diagrams for thought and
knowledge. Based on the general doctrine of diagrams in Charles
Peirce's mature work, Diagrammatology claims diagrams to constitute a
centerpiece of epistemology. The book reflects Peirce's work on the
issue in Husserl's contemporanous doctrine of "categorial intuition"
and charts the many unnoticed similarities between Peircean semiotics
and early Husserlian phenomenology. Diagrams, on a Peircean account,
allow for observation and experimentation with ideal structures and
objects and thus furnish the access to the synthetic a priori of the
regional and formal ontology of the Husserlian tradition.
The second part of the book focusses on three regional branches of
semiotics: biosemiotics, picture analysis, and the theory of
literature. Based on diagrammatology, these domains appear as
accessible for a diagrammatological approach which leaves the
traditional relativism and culturalism of semiotics behind and hence
constitutes a realist semiotics
Diagrams will never be the same. A fascinating and challenging tour
through phenomenology, biology, Peirce's theory of signs and
Ingarden's ontology of literature, all neatly tied together through
the guiding thread of the diagrammatical. A veritable tour de force.
Barry Smith, SUNY at Buffalo, U.S.A.
With his meticulous scholarship, Frederik Stjernfelt shows that
Peirce and Husserl were cultivating a broad and fertile common
ground, which was largely neglected by both the analytic and the
continental philosophers during the 20th century and which promises
to be an exciting area of research in the 21st.
John F. Sowa, CrotononHudson, U.S.A.

J. J. Zeman: The Graphical Logic of C. S. Peirce
You can find a htmlversion of this book at the homepage of Zeman.
This book offers a mathematical elaboration of Peirce's alphagraphs,
Peirce's betagraphs, and the part of Peirce's gammagraphs which
extend the betapart by adding the socalled "broken cut" (this part
corresponds to modal logic). Similar to Roberts, he justifies his
elaboration with a lot of quotations, and he gives some philosophical
background, too.
The only critics I have are: Like Shin and Roberts, Zeman does not provide an
extensional semantics of EGs, `only' translations from graphs to propositional
(for alpha), first order (for beta) and modal (for gamm) logic. These
translatation are correct, but in my eyes a little bit clumsy (you can find a
discussion of this in Shin's book as well). Zeman's definition is an
abstract, mathematical definition (here I have to withdraw a former statement
of mine on this website: sorry for that), but he does not discuss the
relationship of his definition and the graphical representations of
EGs (this relationship is fairly clear to him).
For reading this book, one should be little bit familiar with existential
graphs: It is not as readable like the book of Shin. On the other hand, this
book is in my opinion from a mathematical point of view the best book on
existential graphs so far.
Together with the books of Roberts and
Shin, this is a "standard reading".
More detailed critics can be found here.
Books  containing Existential Graphs

Frithjof Dau: The Logic System of Concept Graphs with Negations
(And its Relationship to Predicate Logic).
PhDThesis. An extended version will appear in Springer Lecture Notes on Computer Science (LNCS 2892).
If you have access to springerlink, you can download this thesis at
springerlink.
Ok. This is advertisement for my thesis. Nonetheless, you will find a short introduction into existential graph
in this treatise.

E. M. Hammer:
Logic and Visual Information.
CSLI Publications, Stanford, California, 1995.
An elaboration of different diagrammatic systems, like
Venn diagrams, Euler circles, or higraphs, containing an chapter
on Peirce's alpha graphs.
I used this book as a textbook for a lecture on logic with diagrams
(the part on venn diagrams). I have to say that from a mathematical
point of view, this book is not precise enough, and it contains some
(minor) flaws.

Derik Hawley: Logic in Pictures: An Examination of Diagrammatic Representations, Graph Theory and Logic.
Thesis requirement for the degree of Master of Arts in Philosophy, Waterloo, Canada, 1994.
pdffile
A master of arts in philosphy thesis. This easytoread thesis (50
pages) provides an abstract definition of Peirce's beta graphs by
means of mathematical graph theory. This definition is similar to the
definition of concept graphs with cuts (see my thesis), and very similar to Pollandts
definition of relation graphs (see her ICCSpaper). Thus this approach has my
full sympathies. But the argumentation does not go into details, some
(in my view important) aspects are discussed only perfunctorily. The
philosophical dimension of existential graphs is nearly discussed not
at all. But this thesis is the only one I found so far which provides
an abstract mathematical definition for existential graphs (which
prescinds from the graphical properties of the diagrams), so it is
definetely worth reading it.

Nathan Houser, Don D. Roberts, James Van Evra (Eds):
Studies in the Logic of Charles Sanders Peirce.
Indiana University Press; 1977.

H. Pape:
Charles S. Peirce: Phänomen und Logik der Zeichen.
German translation of Peirce's Syllabus of Certain Topics of Logic.
Suhrkamp Verlag Wissenschaft, 1983.
Unfortunately, this syllabus, which gives valuable insight into Peirce's understanding
of his graphs, is published only partly in the collected papers.

C. S. Peirce:
Reasoning and the Logic of Things. The Cambridge Conferences Lectures of 1898.
Cambridge, Massachusetts, London, England,
Ed. by K. L. Ketner, H. Putnam, Harvard Univ. Press, Cambridge 1992.
Lecture three is titled "the logic of relatives" and is about existential
graphs. Moreover, you find some discussion in the comprehensive comments
on the lectures as well.
A german translation of this lectures have recently been published by Suhrkamp Verlag.

C. S. Peirce, Collected Papers.
Vol. 16 edited by Charles Hartshorne and Paul Weiss, vol 78 edited b< Arthur Burks, Cambridge: Harvard, 193158.
Including a comprehensive 100 pages elaboration of EGs in Vol. 4 which is very
instructive.
Articles

Robert W. Burch: Peirce on the Application of Relations to Relations..
Published in an anthology edited by Nathan Houser and Don D. Roberts. Indanapolis: Indiana University Press, forthcoming.
Robert W. Burch: Valental Aspects of Peircean Algebraic Logic..
In: Computers Math. Applic. Vol.23, No.69, pp.665677, 1992.

Frithjof Dau: An Embedding of Existential Graphs into Concept Graphs with Negations.
In: Priss, U.,Corbett, D:, Angelova, G.\ (Eds.): Conceptual Structures: Integration and Interfaces.
ICCS 2002, Borovets, Bulgaria, July 15July 19, 2002, Proceedings.
SpringerVerlag, HeidelbergBerlin, 2002.
pdffile
An article on my own which translates Peirce's beta graphs to concept
graphs with cuts (see my thesis). Even if
you are not familiar with concept graphs, you can find some good hints
how and more important, why beta graphs have to be read.

Frithjof Dau: Types and Tokens for Logic with Diagrams: A Mathematical Approach.
See on this site under 'publications'.
Another article on my own, where I discuss how graphs have to be handled in
order to get a rigour formal system. I embedded my argumentation into a case
study, namely Peirce's alpha graphs, thus you find a mathematization of these
graphs, (syntax, semantics, calculus, including a proof that the calculus is
sound and complete) in this paper.

Frithjof Dau: Some Notes on Proofs with Alpha Graphs
See on this site under 'publications'.
There are basically three results in this paper, but I will only refer to two
of them. First, it is shown that the erasre rulecan be removed from the
calculus, and the calculus is still weakly complete (i.e., all tautologies
can be proven). This is nice as the erasure rule is the only rule which
does not fulfill the socalled `finite choice property'. Roughly speaking,
this is like removing the cutrule from a sequent calculus (of course,
Gentzen's proof for this result is much more sophisticated than mine for
removing the erasure rule), i.e. the remaining calculus is as `nice'
as a cutfree sequent calculus. The second result then is interesting:
There are formulas which can be proven in sequent calculi in polynomial
length, but in cutfree sequent calculi, the lengths of the proofs increases
exponentially. For alpha graphs, these formulas can be, even in the
restricted calculus, in polynomial length. Thus this result shows
drastically the fundamental difference between Peirce's transformation
rules and contemporary calculi, like sequent calculi.

Frithjof Dau: Ligatures in Peirce's Existential Graphs.
To appear in a special issue `Peircean diagrammatical logic'
of Semiotika, Elsevier. See on this site under 'publications'.
This paper describes a deeper understanding of ligatures i.e., networks of
lines of identity in Peirce's existential graphs. In constrast to lines of
lines of identity, ligatures do not neccessarily denote a single object. This
makes them in some cases harder to read and understand. The paper introduces
a special case of ligatures, socalled singleobjectligatures, which can
basically be understood like lines of identity, and based on this notion,
a simplified reading of existential graphs is introduced. The paper is based
on some results of my treatise on EGs, but provides
the results of it in a more informal manner.

Frithjof Dau: Constants and Functions in Peirce's Existential Graphs.
Submitted to ICCS 2007. See on this site under 'publications'.
Peirce's existential graphs describe a logic ofrelations, i.e., the
Beta part of existential graphs corresponds to first order logic with
identity, but without constants or functions. This paper investigates
how the syntax, semantics and particularly the calculus of existential
graphs has to be extended in order to capture constants and functions
as well. I provide the paper, as it is submitted to ICCS (it is under review).
pdffile

E. M. Hammer:
Semantics for Existential Graphs.
Journal Philosophical Logic, Vol. 27, 1998, 489503.

J. Hereth Correia, R. Pöschel:
The Teridentity and Peircean Algebraic Logic
In: Schärfe, Henrik; Hitzler, Pascal; Ohrstrom, Peter (Eds.):
Conceptual Structures: Inspiration and Application.
14th International Conference on Conceptual Structures, ICCS 2006, Aalborg,
Denmark, July 1621, 2006, Proceedings.
Springer, LNAI, Vol. 4068
A sophisticated mathematical proof for Peirce's Reduction Thesis in a
very general setting. The proof is ugly (many case distinctions), but
correct (yes, I read it). The result is simply great!

J. Hintikka: The Place of C S. Peirce in the History of Logical Theory.
In: Brunning and Forster (1997), 1333.

Mary Keeler: The Philosophical Context of Peirce's Existential Graphs.
As the title of the paper says, it consideres existential graphs from a philosophical
point of view (and does not contain a single diagram ;)). Not easy to read (at least
not for me), but it cointains some good and important points (e.g., Peirce's purpose
in developping existential graphs).
article

Ralf Müller:
Peirce's Existential Graphs: First Inquiries towards a Proper Understanding.
In: Jaap van Brakel, Michael van Heerden (Eds.):
C.S. Peirce, categories to constantinople,
proceedings of the international symposium of Peirce, Leuven University Press, 1997.

P. Øhrstrøm: Some Peircean Problems Regarding Graphs for Time and Modality
Second International Conference on Conceptual Structures,University of
Maryland, Proceedings, 1994, p.7892.
Together with Jan Schmidt and Harmen van den Berg.

P. Øhrstrøm: Logic and Existential Graphs
Topics in Cognitive Science and HCI 6, (redigeret af Inger Lytje), 1995, p. 137154.

P. Øhrstrøm: Existential Graphs and Tense Logic
in: Conceptual Structures: Knowledge Representation as Interlingua  Lecture Notes in Artificial Intelligence 115.
Peter W. Eklund, Gerard Ellis, Graham Mann (Eds) (44th International Conference on Conceptual Structures,
ICCS '96, Sydney, Australia, August 1996, Proceedings), Springer, Berlin. pp.
203217 ISBN: 3540615342.

P. Øhrstrøm: C. S. Peirce and the Quest for Gamma Graphs
Conceptual Structures: Fulfilling Peirce's Dream, Lecture Notes
in Artificial Intelligence, Springer Verlag 1997, p.357370.
article

P. Øhrstrøm:
A Software System for Learning Peircean Graphs
Published in W.Tepfenhart & W. Cyre (eds.). Conceptual
Structures: Standards and Practices, Lecture Notes in Artificial Intelligence
1640, 1999, p. 184197. Together
with Torben Braüner and Claus Donner.

Silke Pollandt: Relation Graphs:
A Structure for Representing Relations in Contextual Logic of Relations.
In G. Angelova, D. Corbett, U: Priss (Eds.):
Conceptual Structures: Integration and Interfaces.
LNAI 2393, Springer Verlag, BerlinHeidelberg 2002.
A paper, based on Burch's book and
Wille's paper, which provides
a mathematical elaboration of relation graphs (existential graphs
with "pending edges" which describe relations).

D. D. Roberts:
The Existential Graphs.
Computers Math.\ Appl.., Vol. 23, No. 69, 1992, 63963.

SunJoo Shin:
Diagrams and a Theory of Seeing.
article
A 3pages paper on the different ways an existential graphs
ca be perceived.

SunJoo Shin:
Reviving the Iconicity of Beta Graphs.
In:
Theory and Application of Diagrams: First International Conference,
Diagrams 2000, Edinburgh, Scotland, UK, September 2000. Proceedings
Lecture Notes in Computer Science ,SpringerVerlag Heidelberg, 2000.
The document is downloadable from the springersite.
First of all: The results of this paper can be found in
Shin'as book as well.
The paper offers a new translation (Shin uses the term
"reading") of existential graphs to first order logic which
benefits from the "visually clear facts" in a diagram. I
do like her approach, as it unfolds the specific advantages of
diagrammatic systems.
Unfortunately, her reading is not totally correct: see
my paper. But this flaw can be corrected.
If this is done, the translation is indeed very nice
(much better to understand than Zemans translation of EGs (see
Zeman's book).

SunJoo Shin:
Reconstituting Beta Graphs into an Efficacious System.
In: Journal of Logic, Language and Information, Vol. 8, No. 3, July 1999.

SunJoo Shin:
Multiple Readings of Alpha Graphs
In: M.Anderson, B.Meyer, P.Olivier (Eds.): Diagrammatic Representation and Reasoning.
SpringerVerlag, HeidelbergBerlin, 2002.

C. S. Peirce, John F. Sowa:
Existential Graphs: MS 514 by Charles Sanders Peirce with Commentary by John F. Sowa.
article

J. F. Sowa:
Logic: Graphical and Algebraic.
Manuskript, CrotononHudson 1997.

F. Stjernfelt:
Two Iconicity Notions in Peirce's Diagrammatology
In: Schärfe, Henrik; Hitzler, Pascal; Ohrstrom, Peter (Eds.):
Conceptual Structures: Inspiration and Application.
14th International Conference on Conceptual Structures, ICCS 2006, Aalborg,
Denmark, July 1621, 2006, Proceedings.
Springer, LNAI, Vol. 4068
The first paper which introduces two notions of iconicity,
an operational and a optimal (imho, the latter is basically the common
understanding of iconicity in Peirce's graphs). Pretty interesting.

Rudolf Wille: Lectures on Contextual Logic of Relations.
A paper from 2000 based on Burch's book
(see also Markus Arnold: Einführung in die kontextuelle Relationenlogik).
You have to contact Rudolf Wille to get this paper.

J. J. Zeman: Peirce and Philo
article.

J. J. Zeman: Peirce's Philosophy of Logic
article.
Images of original manusscripts of Peirce
A couple of people, most of them from the PORTcommunity (PORT: Peirce Online Resource Testbed),
offer some images of original manusscripts of Peirce. I have to say that, when
I discovered them for the first time, I was touched. Here are some links:
Further Stuff
The following links are not especially on existential graphs.

Stanford Encyclopedia of Philosophy: Peirce's Logic
(Written by E. M. Hammer)

Stanford Encyclopedia of Philosophy: Diagrams
(Written by SunJoo Shin and Oliver Lemon)

Stanford Encyclopedia of Philosophy: Peirce
(Written by Robert Burch)

Robin Catalogue
The annotated catalogue of the papers of Peirce by Richard S. Robin.
Due to the annotation, this site is good to scan which papers
of Peirce you should read for a specific purpose.
 The Peirce Edition Project
A rich source, including the Essential Peirce, lots of links, and a
instructive site how the original manuscripts of Peirce are transcripted
into a digital representation.
 Homepage of the digital Peirce
This is not especially on existential graphs, but you will find a lot of Peircerelated links here.
 Charles S. Peirce
Including htmlversions of some Peircetexts, like
"On a New List of Categories", "The Fixation of Belief " or
"How to Make Our Ideas Clear".

MCI
Another site, containing some photos of Peirce, and a lot of Peircerelated links.

Peirce and Logic
Unfortunately a chinese site, but party in english.
Lots of helpful links, particularly on
REFERENCES.htm.

The Commens Dictionary of Peirce's Terms
Peirce's Terminology in His Own Words. Edited by Mats Bergman and Sami Paavola.

The Peirce studies group
A spanish site, containing lots of spanish readings and a big
english bibliography.
Including a searchfunction. Very helpful.

Louis K. Kauffman: The Mathematics of Charles Sanders Peirce,
Cybernetics & Human Knowing, Vol.8 No12, 2001, pp.79110.
article
Hilary Putnam: Peirce the Logician,
Historia Mathematica, 1982.
A reading I do not know, but they sound related ...
Dr. Frithjof Dau

Dresden, Germany

Letzte Änderung / last change: 20230407
