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Review of  Diagrammatology

Reviewer: Elisabeth Birk
Book Title: Diagrammatology
Book Author: Frederik Stjernfelt
Publisher: Springer
Linguistic Field(s): Psycholinguistics
Book Announcement: 19.3648

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AUTHOR: Stjernfelt, Frederik
TITLE: Diagrammatology
SUBTITLE: An Investigation on the Borderlines of Phenomenology, Ontology, and
SERIES: Synthese Library 336
YEAR: 2007

Elisabeth Birk, Department of Computer Science 5 / Informatik 5 (Information
Systems) and Institute for Linguistics and Communication Studies (ISK), Aachen
University (RWTH Aachen), Germany

Stjernfelt's ''Diagrammatology'' is an investigation into the ontological
foundations of semiotics. On the basis of his interpretations of Peirce and
Husserl, Stjernfelt promises no less than a ''counterrevolution in semiotics''
(ix): conventionalist approaches that privilege the linguistic sign are to give
way to a ''semiotic realism'' (ix). He proposes to fulfill this ''foundational
task'' (ix) by inquiring into the ''phenomenological prerequisites to sign use''
(ix), and diagrams are the type of sign that provides the key to these
prerequisites: Diagrams can make the a priori structures of ontological domains

The first part of the work offers an interpretation of Peirce with a focus on
his ''doctrine of diagrammatical reasoning'' (xiv) and an interpretation of
Husserl. Stjernfelt's aim is to highlight hitherto overlooked parallels between
these two authors, in particular between Husserl's notion of ''categorial
intuition'' in the ''Logische Untersuchungen'' and Peirce's conception of the
epistemological function of diagrams.

The second part (chapters 9 – 18) of ''Diagrammatology'' investigates the role of
diagrammatic reasoning in biosemiotics, visual studies and literary theory.
These case studies are examples of the type of semiological analysis Stjernfelt
seeks to establish; they can also be seen as a demonstration of the scope of the
semiological analyses envisaged by the author.

The overall structure of the book is the following: In chapters 1 to 4
Stjernfelt introduces his reading of Peirce, chapter 5 explores the notion of
transformation in semiotics, chapters 6 to 8 focus on Husserl and his relation
to Peirce; chapters 9 – 12 are devoted to biosemiotics, chapters 13-15 present
Stjernfelt's contribution to visual studies, and chapters 16-18 his take on the
interpretation of literature. The blocks of chapters and some of the chapters
themselves are relatively self-contained; a useful summary (xv-xix) and a
diagram showing the structure of the book (xx) can be found in the Introduction.

The theoretical core of Stjernfelt's ''Diagrammatology'' is his reading of Peirce:
His aim is to establish a connection between a metaphysical idea (the idea of
''real possibilities''), a semiotic position (iconicity and thereby similarity as
the basic semiotic relation), and an epistemological model (Peirce's triad of
abduction-deduction-induction). Diagrams play a role on all three levels: as
structures of real and fictional worlds, as physical tokens of sign types, and
as ''subjective representations'' (334). The correspondences between these three
levels of analysis are what makes diagrams such powerful instruments of
cognition. Many diagrams show explicitly the structures that other semiotic
processes are implicitly based on. This is why, for Stjernfelt, the diagram can
be seen as the paradigmatic sign.

The first chapter of the book outlines Peirce's ''philosophy of continuity'' (5):
Peirce argues for the ''ineradicability of continuity in experience'' (6) and that
is - for Stjernfelt - the (metaphysical) key to our ability to use truly general
concepts, and thereby to a realist semiotics. Only insofar as reality is
experienced as continuous are we capable of using signs that refer not only to
extensionally defined collections of objects, but to the realm of possibility.
This idea is pursued in the second chapter, where Stjernfelt states that the
generalities we note, such as e.g. ''relations, tendencies, patterns, laws,
dispositions'' (47) etc. are to be understood as ''real possibilities'' (46), in
other words, referring to the structural or causal characteristics of a given
(ontological) domain.

Chapter two also presents Peirce's well known classification of signs and
connects the metaphysical and semiotic level of the analysis. Here, Stjernfelt
introduces two ideas that are of central importance for a realist semiotics:
Firstly, the idea that ''any higher sign, index and symbol alike, must contain,
or, by association or inference terminate in, an icon.'' (29); in some respect,
every sign is connected to similarity relations. Secondly, ''the icon, while not
in itself general, is the bearer of a potential generality'' (29); in other
words: icons are not simply mirrors of what there is, they also show (real)
possibilities (and, as Stjernfelt will add later in the book, icons can only
show what is possible, not what is impossible (87)).

Chapter three defends the assumption that similarity plays a foundational role
in semiotics against Goodman and Eco. Chapter three is an attempt to invalidate
conventionalist accounts in semiotics: In particular, Stjernfelt tries to
counter every single one of Goodman's ''Seven Strictures on Similarity''. One of
Stjernfelt's main concerns in this context is that to count as an icon ''a sign
must signify through its similarity to its object'' (50), not simply be similar
to it – the foundational task fulfilled by the icon and the distinction between
icon, symbol and index as different types of reference is – among many other
things – what Goodman is supposed to have failed to understand (54).

Chapter four explores the ''potential generality'' of the icon by introducing what
Stjernfelt calls an ''operational'' definition of similarity (90) and thereby of
the icon (91): ''the decisive test for its iconicity rests in whether it is
possible to manipulate the sign so that new information as to its object
appears'' (90). This extension of the notion of similarity is based on the idea
of the diagram as the prototypical icon: the diagram is an icon that can be
manipulated, as, for example, in geometrical proofs. Stjernfelt chooses the
geometrical proof of the Pythagorean theorem (x sq.) as an example to explain
his notion of ''operational'' similarity: the manipulation of the diagram in a
space conceived as continuous gives rise not only to a new insight, but to a
general proposition, a law. Diagrams are representations of ''rationally related
objects'' (94). Stjernfelt extends this model to all icons and, thereby, to
(elements in) all sign use. ''[D]iagram experimentation'' - i.e. ''various
counterfactual transformations of the phenomenon's real possibilities as the
means of gaining insight into it'' (116) - is a ''basic rational semiotic
behaviour'' (115) present in semiotic processes as different as ''the tropisms
studied by biosemiotics, the contemplation of pictures, metaphorical,
analogical, and poetical reasoning, linguistic and analogical syntax, basic
sensorymotor schemata, as well as mathematics proper'' (115). For Stjernfelt,
this idea is ''the core point of Peircian diagrammatology'' (99).

Chapter five adds historical perspective to this idea by presenting
transformation as a central category in semiotics. Stjernfelt traces the notion
of transformation in Lévi-Strauss, Thom, Greimas, and others, and in
contemporary works in Cognitive Linguistics.

Chapters six to eight turn to Husserl and Stjernfelt's reading of the
phenomenological aspects of diagrammatology. Categorial intuitions in Husserl's
''Logische Untersuchungen'' play, according to Stjernfelt, a role that is
''analogous'' to diagrams in Peirce (158): both permit abstraction by something
like eidetic variation, and ''both point to the necessity of the direct intuitive
access to ideal objects as a prerequisite to a phenomenologically perceived
realism'' (159).

Both, intuition and variation are needed to support Stjernfelt's ''non-inductive''
(137) explanation of abstraction, an abstraction that yields the results
demanded by the author: nothing less than a ''formal ontology'' (162) that takes
its cue from Husserl's mereological analyses. Diagrams make formal ontological
structures explicit: the structure of the diagram may show the mereological
structure of the domain represented (173). Chapter 8 traces these ontological
claims back to an ''Austrian idea of the a priori'' (175) (shared by Brentano and
his disciples, Husserl among them). These authors had, according to Stjernfelt,
a realist conception of the a priori: a priori structures are shared by
propositions and states-of-affairs, and are not the result of a constitution of
the object by a Kantian subject (176).

Diagrams are in this perspective a ''royal road to the investigation of the
synthetic a priori'' (192); but – as Stjernfelt notes – the problem remains
''where [...] the precise borderline [is] between the synthetic a priori laws of
a given domain on the one hand, and the contingent, empirical data and
tendencies recorded in that domain, on the other '' (192). Stjernfelt holds that
this question can only be addressed by analyzing specific domains – and the
remaining chapters of the book do just that: they present three exemplary
domains of investigation in a digrammatological perspective (see 193).

Chapters nine to twelve are devoted to biosemiotics. Biosemiotics claims the
''fundamentally semiotic character of biological processes'' (257) and extends the
range of semiotics far beyond the range of human behavior. For biosemiotics
semiotic processes are embodied: any type of categorial perception is seen as a
semiotic process. Stjernfeld cites von Uexküll's tick as an example: every
organism forms a functional circle with its environment and its interactions
with this environment are interpreted as semiotic processes by biosemiotics.

In this context, an important task for semiotics is to draw up a ''semiotical
ladder of evolution'' that establishes correlations between ''basic body types''
and ''semiotic ability'' (273). Stjernfelt proposes a first draught for such a
''biosemiotic Scala Naturae'' (272), that notes, for example, that it is not the
use of symbols as such, but ''hypostatic abstraction'' (254) – the ''possibility of
making an operation into the object of a new operation'' (251) – that is typical
for (but not exclusive to) human beings.

Chapters 13 to 15 apply ''diagrammatological'' ideas to the domain of visual
studies. Stjernfelt opts for a conception of ''picture'' that is as broad as his
definition of iconicity – it includes non-visual pictures (he thinks of sounds
''picturing'' each other) and ''natural'' pictures such as mirror images (275). For
Stjernfelt, not surprisingly, pictures are defined by similarity (276): all
pictures are ''also'' diagrams or maps (279). By consequence, all pictures must be
representational: every picture represents something, but not necessarily a
material object – some pictures represent emotions or ideas (276). Twentieth
century art, far from being non-representational, is a ''triumph of similarity''

Stjernfelt gives two elaborate examples for a diagrammatical analysis of
pictures. The first is the interpretation of an altarpiece depicting the Last
Supper by the Danish painter C.W. Eckersberg. Stjernfelt bases his description
on an interpretation by Erik Fischer who noted that one place at the table is
conspicuously empty - that of Judas. Fischer takes the empty wooden stool in the
foreground as the starting point of his interpretation. The perspectival horizon
constructed from the stool is different from the horizon constructed from
architectural elements (in particular the room's ceiling). Judas' horizon is
lower than that of the rest of the piece, which is dominated by the figure of
Christ in the middle. Stjernfelt concludes that there is a ''deliberate use of
double perspective with the rhetorical effect of a structural derogation of
Judas'' (282).

The interpretation of the altarpiece is supposed to demonstrate two ideas:
Firstly, that the diagrammatic interpretation of pictures follows a general
pattern of reasoning that can be described in Peircean terms: ''This presentation
demonstrates the characteristic shifting between abduction understood as
qualified guesses faced with strange observations, deduction understood as
diagram experimentation on the picture, abductive helping hypotheses, inductive
probability arguments and a final conclusion measured on the symbolical
governing of the diagram'' (285). Secondly, the interpretation of the painting is
supposed to demonstrate that the ''logical aspects of pictures'' depend on their
very iconicity (285) – the unity of these two aspects is what the diagram
ultimately reveals.

Stjernfelt's second example is Malevich's ''Suprematist Composition: White Square
on White''. Diagram manipulation in a case like this would consist in imagining
variations, e.g. imagining a different size or position for the inner square
(see 286). The difference between the Malevich and the first example is the
''radical underdetermination'' (288) of the former, typical for twentieth century art.

In chapter 14, Stjernfelt turns again to the spatial order of pictures. He
distinguishes two types of pictures, based loosely on Husserl's reflections on
imaginative acts: one type of picture allows the viewer to construct its space
as accessible, as if the viewer could enter into the picture and move around in
the constructed space. The prototype of that kind of picture would be a
landscape painting. The prototype for the second type of picture, the
inaccessible picture, would be a portrait. Stjernfelt suggests that
accessibility could be crucial for the atmosphere of a picture (see 310).

Chapter 15 presents an outline of a theory of the sketch, and its relation to
the diagram. Sketches may be diagrams or proto-diagrams or neither (like the
artistic sketch, which is characterized by the indeterminacy typical for some
works of art).

In chapters 16 to 18 Stjernfelt turns to literary studies. He reconstructs
literary interpretation in Peircian terms, i.e. as an interplay between
abduction, deduction and induction (see 328), and follows Ingarden in his
distinction of levels of interpretation (chapter 17). Chapter 18 offers a final
case study, an analysis of the spy novel, in order to demonstrate the iconic
relation of ''conceptual schemata in literary semantics'' and the ''regional
ontology'' of the world of espionage (365). Features of the regional ontology
would be ''iconically reproduced'' (382) in the novel; for example, ''a tendential
structural difference between foreign and domestic service'' (382) or ''the
positional character of the spy – the possession of secret knowledge as
determination independent of any espionage intention or affiliation of the
person in question''(382).

Stjernfelt's ''Diagrammatology'' is an ambitious book: its main subject is the
foundation of semiotics, but it can also be read as a contribution to the study
of diagrams, to the interpretation of Peirce, Husserl, and a great number of
other authors, to biosemiotics, and to visual and literary studies. Specialists
in any of these areas will find the relevant chapters an interesting read, even
if Stjernfelt rarely refers to the literature in the respective disciplines and
leaves it to the reader to situate his approach within the field. The book's
thematic richness is an asset, but also a liability – the author's efforts to
cover the entire domain of semiotics lets the reader sometimes lose sight of the
main argument. Not all of Stjernfelt's arguments are equally clear and he does
not always entirely avoid polemics. Also, as is almost unavoidable in a book of
this scope, there are loose threads. (The most puzzling of these is in the
chapter on biosemiotics where Stjernfelt says that ''hypostatic abstraction seems
restricted to mankind, even if maybe unevenly distributed among us (which might
in fact be an indication that selection pressure for it is still at work, or has
been until recently).'' (254). This is a very strange thing to say and would
certainly require some explanation.)

Opinions will be divided on Stjernfelt's contribution to the foundation of
semiotics. Those convinced of the necessity of a ''foundational task'' for
semiotics and those leaning towards a semiotic realism will welcome Stjernfelt's
approach. All others will probably remain unconvinced: Stjernfelt's arguments
against Goodman's ''Seven Strictures on Similarity'' are mostly begging the
question (and Stjernfelt himself seems to sense the problem: this is one of the
chapters where his style verges at times on the polemical).

That said, ''Diagrammatology'' provides two essential leads for debates in general
semiotics and in visual studies: firstly, the introduction of phenomenological
problems into semiotic discussions is certainly an important contribution.
Whether under the auspices of a realist or a nominalist approach, semiotics
should not exclude phenomenological questions and the haunting epistemological
problems this implies - in particular the problem of abstraction and the
question of regional ontologies.

Stjernfelt's examples for regional ontologies suffer from the defects all
descriptions of this kind will necessarily be afflicted with: they will be in
part trivial, and in part contestable, because highly dependent on
culture-specific parameters. His analysis of the spy novel is a case in point.
In that sense, Stjernfelt is quite correct in noting that the question of the
borderline between a priori and a posteriori propositions must be asked as soon
as ontologies become ''regional'' (though the reviewer – being a nominalist –
would suggest that the second Wittgenstein's reflections on grammatical and
empirical propositions could provide a useful model). The aim to find ''real
possibilities'' by recognizing similarities adds to the difficulty: in his
reading of spy novels, Stjernfelt tries to identify the real life counterparts
for the laws of a genre. This is arguably not the most interesting way to place
semiotic practices in a real world context – audience studies or narratological
analyses (in a technical sense), for example, would provide alternative
accounts. And, apart from the insistence on similarities, there is no reason to
ignore these accounts in the context of reflections on regional ontologies.

Stjernfelt's second major contribution to debates in general semiotics is his
focus on the study of diagrams: A general semiotics that takes neither pictures
nor language as the prototypical sign provides a fresh start for more
specialized disciplines like visual studies. It could also help relaunch the
debate on a basic methodological question in semiotics, the question whether, in
a semiotic theory, there will always be one type of sign that serves (implicitly
or explicitly) as the prototype for all signs in general.

Diagrams are currently rediscovered as an object of study in their own right. In
this context, the notion of diagram transformation as presented in
''Diagrammatology'' could play a really important part in explaining the
epistemological impact of diagram use. And Stjernfelt addresses, albeit in an
indirect manner, another crucial question in diagram studies: Whether one
subscribes to the metaphysical framework Stjernfelt establishes or not, his
identification of logical structure and iconicity is an attempt to solve one of
the most vexing problems in the study of diagrams, the question of their
classification in relation to digital representations on the one hand, and
analog representations, like pictures, on the other. Again, Stjernfelt offers an
interesting approach to an important question, but just as his universalism
takes him very far from the regional ontologies he wants to explore, his
generalised idea of the diagrammatic will take him very far from the work of
those in search of working definitions for specific types of representations,
diagrams among them.

Stjernfelt identifies a taxonomy of diagrams as one of the future tasks for
semiotics (see 111), but his extension of the scope of semiotics to the natural
world and of the notion of diagram beyond even the visual makes this a daunting
task indeed: In how far can his analysis of the spy novel be called
diagrammatic? In how far is his interpretation of the ''Last Supper'' (that is
based on a visual diagram) prototypical for visual studies – how do other
aspects, from colors to social background, fit into the equation? The
identification of the logic and the iconic comes at a price: the virtual
impossibility to distinguish the diagrammatic from any other form of abstraction
– a price the author willingly pays in the name of realist semiotics. For all
those who do not share this position the question will rather be, in how far
''diagrammatology'' is a useful metaphor for the analysis of the cognitive
strategies inherent in our semiotic practices.

Elisabeth Birk has a background in philosophy and linguistics. She teaches media
theory in the master's program ''Media Informatics'' at Aachen University (RWTH
Aachen), Germany. She finished her PhD thesis on ''Rules and Examples. Goodman
and Wittgenstein on Samples and Their Use'' in 2007. Her current research focuses
on general semiotics and visual studies, in particular on questions of
classification and the use of diagrams in linguistics.

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