Categories, Diagrams, Schemata the Cognitive Grasping of Ideal Objects in Husserl and Peirce

  • Frederik Stjernfelt
Part of the Phaenomenologica book series (PHAE, volume 164)


The question of the status, the presentation, and the representation of ideal objects has received new actuality in recent years as the result of various scientific and philosophical developments. In cognitive science and computer science, concepts like scripts, schemata, frames, diagrams have received renewed attention as opposed to supposedly purely formal logical representations;1 in complexity theory, it has been suggested that all sufficiently complex adaptive systems must include a general, schematic representation of aspects of its environment;2 in the renaissance of Austrian philosophy and phenomenology in general, new attention has been paid to a priori structures and their representation.3 As all of these developments show, the grasping of ideal objects pertains not only to mathematics and logic—even if they form an important case—but also to everyday cognition, as most cognitive acts are not simple and involve general, ideal elements in what Husserl calls “sinnlich gemisschte” form.


Logical Investigation Ideal Object Formal Ontology Steam Engine Empirical Object 
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  1. 1.
    For instance in the cognitive semantics tradition in linguistics, cf. G. LAKOFF, Women, Fire, and Dangerous Things, Chicago: Chicago University Press, 1987; and the diagrammatic reasoning interest in computer science, cf. J. Glasgow, et al. (eds.) Diagrammatic Reasoning. Cognitive and Computational Perspectives, Menlo Park, Cal.: AAA’ Press/MIT Press, 1995.Google Scholar
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    See for instance M. GELL-MANN’S and B. MARTIN’S papers in G. A. Cowan et al. (eds.): Complexity. Metaphors, Models, and Reality, Reading Mass., etc.: Addison Wesley, 1994.Google Scholar
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    See for instance B. SMITH, Austrian Philosophy, Chicago: Open Court, 1994, especially the last chapter; or A. PERUZZI. SMITH, Austrian Philosophy, Chicago: Open Court, 1994, especially the last chapter; or A. PERUZZI, “An Essay on the Notion of Schema”, in L. Albertazzi (ed.), Shapes of Forms, Dordrecht: Kluwer, 1999, 191–244.Google Scholar
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    E. HUSSERL, Erfahrung und Urteil, Hamburg: Felix Meiner, 1985.Google Scholar
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    Peirce’s doctrine of diagrams must be reconstructed from scattered quotes in C. PEIRCE, CollectedPapers, I-VIII, London: Thoemmes Press, 1998 [1931–58], and Elements ofMathematics I-IV, The Hague: Mouton,1976. For adetailed discussion, see F. STJERNFELT, “Diagrams as Centerpiece of a Peircean Epistemology, in Transactions of the Charles S. Peirce Society XXXVI/3, 2000, 357–84.Google Scholar
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    Known as Alpha-, Beta-, and Gamma-graphs, they formalize (a) propositional logic, (b) first order predicate logic, and (c) various brands of modal logic, speech act logic etc.Google Scholar
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    Or, to give Peirce’s definition of what such similarity implies: an icon is a sign which permits us to get more information about the object than what lies in the construction recipe for the sign. Cf. F. STJERNFELT, “How to Learn More. An Apology for a Strong Concept of Iconicity”, in T. D. Johansson et al. (eds.) Iconicity. A Fundamental Problem in Semiotics, Copenhagen: NSU Press, 1999, 21–58Google Scholar
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    Husserl’s own examples of the higher-order objects grasped in categorial intution in the Sixth Investigation include the identity of an object, the relation of part to whole, relations, collections, the “ideierende Abstraktion” and its intiution of essences, the determinate and indeterminate grasping of single objects (“das A”, “ein A”). Sokolowski’s “Husserl’s Concept of Categorial Intuition” presents a thorough analysis of the steps from an unanalyzed experience to its categorial articulation in subject and predicate. Lohmar’s Erfahrung und kategoriales Denken articulates a general 3-step structure for categorial intuition: “Gesamtwahrnehmung, Sonderwahmehmungen, kategoriale Synthesis”.Google Scholar
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    Later, in his drafts of a new version of the Sixth Investigation, Husserl took the position that they always involve such meaning, cf U MELEE, “Husserl’s Revision of the Sixth Logical Investigation”, this vol.Google Scholar
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    We find in the three degenerate act types (imaginative, indexical, and signitive, respectively) a not coincidential parallel to Peirce’s three different ways of signifying an object (icon, index, symbol). This has been noted by D. MUNCH, Intention und Zeichen, Frankfurt am Main: Suhrkamp, 1993, 218.Google Scholar
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    An analogous point is made by R. SOKOLOWSKI, The Formation of Husserl’s Concept of Constitution,59, when he complains that the account given of meanings in the Logical Investigations is “severely limited” because “their origins are not explained.”Google Scholar
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    This point and its relation to the transcendence issue is not always clearly emphasized; a strong exception is D. W1u.ARD, “Wholes, Parts, and the Objectivity of Knowledge”, in B. Smith (ed.), Parts and Moments, M1lnchen: Philosophia, 1982, 379–400.Google Scholar
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    In fact, if categoriality were identified with formal logic only, then some version of logical positivism might be the outcome. But it is not necessary to identify categoriality nor the propositional stance with logic or language. Rather, language is one (prominent, to be sure) instrument developed on the basis of the cognitive potentials of abstraction and categoriality. A very broad definition of categoriality-comprising all higher-level acts founded on perception—is proposed in B. SMITH, “Logic and Formal Ontology”, in Manuscrito (forthcoming).Google Scholar
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    The intimate connection between categorial intuition and this “theory of theories” is highlighted in Coue-SrevENs’s “Being and Categorial Intuition”.Google Scholar
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    Calling the illustration, the diagram token, a “representation” takes up Husserl’s terminology for the way the act content represents its object. In J.-M. ROY, “Saving Intentional Phenomena: Intentionality, Representation, and Symbol” in J. Petitot et al. (eds.), Naturalizing Phenomenology,Stanford, Stanford University Press, 1999, 111–47, Husserl’s distinction between signitive and intuitive based on different representations is taken as the point of departure for a detailed argumentation leading to the claim that “Representation” must not in this context be read symbolically as in the normal Anglo-Saxon use of “representation”. If such a reading is preferred, intuitive representations will lose their direct connection to their object. Husserl’s solution is to take the representational content to be identical and the difference between the two to lie in the “Auffassungsform”. Consequently, diagrams will be categorial representations characterized by an intuitive form of apprehension.Google Scholar
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    In Peirce, this problem is solved by taking general meaning to have a continuum of merely possible (but vague) referents as its extension.Google Scholar
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    Here, Husserl is on a par with Peirce for whom the diagram is not the particular drawing on the page nor the reader’s perception of it. Peirce thus distinguishes between the diagram token—the particular drawing on the page, corresponding to Husserl’s “Anhalt”—and the diagram type which we are able to grasp through a reading of that token, governed by a symbolic sign (which, in Peirce’s terminology, implies generality).Google Scholar
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    As is evident, this variation procedure is modeled upon function analysis in mathematics, even in Husserl’s terminology.Google Scholar
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    On Peirce’s abstraction theory in relation to wholes and parts, see F. STJERNFELT, “Schemata, Abstraction, and Biology” in B. Brogaard and B. Smith (eds.),Rationlity and Irrationality,Vienna:Obvhpt, 2001, 341–61; on mereology in Husserl, Peirce, Jakobson, and Hjelmslev, see F. STJERNFELT, “Mereology and semiotics”, Sign System Studies 28, 2000, 72–98.Google Scholar
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    As has been studied by the cognitive semantics tradition (G. LAKOFF, Women, Fire, and Dangerous Things),this variaiton procedure may be subject to complicated and conflicting constraints in empirical concepts giving rise to a “radial” concept structure with highly variable variation possibilities departing from at prototypical center.Google Scholar
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    J. PETITOT, “Morphological Eidetics for a Phenomenology of Perception”, in J. Petitot et al. (eds.), Naturalizing Phenomenology,330–71.Google Scholar

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© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Frederik Stjernfelt
    • 1
  1. 1.University of CopenhagenDenmark

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