An international, interdisciplinary

conference on the epistemology

of abstract objects



Department of Philosophy and the Study of Religion

University of Southern Denmark, Odense

May 30-31 2003




The conference Access to the Abstract focuses on our knowledge of abstract entities. Forms, relations, types, gestalts, meanings, propositions, categories, classes and numbers play a crucial role in both ordinary life and the sciences. They are dealt with and spoken about almost as often as concrete objects. And many contemporary philosophers insist that they be taken  seriously – they are not merely “shadows of our language” or convenient fictions, but should be counted among the basic furniture of the world. But how can we acquire knowledge of such intangible objects? And what role – if any – does sense experience, abstraction, schematising, visualising or symbolisation play in this process? These and other questions concerning the epistemology of abstract objects will be addressed at the conference, which is intended to bring together scholars and students from various traditions and disciplines, such as phenomenology and analytical philosophy, and the humanities and the natural sciences.




Friday 30 May (Auditorium U100)


9.00                Registration


9.15                Welcome by Frederik Stjernfelt and Søren Harnow Klausen


9.30                Kevin Mulligan (Univ. of Geneva): Intuiting the Formal


10.30                         Roberto Casati (Institute Jean Nicod, Paris): Numerals and the Accessibility of Numbers


11.30              Søren Harnow Klausen (University of Southern Denmark)

Categorial Intuition as Mental Modelling


12.30-13.30  Lunch


13.30                         Frederik Stjernfelt (Univ. of Copenhagen): Reasoning with Diagrams          


14.30              Stevan Harnad (Univ. of Southampton): There is no Concrete


15.30              Coffee Break


16.00              Johanna Seibt (Univ. of Aarhus): The Categorization of Change

and Dynamicity


19.00              Dinner



Saturday 31 May (Auditorium U100)


9.30                     Peer F. Bundgaard (Univ. of Aarhus): The Ideal Scaffold of

Language. On Husserl’s Abstraction of a Grammatical A priori in the IV. Logical Investigation


10.30              Wolfgang Künne (Universität Hamburg): Access to Propositions


11.30                         Anders Hougaard (Univ. of Southern Denmark): Conceptual Disintegration as a Means to Access the Abstract


12.30-13.30  Lunch 


13.30                         Gianfranco Soldati (University of Fribourg): Perceiving Abstract Objects


14.30                         Michael May ( Danish Maritime Institute): Categorial Aspects of Sign Types


15.30              Coffee Break


16.00              Cynthia M. Grund (Univ. of Southern Denmark): Musical Experience and Abstract Objects




The conference is arranged by Frederik Stjernfelt and Søren Harnow Klausen ( It is sponsored by the Carlsberg Foundation, The Danish Research Council, The Department of Philosophy and the Study of Religion, University of Southern Denmark, and The Danish Research School in Philosophy and the History of Philosophy. 






An Interdisciplinary Conference on the
Epistemology of Abstract Objects

University of Southern Denmark
Department of Philosophy and the Study of Religions
Campusvej 55
DK-5230 Odense M

Friday 30 May (U100)

9.45 Roberto Casati: Numbers: the limited access theory
Numerals are a part of language, but they are unlike any other part, both in the way they
are learned, and in the way they are structured. A certain learning sequence (one-two-
three...) is mandatory (you never learn seven-eighteen-etc.). Up to ten, and actually up to
twenty, the morphology of the items in the sequence does not mirror any syntax (as
opposed to "twenty-three", say). My bet is that when you learn a series of numerals you
build a map. NB: the map "is" the sound sequence itself. But only later on the map is
used representationally, by making some of its elements correspond to numbers. It is
holistic as maps are in general: the meaning of one part depends from a simultaneous
assignment of meaning to all other parts, etc.
Now, the question is, could this map be not linguistic at all? I think so. If we had
absolute pitch ear, we could learn the map by learning to sing a scale, say. If this is correct,
language does not play a crucial role in accessing numbers. Something else does, the
ability to interpret maps. So here I have to say something about map semantics.
Why are numerals unstructured up to ten or twenty? A design feature of learning
applies which is explained by a bridge hypothesis suggested by Elizabeth Spelke. One
needs to build a bridge that takes you from the jurisdiction of the individuation-and-
tracking system to the jurisdiction of the large-and-approximate-set system. Somewhere
between four and twenty is a good bridge. But why do we not use syntactically structured
numerals from the very beginning (a unary or binary system?). Because the syntax aspect
would dominate the map-like aspect of the numerals series, and it would be hard to use the
series as a map. The punchline is that there is no number cognition at all, except for very
small integers. All the rest is map and symbol manipulation.

11.00 Gianfranco Soldati (Univ. of Fribourg): Abstraction & Abstract Concepts.
Much work has recently been dedicated to the discussion of abstraction theory within the
fregean framework of philosophy of mathematics. In the present paper I intend to revist
certain aspects of Husserls early theory of abstraction, as it was presented in his
Philosophy of Arithmetics and elaborated in the Logical Investigations. It is especially on
the epistemological side that the husserlian approach appears to present a number of

12.15-13.15 Lunch

13.15 Frederik Stjernfelt (Univ. of Copenhagen): Abstraction and diagrammatical

The elder Peirce's theory of the role of diagrams in reasoning constitutes an overlooked
gem in his mature work. This paper investigates Peirce's detailed theories of different
abstraction types Ð discrimination, prescission, dissociation, hypostatic abstraction Ð in
their relation to the construction of and experimenting with diagrams. Peirce's general idea
is that diagrams provides the means for the access to ideal objects and to the gaining of
insight in them by diagram manipulation - both in pure and applied versions. But the
different versions of abstractions are seen as basic prerequisites to the construction of
such diagrams. Peirce's pragmatical semiotics of diagrams and abstraction types thus
forms an
important complement to the phenomenological theories of abstraction, eidetic variation,
and Wesenschau.

14.30 S¿ren Harnow Klausen: Categorial Intuition as Mental Modelling
In spite of the growing recognition of the need to posit abstract objects of various sorts,
little work has been devoted to the question of how we can have epistemic access to them Ð
and to the exact nature of this relationship, which seems to involve, at least in some cases, a
distinctive sort of experience, often referred to as intuition or rational insight. For a more
detailed account of the mental processes that underlie our ability to think about and
experience the abstract features of reality, we still have to consult historical theories like the
British empiricistsÕ theories of abstraction, KantÕs doctrine of "schematism", PeirceÕs
theory of diagrammatic reasoning and, last but not least, HusserlÕs theories of categorial
intuition and eidetic variation. The paper discusses how more recent developments in
cognitive science and psychology, in particular the mental models approach to cognition
(Craik, Johnson-Laird) and theories of mental imagery (Kosslyn), might be able to
support and supplement the traditional views.

15.30 Coffee

16.00 Kevin Mulligan (University of Geneva): How (Not) to Intuit Values
According to extreme value realism (Husserl, Moore, Scheler, Hartmann, Tappolet,
Johnston), values or monadic axiological properties are instantiated or exemplified by
natural objects and our grasp of values is, at bottom, a type of affective intuition.
According to weak value realism, natural objects really do have axiological properties but
these properties are to be understood as dispositions to produce affective responses
(response dependence theories), perhaps appropriate affective responses (Hutcheson,
Zimmermann, Brentano, McDowell, Wiggins, Mulligan). Accounts of the latter sort are
sometimes Ð unfortunately Ð described as forms of "neo-sentimentalism" (dÕArms). One
apparent weakness of neo-sentimentalism is that the very idea of an affective response to a
natural situation seems to presuppose a prior grasp of the object of the response. Can fear
be an appropriate response to a situation if it is not rooted in some grasp of danger? There
are, certainly, many important differences between affective responses such as admiration,
fear, enthusiasm, scorn, on the one hand, and feeling and preferring, on the other hand. In
particular, feeling and preferring are not any sort of responses. I examine some replies to
this objection to neo-sentimentalism. One such reply has it that feeling and preferring have
as their objects values and relations between values but no natural situation exemplifies
any monadic axiological property or instantiates any value. Value properties are indeed
monadic, as the extreme realist says. But in our world nothing exemplifies them, a claim he
denies.This view has one advantage. It allows us to make sense of our grasp of the
internal relations between values in value space Ð the logics of value and of betterness
(preferability). And it combines nicely with the view that axiological instantiation and
exemplification differ from ordinary exemplification and instantiation. It also resembles
one theory of colours: colours are monadic properties but in our world no natural objects
exemplify these (Maund).

19.00 Dinner

Saturday 31 May (U100)

10.00 Stevan Harnad (Univ. of Southampton): There Is No Concrete.
We are accustomed to thinking that a primrose is "concrete" and a prime number is "abstract," that  "roundness" is more abstract than "round," and that "property" is more abstract than  "roundness." In reality, the relation between "abstract" and "concrete" is more like the relation between "abstract" and "concave," "concrete" being a sensory term [about what something feels like] and "abstract" being a functional term (about what the sensorimotor system is doing with its input in order to produce its output): Feelings and things are correlated, but otherwise incommensurable. Everything that any sensorimotor system such as ourselves manages to categorize successfully is based on abstracting sensorimotor "affordances" (invariant features).  The rest is merely a question of what inputs we can and do categorize, and what we must abstract from the particulars of each sensorimotor interaction in order to be able to categorize them correctly. To categorize, in other words, is to abstract. And not to categorize is merely to experience. Borges's Funes the Memorious, with his infinite, infallible rote memory, is a fictional hint at what it would be like not to be able to categorize, not to be able to selectively forget and ignore most of our input by abstracting only its reliably recurrent invariants. But a sensorimotor system like Funes would not really be viable, for if something along those lines did exist, it could not categorize recurrent objects, events or states, hence it could have no language, private or public, and could at most only feel, not function adaptively (hence survive). Luria's "S" in "The Mind of a Mnemonist" is a real-life approximation whose difficulties in conceptualizing were directly proportional to his difficulties in selectively forgetting and ignoring. Watanabe's "Ugly Duckling Theorem" shows how, if we did not selectively weight some properties more heavily than others, everything would be equally (and infinitely and indifferently) similar to everything else. Miller's "Magical Number Seven Plus or Minus Two" shows that there are (and must be) limitations on our capacity to process and remember information, both in our capacity to discriminate relatively (detect sameness/difference, degree-of-similarity) and in our capacity to discriminate absolutely (identify, categorize, name), The phenomenon of categorical perception shows how selective feature-detection puts a Whorfian "warp" on our feelings of similarity in the service of categorization, compressing within-category similarities and expanding between-category differences by abstracting and selectively filtering inputs through their invariant features, thereby allowing us to sort and name things reliably. Language does allow us to acquire categories indirectly through symbolic description ("hearsay," definition) instead of just through direct sensorimotor trial-and-error experience, but to do so, all the categories named and used in the description must be recursively grounded in direct sensorimotor invariants. Language is largely a way to ground new categories by recombining already grounded ones, often by making their implicit invariant features into explicit categories too. If prime numbers differ from primroses, it is hence only in the degree to which they happen to be indirect, explicit, language-mediated categories. Like everything else, they are recursively grounded in sensorimotor invariants. The democracy of things is that, for sensorimotor systems like ourselves, all things are just absolute discriminables: they number among those categories that our sensorimotor interactions can potentially afford, no more, no less. A primrose affords dicotyledonousness as reliably (if not as surely) as a numerosity of 6 (e.g., 6 primroses) affords factoring (whereas 7 does not).

11.15 Peer F. Bundgaard (Univ. of Aarhus): The Ideal Scaffolding of Language.
On HusserlÕs Abstraction of a Grammatical A priori in the IV. Logical Investigation
One of the central issues in actual linguistics is whether or not language should be
considered a self-contained, autonomous formal system, essentially reducible to the
syntactic algorithms of meaning construction (as orthodox Chomskyan grammar would
have it), or a holistic-functional system serving the means of expressing pre-organized
intentional contents and thus accessible only with respect to features and structures
pertaining to other cognitive subsystems or to human experience as such (as Cognitive
Linguistics would have it). The latter claim depends critically on the existence of principles
governing the composition of semantic contents. HusserlÕs IVth Logical Investigation is
well known as a genuine precursor for Chomskyan grammar. The "ideal scaffolding" of
language it eventually establishes through "formal abstraction" is indeed purely syntactic.
However, I will establish the heterogeneous character of the investigation and show that the
whole first part of this investigation is devoted to the exposition of a semantic
combinatorial system cognate to the one elaborated within cognitive linguistics. In other
words, Husserl abstracts not one, but two grammatical a prioris, a semantic and a syntactic
one, riding on essentially different principles of composition. My heart belongs to the

12.30-13.30 Lunch

13.30 Thor GrŸnbaum (Center for Subjectivity Research, Copenhagen): R.
Ingarden and the Dynamics of Schematized Profiles through the Structures of Bodily
Roman Ingarden's theory that verbal texts contain a stratum of schematised profiles
(aspects) has perhaps been the most disputed and the most influential part of his general
theory of literature and aesthetics. My paper will contain three parts; exposition,
limitations, and perspectives: 1) A short exposition of IngardenÕs theory of schematised
profiles. Sound, meaning, and referent are old friends to semiotic theories of language; but
Ingarden's stratum of schematised profiles is a genuine phenomenological innovation, pin-
pointing the borderlines between experience, imagination, and linguistic structure. 2) There
is a central limitation as to the way Ingarden formulates his theory: It's formulated in
analogy with the perception of a static object, and as a consequence the theory only seems
to cover static representation. 3) Recent cognitive theories of language have reached
insights comparable to those of Ingarden: Language is not only a matter of sound,
meaning, and reference, but also a matter of forming schematised representations of a
referent-situation. Drawing on some of these "cognitive" insights itÕs possible to trace
specific grammatical and lexical features back to experiences of bodily motion. In this way
Ingarden's theory can be formulated so as to describe how language schematise a dynamic
perceptual space.

14.15-14.45 Coffee

14.45 Cynthia M. Grund (Univ. of Southern Denmark): Name That Tune:
Abstraction and Concretion in our Experience of Music
Music is a fertile source of topics which exploit and challenge our theoretical notions of
abstraction and concretion, the relationship of these notions one with another, and our
intuitions as to where the boundary between them lies. The ontology of a work of music,
the relationship of score to work, demarcation problems inherent in work identification and
the relation of performance to score are four such topics. Indeed, much important work
within the last generation or two of aesthetics and philosophy of music has dealt with these
matters. This talk will survey and address some of the salient aspects of this theoretical
work and its relevance for discussion of abstraction v. concretion. We will then move on to
an area which, although outside traditional philosophy and aesthetics, readily provokes
further re-examination of the abstract-concrete dichotomy in a musical context.
Known as Music Information Retrieval, it is an area of truly cutting-edge digital
technology. Thanks to the prior aid and assistance of colleagues within the The Danish
Network for Cross-Disciplinary Studies of Music and Meaning (acronym: NTSMB),
examples of MIR and related technologies will be included in the presentation.