Time Granularity and the Formal Ontology of Time-Awareness. A Husserlian Argument for a Topology of Temporal Information

Stefano Papa (University of Vienna)

Time Granularity and the Formal Ontology of Time-Awareness. A Husserlian Argument for a Topology of Temporal Information

Abstract  

The Phenomenological Analysis of Inner or Immanent Time-Consciousness is meant to make explicit structural dependencies in the field of predication and imagination. Reasoning about temporal information (which is central in modern systems of temporal logic) is touched upon only insofar, as an explication of abstractive reflection itself can be made available. Husserl proposes a fourfold sense of „absence“ in his analysis of temporal awareness: .“representation“; what is here absent, is the object denoted by a predication. Representation is dependent upon imagination. An object absent in an act of imagining is „vacant“ in the sense that the item itself is not to be retrieved by imagining it. Vacancy itself is dependent upon a third more radical absence, the absence of Time-Consciousness. Absence in this third sense is to be further explicated as awareness of time as immanent duration and inner sequence of given items. The methodical points of view which are operational in the interpretaion of temporal awarenes, and are to be applied to the experience of linear ordering of information items (for example, a musical gestalt); are the ones of the formal ontology developed in the Logical Investigations. The expressions „stream in a stream“, or „transcendence in the immanence“ (in Cartesian Meditations, with an eye to intersubjectivity), or else „living present“ are metaphorical. They point to the fourth sense of absence.
From the point of view of Phenomenology, the formal methods used in contemporary logics to model temporal reasoning are idealizations and abstractive formalizations, onesidedly founded in the above mentioned structures of dependency. As an example of such idealizations, one could mention Kamp’s theorem: the definability of all temporal operators in terms of „since“ and „until“, is bound to the condition that „time“ is interpreted as a continuous linear ordering. Indipendently from the completeness-result, this theorem is important also because it poses the issue of referring to the same language to describe a situation with respect to different temporal scalings (granularity).Time granularity is linked to semantic properties of representation systems. In contemporary logics it is formally treated by defining an algebra for granularities (set-theoretical approach) and by combination of simple temporal logics into a system for time granularity (logical approach). At this point, however, phenomenological considerations could motivate a shift in the study of time granularity: Since, as stated above, time-awareness is an eidetic layer to be abstracted from the presentation of some sequential items (melody), frames (algebras) as formalizations of finite operations have a shortcome, because they don’t contain a formalization of what they might be about (but this might be at the root of the problems posed by granularity, as illustrated by the synchronization problem). This situation can be changed by enriching a given frame (operations) with a set of points (observations), and a subset of their cartesian product. This construction is called a topological system. The introduction of a topology has thus been motivated by phenomenological considerations on time-awareness and its structural role in systems of formal representation. That is, the aim of this paper is to vindicate a systematic function of phenomenological reflections for the representation of formal categories in a given formalized system.E. Husserl, Logical Investigations (J. Findlay). 1970
E. Husserl, On the Phenomenology of the Consciousness of Internal Time (1893–1917), 1990 [1928]. (Brough, J.B).
E. Husserl, Formal and Transcendental Logic, 1969 [1929], Cairns, D., trans. The Hague: Nijhoff.
H. Kamp. Formal Properties of ‘now’. Theoria, 37:227–273, 1971.
H.Kamp. Events, Instantsand Temporal Reference. In: R.Bäuerle, U.Egli, and A.von Stechow, editors, Semantics from Different Points of View, pages 376–417. Springer-Verlag, 1979.
Jerome Euzenat, Angelo Montanari. Time granularity. In: Michael Fisher, Dov Gabbay, Lluis Vila. Handbook of temporal reasoning in artificial intelligence, Elsevier, pp.59-118, 2005, Foundations of artificial intelligence
S. Vickers, Topology via Logic. Cambridge 1989 (1996)