Bartłomiej Skowron

Formal Ontology

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Husserl's part-whole theory

"We interpret the word ‘part’ in the widest sense: we may call anything a ‘part’ that can be distinguished ‘in’ an object, or, objectively phrased, that is ‘present’ in it. Everything is a part that is an object’s real possession, not only in the sense of being a real thing, but also in the sense of being something really in something, that truly helps to make it up:1 an object in itself, considered in abstraction from all contexts to which it is tied, is likewise a part. Every non-relative ‘real’ (reale) predicate therefore points to a part of the object which is the predicate’s subject: ‘red’ and ‘round’, e.g., do so, but not ‘existent’ or ‘something’. Every ‘real’ (reale) mode of association, e.g. the moment of spatial configuration, likewise counts as a proper part of the whole." [Husserl, Logical Investigations, s. 165]

''By a Whole we understand a range of contents which are all covered by a single foundation without the help of further contents. The contents of such a range we call its parts. Talk of the singleness of the foundation implies that every content is foundationally connected, whether directly or indirectly, with every content.''. [Husserl, Logical Investigations, s. 176]

Proposition 1. If an α as such requires to be founded on an μ, every whole having an α, but not an μ, as a part, requires a similar foundation.

Proposition 2. A whole which includes a non-independent ‘moment’, without including, as its part, the supplement which that ‘moment’ demands, is likewise non-independent, and is so relatively to every superordinate independent whole in which that non-independent ‘moment’ is contained.

Formal ontology

''We owe the idea of a formal ontology to the philosopher Edmund Husserl, whose Logical Investigations (1900/01) draws a distinction betweenformal logic, on the one hand, andformal ontology, on the other. Formal logic deals with the interconnections of truths (or of propositional meanings in general) with inference relations, with consistency and validity. Formal ontology deals with the interconnections of things, with objects and properties, parts and wholes, relations and collectives. As formal logic deals with inference relations which are formal in the sense that they apply to inferences in virtue of their form alone, so formal ontology deals with structures and relations which are formal in the sense that they are exemplified, in principle, by all matters, or in other words by objects in all material spheres or domains of reality. Husserl’s formal ontology is based on mereology, on the theory of dependence, and on topology. The title of his third Logical Investigation is On the Theory of Wholes and Parts and it divides into two chapters: The Difference between Independent and Dependent Objects and Thoughts Towards a Theory of the Pure Forms of Wholes and Parts. Unlike more familiar extensional theories of wholes and parts, such as those propounded by Lesniewski, and by Leonard and Goodman (see Simons 1987), Husserl s theory does not concern itself merely with what we might think of as the vertical relations between parts and the wholes which comprehend them on successive levels of comprehensiveness.Rather, Husserl s theory is concerned also with the horizontal relations between co-existing parts, relations which serve to give unity or integrity to the wholes in question. To put the matter simply: some parts of a whole exist merely side by side, they can be destroyed or removed from the whole without detriment to the residue. A whole all of whose parts manifest exclusively such side-by-sideness relations with each other is called a heap or aggregate or, more technically, a purely summative whole. In many wholes, however, and one might say in all wholes manifesting any kind of unity, certain parts stand to each other in formal relations of what Husserl called necessary dependence (which is sometimes, but not always, necessary interdependence). Such parts, for example the individual instances of hue, saturation and brightness involved in a given instance of colour'' (Barry Smith)