General Formal Ontology (GFO)
First we present and discuss our philosophical position. We consider
two topics: the notion and ontological status of categories, and
the problem of existence. We support a realistic position in philosophy,
but there is the need to clarify more precisely the term ``realism''.
There is a close relation between categories and
language, hence the analysis of the notion of category cannot be - in our
opinion - separated from the investigation of language. Concerning
the notion of existence we draw our inspiration partly from Ingarden
but mainly from our own ontological investigations and analyses. We use the
term entity for everything that exists.
The discussion in this section is inspired by Jorge Gracia's ideas presented in
(23), which proved to be useful for the purpose of
conceptual modelling and computer-science ontologies.
A general ontology is concerned with the most
general categories, with their analysis and axiomatic foundation.
Categories are entities that are expressed by
predicative terms of a (formal or natural) language and that can be
predicated of other entities.
Predicative terms are linguistic expressions which
state conditions to be satisfied by an entity. Categories are
what predicative terms express, their content and meaning, not
the predicative terms themselves, understood as a string of letters in a
language. Hence, we must distinguish: the category, the
predicative term - as a linguistic entity - expressing
the category, and the entities that satisfy the conditions stated by the
The predicative term , the expressed category , and the satisfying
are mediated by two relations, and . We stipulate
that a category is predicated of an entity if and only if satisfies
that are associated to . Equivalently we say that an entity
is an instance of a category , or that instantiates .
Hence, we hold that the following three conditions are
equivalent: instantiates , is predicated of , and satisfies
the conditions of .7 Categories are designated and
expressed by terms of a language. Terms of a language are words,
sentences, texts, i.e., every
expression that is well-formed according to the grammatical rules of the
We assume that categories are conceived in such a
way that we are not forced to commit ourselves to
realism, conceptualism, or nominalism
(23). This assumption
is compatible with our
pluralistic approach discussed in the introduction above
and it seems to be the most adequate for the purpose
of computer-science ontologies and conceptual modelling.
According to the approach of (23) we derive several
kinds of categories from basic philosophical assumptions. We restrict
these to the following basic kinds of categories: immanent
categories (also called in the following
universals), concepts (conceptual structures)
, and symbolic
Immanent categories are not outside the world of human
experience, but are constituents of this world. Concepts are
categories that are expressed by linguistic signs and are
present in someone's mind. Symbolic structures are signs or
texts that may be instantiated by tokens.
There are close relations between
these three kinds of categories: an immanent
category is captured (grasped) by a
concept which is denoted (designated) by a symbolic
structure. Texts and symbolic structures may
be communicated by their instances that are physical tokens.
An important problem in conceptual modelling is to present (specify) categories
in a formal modelling language, and to determine which
conditions a formal language should satisfy to capture categories
of several kinds adequately.
Sets play a particular role in GFO. We hold that a set cannot be predicated
of its members, but there are, of course, specifications of sets expressing
categories which can be predicated of sets.9For this reason we do not consider sets as categories. Sets serve as a formal
modelling tool and are associated to the abstract top level of GFO.
In (32) a classification of modes of existence is
discussed that is
useful for a deeper understanding of entities of
According to (32) there are - roughly -
the following modes of being:
absolute, ideal, real, and intentional entities. This classification can
be to some extent related to Gracia's approach and to the levels of reality in
the spirit of Nicolai Hartmann (29). But, the
theory of Roman Ingarden is not sufficiently
elaborated compared with Hartmann's large ontological system.
For Ingarden there is the (open) problem, whether material things are real
spatio-temporal entities or intentional entities in the sense of the later
Husserl. We hold that there is no real opposition between the realistic
attitude of Ingarden and the position of the later Husserl, who considers the
material things as intentional entities being constructed by a
transcendental self. Both views provide valuable insights in the modes
of being that can be useful for conceptual modelling purposes.