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| | Definitions of Ontology. First Part: from Christian Wolff to Edmund Husserl | |
Nicolai Hartmann to the Present TimeINTRODUCTION: DEFINING "ONTOLOGY"a) One of the best available dictionaries gives the following definition of Ontology: "1. A science or study of being: specifically, a branch of metaphysics relating to the nature and relations of being; a particular system according to which problems of the nature of being are investigated; first philosophy. 2. a theory concerning the kinds of entities and specifically the kinds of abstract entities that are to be admitted to a language system." (1) b) The first sense is commonly used in the philosophical tradition: "In contemporary philosophy, formal ontology has been developed in two principal ways. The first approach has been to study formal ontology as a part of ontology, and to analyse it using the tools and approach of formal logic: from this point of view formal ontology examines the logical features of predication and of the various theories of universals. The use of the specific paradigm of the set theory applied to predication, moreover, conditions its interpretation. The second line of development returns to its Husserlian origins and analyses the fundamental categories of object, state of affairs, part, whole, and so forth, as well as the relations between parts and the whole and their laws of dependence - once all material concepts have been replaced by their correlative form concepts relative to the pure 'something'. This kind of analysis does not deal with the problem of the relationship between formal ontology and material ontology." (2) c) The second sense is used in research on Artificial Intelligence and Knowledge Representation; one of the best known definitions is Tom Gruber's: "An ontology is an explicit specification of a conceptualization. The term is borrowed from philosophy, where an ontology is a systematic account of Existence. For knowledge-based systems, what “exists” is exactly that which can be represented. When the knowledge of a domain is represented in a declarative formalism, the set of objects that can be represented is called the universe of discourse. This set of objects, and the describable relationships among them, are reflected in the representational vocabulary with which a knowledge-based program represents knowledge. Thus, we can describe the ontology of a program by defining a set of representational terms. In such an ontology, definitions associate the names of entities in the universe of discourse (e.g., classes, relations, functions, or other objects) with human-readable text describing what the names are meant to denote, and formal axioms that constrain the interpretation and well-formed use of these terms." (3) This definition has been criticized by Nicola Guarino that, after examining seven possible interpretations of ontology, (4) writes: "A starting point in this clarification effort will be the careful analysis of the interpretation adopted by Gruber. The main problem with such an interpretation is that it is based on a notion of conceptualization (introduced in: Genesereth, Michael R. and Nilsson, L. "Logical Foundation of Artificial Intelligence" Morgan Kaufmann, Los Altos, California, 1987) which doesn't fit our intuitions, (...): according to Genesereth and Nilsson, a conceptualization is a set of extensional relations describing a particular state of affairs, while the notion we have in mind is an intensional one, namely something like a conceptual grid which we superimpose to various possible state of affairs. We propose in this paper a revised definition of a conceptualization which captures this intensional aspect, while allowing us to give a satisfactory interpretation to Gruber's definition." (5) Guarino gives this definition: "Since this paper is deliberately addressed to an interdisciplinary audience, it is advisable to pay attention to some preliminary terminological clarifications, especially because some crucial terms appear to be used with different senses in different communities'. Let us first consider the distinction between "Ontology" (with the capital "o"), as in the statement "Ontology is a fascinating discipline" and "ontology" (with the lowercase "o"), as in the expressions "Aristotle's ontology" or "CYC's ontology". The same term has an uncountable reading in the former case, and a countable reading in the latter. While the former reading seems to be reasonably clear (as referring to a particular philosophical discipline), two different senses are assumed by the philosophical community and the Artificial Intelligence community (and, in general, the whole computer science community) for the latter term. In the philosophical sense, we may refer to an ontology as a particular system of categories accounting for a certain vision of the world. As such, this system does not depend on a particular language: Aristotle's ontology is always the same, independently of the language used to describe it. On the other hand, in its most prevalent use in AI, an ontology refers to an engineering artifact, constituted by a specific vocabulary used to describe a certain reality, plus a set of explicit assumptions regarding the intended meaning of the vocabulary words. This set of assumptions has usually the form of a first-order logical theory, where vocabulary words appear as unary or binary predicate names, respectively called concepts and relations. In the simplest case, an ontology describes a hierarchy of concepts related by subsumption relationships; in more sophisticated cases, suitable axioms are added in order to express other relationships between concepts and to constrain their intended interpretation. The two readings of ontology described above are indeed related each other, but in order to solve the terminological impasse we need to choose one of them, inventing a new name for the other: we shall adopt the AI reading, using the word conceptualization to refer to the philosophical reading. So two ontologies can be different in the vocabulary used (using English or Italian words, for instance) while sharing the same conceptualization." (6) (1) Webster's Third New International Dictionary (2) Liliana Albertazzi - "Formal and material ontology" in: Roberto Poli & Peter Simons (ed.) - "Formal Ontology" - Kluwer 1996 p. 199 (3) Tom Gruber "A translation approach to portable ontology specifications". In: Knowledge Acquisition 5, (1993) pp. 199-220 (4) Nicola Guarino - "Ontologies and Knowledge Bases. Towards a terminological clarification" (1995) p. 1 (5) ibid. p. 2 (6) Nicola Guarino "Formal ontology and information systems". In: N. Guarino (ed.), Formal Ontology in Information Systems. Proceedings of the First International Conference, Trento, Italy, 6-8 June 1998. IOS Press, 1998 p. 4DESCRIPTIVE, FORMAL AND FORMALIZED ONTOLOGY"I shall distinguish descriptive, formal and formalized ontology. Each of these ontologies comes in two guises: domain-dependent and domain-independent. Domain-dependent ontologies concern categorically closed regions of being; on the other hand, a domain independent ontology may be properly called general ontology. (...)Descriptive ontology concerns the collection of such prima facie information either in some specific domain of analysis or in general. Formal ontology distills, filters, codifies and organizes the results of descriptive ontology (in either its local or global setting). According to this interpretation, formal ontology is formal in the sense used by Husserl in his Logical Investigations. Being 'formal' in such a sense therefore means dealing with categories like thing, process, matter, whole, part, and number. These are pure categories that characterize aspects or types of reality and still have nothing to do with the use of any specific formalism. Formal codification in the strict sense is undertaken at the third level of theory construction: namely that of formalized ontology. The task here is to find the proper formal codification for the constructs descriptively acquired and formally purified in the way just indicated. The level of formalized constructions also relates to evaluation of the adequacy (expressive, computational, cognitive) of the various formalisms, and to the problem of their reciprocal translations. The close similarity between the terms 'formal' and 'formalized' is somewhat unfortunate. One way to avoid the clash is to use 'categorical' instead of 'formal'. Most contemporary theory recognizes only two levels of work and often merges the level of the formal categories either with that of descriptive or with that of formalized analysis. As a consequence, the specific relevance of categorical analyses is too often neglected. The three levels of ontology are different but not separate. In many respects they affect each other. Descriptive findings may bear on formal categories; formalized outcomes may bear on their twin levels, etc. To set out the differences and the connections between the various ontological facets precisely is a most delicate task." From: Roberto Poli - Descriptive, formal and formalized ontologies - In: Denis Fisette (ed.) - Husserl's Logical Investigations reconsidered, Dordrecht, Kluwer, 2003 pp. 183-210 "The idea of a formal ontology arose around the turn of the present century in the work of Edmund Husserl. It coincides in many respects with what is nowadays sometimes called 'analytic metaphysics' or with attempts to use formal methods to solve classical philosophical problems relating to the notions of being, object, state of affairs, existence, property, relation, universal, particular, substance, accident, part, boundary, measure, causality, and so on. Formal ontology thus includes several sub-disciplines, of which the most developed is the theory of part and whole, as sketched by Husserl in the third of his Logical Investigations and later worked out as a formal theory by Lesniewski. Formal-ontological ideas are present also in much contemporary work on naïve physics and in the formal theories of the common-sense world canvassed by workers in the field of artificial intelligence research. The idea of a formal ontology is placed in a network of conceptual oppositions: it admits of different senses according to which of its two constituent elements is given priority. If the emphasis is placed on 'ontology' then the principal distinction is between 'formal' and 'material' (that is between 'formal ontology' and 'material ontology'); if instead the emphasis falls on 'formal', the contrast is between 'ontology' and 'logic' ('formal ontology' vs. 'formal logic'). This situation raises some important questions: When one speaks of 'ontology', how can its formal aspects be distinguished from its material ones? When we talk about the 'formal', how can we distinguish between logic and ontology?" From: Roberto Poli and Peter Simons (eds.) - Formal ontology - Dordrecht, Kluwer, 1996 - Foreword by the Editors p. VII. "One hundred years ago, Edmund Husserl was perhaps the first philosopher to pay any interest to the formal treatment of some of the most fundamental questions of ontology. Powerful tools of logic were developed in those days, and this new development inspired in a natural way various attempts to use these techniques within this prestigious area of philosophical inquiry. Through Husserl's younger colleague, Roman Ingarden, and in the light of related ideas of Lesniewski and other members of Lwow-Warsaw School, these ideas spread rapidly, particularly in the Polish scientific community. Philosophical inquiries into ontology in an advanced formal setting were put forward first by Stanislaw Lesniewski. Inspired by the contemporary discussion on the foundations of mathematics, Lesniewski was interested in finding a formal framework appropriate for the ontological grounding of both mathematics and logic. The basic system was Mereology, i.e. the general theory of collective sets. Ontology itself arises from Protothetic. All his axiomatic systems came about in an elegant yet somewhat exotic notation. (1) Lesniewski's mereology was intended to play the part of an alternative to set theory. Later -- as an axiomatic 'calculus of individuals' -- it appears to be a proper extension of set theory rather than a competitive calculus. Thomas Mormann's article 'Topological Representations of Mereological Systems' (2) can be seen as a recent example of that line of research. He shows that nothing is lost when a reasonable mereological system is substituted by its topological model. That brings mereology into contact with well developed mathematical theories and may help mereology, as Mormann concludes, "to leave its present state of theoretical immaturity". In any case, mereology can be treated as a contribution to formal ontology only if it carries a meaningful theory of (the construction of) universes. The same holds for (pure) set theory itself, which is sometimes taken to be the most usable and convenient base for any formal ontological system (cf. Quine's discussion of this topic in various places, and for several other approaches see e.g. Poli and Simons (eds.) Formal ontology Dordrecht, Kluwer, 1996; Scheffler and Urchs - Ontologic. Essays on formal ontology - Logic and logical philosophy, Torun, Copernicus University Press, vol. 2, 1995)." (1) Tadeusz Kotarbinski served as a faithful translator of Lesniewski's rather esoteric writings for the broader public. Most of Lesniewski's successors both within and outside the Lwow-Warsaw School set out their own considerations on formal ontology in the spirit of his systems. They often, however, use Kotarbinski's explication of these ideas. (2) [Same volume, pp. 463-486] From: Philosophical entities. A introduction - by Jan Faye, Uwe Scheffler and Max Urchs in: Things, facts and events - edited by Jan Faye, Uwe Scheffler and Max Urchs - Amsterdam, Rodopi, 2000 p. 11."If you wish to study philosophy fruitfully, then logic must be given the very first place. Logic treats the rules which direct the cognitive faculty to the knowledge of truth. Now we should study philosophy in such a way as to acquire complete certitude. Hence, he who studies philosophy should know how to proceed in the knowledge of truth. Consequently, he should be acquainted with logic. Hence, logic must be given the very first place. It might also be mentioned that those who are beginning in philosophy overcome their inexperience by studying logic. We have already given the reason for this. He who is unacquainted with logic does not know how to examine definitions and demonstrations with rigor. Therefore, he easily admits as certain things which greatly disagree with evidence. And he often thinks he understands things which he has not examined. However, if everything in logic is to be demonstrated, then principles must be borrowed from ontology and psychology. Logic treats of the rules which direct the intellect in the knowledge of all being, for the definition of logic does not restrict it to any species of being; therefore, it ought to teach us what to look for in order to know things. Now that which pertains to the general knowledge of being is derived from ontology. Hence it is clear that, in order to demonstrate the rules of logic, principles must be taken from ontology. Furthermore, since logic explains how to direct the intellect in the knowledge of truth, it ought to teach how the operations of the intellect are used in knowing truth. Now we must learn from psychology what the cognitive faculty is and what its operations are. Hence it is also clear that, in order to demonstrate the rules of logic, principles must be taken from psychology. This will be clearer when you have learned logic and have compared it with ontology and psychology. We have experienced this many times while carefully investigating the rules of logic and their reasons. If all things in logic are to be rigorously demonstrated with genuine proofs, then logic must come after ontology and psychology. Logic derives its principles from ontology and psychology. Now the parts of philosophy should be ordered in such a way that those parts come first which provide principles for other parts. Therefore, ontology and psychology should precede logic if everything in logic is to be rigorously demonstrated and if its rules are to be genuinely proven. Demonstrative method requires that logic be treated after ontology and psychology. However, the process of learning requires that logic precede all the other parts of philosophy, including ontology and psychology. Both methods cannot be observed. Weighing this more carefully, we should realize that he who does not know logic cannot be usefully acquainted with ontology and psychology. However, the principles of ontology and psychology which pertain to logic can be easily explained in logic. Therefore, we choose the method of learning in preference to the method of demonstration. Another reason why this approach is preferable is that ontological principles are definitions and psychological principles are established from experience. Consequently, ontological principles can be understood and admitted as true, even though the other things which are treated in ontology have not yet been examined. And the presuppositions of logic which can be demonstrated in psychology can be grasped a posteriori." From: Christian Wolff -Preliminary discourse on philosophy in general (1728) - Translated, with an introduction and notes, by Richard J. Blackwell - Indianapolis, The Bobbs-Merrill Company, Inc. 1963 p. 17 "Philosophy is the science of the possibles insofar as they can be." ibid., pp. 39-40 "There are some things which are common to all beings and which are predicated both of souls and of natural and artificial bodies. That part of philosophy which treats of being in general and of the general affections of being is called ontology, or first philosophy. Thus, ontology, or first philosophy, is defined as the science of being in general, or insofar as it is being. Such general notions are the notions of essence, existence, attributes, modes, necessity, contingency, place, time, perfection, order, simplicity, composition, etc. These things are not explained properly in either psychology or physics because both of these sciences, as well as the other parts of philosophy, use these general notions and the principles derived from them. Hence, it is quite necessary that a special part of philosophy be designated to explain these notions and general principles, which are continually used in every science and art, and even in life itself, if it is to be rightly organized. Indeed, without ontology, philosophy cannot be developed according to the demonstrative method. Even the art of discovery takes its principles from ontology." ibid., pp. 45-46GOTTFRIED WILHELM LEIBNIZ (1646-1716)"Ontologiam seu scientiam de Aliquo et Nihilo, Ente et Non ente, Re et modo rei, Substantia et Accidente" ("Ontology or the science of something and of nothing, of being and not-being, of the thing and the mode of the thing, of substance and accident." From: Louis Couturat - Opuscules et fragments inédits de Leibniz - Paris, Alcan, 1903. Reprinted Hildesheim, Georg Olms, 1961, p. 512 (Introductio ad Encyclopaediam Arcanam) (Now in: G. W. Leibniz Sämtliche Schriften und Briefe, VI Sektion: Philosophische Schriften, Band IV, Text n. 126 p. 527.) In a fragment titled by the Editors De duobus systematis scientiarum (1693?) on the classification of books in a library Leibniz in a deleted paragraph wrote: "Philosophici doppelt unterstr. (aaaa) Dida (bbbb) Logicam, Mnem (cccc) Didacticam, (aaaaa) Mnemonicam, (bbbbb) Logicam (aaaaaa) Rhet (bbbbbb) oratoriam seu (aaaaaaa) Persuasoriam (bbbbbbb) partem Rhetoricae persuasoriam, Mnemonicam; (aaaaaaaa) Metaphysicam, (bbbbbbbb) Ontologiam". (Sämtliche Schriften und Briefe, Akademie Verlag, Berlin 2004, Reihe IV, Bd. V, p. 592, ad. l. 25. The third occurrence was published by Nicholas Jolley, "An Unpublished Leibniz MS on Metaphysics", Studia Leibnitiana, 7 (1975), 2, p. 179, l. 81 and var. ad l. 81: "Scientiam autem genera lis quam vulgo Ontolog", but he later altered his text to read: "Scientia autem generalis quam dicam Metaphysicam vocant". (see: Michaël Devaux & Marco Lamanna, "The Rise and Early History of the Term Ontology (1606-1730)", Quaestio.Yearbook of the History of the Metaphysics, 9, 2009, pp. 173-208 (on Leibniz see pp. 197-198).ALEXANDER BAUMGARTEN (1714 - 1762)“Prolegomena to Metaphysics [ 1-3] 1. METAPHYSICS is the science of first principles in human cognition. 2. Ontology, cosmology, psychology, and natural theology belong to metaphysics. 3. NATURAL METAPHYSICS is the cognition of matters treated in metaphysics that are attained through the mere use of these matters. If artificial [metaphysics] explained in 1 is also added to it, then it is useful (1) for the development of its concepts, (2) for the determination and conception of its first principles, and (3) for the continuation and certainty of its proofs, etc. PART ONE: ONTOLOGY [ 4-35c] Prolegomena [ 4-6] 4. ONTOLOGY (ontosophy, metaphysics, cf. 1, universal metaphysics, architectonic, first philosophy) is the science of the general predicates of a thing. 5. The predicates of a thing that are more general are the first principles of human cognition, thus ontology belongs ( 2), with reason, to metaphysics ( 1, 4). 6. Ontology contains the predicates of a thing ( 4), (I) [that are] internal, (I) universal, which are in each thing, (2) disjunctive, one of which is in each thing; (II) relative.” Translated from Alexander Baumgarten – Metaphysica – (Frankfurt, 1757, 4th ed., 1739 1 ed.), reprinted at 15:4-54 and 17:23-226 of Immanuel Kant's Gesammelte Schriften (Berlin: Königlich-Preussischen Akademe der Wissenschaften zu Berlin, 1902-). Cited from: Eric Watkins – Kant's Critique of Pure Reason. Background Sources Materials – Cambridge, Cambridge University Press, 2009, p. 89. | |
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