Papers on the Logic and Ontology of Dependence Relations



Barry Smith, “Logic, Form and Matter”, Proceedings of the Aristotelian Society, Supplementary Volume 55 (1981), 47–63.

It is argued, on the basis of ideas derived from Wittgenstein’s Tractatus and Husserl’s Logical Investigations, that the formal comprehends more than the logical. More specifically: that there exist certain formal-ontological constants (part, whole, overlapping, etc.) which do not fall within the province of logic. A two-dimensional directly depicting language is developed for the representation of the constants of formal ontology, and means are provided for the extension of this language to enable the representation of certain materially necessary relations. The paper concludes with a discussion of the relationship between formal logic, formal ontology and mathematics.


Barry Smith and Kevin Mulligan, “Framework for Formal Ontology”, Topoi, 3 (1983), 73–85.

The paper draws on the distinction, first expounded by Husserl, between formal logic and formal ontology. Formal logic concerns itself with meaning-structures; formal ontology with structures amongst objects and their parts. We show how, when formal-ontological considerations are brought into play, contemporary extensionalist theories of part and whole, and above all the mereology of Lesniewski, can be generalised to embrace not only relations between concrete objects and object-pieces, but also relations between what we shall call dependent parts or moments. A two-dimensional formal language is canvassed for the resultant ontological theory, a language which owes more to the tradition of Euler, Boole and Venn than to the quantifier-centred languages which have predominated amongst analytic philosophers since the time of Frege and Russell. Analytic philosophical arguments against moments (accidents, tropes, individual qualities), and against the entire project of a formal ontology, are considered and rejected. The paper concludes with a brief account of some applications of the theory presented.


Barry Smith and Kevin Mulligan, “Pieces of a Theory”, in Barry Smith (ed.), Parts and Moments. Studies in Logic and Formal Ontology, Munich: Philosophia, 1982, 15–109.

The chapter surveys the history of treatments of the logic and ontology of dependence relations with special reference to the work of Husserl and of the Gestalt theorists. It is divided into 6 sections:

1.     From Aristotle to Brentano

2.     Stumpf’s Theory of Psychological Parts

3.     Husserl’s 3rd Logical Investigation: The Formal Ontology of the Part-Whole Relation

4.     The Theory of Material A Priori Structures: Phenomenology and Formal Ontology

5.     The Influence of the Logical Investigations on Logical Grammar and Linguistics: Husserl and Leśniewski

6.     Further Developments: Köhler, Lewin Rausch

For treatments of a diagrammatic representation of dependence relations see especially the final sub-section (6.4).


Barry Smith, Characteristica Universalis”, in K. Mulligan (ed.), Language, Truth and Ontology (Philosophical Studies Series), Dordrecht/Boston/London: Kluwer, 1992, 48–77.

We construct portions of a directly depicting language that is designed to enable the representation of the most general (dependence, and part-whole) structures of reality. We draw not on standard logical treatments of the contents of epistemic states as these are customarily conceived in terms of sentences or propositions. Rather, we adopt an approach to formal ontology which takes its starting point from maps and diagrams. The approach embraces elements of the conception of picturing outlined by Wittgenstein in his Tractatus, of Peirce’s logical graphs, and of chemical notation.


Barry Smith, On Substances, Accidents and Universals: In Defence of a Constituent Ontology”, Philosophical Papers, 26 (1997), 105–127.

The essay constructs an ontological theory designed to capture the categories instantiated in those portions or levels of reality which are captured in our common sense conceptual scheme. It takes as its starting point an Aristotelian ontology of “substances” and “accidents”, which are treated via the instruments of mereology and topology. The theory recognizes not only individual parts of substances and accidents, including the internal and external boundaries of these, but also universal parts, such as the “humanity” which is an essential part of both Tom and Dick, and also “individual relations”, such as Tom’s promise to Dick, or their current handshake.


Thomas Bittner, Maureen Donnelly and Barry Smith, “Individuals, Universals, Collections: On the Foundational Relations of Ontology”, in Achille Varzi and Laure Vieu (eds.), Formal Ontology in Information Systems. Proceedings of the Third International Conference (FOIS 2004), Amsterdam: IOS Press, 2004, 37–48.

This paper provides an axiomatic formalization of a theory of foundational relations between three categories of entities: individuals, universals, and collections. We deal with a variety of relations between entities in these categories, including the is-a relation among universals and the part-of relation among individuals as well as cross-category relations such as instance-of, member-of, and partition-of. We show that an adequate understanding of the formal properties of such relations—in particular their behavior with respect to time—is critical for formal ontology. We provide examples to support this thesis from the domain of biomedicine.


Fabian Neuhaus, Pierre Grenon and Barry Smith, “A Formal Theory of Substances, Qualities, and Universals”, Achille Varzi and Laure Vieu (eds.), Formal Ontology in Information Systems. Proceedings of the Third International Conference (FOIS 2004), Amsterdam: IOS Press, 2004, 49–58.

One of the tasks of ontology in information science is to support the classification of entities according to their kinds and qualities. We hold that to realize this task as far as entities such as material objects are concerned we need to distinguish four kinds of entities: substance particulars, quality particulars, substance universals, and quality universals. These form, so to speak, an ontological square. We present a formal theory of classification based on this idea, including both a semantics for the theory and a provably sound axiomatization.