Ontology

Quartet 2

Why Ontology?

“If we only knew what we know, namely, in the use of certain words and concepts that are so subtle in application, we would be astonished at the treasures contained in our knowledge.”                  Immanuel Kant, Vienna Logic.

My interest in Ontology might be traverse to that of other people, being mainly motivated by psychology: the question I ask is – might the idea that the mind operates with an ontology help us to understand how the mind does the sorts of things that we know it does do? Other people come to Ontology from Philosophy, asking something like – what are the basic categories of reality? – or from Computer Science, asking something like – what is the best way to organize information?

To steal from Giuseppina D’Oro’s book on Collingwood, my approach is “Kantian … in so far as it seeks to uncover not the ultimate structure of reality but the presuppositions which govern our experience of the world.”

Ontology can mean many things – sometimes it seems almost synonymous with metaphysics. Here, my main interest in ontology is focused on the viability of the categories, sometimes called top-level categories, or ontological categories.

I will sketch my route via concerns with psychology to an interest in ontology.

The mind accomplishes remarkable things, and it seems to do this with recourse to generalization. A way of looking at this, is that it identifies patterns. At least one of the jobs of the mind is pattern identification.

Generalization and the identification of patterns – The mind sees similarities, or regularities, between different “things”, and then, either implicitly or explicitly, identifies certain sections of its sensory flux as being the same, and being a concept. (or, if you like, the identification of regularities IS conceptualization.)

We now have the idea that “concepts” might help us to understand the mind. It might next be useful to see whether concepts could be differentiated from each other by whether they fall into different broad categories.

It seems that they might – language often treats object concepts, e.g. “cow”, differently from property concepts, e.g. “brown”, so language might indicate a way of breaking down concepts into different categories; objects correspond to nouns, and properties correspond to adjectives. Other categories, for example relation, state, process and event, can fall under consideration in the same way.

Another approach is to analyse, logically, the different categories of concept that there may be. Aristotle and Kant are the foremost traditional thinkers on this, and contemporary thinkers such as Barry Smith and John Sowa are taking the field forward today. It may look a bit too a priori for some, but if held to account by real-world knowledge engineering, it might provide us with useful insights.

Included in this, it might give me and people with similar interests an insight into how the brain does the mind. None of this proves that the mind has an ontology, but indicates that ontology might help us to understand how the mind does its job.

It is possible that Ontology is a wild goose chase for understanding the higher levels of the organization of the mind, but I’m yet to read anything which convincingly argues that it is likely to be so; it seems best to pursue all avenues of inquiry into the nature of our minds.

To put the argument presented here assertively –

1) The mind uses concepts.

2) Concepts can be differentiated from each other, and articulated with each other, by the use of something like the Categories.

NOTE: The linguistic approach is fraught with dangers – for example, it is all too easy to think of noun phrases as corresponding to concrete objects, but this is often not the case. It is salutary in this regard to look down a list of most-used words in English, and to note how far down that list you have to go before you reach a genuinely concrete common noun. Similar considerations apply to other parts of speech – not all verbs are really actions, and so on. Nevertheless, the syntax / semantics interface affords insights if properly checked and treated with due caution.

Upper-Level Ontology

Aristotle gives the best early attempt to develop a list of the most fundamental ontological categories, now often called the top-level categories, in his work “The Categories”. He lists ten of these (emphasis added) –

“CHAPTER 4
1b25. Of things said without any combination, each signifies either substance or quantity or qualification or a relative or where or when or being-in-a-position or having or doing or being-affected. To give a rough idea, examples of substance are man, horse; of quantity: four-foot, five-foot; of qualification: white, grammatical; of a relative: double, half, larger; of where: in the Lyceum, in the market-place; of when: yesterday, last-year; of being-in-a-position: is-lying, is-sitting; of having: has-shoes-on, has-armour-on; of doing: cutting, burning; of being-affected: being-cut, being burned.”

Aristotle's Categories

As the above diagram indicates, there is a major division between substances, which are independent, that is, not dependent for their existence on something else, and all the other categories, which are dependent – on substances. Thus, the redness (a quality) of the apple depends on the apple (a substance). (I leave it to my dear reader to spot which of Aristotle’s categories has gone walkabouts from the diagram!)

All of these top-level categories are what are known as universals. They, or those within such modern developments from Aristotle’s initial work as the Basic Formal Ontology (see below), are not, however, the only universals – lower-level universals would be such terms as “dog”, and so on. I will leave open for now the important question of just how “top” a top-level category need be.

Beside universals, our main concern, we need some other ideas to show how ontology locks on to reality. As well as universals, such as “dog”, we need the concept of particulars, such as Boz, my family’s dog. Boz is a particular, and instantiates the universal of dog. Regarding this instantiation, we can say he is an instance of the universal dog. Dog is itself, in terms of Aristotle’s top-level categories, a substance. The diagram at the start of this article, derived from the work of E. J. Lowe, indicates the relationship between universal and particular (sometimes also called individual). It also indicates the relationship between substance and property (property is a near synonym for quality, or qualification in the Aristotle quotation above) and sort of shows how the four terms might work together. Substance and property are very important top-level categories.

There are a few more insights from Aristotle which are important for us. Regarding the “is a kind of” relationship, higher universals subsume lower – dog is a kind of mammal, mammal is a kind of animal, animal is a kind of living thing, and living thing is a kind of substance. The relationship between the higher and lower terms are, relationally, called genus and species respectively. (Note that for the Linnean taxonomy, as used by biologists to classify living things, genus and species have more specialized meanings, as two particular levels amongst others). This relationship gives us the terms generalization (very important) and specification. Other useful terms for such higher / lower relationships are superordinate / subordinate.

A species falls under a genus, and inherits its qualities, properties, etc. All that is true of a higher universal is true of any lower universal which it subsumes. But any species is also differentiated from other species that fall under the same genus. This is called its differentia. For a species, its genus together with its differentia define it:

genus + differentia = species.

The taxonomy of ontological categories, like other taxonomies, is hierarchical, having a tree-like structure, and can be perspicuously represented by tree-like diagrams. A tree, in this sense, is, mathematically, a kind of graph. Wikipedia has – “In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path. In other words, any acyclic connected graph is a tree.” [for now, I quibble “undirected”, since I think a tree of ontological categories needs to be directed.]

Some additional ideas I should at least mention, though at the risk of terminological overload, (the field of ontology just IS a terminological nightmare!), are –

  • Dependence – I’ve already mentioned this, but it will be as well to repeat here, bringing in some related terms: properties or qualities, (usage varies), depend upon substantial entities, such as substances (also known as objects). Substances are independent entities. Properties or qualities are dependent entities. Characterization is a related term: a property characterizes a substance.
  • Object and Stuff – Both these terms are close to that of substance, with object perhaps a synonym for substance. As in grammar, a distinction can be made between objects, or things in common parlance, and stuff. It is the difference between dog and water. Grammarians should think of countable and uncountable nouns, and number and measure. Discrete and continuous is a related duality.
  • Whole and Part (consideration of which is termed Mereology) – Both whole and part are substantial or processual entities, and a whole made of parts can also be a part of a larger whole; whole and part, like genus and species, are relational concepts, so often don’t appear in taxonomies as entities in their own right. However, the whole-part relationship is very important within ontology. It, too, has a hierarchical, tree-like structure. Composition and composite are very much to do with wholes and parts, and can be contrasted with aggregation and aggregate, an important category. Note also the term component: a part of a composition or composite.
  • State – States seem to me to be non-essential properties or qualities. Non-essential in this sense is sometimes called accidental, and non-essential properties or qualities are accidents. However, states are also often put on the dynamic, “occurent” side of things, along with processes and events.
  • Continuant and Occurent – Continuants are the sorts of things we have already considered – such as objects and qualities. Occurents bring in the more dynamic entities of reality – such as processes and events. Nearly synomymous terms are endurant and perdurant.
  • Relation – Relations are in many ways of great concern to me. There are some attempts at taxonomies of relations below.  Relation covers a wide range, and its analysis is very difficult.

A Detour Through Kant

Immanuel Kant, one of the most influential thinkers in the history of philosophy, was dissatisfied with Aristotle’s treatment of the categories, which he regarded as being a congeries, lacking any real structure. Kant, a sort of super-systematizer, tried to tidy up the categories into a table with a 4 x 3 structure, rendering 12 categories, which have similarities to and differences from Aristotle’s 10 categories. An interesting aspect to this, displayed in the tables below, is that Kant saw an isomorphism between the organization of judgements, which we would now regard as the province of formal logic, also with a 4 x 3 structure, and that of the categories: the categories are founded in the nature of reason. I have neither the time nor the intellectual confidence to explore these ideas properly, but include them here to indicate intriguing possibilities. Curious readers can look elsewhere for more adequate expositions.

Kant's Categories

Basic Formal Ontology

The Basic Formal Ontology, developed by Barry Smith et al, is a present-day endeavour in the field of ontology. Of the upper-level ontologies on offer, their approach is the one which, for me, makes the most sense and shows the most promise. I recommend a glance at their literature, as it gives an idea of what contemporary work on ontology looks like. The websites of the project are at –

http://basic-formal-ontology.org/

and http://ontology.buffalo.edu/smith/

and the best reference work seems to be –                                                                                “Building Ontologies With Basic Formal Ontology”                                                                       by Arp, Smith and Spear.

The diagrams below (click on them for higher resolution) are my own interpretation of their project. Note, however, that none of these diagrams should be directly attributed to the BFO project – I am not part of it, so the diagrams are not canonical or authoritative. Specifically, the diagrams are not completely in accord with the latest version of BFO, though I hope to amend them soon. The second Relations diagram, asterisked, in particular might have been superseded, but it is suggestive of matters left out of later developments. It is based on the paper “The Cornucopia of Formal-Ontological Relations” by Smith and Grenon, which may have been quite speculative and conjectural in the first place. Given all these provisos, I have nevertheless tried to be faithful to the work of the BFO group, and hope I have not been fanciful or, indeed, unduly original.

Entities

BFO

Relations

BFO Relations New

Relations*

BFO Relations

                                                                An older diagram
Smith et al do not regard their project as psychologistic, so do not present their categories as pointing to concepts, that is, as illuminating how the mind works, but rather directly realist, referring to reality. They are also very concerned with the Computer Science orientation, though with a sophisticated background knowledge of philosophical matters, and are directly involved in developing computer systems. They see ontology as being vital to enhancing the interoperability of databases, and thus helping to make scientific advance more efficient and more swift.

Smith et al give good reasons for their referential position, and though my own approach is motivated by cognitive or conceptualist concerns, based perhaps on sense rather than reference, as long as there is a general convergence we need not worry too much. Since within epistemology my position is realist, my Kantianism is, in this regard, attenuated. Ultimately, I regard categories, schemata, frames, etc. as enabling us to know and to navigate the world – they work, at least enough of the time, because they help us to identify patterns and regularities which are real. How this has come about is explicable by recourse to Darwinian evolutionary theory. Pre-Darwinian philosophers like Aristotle and Kant could not, of course, avail themselves of the insights afforded by such an approach to epistemology. Konrad Lorenz observes, somewhere, that what for Kant is a priori, is, from the point of view of an evolutionist, a posteriori. Given this, it is reasonable to follow Smith et al’s realism rather than conceptualism, not the least reason being that it helps keep ontologies consistent, and helps avoid some of the gobbledegook they have identified in efforts which muddle realist terms with conceptualist terms.

Related to this matter, note that in this article I have rode roughshod over use / mention distinctions: I have often ignored the need to put quotation marks around terms, and so on. For my purposes now, such considerations would be a distraction, and would amount to clutter.

As something of a side issue, I am sceptical of the aims of Smith et al to impose a logical / ontological language on scientific researchers. It seems to me that this would be to demand of researchers that, as well as presenting their findings, they should fulfil the additional task of translating their findings into the latest ontologese, a double burden. Perhaps we simply need to accept the likelihood of a time-lag between cutting-edge research and the tidying up of any viable results into the ontology.

Sowa

Another approach to ontology can be found in the work of John Sowa and his team on knowledge representation, the KR Ontology. The website for this project, which is very well organized and extremely detailed, can be found at –

http://www.jfsowa.com/ontology/index.htm

and the core book is –                                                                                                        “Knowledge Representation: Logical, Philosophical, and Computational Foundations”         by Sowa.

Like Smith, Sowa is very knowledgeable of philosophy and its history, and indeed, this may be part of the attractiveness to me of their approaches over more merely computer-based orientations.

The diagram below represents Sowa’s top-level ontology.

1 Top Level

[UNDER CONSTRUCTION rather mystifying use of Peirce and Whitehead to derive trichotomies]

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About David Ruaune

My main interests are philosophy, psychology and semiotics.
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