Concepts and Schemas

In my last note I suggested that personal identity was the outcome of a particular mode of individuation. While everything is individuated in some way, only human beings are self-consciously individuated. Self-consciousness or introspective awareness is a form of individuation that is particular to human beings.

However, this generates something of an ironic paradox. Conceptual thinking is the most distinctive component of introspective awareness and the basis of rationality. But conceptual thinking is driven away from the individual by abstraction and generalisation. In conceptual thinking, individuated entities become the instantiations of an abstract type and the idiosyncrasies of individuality are bypassed in generalisations about populations.

The irony is that in this way the exercise of introspective awareness tends towards rationality and therefore towards the elimination from view of its own grounding in self-conscious individuation. Science is one example: Erwin Schrödinger called the objectification of nature through the elimination of the subject of cognizance science’s opening gambit. Another, travelling in the opposite direction, is Kant’s categorical imperative, in rational adherence to which the self exercises its freedom, but which removes every specificity of time and place and situation from moral significance.

A collection of individuated entities will form a population if the entities can be mapped to a type. For example, pine is a type, as are tree, plant, living organism and entity. This set of types forms a hierarchy. For every type hierarchy there is a matching population hierarchy. The more abstract the type, the larger the population: for example, the population of pines is smaller than the population of trees and the population of trees is smaller than the population of plants.

At each level of abstraction in the hierarchy there are attributes that characterise the entity at that level of abstraction: cellular composition is a characteristic of living organisms, cell walls containing cellulose is a characteristic of plants and supported on a rigid stem or trunk is a characteristic of trees. The type at each level of abstraction inherits the attributes of all the higher levels of abstraction, so pine trees inherit the characteristics of trees generally, of plants and of living organisms.

There are many conceptual hierarchies of this kind and any entity will belong to multiple hierarchies. Abstraction isn’t excluding.  The one for human beings might run human…living organism…entity or, alternatively, person…being… entity depending on whether you wanted to focus on the biological or the subjective entity.

The same applies to every individuated event. An event, at the most abstract level, is a change of state. For example, accompanying the entity hierarchy plant…living organism…entity we might have the event hierarchy photosynthesis…metabolic process…event. Entities and events are linked in that an event is a change in state of an entity. Modelling in terms of entities creates the synchronic perspective, describing the state of something at a moment in time; modelling in terms of events creates the diachronic perspective, describing changes in state between two moments in time.

These conceptual hierarchies are schemas. I have taken the term from software development where schemas are used to specify the design of the data stores and messages in a computer system. Schemas specify the form in which information is to be organised. They describe what entities there are, what attributes each entity may have and from what domain of values the content of the attributes may be drawn. It is also possible to have a meta-schema which describes how schemas are to be specified. As meta-schemas are self-referential there is, happily, no need for a further level.

However, there is also a philosophical precedent in Kant’s Critique of Pure Reason, where schemas are the link between the abstract categories of thought and empirical observation. Kant’s concept of a schema is considered particularly difficult to interpret and I wouldn’t want to claim too much but as multi-level structures of classification the congruence with software schemas is striking.

The problem Kant was trying to solve was how to bring together concepts and sensory experience. Concepts are formed out of words whereas experience is formed from sensory inputs. How are these two disparate ontologies connected together so that concepts remain anchored in sensation. The solution was to imagine that the mind can form a kind of temporary sketch according to a set of rules and through this process the imagination can give a tentative image to a concept.

Kant proposed three kinds of schema: empirical, mathematical and categorical. Trees, as an example of an empirical input, come in multiple shapes and sizes. The mental image of the empirical concept tree will necessarily resemble a particular type of tree: a pine, an oak or a palm, but at the same time must be understand as a representation of the abstraction which applies to all of them. An empirical concept is the set of rules or schema for forming this fleeting representation.

Similarly, it’s not possible to form an image of a mathematical concept such as a triangle that isn’t also one of equilateral, isosceles or scalene. It’s therefore not possible to instantiate the concept triangle, even in imagination, without instantiating a more particular type of triangle. To solve this problem, the schema associated with the concept triangle functions as a set of rules that governs how we can form a representational sketch of the more abstract concept in imagination.

In addition to these mathematical and empirical concepts, Kant proposed that at a more abstract level there were a set of concepts, the categories, that were required in order for the mind to make sense of any experience. The categories are very abstract concepts concerning quantity and quality, relation and modality. The categories are the condition of unifying disparate components into a single integrated experience. For this reason, Kant considered them to be a priori, given to experience rather than taken from it.

There are obvious advantages to having this multi-level structure. Kant was concerned to bridge the gap between perception and concept which is a wider gap than the one between individual and type which is the concern of information technology. Before we can consider individual entities as instantiations of a type, we first have to resolve incoming sensory information into a set of individuated entities. Visual information in particular is very noisy and, confronted with a noisy environment, the first priority of the mind might be to individuate the components simply as separate entities before trying to identify their type more concretely. This process could be interpreted as the imposition of an a priori structure onto experience.

My own view is that the most abstract categories are products of conceptual thinking rather than functions either of reality or of the mind. The reason is that wherever you start from and whatever domain of application you are considering, the process of abstraction will always end in the same place. At the top level of any and every conceptual schema there will always be the same ultimate abstractions: entity or event. These are artifacts of abstraction, so to speak.

Associated with these abstractions will be a further set of very abstract attributes. Entity implies boundary, extent, location and state; event implies sequence and duration. Both entity and event imply type; type implies abstraction, population and instantiation and instantiation implies actuality and possibility. These categories appear to be a priori because they are universal, and universal beyond what is actual or even possible because the same conceptual models can be applied to impossible imaginary worlds.

I think there are also more strategies available with regard to the representation of abstract concepts; strategies such as analogues, proxies and placeholders. In my mind, for example, the placeholder for the concept entity looks a bit like a drawing of an amoeba, an irregular line which closes in a loop to form the image of a blob. However, the loop creates a boundary and therefore an extent, a location and a state, an image that can be projected topographically onto the image of any other concept.

With regard to events, I tend to use the image of a switch as a proxy. A switch is an entity that has only two possible states, say on and off, and therefore the only events or changes of state possible are to toggle between them. In this case, simplicity is a proxy for abstraction.

Abstraction is a process of understanding that creates conceptual models that can be applied to reality in order to recognise and identify and then to understand and explain. Our ability to makes rational sense of the world to a large extent depends on how far the generalisations applicable to an abstract type capture the possibilities that inhere in an individuated totality. In this way, our understanding and explanation will be limited by the gap between type and individual.

This is an ontological gap rather an epistemological one. The scale of the gap is determined by the mode of individuation of the target entity or event. It is at its narrowest when we are considering material substances and at its widest and most unbridgeable when we are considering human beings and their behaviour. Plants and animals fall somewhere in between. Oceans are as much individuated entities as pines, octopus and human beings, but conceptual modelling captures the possibilities inherent in the existence of an ocean more completely than in the existence of a plant or an octopus and much more completely than in the subjectivity of a human being.

What this means is that the best tools for rationally explaining the world acquire their power from abstraction and generalisation but we ourselves are the least adapted of all entities to be the target of such explanations. The inscrutability of human beings is a consequence of the integrated subjectivity that is both the necessary platform for conceptual thinking and at the same time the most intransigent target for such thinking.