Ontology of Relations

Ontology of Relations


the notion of a thing is grounded in an insight that grasps, not relations between data, but a unity, identity, whole in data; and this unity is grasped, not by considering data from any abstractive viewpoint, but by taking them in their concrete individuality and in the totality of their aspects. For if the reader will turn his mind to any object he names a thing, he will find that object to be a unity to which belongs every aspect of every datum within the unity. Thus, the dog Fido is a unity, and to Fido is ascribed a totality of data whether of color or shape, sound or odor, feeling or movement. Moreover, from this grasp of unity in a concrete totality of data there follow the various characteristics of things.

Lonergan, Bernard; Crowe, Frederick E.; Doran, Robert M. (2012-05-23). Insight: A Study of Human Understanding, Volume 3: 003 (Collected Works of Bernard Lonergan) (Kindle Locations 5728-5733). University of Toronto Press. Kindle Edition. 


This unity and identity in a given set of data taken in its totality assumes the data taken is a priori grasped as a unity ontologically, and is thus relevant to the person making the determination.  As a result the “things” of the physicist, while they relate to the same unity, will necessarily grasp different aspects present in that given unity than will the “things” of the historian or psychologist.  The question left unanswered is, of course, what is unified in this ontological unity.  The apparent answer is the individual datums but this is obviously not correct, since, for instance, we grasp no unity between the heart and the toes in the unity we grasp as a human being.  The unity is a unity specifically of relations.  We do in fact grasp the relations, and it is in grasping them as a unity of reciprocal relations that we grasp the unity in a given set of data.

That a thing, ontologically, is a unity of relations answers part of the question but raises another: what is a relation?  In particular, at the lowest genus and at the highest, the relations can’t be said to obtain between ‘things’ in the sense that we understand things as physically manifest, as presented.  We can find a clue in Heidegger’s fundamental ontology as a topological ontology: a topology of being.  However this is initially a difficult notion to understand in concrete terms.  How does topology, specifically a topology of place, lead to an ontology of things outside of the human experience of things ‘having’ a place, and spatiality and temporality being abstractions of place that we ascribe to the things themselves when we strip them of context?  Spatiality and temporality as derived from the topology of the things makes a certain sense in terms of the lack of absolute locality and temporality between things: if locality and temporality are both relative to different things then both have to originate within the system of each thing. 

The other issue is how to find a commonality that can be said to be intrinsic to the notion of relation, given the wide variety of types of relation that can be said to obtain:

Types of Systemic Relations


In our work we realized that we need to keep more attnetion to the relations. A simple line or arrow or a plus o minus like in casual loop diagrams is not sufficient. Therefor i developed this list of possible types of relations. is probably incomplete and needs development. Go to the Forum to comment the list.


The colours are suggestions for colour coding arrows or lines in a diagram. In addition to these one should us differentiation of fonts for lines and one should also label relations with descriptions.


1. RELATIONS IN SYSTEMS THAT ARE DEPICTED WITH NODES AND CONNECTORS (typically objects connected with lines or arrows)





1.1.1 Structural relations (Functional relations)

Very often systems are described as the assembly of parts where the sum is more than its parts. This is not a cause effect relationship but structural relationship.

Example: there is not a causal relationship between the wheels and the frames of a bicycle in the sense that e.g the frame decreases if the wheels increase. They are assembled in a structure where they generate together a surplus output. The whole is more than the sum of the parts.
Example: The relation in the air traffic system between the planes and the control system. The amount of plains do not automatically decrease if the control system is reduced. It only happens through institutional regulations.



1.1.2. Macro systemic relations (MSR):

Relations that are caused by the entities being subsystems in the same “supra-system” but without necessarily being inn direct contact with each other.

Example: Bikes and cars are related because they are sharing the same macro system: the roads. (They are related in additional ways than this)
Examples: The winter coat and the bikini are both part of the clothing wardrobe of the same person.



1.1.3. Micro systemic relations (MiSR):

Systems that are related because they share a relation through a sub system:

Example: The rubber in the tires of the cars and the bikes come from the same producer.
Example: A Mixmaster and a hair dryer can share similar electronic parts from the same manufacturer.





1.2.1. Thematic relations (TR):

Thematic relations are entities being part of the same thematic field or category. Themes are manmade sorting devices and there needs not necessarily to be e.g. a causal relation between members of a theme.

Example: the relation between Universal Design and Ergonomics
Example: Genres of music. There are many possible relations between genres of music but if we think of the relation between the music of the Australian aborigines and a symphony by Bach we can only think of very few like biological (music being programmed in our genes) and thematic relations (both being music).


1.2.2. Representational relations (RR):

Images, representation, videos, simulations, AR

Example: The relation between a map and a landscape



1.2.3. Associative relations (AR):

Metaphors and analogies: These are the types of relations that pop up in brain storms by associations.

Example: If two people are very similar to each other in their look there is an associative relation.
Example: If I say bird, you say fish….


1.3. SOCIAL RELATIONS (Yellows) (SR)



1.3.1. Structural social relations (SSR)

Example: Family, friends etc



1.3.2. Institutional social relations (ISR)

Example: Work, municipality, nation, culture, language etc.



1.2.3. Actions (ASR)

Social relations created through action

Example: Sharing political interests.





1.3.1 Causal relations (CR)

Cause and effect models: The nodes depict what entities causes an effects and what entities are being affected while the relations (normally arrows) depict the effect.

Example: If the heat is turned on the kettle starts to boil
Example: If the tolls for entering the city by car increases the passengers on public transportation go up.


1.3.2. Qualitative Causal Relation (QCR)

The amount or intensity will not be influenced but the quality will be changed

Example: The relation between architectural space and micro climate


1.3.3. Tools (CRT):

Tools are typically modifying and influencing the relations and not the entities directly.

Example: AR used to increase cultural understanding of biological systems.



1.3.4. Flows in human systems (FHS):

These are the concrete flows of values in our society. They are driven by needs and economic forces.

Examples related to human society: Material flows, Energy flows, Information flows, knowledge, Economic flows, Stock markeds.
Examples: Traffic flow, crowding of people.



1.3.5. Flows in natural systems (FNS)

These are driven by pressure differences (field conditions) and/ or by nuclear processes. On the high level these might be understood as causal relations, but on a detailed level they need to be understood as differentiations in uniform fields, like e.g. flows in water. They are caused by heat impact causing internal differentiation of pressure, but the shapes of the flows themselves are generated by internal chaotic principles resisting simple cause effect analyses.

Examples related to natural phenomena: water, air, magma, cosmic particle flows etc.


1.3.6. Variables, stocks and flows

This is the normal way of describing systems in Systems Dynamics. Variables are nodes that might change under the influence of other nodes. Flows are the flows of the content of the nodes form one to the other or the influence from one node to the other. Stocks are the storing capacity of the nodes.

Example: Classic example is a bath tub: if the inflow is bigger than the flow out of the drain the bathtub will be filled and flooded. If the flow out of the tub is bigger the tub will eventually be empty.
Example: The amount of predators and prey will influence each other. If the amount (stock) of rabbits is increasing the amount of foxes will increase which will lead to a decrease of rabbits which will lead to a decrease of foxes which will lead to an increase of rabbits…etc…
Example: the relation between the price of goods and the availability



1.3.7. Negative relation (NCR)

If node A increases, node B decreases

Examples: The fox and rabbit example, (this tends to be a self stabilizing system)



1.3.8. Positive relations (PCR):

If node A increases, the node B increases or if node A decreases node B decreases:

Example: The increase of profit on the stock market leads to the increase of the amount of traders


1.3.9. Feedback loops (Floop):

The effect of a chain of causal relations between variables returns to the “starting node”

Positive feedback loop (+Floop):

The sum of the relations is positive, The system is unbalanced

Example ? (I find these very hard to get right because it is very difficult to interpret and it is all dependent on the variables one makes up) Hostile negotiations accelerating into war.

Negative feedback loop (-Floop):

The sum of the relations is negative: the system is balanced.

Example? Fox and rabbit.
Example: if the price goes up the sales go down (-) then the price goes down (+) and then the sales goes up (-) and the price goes up (+). This is seemingly a self stabilising system but it’s not a negative feedback loop because it’s neutral (two –  and two +). The model is never quite like reality.



Not all systemic relations can be abstracted to nodes with connections. they will have to be diagrammed with spatial maps, intensity maps or along time lines.


2.1. Spatial proximity (SP):

Elements sharing the same space within an operational proximity for the agent (e,g, user)

Examples: The relation between a chair and a table. There is of course also a thematic relationship because they both are furniture and also maybe a historic relationship because both belong to the same style. There is also a functional / structural relationship. (Who said this is simple?)

Example: the proximity between a neighbourhood and a park.

Example: the proximity of the Bygdøy museums

2.2. Temporal proximity (TP):

Elements share a temporal proximity in relation to an agent (e.g. user)

Example: Traffic regulation systems that are timed according to rush hours that again are caused by the working hours which again are influenced by the planetary system (day length).

Example: A cafe serving lunch at lunch hours.

2.3. Spatial distribution (SD):

Intensity fields, variation and differentiation of the distribution of similar elements in space.

Example: temperature across a room with a stove in one corner.

Example: The density and distribution of sunbathers in a park.


2.4. Temporal distribution (TD)

2.4.1. The distribution of elements over time,

Example: the distribution of intensities in a music composition.

Example: The distribution of traffic density during one day


2.4.2 Timing, rhythms, repetitions (TRR):

Same elements are appearing in a recognisable pattern.

Example: The repetitions in a music compositions.

Example: The rhythms of intensity in the density of traffic.

Example: the rhythms and patterns of usage of the rooms in a house.


How  a single type of relation could form aggregates of relationality that encompass all of these types of relations is not immediately obvious, nor of course how that type could obtain at the lowest and highest genera between non-physical things, or in our usual terminology no-things.  

The type of relation that satisfies this multitude of requirements is known mathematically as a Topological Recursive Relation.  It is topological, satisfying Heidegger’s topology of being; it is recursive and can result, through various recursions and recombinations, in all of the types of direct relation we observe ontologically (indirect relations, such as those obtaining through the mind, are inherently combinations of simpler relations); it is also generic, i.e. how the relation obtains changes from one genus to another, while retaining the same relational rules.



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