How we use coherence of concepts to build ideologies and make sense of our world.

Much of human cognition can be though of as ‘constraint satisfaction’ according to philosopher Paul Thagard. For example, think of applying to a university. One college is in a beautiful setting, but another college has a professor who is an expert in your desired major. The first college is in a quaint town with a low crime rate, the second one is in an city with a high crime rate. You have a scholarship to the first college, but the second college charges less for tuition. And so forth.
Or suppose you are a detective in a murder case where the prime suspect is the daughter of the victim, a rich industrialist. The daughter was in line to inherit the family fortune. You interview the daughter, and find out she dedicates her spare time to helping the needy. Then you find out that her boyfriend is a fellow she rescued from jail. So again, there is information that leads you in conflicting directions.
One way to manage all the conflicts (or even just priorities) is by constraint satisfaction.

The following is a diagram of a simple situation. You are thinking of hiring a local carpenter named Karl, but you need to know whether you can trust him alone in your house. You know he’s a gypsy, and that the gypsy culture has allowed thievery from outsiders. So that knowledge would push you in one direction. But then you hear that he returned a lost wallet to your neighbor. So that pushes you in another direction. (I scanned the next figure, which illustrates the Karl scenario) from a small paperback, so the orientation is disturbing my coherence, but here it is)


The dotted lines are inhibitory, and connect incompatible nodes or hypotheses. The normal lines are excitatory. All connections are bidirectional – so that if node-A reinforces node-B, then node-B reinforces node-A also.

In this picture, the hypothesis of being honest is incompatible with being dishonest, so there is a dotted line between them. The action of returning the wallet is compatible – in fact is evidence for – honesty, and so there is a full line – an excitatory connection between them.

But decisions aren’t just made based on evidence, there is often an emotional component. Another diagram, a cognitive affective map, can show the influence of emotions:


Ovals are used for positive valences (a positive emotion) so in this example the oval around ‘food’ indicates that food is a desirable concept’. Hexagons have negative valences (and so the shape used in the diagram for hunger is a hexagon). Rectangles are neutral – you are not pro-or anti-broccoli in this example.

The diagrams can apply to political attitudes. For instance, in Canada, the law says you should refer to ‘trans’ people by their preferred pronoun (which might be neither ‘he’ nor ‘she’). Some Canadian libertarians, notably Jordan Peterson, have objected to this. Here are two diagrams from a 2018 article by Paul Thagard showing how a liberal, for whom equality ia a paramount value, might look at the issue, versus how a libertarian might look at the issue..


The green ovals with the strong borders show what the liberal prioritizes (equality) versus what the libertarian prizes (freedom).  In the lower diagram, the libertarian considers freedom as somewhat incompatible with regulation, and with taxation, but compatible with private property and economic development.    As a libertarian, you may take it as inevitable that economic development will result in income inequality, which is why the desirable value of ‘economic development’ has a inhibitory link with ‘income equality’ in the second diagram.   As a liberal, prioritizing equality, you might see the positive links between capitalism and the negative nodes of ‘exploitation’ and ‘inequality’, so even though there is a positive link between ‘capitalism’ and ‘freedom’ in the first diagram, you might, after the various constraints interact and settle down on a solution, want to modify Capitalism.

One way of learning about an opponent’s perspective is to draw the diagrams of how you believe your opponent he thinks -and then have him critique it and redraw it.

One advantage of such diagrams is that you can use an iterative (repetitive) process to spread the activations and find out, after the dust settles, which nodes are strongly activated.

You start by assigning activations to each node. We can assign all of the nodes an initial activation of .01, for example, except for nodes such as ‘evidence nodes’ that could be clamped at the maximum value (which is 1, the minimum value it can take is -1 ).  Evidence might be an experimental finding, or an item in the newspaper or an experience you had.

The next step is to construct a symmetric excitatory link for every positive constraint between two nodes (they are compatible) . For every negative constraint, construct a symmetric inhibitory link.

Then update every node’s activations based on the weights on links to other units, the activations of those other units, and the current activation of the node itself. Here is an equation to do that:


Here d is a decay parameter (say 0.05) that decrements each unit at every cycle, min is a minimum activation (-1) and max is (1). ‘net’ is the net input to a unit, it is a sum of the product of weights * activations of the nodes that the unit links to.

The net updates for several cycles, and after enough cycles have occurred, we can say that all nodes with an activation above a certain threshold are accepted. You could end up with the net telling you to go to that urban college, or the net telling you that the daughter of the industrialist is innocent, or that a diagnosis of Lyme disease is unwarranted, or that you should not trust Karl.

There are several types of coherence, and they often interact. Professor Thagard gives an example:

In 1997 my wife and I needed to find someone to drive our six-year-old son, Adam, from morning kindergarten to afternoon day care. One solution recommended to us was to send him by taxi every day, but our mental associations for taxi drivers, largely shaped by some bizarre experiences in New York City, put a very negative emotional appraisal on this option. We did not feel that we could trust an unknown taxi driver, even though I have several times trusted perfectly nice Waterloo taxi drivers to drive me around town.
So I asked around my department to see if there were any graduate students who might be interested in a part-time job. The department secretary suggested a student, Christine, who was looking for work, and I arranged an interview with her. Very quickly, I felt that Christine was someone whom I could trust with Adam. She was intelligent, enthusiastic, interested in children, and motivated to be reliable, and she reminded me of a good baby-sitter, Jennifer, who had worked for us some years before. My wife also met her and had a similar reaction. Explanatory, conceptual, and analogical coherence all supported a positive emotional appraisal, as shown in this figure:


Conceptual coherence encouraged such inferences as from smiles to friendly, from articulate to intelligent, and from philosophy graduate student to responsible. Explanatory coherence evaluated competing explanations of why she says she likes children, comparing the hypothesis that she is a friendly person who really does like kids with the hypothesis that she has sinister motives for wanting the job. Finally, analogical coherence enters the picture because of her similarity with our former baby-sitter Jennifer with respect to enthusiasm and similar dimensions. A fuller version of the figure would show the features of Jennifer that were transferred analogically to Christine, along with the positive valence associated with Jennifer.

If we leave out ’emotion’ then we just spread activations and compute new ones. To include emotions, we assign a ‘valence’ (positive or negative) to the nodes as well, and those valences are like the activations, in that they can spread over links, but with a difference – their spread is partly dependent on the activation spread.

Take a look at this diagram:


There is now a valence node at the top, that sends positive valence to honest’ and ‘negative’ valence to ‘dishonest’. When the net is run, first the Karl node is activated, which then passes activations to the two facts about him, that he is a gypsy, and he also returned a wallet. If ‘honest’ ends up with a large activation, then it will spread its positive valence to ‘returned wallet’ and then to Karl.

The equation for updating valences is just like updating activations, plus the inclusion of multiplying by valence.

Some interesting ideas emerge from this. One is the concept of ‘meta-coherence’. You could get a result with a high positive valence, but it is just above threshold, and you therefore not sure of it, which could cause you distress. You might have to make a decision that is momentous, which you really can’t fully be confident is the right one.
Another emotion, surprise, could result from many nodes switching from accepted to rejected or vice versa as the cycles progress. You may find that you had to revise many assumptions.
Humor is often based on a joke leading you toward one interpretation, and then ending up with a different one at the punch line. Professor Thagard says that the punch line of the joke shifts the system into another stable state distant from the original one.

In an actual brain, concepts are not likely to be represented by a single neuron, it is more likely that population codes (such as semantic pointers) would be used. So an implementation of the above relationships between concepts would be more complicated. Moreover, the model doesn’t explain how the original constraints between concepts are learned. I would guess that implementation details might modify the model somewhat. Coherence doesn’t ‘mean that multiple rational people will come to the same conclusions on issues – even scientists who prize rationality often disagree with each other. Sometimes, even the evidence you will accept depends on a large network of assumptions and beliefs. What nodes do you include? What weights to you assign to the constraints?

Still, the model is intuitive and makes sense.

You can get a link to the various programs mentioned at   There is also  more info at

Coherence in thought and action – Paul thagard 2000 MIT press
Emotional Consciousness: A neural model of how cognitive appraisal and somatic perception interact to produce qualitative experience
Thagard, P. (2018). Social equality: Cognitive modeling based on emotional coherence explains attitude change. Policy Insights from Behavioral and Brain Sciences., 5(2), 247-256.


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