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Mental Models: Excerpt from Brief Introduction to Philosophy of Sport (De Villa, et. al., 2020)

Updated: Jul 5

While it is so easy for the public to get interested in the most abstruse claims, it is so difficult for this same public to give some attention to simple ideas that affect so much of its very existence.


“Philosophy” comes from the Ancient Greek term “philos,” meaning “love of,” and “sophos,” or its plural form “sophia,” meaning wisdom. Thus the expression literally means “love of wisdom.” This is what is today referred to as the classic, or Ancient Greek Thought, meaning of the term.


The Erechtheum. Photograph by Jebulon (WikiMedia)

In addition to the term, Pythagoras has also given Philosophy a dimension that even today remains valuable to all civilizations. Ancient Greeks, like Pythagoras and his followers, have considered knowledge as some basis for predicting the future, therefore basis for explaining the behavior of nature. They have believed, in addition and quite importantly, that between all the pieces of knowledge that men bear in their minds is a harmony, a coherence, that binds them all in some unity.


Thus, for Pythagoras for example, knowledge of the shape of triangles involves not only the observation that it has three sides. It also involves observation of some principle or rule that relates the angles of the triangle to one another. Knowledge, for him, of the many principles one can learn in his life has to involve knowledge also of how all of these principles are themselves governed by some overarching principle or principles that combine all of these into one coherent body.

For purposes of modern life in an industrialized world, this Ancient Greek Thought definition is inadequate — not wrong but in adequate. Accordingly, scholars have refined the use of the term “philosophy.” For these scholars, at large, there are, in modern life, three senses, or uses, of the term “philosophy.”


This is one of those uses. Contemporarily, the term “philosophy” is used to refer to a particular type of method of reflection unique to the Ancient Greeks and still prevalent among Westerners. For instance, when it comes to numbers, ancient Egyptians and Persians alike consider knowledge of the rules that govern numbers as gifts of the gods and the deities, meant only for the chosen few. Indeed, among many ancient civilizations, knowledge of numbers involves, at times, esoteric religious ceremonies. For the Ancient Greeks, knowledge of numbers, while may still involve some religious dimension, largely involve mental exercise that, given enough patience and practice, can be available to everyone. Knowledge of geometry, for example, for them involves rules of logic and rules of mathematics that can, in principle, be taught to anyone with the right amount of reasoning skill — skill that can be learned by anyone with enough patience.

When some individual reflects upon his problems in life, for example, using one’s reasoning as the Ancient Greeks have done, one may be said to be having a philosophical moment.

One more use of the term “philosophy” is to use it to refer to some intellectual presupposition. As has been pointed out, for the Ancient Greeks like Pythagoras, knowledge of men involve some harmony or coherence. If knowledge be beliefs or thoughts in one’s mind, the assumption is that these thoughts cohere in a body, as if an organism, under some harmony. Among these thoughts, there is a matrix and there is a hierarchy. Some thoughts are more basic than others, meaning that the existence of some thought is dependent on some other thought, which itself is dependent on some other thought, and so on. In the end, one might surmise that some thoughts are more important than others. Some of these thoughts are so important, to think that these thoughts are trivial may mean that the entire body of thoughts itself is trivial. The point is that these thoughts upon which many other thoughts depend on are so vital as to be like the heart is itself vital to an organism. Thoughts like these are called intellectual presuppositions.

In the world of Geometry, these intellectual presuppositions are called axioms. Thus one can distinguish between Euclidean Geometry and Non-Euclidean Geometry precisely on account of some difference in some axiom.

To identify an intellectual presupposition, in a way, is to identify a philosophy. For instance, one may believe that, as basic belief, there is only one god. Thus one can be said to have a monotheistic intellectual presupposition, a monotheistic philosophy.


Another use of the term “philosophy” is to use it to refer to some belief system on a wholesale basis. It may actually happen that two individuals may end up having the same intellectual presupposition and yet cannot be described as having the same philosophy. A Muslim and a Christian may both believe in the presupposition that there is one and only one god. For some practical purpose, however, they cannot be said to have the same philosophy. It may still be important to draw some distinction between their “philosophies.” It is in this and similar cases that one needs to use the term “philosophy” to refer to an entire repertoire of thoughts unique as a body of beliefs, as in distinguishing between a Muslim philosophy and a Christian philosophy.


Overall, the Ancient Greek caveat still holds, that is, between all of these three senses, or uses, of the term “philosophy” is some harmony or coherence. They relate to one another under some matrix in the way all of one’s thoughts are related to one another in some web of belief.

There are many contemporary expressions that actually are treated in very much the same way as the term “philosophy.” These are some of them: world view, paradigm, theoretical framework, conceptual framework, and mental model. There are unique reasons for using these and similar terms instead of “philosophy” but overall, these all presuppose themselves both the classic and the modern definitions of the term.

Focus on the expression, noted above, “mental model.”

Think of “mental model” as a machine. Like any other machine it may work, or it may not. Like any other machine, it may work well or it may not work well. One of the measures of whether it works or works well is fitness of its parts along with all the others — how well one part works with all the others. Do the parts fit together well or not?

In addition, think of this machine as a time travel spacecraft. With this craft, you can go into the past, or you can go into the future. This means you can have a vision of the future with it as your tool.

A farmer who knows which months of the future promise no rain and which months promise rain, of course, is the farmer expected to have better harvest than those who have no such knowledge of the future. This means he has more chances of survival, meaning, too, more control over his destiny.

This is, of course, if the farmer has a reliable tool, a reliable craft with which he is able to get into the future.

For mental models to work well, all the parts of it have to fit together well with all the other parts. When some parts do not fit well with the others, meaning there are pain points involved, the mental model is not expected to work well, meaning the mental model does not give accurate predictions about the future.

What does it mean for a mental model to have pain points? It means that the mental model has contradictions. It has conflicts that put the model, the system, in some state of chaos.

A coherent mental model is a reliable mental model. Coherent means not having contradiction as much as the system can afford. The more coherent, the less contradiction is involved. The more contradiction involved, the less coherent the system is.

Mental models are philosophies. On the basis of the knowledge content that we have within our mental models plus the system with which this content is organized, the future may be predicted with much reliability. That is, so long as the system involved is coherent or as coherent as it can be made.

This is how we predict the paths of typhoons, for example, or the trajectories of satellites. We use models, in the case of humans, mental models.

Contradictions are pain points that indicate challenge. Someone produces a vacuum and lights up a candle. He observes that light can travel through a vacuum. Contradiction is noted. How can light travel through nothing? Same with electricity, how can electricity travel through nothing? In Physics, for example, such contradictions pose challenge to become creative. In this case of the behavior of light and the behavior of electricity, these have led to reinvention of the concepts of Physics as a discipline and has led to invention of Einsteinian Physics.

This is the reason why it pays to be involved with Philosophy. It may be Philosophy of Physics that deals with the pain points of Physics. It may be Philosophy of Science that deals with the pain points of Science. It may be Philosophy of Mathematics that deals with the pain points of mathematics.

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