5.2 The Trivium

{Section under development}

This section couples modern cognitive science to the age-old concept op the trivium to the recent definition of Open-ended development. Whatever open-ended development is, it is definitely not development aimed at interacting in a closed environment: that would only require a finite development. Open-ended development is essentially aimed at dealing with reality as it is and not with reality is it appears to be or as we can simplify it to. This entails that reality is leading. Like it is in science.

Developing a reality-tested belief base

Every act you do, every step you take, every choice you make is a test of your beliefs. For example every step you make relies on the ground not changing into water or disappearing altogether. And each act that has the expected/desired outcome is evidence that your beliefs and your reasoning capacity is reliable. But the very fact that you initiate an act is a sign that you believe you expect you can deal with the consequences of your actions. Ideas as expressed in words are of a different quality than ideas tested out in reality with whatever intended or unintended consequences. Note that this directly refers to (raw) power as the capacity to produce intended effects without taking into account the full consequences and wisdom as the capacity to produce intended effects while taking into the full consequences into account.

The more your beliefs and thought processes pass a wide variety of tests, the more reliable they are. In addition, the more your understanding or the world extends itself, the further in the future and the wider in spatial, cultural, technical, social, or scientific terms one’s plans work will out as expected. This entails that, if all is well, our interactions with the world ensure that beliefs become gradually more reliable in terms of how pervasively they can be used to base successful courses of action on. This results in a reality-tested globally consistent belief base.

Unfortunately the development of a high quality reality-tested belief base is a process that, although it works in all of us, may be derailed at some point. And it is typically derailed when authority derived belief systems (ideologies, religions, or cultural biases) or authoritarian parent, teachers, or authorities limit the freedom to “consider facts” critically and to either adopt them in your belief-base or refute them as false or unreliable. Without this freedom people will not fill their minds with ever more reliable and self-empowering knowledge and skills. The result is dependency on authorities to maintain the conditions in which the mind functions adequately: authoritarianism.

It is therefore important that the mind can fully self-develop, without externally (authority) imposed limitations. This is probably the reason why the type of learning that leads to a reality-based belief system is called liberal education.

Liberal education (New Oxford Dictionary)
concerned mainly with broadening a person’s general knowledge and experience, rather than with technical or professional training

Note the use to the word education for “broadening a person’s general knowledge and experience” and the word training for “technical or professional training.”

Only very few of us in Western Societies have received an education that allows the mind to self-develop without imposed limitations and constraints. Yet a sizable minority has still has learned to think properly and critically. The reason for that is that learning to think properly is natural process, it might well be that low quality thought occurs only in societies, like ours, that make an [effective effort[disempowerment to suppress the development of high quality thought.

The Trivium and open-ended development

How to develop a reality-tested consistent belief system has been known since classical times (and probably well in advance of that) and it is described in the so-called Trivium of ‘grammar’, ‘logic’ or ‘dialectic’, and ‘rhetoric’. There are many descriptions of these concepts. Here we add another that takes the scientific basis in this website, and in particular the [open-ended development loop] into account. It is loosely based on trivium education and [Sayers, 1947]. The ancient Greeks used the term dialectic to refer to various methods of reasoning and discussion in order to discover the truth (see entry ‘dialectic’ the New Oxford Dictionary) and in this context it might be better term than ‘logic’.

The Open-ended development loop depends, just as the Trivium, on three different concepts. And interestingly, these two sets of concepts are easily connected and possible references to the same phenomena.

Open-ended development loop
Open-ended development loop

Table Trivium vs open-ended development provides a comparison between the three components of the Trivium and the three components of the open-ended development loop and interprets each components

Trivium vs open-ended development
Trivium Open-ended development loop Interpretation
Discovery of the Who, What, Where, and When through interaction
Exploration quadrant
Extending behaviors through exploration
Exploration via direct experiential evidence or critically evaluating factual evidence
Why of the world through contemplation and reasoning
Consolidation quadrant
Generalization of behaviors and consolidating them
Consolidation of the knowledge and skills acquired from the grammar-process through a coupling with as of yet unrelated domains of knowledge and skills
The how of the world through interaction
Problem solving quadrant
Fine-tuning and testing of behaviors and real world problem solving
Problem solving associated with the realization of ideas in an open world
Frustration quadrant
Deactivating or unlearning behaviors
The antithesis of education, but nevertheless important since not all behaviors are productive and some should be unlearned if they do not work out in reality

The next few paragraphs are in part a verbatim copy of text in section Open-ended development (if so in italic), but extended to be more useful for the connection with the Trivium.

Grammar — Exploration

In the exploration quadrant one expresses autonomy and agency and extends one’s behavioral repertoire. Like anything on the right site of the [core-affect] plane, exploration must be unforced and self-initiated. This ensure that one is in the [Vygostsky’s] zone of proximal development](https://en.wikipedia.org/wiki/Zone_of_proximal_development) where learning and ultimate consolidation is (almost?) guaranteed. Exploration should however become a structured and effective process in which, if at all possible, a learner should be aware of the completeness extend of the exploration so that exploration does not leave important answers open that could have been easily filled with somewhat more strategic exploration.

Logic/dialectic — Consolidation

In the consolidation quadrant one develops — in the absence of environmental pressures — new relations between oneself and the environment and one relates and combines hitherto unrelated knowledge and experiences. In doing so one generalizes, stabilizes, and consolidates knowledge and relations (whether mental, social, or otherwise). The consolidated knowledge, (social) relations, and skills, no longer new and unpredictable, become more and more suitable for general utility and in particular problem solving (a left-hemispheric activity).

This corresponds to the problem-solving quadrant in which the agent can prove its increased competence and test and fine-tune its extended behavioral repertoire. Successful real-world problem solving leads to confidence, which is a basis for further exploration, consolidation, and testing.

This ‘open-ended development loop’ is depicted in Figure [open-ended development loop]

Grammar process: exploration via direct experiential evidence or critically evaluating factual evidence

Logic process: consolidation of the knowledge and skills acquired from the grammar-process through a coupling with as of yet unrelated domains of knowledge and skills.

Rhetoric-process: problem solving associated with the realization of ideas in an open world.


The grammar process leads to the discovery of the Who, What, Where, and the When of the world.

The grammar process is about small-scale structure and in particular about exploring the dynamics of symbols, objects, and processes. Play of any sort is a great way to explore and discover the structure/dynamics of any system and the more one plays, the more one samples and discovers the space of opportunities afforded. Grammar is traditionally used to refer to the symbols of language and is as such important. In the middle ages a pupil of liberal education learned a second language (usually Latin) explicitly on the basis of the grammar of the second language. This engrained the belief that any system, however intractable it might appear initially, is subject to regularities and that these regularities can be discovered and used. This is a highly empowering realization on which all further learning .

Grammar, in de sense of allowed (often sequential) relations between symbols, matches left hemispheric strengths because symbols refer to abstract entities without individuality that can however be specified to particular situations. Mathematics and Computer Science tap into this type of ability. Grammar in the sense of causal (local) structures that can be discovered via (playful) interaction with the world is equally important and more attune with right hemispheric strengths. Here the object of play is a particular real-world system, with all its particular idiosyncrasies and fullness. In this case the discovery process is more aimed at learning to generalize the experience by learning to discount the particulars of the instance. An important point in both cases is that grammar is local in the sense that it, at least initially, pertains to things that are simultaneous or sequential and typically part of a single system or process. Grammar is therefore aimed at a local environment.

The result of discovering and ordering the small-scale structure includes the answers to the Who, What, Where, and the When of individual processes that are randomly sampled from the world. Trained thinkers are very good in discovering facts and experiences in ways that reliably answers all W-questions from raw data. They have developed an uncanny ability to discover local inconsistencies and to discover factual errors or lies; and they will not be satisfied or put of by inconsistencies. In addition they know to judge the quality of information given by (so called) experts and authorities and to check both key-facts and random factoids pertaining to a situation. As such they fill their minds with a huge variety of reliable facts and experiences that can be summoned when necessary and that can be used to discover and judge new raw data.

This leads to a large network of connected facts and experiences from a wide range of domains. The nature and character of these domains is by and large irrelevant as long as its diversity is large and the facts and experiences derived from it mainly reliable.


The logic-process produces the Why of the world.

Logic-process is about the interconnectedness of knowledge in as globally consistent manner. Small-scale logic plays a role in fact-discovery and fact-evaluation. But the key point of the logic-process is providing answers to the Why of a subject, i.e., it is about the history and complete set of influences that gave rise to it and maintain it. Or phrased differently: to understand a situation. For example, one might reflect on a bridge and why it was build just there, why it has the features it has, and why it is in the state it is. This requires the flexible combination of facts, skills, and knowledge from many different domains.

A proficient thinker is can rely on a huge basis of facts and experiences and use this to come up with a globally consistent belief-base that approaches the consistency of reality itself. Proficient thinkers know that inconsistencies in their thoughts cannot be a reflection of (ever-consistent) reality and as such it require attention in the form of new or additional fact-checking or other research.

Not yet competent thinkers on the other hand are characterized by what George Orwell termed doublethink in his novel Nineteen Eighty-four: “Doublethink is the act of simultaneously accepting two mutually contradictory beliefs as correct, often in distinct social contexts” wikipedia. Doublethink is only possible when different domains of knowledge are not integrated in a (globally) consistent whole. So the purpose of logic is to connect all types of different forms of knowledge and experiences.

While the grammar-process is about going to the world and acquiring facts, the logic-process is more introvert and contemplative. It requires quietness and a playful contemplative state of mind which allows relevant knowledge to present itself to be fit into the larger reality-tested (and therefore consistent) belief-base. Daydreaming, fantasizing, playful planning, discussions, and listening to real-world accounts can all be ways to connect previously unconnected knowledge, experiences, and skills. The logic-process can be tedious step-by-step work (especially in the case of formal logic), often it involves a more day-dreaming or playful state of mind in which all kinds of (possibly) relevant knowledge domains and experiences are combined in search for inconsistencies to be resolved and for new relations to be discovered.

The natural result of the logic-process is the gradual merging of initially isolated knowledge and experiential domains into a single connected reality-based understanding of the world. In this understanding of the world, everything has a history that may not be known in full, but that can be envisioned as the result of complex real-world dynamics context , which can be extrapolated to the future. In many cases this requires some filling in, which necessitates additional research (grammar).

Eventually the logic-phase allows one to understand every scene and every situation in terms of relationships and dynamics. And part of these relations and dynamics can be separated from the whole of existence and analyzed as a closed system (with typical left hemispheric approaches) to solve particular problems. The result can always can be reintegrated in the whole of understanding.

The result of the logic-process is a progressively more pervasive integrated belief-base on which action can be reliably be based.


Rhetoric-process proofs that one knows the How of the world.

While the logic-process is primarily a mental and therefore an individual process, the rhetoric-process is essentially a participatory one of (again) going out in the world to test one’s ability to understand aspects of the world by [co-creating] new and desirable contributions to the world. The narrow meaning of rhetoric is “the art of effective or persuasive speaking or writing”. But this is only one way of persuasion: the best way of persuasion is by actually contributing something new and useful in a more tangible form than mere words.

The key-feature of the rhetoric process is realizing: and successful realization is a measure of a realistic belief base, because realizing something, and especially something new, is the culmination of a long sequence of actions.

Applying knowledge and understanding expressively comprises Wisdom or, in other words, it is systematically useable knowledge and understanding- to explore and find the proper choice of methods for cogently expressing the conclusions of grammar and logic on a subject in writing and/or oral argumentation (oratory). The annunciation of those conclusions is called a statement of rationale, the set of instructions deduced from the rationale for the purpose of application (of those conclusions) in the real world is called a statement of protocols.

Many beliefs are false. Some seem reliable. Some are reliable. And some beliefs are true in a particular — closed world — situation. No belief is generally true (which leads to the problem of whether this statement is true :-) )

. That does not make your beliefs true in general

Given the fact that many of our belief

Every act is a test of our beliefs. We only act if we expect to be able to handle its consequences.


  • Sayers, D. (1947). The Lost Tools of Learning. In The Poetry of Search and the Poetry of Statement. Gollancz.