I read that Edmund Gettier died recently, famous for the problem of knowledge named after him. He argued that justified true belief may not really be knowledge, and gave counterexamples for it not being so.
Here I show a diagram for those three conditions (Justified, True, Belief) and their opposites (Baseless, False, Doubt). The Wikipedia page on the Gettier problem states simply that the solution for it is that the justification must be true also, as the belief.
I don’t want to be posing as Pilate, but it does seems that truth is the most difficult and elusive of the three criteria, conditioning as it must the other two. In this age of disinformation, you could do worse than read the articles below.
The Kabbalah (correspondence) is a traditional and esoteric school of thought in Jewish mysticism. The ten Sephirot (emanations) of the Kabbalah in the Tree of Life diagram can be divided into Four Worlds as follows, and correspond with the Four Suits of the Tarot and the Four Elements:
Atziluth (אֲצִילוּת): World of Emanation (Wands, Fire, Spirit)
Beri’ah (בְּרִיאָה): World of Creation (Swords, Air, Intellect)
Yetzirah (יְצִירָה): World of Formation (Cups, Water, Emotion)
Asiyah (עֲשִׂיָה): World of Manifestion (Disks, Earth, Action)
Memory is the treasury and guardian of all things.
Before the internet and before even writing, memory served as the treasury and the guardian of the past, as the imagination served as the vanguard and the promise of the future. Today, our memory is weakened by the onslaught of the new and the now, leaving us open to attack from forgetfulness and apathy. Well-documented techniques of the past exercised our “artificial” memory, over and above that of our “natural” memory. One such method was the use of a “memory palace,” a spatial geography or edifice that enabled a visualization and recall of structural sequence, ornamented by real or imaginary decoration to link things or words into this order.
The art listed four main constituents: the rules for the places (or loci), the rules for the images, and (rules for) the memories of the things or the words to be remembered. As the art originated in antiquity, the records of its use and evolution come to us only in written or printed form. Perhaps this is like trying to reconstruct a living, breathing life-form from the bits and pieces of its fossilized body. And so, perhaps this arcane art was nothing like what we imagine it is today, but something else, rich and strange, that enabled techniques and skills beyond mere recall.
Rules for Places
Rules for Images
Memory for Things
Memory for Words
And so as Plato recounts Socrates’ dialog with Phaedrus, wherein Thamus says to Thoth, inventor of the written word:
This discovery of yours will create forgetfulness in the learners’ souls, because they will not use their memories; they will trust to the external written characters and not remember of themselves. The specific which you have discovered is an aid not to memory, but to reminiscence, and you give your disciples not truth, but only the semblance of truth; they will be hearers of many things and will have learned nothing; they will appear to be omniscient and will generally know nothing; they will be tiresome company, having the show of wisdom without the reality.
The former four now ending their discourse, Ceasing to vaunt their good, or threat their force. Lo other four step up, crave leave to show The native qualityes that from them flow: But first they wisely shew’d their high descent, Each eldest daughter to each Element.
— From The Four Humours in Man’s Constitution, by Anne Bradstreet
As a young puritan poet, Anne Bradstreet (1612-1672) wrote several poems in fourfold arrangements, dealing with fourfold topics, she called Quaternions.
Four Life Ages
She later added another to her oeuvre, writing one dealing with Monarchies or Empires.
“How to Solve It” (first published in 1945) is a small volume by mathematician George Pólya describing methods of problem solving. The book suggests the following steps when solving a mathematical problem:
1. Understand the problem.
2. Devise a plan to solve it.
3. Carry out the plan.
4. Revise and extend: look back on your work.
What is the best way to educate, to teach and learn? Ideally, students shouldn’t merely memorize facts and recall them on demand, although retaining well accepted knowledge is important. Certainly, students need mental structures to organize these facts, so that they form associated groups of categories and classification. Additionally, methods are needed for accepting and rejecting facts, and procedures for organizing facts, although facts may often be revisited for truth, or to reorganize them, and so on.
Benjamin Bloom et al. developed a taxonomy for educators of six mental aspects for the acquisition of knowledge, which was revised later into six cognitive actions or processes by L. Anderson, B. S. Krathwohl and others. These six actions form a sort of food pyramid for knowledge, so that lower actions form a broader base for higher ones. Both taxonomies sort a dimensional hierarchy of knowledge operated by these aspects or actions from concrete to abstract: Factual, Conceptual, Procedural, and Metacognitive (the last added when revised).
In the revised taxonomy, “Remember” is the lowest cognitive action, described by “remember facts and basic concepts,” which deals with the Factual and Conceptual. Above it is “Understand,” described by “explain ideas or concepts,” and I imagine an idea can be a fact. Next is a procedural action “Apply: use information in new situations,” and in fact all six actions are procedural by being actions. At the top of the pyramid is “Analyze,” “Evaluate,” and “Create”. The Metacognitive dimension (“thinking about thinking”) is for thinking about these six actions and these four dimensions, as to how they are related and differ.
These taxonomies are well considered and there are many resources to investigate.
Anderson, L., Bloom, B. S., Krathwohl, D., & Airasian, P. (2000). Taxonomy for learning, teaching and assessing: A revision of Bloom’s Taxonomy of Educational Objectives (2nd ed.). New York: Allyn & Bacon, Inc.
Anderson, L. W., Krathwohl, D. R., Airasian, P. W., Cruikshank, K. A., Mayer, R. E., Pin- trich, P. R., … & Wittrock, M. C. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives, abridged edition. White Plains, NY: Longman.
A Yojijukugo (四字熟語) is a unit of four kanji characters that usually represents an idiomatic saying in Japanese. It is itself a yojijukugo, even though it isn’t idiomatic, since the term can also broadly refer to a non-idiomatic phrase of four characters.
Shunkashūtō (春夏秋冬) is a nice one that means the four seasons of the year, and so is a fourfold written in four kanji characters.
Eshajōri (会者定離) is hopefully appropriate, meaning “every meeting must involve a parting”.