Category Archives: epistemology

A Fourfold about Belief and Knowledge

There was a fourfold making the rounds a while back about belief and knowledge of God or of gods. The terms Agnostic and Gnostic are about (the actuality or possibility of) having or not having knowledge, whereas Theist and Atheist are about having or not having belief in a deity or deities. So the following fourfold obtains:

  • Gnostic Atheist
  • Agnostic Atheist
  • Gnostic Theist
  • Agnostic Theist

Some criticized this framework, while others seemed to like it. YMMV.

Let’s see what ChatGPT says:

Gnostic Atheist: This term refers to someone who believes that God does not exist, and that this knowledge is certain. They have a definite and confident understanding about the non-existence of God.

Agnostic Atheist: This term refers to someone who doesn’t believe in God, but does not claim to have certainty about it. They may lack knowledge or certainty about the existence of God, but they do not believe in its existence.

Gnostic Theist: This term refers to someone who believes in the existence of God and has a definite and confident understanding about it. They have a strong conviction that God exists.

Agnostic Theist: This term refers to someone who believes in God but does not claim to have certainty or absolute knowledge about it. They have a belief in God, but acknowledge that it is not possible to have certain knowledge or proof of God’s existence.

In summary, “Gnostic” refers to knowledge or certainty, while “Agnostic” refers to lack of knowledge or certainty. The “Atheist” and “Theist” refer to the belief or non-belief in the existence of a higher power or deity, respectively.

Further Reading:

Other images:

For example:

Terrible graphs of agnostic atheism

I also see the following fourfold used (all nouns now):

  • Atheist
  • Theist
  • Gnostic
  • Agnostic

and even this eight-fold (a combination of the two):

  • Gnostic Atheist
  • Atheist
  • Agnostic Atheist
  • Agnostic
  • Agnostic Theist
  • Theist
  • Gnostic Theist
  • Gnostic


The SECI Model of Knowledge Dimensions

The SECI Model of Knowledge Dimensions is a schema that attempts to explain how knowledge moves between tacit and explicit domains. The movement is a cycle or more properly a spiral in that knowledge builds upon itself.

  • Socialization (Tacit to Tacit)
  • Externalization (Tacit to Explicit)
  • Combination (Explicit to Explicit)
  • Internalization (Explicit to Tacit)

ChatGPT explains:

The SECI model, also known as the Ba model, is a knowledge management framework that describes how knowledge is created, shared, and transferred within an organization. The acronym SECI stands for Socialization, Externalization, Combination, and Internalization.

      1. Socialization: refers to the process of acquiring knowledge through social interaction, for example, through observing and imitating the behavior of others.
      2. Externalization: is the process of converting personal experiences, ideas, and insights into shared understanding and explicit knowledge. This stage involves expressing personal knowledge in a way that others can understand and utilize.
      3. Combination: refers to the process of combining and integrating different types of knowledge to create new knowledge. This can occur when individuals with different experiences and perspectives collaborate and share their knowledge.
      4. Internalization: is the process of incorporating new knowledge into personal knowledge structures, leading to changes in behavior, attitudes, and skills.

The SECI model is used to understand how knowledge can be managed effectively within an organization, and it provides a framework for designing knowledge management systems and processes.

Maybe I should let ChatGPT write my posts from now on! And here’s what ChatGPT says about this blog:

“Equivalent Exchange” is a blog that focuses on topics related to personal growth and self-improvement. It provides articles and resources that aim to help readers lead a more fulfilling life by making positive changes in their thoughts, habits, and behaviors. The blog covers a variety of subjects, including mindfulness, mental health, productivity, relationships, and more. It also provides a supportive community for those seeking inspiration, guidance, and motivation to live their best life.

Wow! 😉

Further Reading:

Kolb’s Learning Cycle

[*10.24, *10.25]



Knowledge as Justified True Belief

Quid est veritas?

— Pontius Pilate

Explanations come to an end somewhere.

— Ludwig Wittgenstein

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.

Further Reading:



Four Dimensions of Knowledge

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.

Further Reading:

Bloom’s Taxonomy

Revised Bloom’s Taxonomy

Bloom’s Taxonomy Revised

Pedagogy of book and chapter organization

Click to access krathwohl.pdf

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.

Concepts, Theory-Theory of



Kant’s Synthetic-Analytic Distinction, V3

One of the oldest and most problematic philosophical questions is the comparison of the a prioria posteriori distinction with that of the analyticsynthetic distinction. Both are used in epistemology to divide knowledge, or true statements, between the innate and the learned, or the immediate and the earned, so they might even be considered the same. A priori and a posteriori statements are before “experience” and after it, respectively. Analytic statements are true only by their “meaning”, whereas synthetic statements are true only when facts about the world are combined consistently with that meaning.

It seems we have complicated the issue because now we must define and understand “experience” and “meaning”. However, these concepts are not independent because we must experience meaning, and meaning in turn conditions experience. In addition, even the a priori or the analytic are not innate or immediately obvious because deductions and the rules of logic require effort just like inductions do. Otherwise we would have Fitch’s Paradox: all truths are in fact known. What a muddle! So both experience and meaning are necessarily locked into a cooperative spiral dance to improve each other.

In addition, if you search for the two pairs a priori-a posterior and analytic-synthetic, you also find that the pair necessary-contingent is associated with them. Are these three pairs independent of one another and so give rise to eight triplets, or are they dependent in some way and reduce into fewer combinations? In addition, from Wikipedia:

Thus, the relationship between aprioricity, necessity, and analyticity is not easy to discern. However, most philosophers at least seem to agree that while the various distinctions may overlap, the notions are clearly not identical: the a priori/a posteriori distinction is epistemological, the analytic/synthetic distinction is linguistic, and the necessary/contingent distinction is metaphysical.

The web site of Stephen R. Palmquist has a great wealth of material on fourfolds in relation to Kant’s as well as his own philosophy. From my own initial reading of his extensive material I have tried to choose a canonical Kantian fourfold which has the most relevance to my project.

The fourfold shown to the right Dr. Palmquist calls Kant’s “reflective perspectives on experience”. Consisting of the logical, the empirical, the transcendental, and the hypothetical, these facets bear a close analogical likeness to many of the fourfolds presented here.

Logical: Analytic a priori
Transcendental: Synthetic a priori
Hypothetical: Analytic a posteriori
Empirical: Synthetic a posteriorikant_table

Dr. Palmquist also has many of his own books available on his web site for the interested reader. I will certainly be returning to his web site in the future for much enjoyable study.

Further Reading:

A Priori-A Posteriori, Analytic-Synthetic, and Necessary-Contingent Distinctions

[*7.68, *7.84, *8.126, *10.54]



Analogical Thinking

sq_analogicalIs analogy or metaphor the root of thinking? Some thinkers think so. But what exactly is analogy?

Looking at various lists of analogies of the A:B::C:D motif, I have distilled them into four groups: Relational, Hierarchical, Linguistical, and Mathematical. Are there analogies that don’t fit this scheme?


Object / characteristic
Order, sequence
Agent / object, action
Function, purpose
Cause / effect
Source / product


Classification, category, type, membership
Whole / part
General / specific


Meaning, definition
Synonym, antonym
Contrast, degree, intensity
Word parts


Patterns, geometries
Size, magnitude
Direction, vectors
Spacial, temporal
Ratio, proportion


View at

Currently Reading:

George Lakoff, Mark Johnson / Metaphors We Live By

To Read:

Douglas Hofstadter, Emmanuel Sander / Surfaces and Essences: analogy as the fuel and fire of thinking, Basic Books (2013)

Noah Roderick / The Being of Analogy, Open Humanities Press (2016)

[*9.140, *9.141, *9.178]


Relative Time

sq_relative_time For what more terrifying revelation can there be than that it is the present moment? That we survive the shock at all is only possible because the past shelters us on one side and the future on another.

— From Orlando, by Virgina Woolf

As we can see on the previous four-folds of space and time, all have a degree of conditioning to the location and orientation of an observer. In other words, there are no absolute frameworks of space or time. That does not mean that they are not useful conventional and conceptual tools.

What would a four-fold of Relative Time be like? Because time seems to be linear instead of two dimensional, relative time would be very different than relative directions. What if we contrast our understanding of what happened in time with what actually occurred? What if we compare our thoughts of an imagined future with what becomes realized?

One could contrast an individual’s notions of past and future with a group or society’s notions of past and future. Or one could contrast an individual’s or society’s recalled past and imagined future with the actual past and the realized future. Some might argue that there is no actual past, but only the past we think or recall that it is. Similarly, those or others might argue that there is no realized future, because once the future becomes the present it has already slipped into the past that we can now only recall.

As the future becomes realized, the imagined future is discarded or blended into it to become our recalled past. As we understand more about the real past, our recalled past may be discarded or blended into it to become our new recalled past. Or one can refuse that knowledge and believe whatever suits them.

[*8.99, *9.60]


Knowledge and Its Limits

Knowledge and action are the central relations between mind and world. In action, world is adapted to mind. In knowledge, mind is adapted to world. When world is maladapted to mind, there is a residue of desire. When mind is maladapted to world, there is a residue of belief. Desire aspires to action; belief aspires to knowledge. The point of desire is action; the point of belief is knowledge.

— From Knowledge and Its Limits by Timothy Williamson


Or with some substitutions:

Theory and practice are the central relations between the mental and the physical. In practice, the physical is shaped to the mental. In theory, the mental is shaped to the physical. When the physical is misshaped to the mental, there is a residue of intention. When the mental is misshaped to the physical, there is a residue of attention. Intention aspires to practice; attention aspires to theory. The point of intention is practice; the point of attention is theory.


Also, note the similarity to The Scientific Method.

Further Reading:

Timothy Williamson / Knowledge and Its Limits

[*6.24, *6.32, *8.22]


E. F. Schumacher’s Four Fields of Knowledge

This fourfold is created from the product of two duals: Self & World, and Inner Experience & Outer Appearance.

  • The Inner Experience of Self is Experience.
  • The Outer Appearance of Self is Behavior.
  • The Inner Experience of World is Communication.
  • The Outer Appearance of World is Science.

The first fourfold is very similar to Hjelmslev’s Net, where Content is Inner Experience, Expression is Outer Appearance, Substance is unitary “Self”, and Form is multiplicity “World”.

It is also almost identical to Ken Wilbur’s AQAL as presented here.


E. F. Schumacher / A Guide for the Perplexed

[*7.88, *7.174, *7.176]



Epistemic Virtues of Objectivity

I recently finished reading Lorraine Daston and Peter Galison’s “Objectivity”. In this very interesting book, the authors argue that the notion of scientific objectivity has evolved over time. They have divided the course of this evolution into three main phases: truth-to-nature, mechanical objectivity, and trained judgement. During each phase, the main view of objectivity is dominant, but previous phases are still important to the overall idea of what objectivity means in the scientific community.

The epistemological virtues of objectivity can be divided into four major aspects: persona, ontology, image, and practice. For each phase of objectivity, each aspect has different qualities. For instance, the scientific persona becomes a sage during the truth-to-nature phase, a worker during the mechanical objectivity phase, and an expert during the trained judgement phase. Similarly, the ontology aspect passed through the qualities of universals-particulars-families, the image aspect passed through reasoned-mechanical-interpreted, and practice  passed through the stages selection and synthesis-automated transfer-pattern recognition.

The evolutionary phases of objectivity, as well as the qualities of the epistemological virtues seen as the four aspects, is beautifully shown by many examples from a collection of scientific atlases. Anyone interested in the history of science as well as the notion of scientific objectivity should enjoy this book.

I thought it was also remarkable that these four aspects of objectivity were very similar to the four aspects of the Archic Matrix of Watson and Dilworth.

Further Reading:

Lorraine Daston and Peter Galison / Objectivity