Category Archives: Philosophy

Direction of Fit

The notion of “Direction of Fit” can describe several associated concepts, from a specific one in “Speech Act Theory” (SAT) to the more general one in the “Philosophy of Mind” (POM). For SAT, the concept depends on whether words accurately describe the world (word-to-world), or if the world is actually altered by words (world-to-word) (or possibly both or neither). For POM, the concept is generalized to be between mind (or thought) and world, and of course, word could serve to mediate between mind (or thought) and world.

I propose that direction of fit could also be enlarged to encompass the fits of world-to-world and word-to-word.

Perhaps the notion of world fitting to world is tautological, that it is always true by necessity. For any fit of world to world is natural, in as much as we understand it, because anything else would be super-natural. This is the realm of science then, when we try to explain how the mechanism of the world behaves in its ordered operation. I imagine that we could also put engineering and technology in this case, since we are trying to create an artifact in the world that meshes with the normal goings on of nature. If it meshes very poorly, it either breaks or nature does instead.

The notion of word fitting to word is interesting as well. It is not given that words I write will fit with the words that you read, or there is a proper fit between speaking and listening. I guess the art of rhetoric can be placed here, as how we can fashion our words best to convince or explain or engage. In the POM sense, perhaps any art could be included as well, from literature to music to visual arts, since they strive to convey thoughts to thoughts. I am reminded of the notion of the perfect language in accurately describing the world or of complete understanding between minds.

Maybe words describing world could also be science, but perhaps its proper realm should be more of history or the states of human affairs. This is more in agreement with the opposite direction of World-to-Word, or world fitting to word.

Maybe I’m just thinking of a certain fourfold of Richard McKeon, and want to make a correspondence of

  • Word-to-World => Thought
  • World-to-Word => Action
  • Word-to-Word => Word
  • World-to-World => Thing

although I’m not sure this works.

Further Reading:

Things, Thoughts, Words, and Actions

[*12.96, *12.98]




The Four Paths of Yoga

According to the Vedanta, the 4 major margas (paths) are Jnana Yoga (the path of wisdom and knowledge), Bhakti Yoga (the path of devotion), Karma Yoga (path of selfless action or service) and Raja Yoga (path of self-discipline):

  • Jnana Yoga: The path of wisdom and knowledge
  • Bhakti Yoga: The path of devotion
  • Karma Yoga: The path of selfless action and service
  • Raja Yoga: The path of self-discipline

Further Reading:



The Three Pillars of Stoicism

The Four Cardinal Virtues of Wisdom, Justice, Temperance, and Courage are often linked to the “Three Pillars” of Stoicism: Logics, Ethics, and Physics. Logics and rational thought enables the virtue of (practical) wisdom to produce intelligent assent or rejection. Ethics and moral strivings condition the virtue of justice (and courage) to inform proper action or non-action. Physics and natural constraints temper the virtue of courage (and temperance) by proportionate or bounded desire or aversion.

    • Logics (Rational Domain): Assent for (practical) Wisdom
    • Physics (Natural Domain): Desire for Courage and Temperance (restraint)
    • Ethics (Moral Domain): Action for Justice

Note the mismatch between Four Cardinal Virtues and the Three Pillars. Some add Metaphysics to get Four Pillars, although what domain does it inform? (Supernatural? Speculative? Philosophical?) Also note my use of the term “Logics”. If the British can use the term “Maths” then I can certainly use “Logics,” because logic can now come in many different formulations.

Further Reading:

The Highest Good: An Introduction To The 4 Stoic Virtues

Disciplines, Fields, and Virtues: The Full Stoic System in One Neat Package


The Spheres of Human Understanding

The Four Cardinal Virtues

Images of Logic, Ethics, Physics:



The Passions of the Stoics

I will show you fear in a handful of dust.

— From “The Waste Land”, by T. S. Eliot

The Stoics divided the passions into four parts, consisting of a two by two matrix of “good” or “bad” emotions versus whether they occur during the present or while thinking about the future.

  • Delight (or Pleasure): present and good
  • Distress: present and bad
  • Desire (or Appetite) : future and good
  • Dread (or Fear): future and bad

To Stoics all these passions were actually harmful, in the sense that they are irrational and instead should be thoughtfully managed. Instead one should have Three Good Feelings and but not Three Not-as-Good Feelings:

  • Joy (chara) instead of Pleasure
  • Wish (or Hope) (boulesis) instead of Appetite
  • Care (eulabeia) instead of Fear

What about Distress and its Stoic version (which might even be Calm or Ease)? And what of emotions for past memories? They might be  Relief (past and “bad”) and  Regret (past and “good”).

Further Reading:

Stoic Ethics




On the Death of a Giant

Renowned physicist Steven Weinberg passed away recently. He was a giant in the world of physics and winner of the Nobel prize, advancing knowledge about the Standard Model and the unification of physical forces. He was also, famously, a materialist and atheist.

In his book “The Sophist”, Plato wrote (metaphorically?) about the battle of the gods and the giants. He related how the gods were friends of Platonic forms (perhaps being close to forms themselves) whereas the giants were materialists. Plato, being partial to forms, painted the giants as militant and unreasonable materialists, and the gods as a friendly and peaceful sort.

The Greek gods were friendly and peaceful? Perhaps the giants of the legend were the easy-going and reasonable sort, since the gods of the Greeks seemed the opposite. They say that history is rewritten by the victors.

Further Reading:

With Steven Weinberg’s death, physics loses a titan

A very nice article:

Steven Weinberg (1933-2021): a personal view


John Buridan’s Octagon of Opposition

Medieval logician John (or Jean) Buridan was a scholar of Aristotle, and wrote many works of commentary and elaboration on Aristotelian philosophy. Several items in logic and philosophy are tied to Buridan (such as Buridan’s Bridge and Buridan’s Ass) but he may now be more widely known for his Octagon which combines Aristotle’s Square of Opposition with a Square of Modality.

Below and to the right is a fourfold diagram of Aristotle’s Square of Opposition. The modern universal and existential (or particular) qualifiers are ∀ (meaning All) and ∃ (meaning Some), respectively. Also in these diagrams, ¬ means logical Not.

  • ∀ S are P
  • ∃ S are P
  • ∀ S are ¬ P
  • ∃ S are ¬ P

Next I show a fourfold of modal operators and their equivalents. The modern modal symbols are (meaning Necessarily) and or ◊ (meaning Possibly).

  • P ≡ ¬ ◊ ¬ P
  • ◊ P ≡ ¬ ¬ P
  • ¬ P ≡ ◊ ¬ P
  • ¬ ◊ P ≡ ¬ P


Further Reading:

The Art of the Syllogism

Click to access Demey_DWMC2015_Buridan_Avicenna_slides.pdf

Click to access Buridan_Octagon.pdf

Click to access hughes-buridan.pdf





The Twelve Virtues of Aristotle

The Twelve Virtues of Aristotle:

  • Brave
  • Temperate
  • Generous
  • Munificent
  • High-minded
  • Ambitious
  • Patient
  • Friendly
  • Truthful
  • Witty
  • Modest
  • Indignant

Further Reading:

Aristotle’s 12 virtues: from courage to magnificence, patience to wit




The Square of Epictetus

Here is a nice two-by-two matrix by engineer David E. Goldberg derived from the stoic philosophy of Epictetus. For each and every concern, it’s the cross product of one’s Activity (control vs. no control) and State of Mind (concerned vs. not concerned). And so we have the four combinations:

  • Concerned with Control: Accomplishment
  • Unconcerned with Control: Forgone Opportunity
  • Concerned but No Control: Needless Worry
  • Unconcerned and No Control: Peace of Mind

Of course the key is to dwell within the positive Accomplishment and Peace of Mind regions, and not to inhabit the negative ones of Needless Worry and Forgone Opportunity.

Further Reading:

More Accomplishment, Less Worry: Follow the Epictetus Square




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 Anderson-and-Krathwohl_Revised-Blooms-Taxonomy.pdf

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