Category Archives: twelvefolds

Kant’s Tables of Judgments and Categories

Even though Immanuel Kant’s tables of Judgments and Categories are each made up of four triples, both are divided into the same four headings: Quantity, Quality, Relation, and Modality. And as to the tripartite structure of their divisions, I can’t say I’m convinced of their coherence and completeness, c.f. Lovejoy’s article below.


  • Quantity: Universal, Particular, Singular
  • Quality: Affirmative, Negative, Infinite
  • Relation: Categorical, Hypothetical, Disjunctive
  • Modality: Problematic, Assertoric, Apodictic


  • Quantity: Unity, Plurality, Totality
  • Quality: Reality, Negation, Limitation
  • Relation: Substance, Cause, Community
  • Modality: Possibility, Existence, Necessity

Further Reading:

Immanuel Kant: Logic

Kant, Immanuel

Arthur O. Lovejoy / Kant’s Classification of the Forms of Judgment, The Philosophical Review, Nov. 1907, Vol. 16, No. 6, pp. 588-603

Click to access 2177294.pdf


Some researchers discussing Kant’s judgments that look interesting:

[*4.136, *7.114]


The Wind’s Twelve Quarters

From far, from eve and morning
And yon twelve-winded sky,
The stuff of life to knit me
Blew hither: here am I.

Now — for a breath I tarry
Nor yet disperse apart —
Take my hand quick and tell me
What have you in your heart.

Speak now, and I will answer;
How shall I help you, say;
Ere to the wind’s twelve quarters
I take my endless way.

— “From Far” (A Shropshire Lad), by A. E. Housman

The Rose of the Twelve Greek Winds:

  • Thrascias
  • Aparctias
  • Boreas
  • Caecias
  • Apeliotes
  • Eurus
  • Euronotos
  • Notos
  • Libonotos
  • Lips
  • Zephyrus
  • Argestes

Further Reading:



The Twelve Houses of the Zodiac

How does one circumscribe the totality of human experience, both for the individual as well as for culture? One of the oldest ways is the twelvefold division of the Houses of the Zodiac, which may have its origins in Babylon. Other similar systems were used in India, China, Europe, etc. In my diagram above I’m using Latin numerals along with the Latin names of the houses.

For Western Astrology, four groups of three houses are divided by the four classical elements and then into triplicities (from Wikipedia):

  • Fire : Identity (I, V, IX)
  • Earth : Material (II, VI, X)
  • Air : Social and intellectual (III, VII, XI)
  • Water : Soul and Emotional (IV, VIII, XII)

And somewhat similarly for India, the divisions of Vedic Astrology are broken into four Bhavas or “needs” (from Wikipedia):

  • Dharma : (Duty) The need to find our path and purpose
  • Artha : (Resources) The need to acquire the necessary resources and abilities to provide for ourselves to fulfill our path and purpose
  • Kama : (Pleasure) The need for pleasure and enjoyment
  • Moksha : (Liberation) The need to find liberation and enlightenment from the world

There are more recent and scientific divisions of human universals, such as those by George Murdock, Robin Fox, and Donald Brown, as mentioned by Jungian analyst Anthony Stevens in his book “Archetype Revisited”. These are also grouped into four categories (from Wikipedia):

  • Language and cognition
  • Technology
  • Society
  • Beliefs

Further Reading:

Anthony Stevens / Ariadne’s Clue: a guide to the symbols of mankind

Note that John Crowley’s “AEypgt Quartet” uses the Latin names of the Houses as “books”, three to a volume.





The Rosetta Stone of Arthur M. Young

In his book “The Geometry of Meaning”, Arthur M. Young developed a system which he called his “Rosetta Stone” because he claimed that it associated mental attributes to some physical measurements, giving a kind of map to mind-body dualism. In the above diagram the expressions and names of these twelve objective values or physical units are shown. Examine the list below to see the twelve subjective values or mental attributes (shown in parentheses) that Young ascribed to them.

I’ve rearranged the sequence of these somewhat because I don’t quite understand the reasons for the organization Young gave them. I’ve also relabeled the units using the more standard derivative notation L’ = dL/dT, L” = d^2 L/ dT^2, etc. His notation is given at the end of each line below in parentheses for comparison (essentially he removes the d’s from the derivatives, writing dL/dT as L/T, which seems confusing to me when then multiplied by L).

Given the measurement Position or Length (L), Moment is Mass (M) times Position giving ML, and Moment of Inertia is Moment (ML) times Position giving ML^2. Velocity (L’), Acceleration (L”), and Control (L”’) have similarly related pairs of values by multiplying each by M and by ML. This gives four sets of similar expressions differing by their common derivative. I should have probably named the 1st set to be 0th, 2nd set to be 1st, 3rd set to be 2nd, and 4th set to be 3rd after the order of the common derivative.

  • Position (Observation): L
  • Moment (Significance): ML
  • Moment of Inertia (Faith): ML^2
  • Velocity (Change): L′ (L/T)
  • Momentum (Transformation): ML′ (ML/T)
  • Action (Impulse): MLL′ (ML^2/T)
  • Acceleration (Spontaneous act): L” (L/T^2)
  • Force (Being): ML” (ML/T^2)
  • Work (Fact): MLL” (ML^2/T^2)
  • Control (Control): L′′′ (L/T^3)
  • Mass Control (Establishment): ML′′′ (ML/T^3)
  • Power (Knowledge): MLL′′′ (ML^2/T^3)

How does Young justify associating, for example, the mental attribute “Faith” with the physical unit “Moment of Inertia”? It seems to have something to do with his original cyclic order of these twelve measurements and the associations he gives them to the Astrological Signs of the Zodiac. This mapping is not shown but can easily be found in the links below.

Further Reading:

Arthur M. Young / The Geometry of Meaning

The only early entry in my blog without a leading figure (and poor tables as well):

[*7.78, *7.79, *8.2, *11.38]


The Seasons and the Zodiac

This isn’t a bad little diagram of the four seasons along with the twelve zodiac names and symbols. However, it might be oriented wrong by convention or going clockwise instead of counter-clockwise.  Interestingly, old horoscope charts that show what was in the sky (the positions of the zodiac stars and the eight or nine planets in regards to the twelve “astrological houses”) at the time of a person’s birth were shown using the outside ring of twelve triangles instead of the more familiar circle that is used today. The inner square might be for notes or some nice drawing.

Further Reading: