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:

https://en.wikipedia.org/wiki/Classical_compass_winds

https://en.wikipedia.org/wiki/The_Wind%27s_Twelve_Quarters

https://en.wikipedia.org/wiki/A_Shropshire_Lad

https://en.wikisource.org/wiki/A_Shropshire_Lad/XXXII

https://en.wikipedia.org/wiki/Anemoi

https://www.greekmythology.com/Other_Gods/Anemoi/anemoi.html

https://www.theoi.com/Titan/Anemoi.html

[*12.9]

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The Art of the Syllogism

The syllogism is a logical system that was invented by Aristotle which deduces valid inferences from given premises. It is categorical in nature because each of two premises and the conclusion has an internal relationship of belonging or inclusion. Specifically, there is a major premise of a general nature and a minor premise that is usually specific, or of reduced generality. Both are combined deductively to reach or prove the conclusion.

Both premises and the conclusion deal with three categories two at a time, a subject term (S), a middle term (M), and a predicate term (P), joined by one of four binary inclusion relations. The major premise deals with M and P, the minor premise deals with S and M, and the conclusion with S and P. The four types of relations are denoted by the letters A, E, I, O (also a, e, i, o) and are described below. The premises may have M first or second, but the conclusion always has the S first and the P second.

S = Subject
M = Middle
P = Predicate

A = a = XaY = All X are Y
E = e = XeY = All X are not Y
I = i = XiY = Some X are Y
O = o = XoY = Some X are not Y

Major premise: MxP or PxM, x = a, e, i, or o
Minor premise: SxM or MxS
Conclusion: SxP

The distinction between the four Figures concerns the placement of the middle term M in each of the premises. In order to highlight this order, I’ve written them with ( and ) on the side of the relation where the M is.

Figure 1: MxP, SyM, SzP: (xy)z
Figure 2: PxM, SyM, SzP: x(y)z
Figure 3: MxP, MyS, SzP: (x)yz
Figure 4: PxM, MyS, SzP: x()yz

There are only 24 valid inferences out of all possible combinations, six for each of the four Figures (and some of these may be erroneous sometimes due to the existential fallacy). In addition, they were given mnemonic names in the Middle Ages by adding consonants around the vowels of the relations. And so the valid inferences and their names (or something close to it) are as follows (by my notation and in no special order):

(aa)a, B(arba)ra
(ea)e, C(ela)rent
e(a)e, Ce(sa)re
a(e)e, Ca(me)stres
a()ee, Ca(l)emes
(ai)i, D(ari)i
(a)ii, D(at)isi
(i)ai, D(is)amis
i()ai, Di(m)atis
(ei)o, F(eri)o
e(i)o, Fe(sti)no
(e)io, F(er)ison
e()io, Fre(s)ison
a(o)o, Ba(ro)co
(o)ao, B(oc)ardo
(aa)i, B(arba)ri
a()ai, Ba(m)alip
(ea)o, C(ela)ront
e(a)o, Ce(sa)ro
a(e)o, Ca(me)stros
a()eo, Ca(l)emos
(e)ao, F(el)apton
e()ao, Fe(s)apo
(a)ai, D(ar)apti

For example, (aa)a, or Barbara, is a syllogism of the form: All Y are Z; All X are Y; thus All X are Z.

Further Reading:

https://en.wikipedia.org/wiki/Syllogism

http://changingminds.org/disciplines/argument/syllogisms/categorical_syllogism.htm

http://www.philosophypages.com/lg/e08a.htm

https://plato.stanford.edu/entries/medieval-syllogism/

[*11.8]

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Ouroboros

Lo! ’t is a gala night
Within the lonesome latter years!
An angel throng, bewinged, bedight
In veils, and drowned in tears,
Sit in a theatre, to see
A play of hopes and fears,
While the orchestra breathes fitfully
The music of the spheres.

— From The Conqueror Worm, by Edgar Allen Poe

The worm, turns.

Further Reading:

https://en.wikipedia.org/wiki/Ouroboros

https://www.poetryfoundation.org/poems/48633/the-conqueror-worm

https://en.wikipedia.org/wiki/The_Conqueror_Worm

https://en.wikipedia.org/wiki/Even_a_worm_will_turn

https://en.wikipedia.org/wiki/The_Worm_Ouroboros

[*12.64]

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Agent, Actor, Critic, and Spectator

To understand all (causally) is to forgive all (normatively). To understand all (normatively) is to forgive nothing, for it is to talk about norms, not people; about mathematics, in which there is no error and no responsibility, and not about mathematicians, who do make mistakes.

— Lewis White Beck

Here is a set of distinctions by philosopher Lewis White Beck that may have some relevance to thinking about human determination and action. Beck was most renowned as a scholar of Kant.

  • Agent: a person X who thinks they are responsible and free in choices and actions (essentially a “free” agent), with motives and reasons
  • Actor: a person X who thinks they are an agent but is judged by a Spectator Y to not be free and instead determined by external causes
  • Spectator (diagrammed as Viewer): a person Y who observes any X and explains their actions exclusively by causal terms, and so judges them to be an Actor
  • Critic: a person Z who is in a position to agree with X that X is indeed an Agent or a Spectator Y that X is instead an Actor

A great deal of language revolves around explaining our behavior and that of others, both for the benefit or detriment to ourselves and others. All of us would usually rather be free and responsible agents than causally determined actors, but certainly we are not entirely free to act no matter how little we are not. Philosophical discussion of human action continues to be commonly cast into terms such as agency, action, intention, and even authenticity.

Beck later returned to these ideas for his Ernst Cassirer lectures, and a book of them was published in 1975. By the title and a short description, it appears that Beck reduced the fourfold to a mere dual, in order to simplify as well as elaborate his ideas (but I cannot say for sure as I have not read it). Still, I like the original fourfold scheme that in my mind bears likenesses to others presented here (for example, Modal Verbs.)

Further Reading:

Lewis White Beck / Agent, Actor, Spectator, and Critic, The Monist , April, 1965, Vol. 49, No. 2, pp. 167-182
http://www.jstor.com/stable/27901588

Lewis White Beck / The Actor and the Spectator: foundations of the theory of human action (1975)

https://en.wikipedia.org/wiki/Lewis_White_Beck

https://en.wikipedia.org/wiki/Agency_(philosophy)

https://plato.stanford.edu/entries/agency/

https://en.wikipedia.org/wiki/Action_(philosophy)

https://plato.stanford.edu/entries/action/

https://en.wikipedia.org/wiki/Intention

https://plato.stanford.edu/entries/intention/

https://en.wikipedia.org/wiki/Authenticity_(philosophy)

https://plato.stanford.edu/entries/authenticity/

[*4.40, *4.108, *7.38, *9.66]

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A Man, a Plan, a Canal, Panama

You may think I’m just being silly by presenting everyone’s favorite palindrome.

But now notice the rough correspondence of these four things to the Four Causes.

Further Reading:

https://www.americanheritage.com/man-plan-canal-panama

[*12.62]

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The Canonical Formula of Myth

Further Reading:

Claude Lévi-Strauss / The Structural Study of Myth, The Journal of American Folklore, 68, 270, Myth: a symposium, American Folklore Society, http://www.jstor.org/stable/536768

https://www.webpages.uidaho.edu/~sflores/KlagesLevi-Strauss.html

https://www.webpages.uidaho.edu/~sflores/KlagesPoststructuralism.html

Lévi-Strauss’s ‘double twist’ and controlled comparison: transformational relations between neighbouring societies

Jack Morava / On the Canonical Formula of C. Lévi-Strauss, arXiv:math/0306174v2 (2003)

James B. Harrod / A post-structuralist revised Weil–Lévi-Strauss transformation formula for conceptual value-fields, November 2018, Sign Systems Studies 46(2/3):255

Jean-Loïc Le Quellec, Marc Thuillard / A phylogenetic interpretation of the canonical formula of myths by Levi-Strauss, December 2016

Mark S. Mosko / The Canonic Formula of Myth and Nonmyth, American Ethnologist, Feb., 1991, Vol. 18, No. 1 (Feb., 1991), pp. 126-151, http://www.jstor.com/stable/645568

[*9.128, *12.64]

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