Political Fourfolds

November 8, 2016

sq_politicalToday I present an example of a political fourfold. Frequently they have two factors: first, between the personal and the economic, and second, between liberty and security, or freedom and control. The quadrants that result can have different labels, but the one above is essentially the Nolan Chart, consisting of Authoritarian, Conservatism, Libertarian, and Liberalism.

  • Libertarian (personal freedom, economic freedom)
  • Authoritarian (personal control, economic control)
  • Conservatism (personal control, economic freedom)
  • Liberalism (personal freedom, economic control)

But you can read this anytime! This is an important day in United States politics so I urge everyone that can to please get out and vote!



Images of “Political Quadrants”:


[*7.31, *9.172]


A Game of Fourfolds, Part 4

October 4, 2016


Many of the fourfolds presented here are roughly a combination of two dualities, a double dual if you will. Their diagrams could be considered as a crossed pair of rectangular cards, with each card showing a single pair of opposites. If one creates cards for every unique and important dual, new juxtapositions not thought of previously may be revealed by random and spontaneous association.

Of course many fourfolds cannot be reduced to the simple sum of their parts, or even the sum of their pairs. All four concepts often ramify themselves and each other due to binary, tertiary, and quaternary relations. Then the fourfold is greater than its individual constituents.

For example, the Four Elements are more than the opposite pairs of Air and Earth, Fire and Water. In Hjelmslev’s Net, Substance and Form combines with a superficially similar Content and Expression. However, above is an example of what I am striving for when Space and Time is combined with Matter and Energy.

Below is a list of dualities that might be used to create a useful set of cards. Some duals will come from fourfolds mentioned here but others will be new. Dualities or dichotomies are usually included in lists of opposites or antonyms, although they are usually more philosophical in nature.

Fourfolds that cannot be readily divided into two duals may by presented by square cards, perhaps called “trumps” or “major arcana” (or perhaps even “arcana quadra”). If cards are picked randomly but placed by choice, the rules of such actions must next be determined.

List of Duals (alphabetic):

Above, Below
Absence, Presence
Absolute, Relative
Abstract, Concrete
Active, Passive
Actual, Potential (Actual, Possible)
Addition, Subtraction
All, None
Analytic, Synthetic
Answer, Question
And, Or
A Posteriori, A Priori
Artificial, Natural
Asymmetric, Symmetric
Atom, Void
Beautiful, Horrible
Begin, End (Start, Stop)
Being, Becoming
Big, Little
Birth, Death
Black, White
Body, Mind
Bounded, Infinite
Cause, Effect
Chaos, Order (Discord, Harmony)
Child, Parent
Clean, Dirty
Combine, Separate
Complex, Simple
Content, Expression
Contingent, Necessary
Continuous, Discrete
Create, Destroy
Crooked, Straight
Dark, Light
Dawn, Dusk
Day, Night
Dead, Live
Decrease, Increase
Demand, Supply
Difference, Sameness (Distinction, Similarity)
Disease, Health (Sick, Well)
Division, Multiplication
Down, Up
Dynamic, Static
Electrical, Magnetic
Emotion, Reason (Irrational, Rational)
Empirical, Rational
Empty, Full
Enemy, Friend
Energy, Matter
Ends, Means
Even, Odd
Evil, Good
False, True
Far, Near
Fast, Slow
Female, Male
Fool, Sage
Forget, Remember
Found, Lost (Find, Lose)
Form, Substance
Future, Past
Gather, Scatter
Give, Take
Global, Local
Greater, Lesser
Guest, Host
Happiness, Sadness
Hate, Love
Hero, Villain
Hidden, Revealed (Invisible, Visible)
Higher, Lower
Holoscopic, Meroscopic
Illusion, Reality
Immanent, Transcendent
Inside, Outside (Internal, External)
Left, Right
Listen, Speak
Long, Short
Many, One
Me, You (Them, Us)
Mix, Sort
Moon, Sun
Nature, Culture
Nature, Nurture
Negative, Positive
New, Old
Object, Subject (Objective, Subjective)
Ontic, Phenomenal
Other, Self
Part, Whole
Particle, Wave
Particular, Universal
Peace, War
Permanent, Temporary
Play, Work
Practice, Theory
Quality, Quantity
Reap, Sow
Religion, Science
Read, Write
Right, Wrong
Rough, Smooth
Private, Public (Personal, Social)
Profane, Sacred (Secular, Spiritual)
Pull, Push
Space, Time
Strong, Weak
Vice, Virtue

List of Trumps:

Air, Earth, Fire, Water
Cold, Hot, Dry, Wet
East, West, North, South
Fall, Winter, Spring, Summer



Vocabulary list by Opposites (or Antonyms)





[*9.34, *9.37]


Distinctions with and without Differences

September 24, 2016

sq_distinction2It is often asked, why is there something rather than nothing?

Instead why not ask, why is there a rich diversity of things, rather than a dull sameness? And even though the closer and the further one looks the diversity is almost without limit, one also sees the world divided into natural kinds that partition it into a differentiated but interrelated mixture.

Several ancient philosophers thought that the entire world was an indivisible whole, a solid “being”. Others thought that you can’t even step into the same river twice, thus a fluid “becoming”. The real world seems to be somewhere in-between these two poles, moving continuously back and forth to now generate difference and newness, and then returning to sameness and oldness, and next continuing on to newness again.

Why drives these generative processes? One could say evolution, but evolution merely means “change over time”. And it would need to be an evolution at all levels of the cosmos, from the physical constituents of matter to the psychological constructs of culture. What do these disparate systems have in common?

Perhaps the commonality lies in the relations between small and large ensembles of chunks of space and time. In theories of statistical thermodynamics, the associations between micro states and macro states as well as micro events and macros events may drive entropy.

Here I present a schema that divides the continuum between one and many into four: Sameness, Similarity, Distinction, and Difference.
A member of the “being” camp might say these aren’t really different, whereas one from the “becoming” camp could say there really isn’t any sameness to begin with. Here I’ve chosen neither camp but struggled to bridge the gap between them.





Also see:

Statistical Thermodynamics

One and Many



Statistical Thermodynamics

September 22, 2016

sq_statisticalWhat drives the arrow of time? How does macroscopic irreversibility arise from microscopic reversibility? What makes entropy increase for closed systems, but decrease in certain open systems?

From the viewpoint of statistical thermodynamics, one can model the evolution of any discrete system by its possible macro states and micro states.

Those macro states having more possible micro states will be more likely to occur, and the macro states having less micro states will be less likely.

Similarly, those macro events caused by more possible micro events will be more likely to obtain, and the macro events caused by less micro events will be less likely.

Therefore, the probabilities of how the past effects the future are determined by the arrangements of the parts making up the micro states and macro states, and similarly the chains of causes constituting the relations between the micro events and macro events.

Apparently time is a progression of events unfolding from the more ordered to the less ordered. However, we know that local order can increase while global order decreases, even if we are unclear as to why. Information and organization can grow; nature and biological evolution are proof of it.

So there is an arrow of time, yet one might think that time is more like a river. (Heraclitus said you could not step into the same river twice.) There is a main flow of the current that carries most everything downstream to disorganization and increasing entropy, but there are eddies here and there that actually increase information and organization.

What enables this to happen? Some say thermodynamic gradients. Some say quantum entanglement. Some say gravity. Some say by the expansion of the universe. Some say dark matter or dark energy. Some say sorting processes.

Can we think of time as being “reversed” in these eddies where information and organization increase locally? No, but it’s an interesting (unscientific) thought.

References and Further Reading:












Italo Scardovi / Time and Chance: a statistical hendiadys


Time’s Arrow Traced to Quantum Source, Quanta Magazine

Time’s Arrow Traced to Quantum Source

[*7.136, *8.43]


Laws of Form

September 19, 2016

sq_laws_of_formGeorge Spencer-Brown, author of Laws of Form, recently passed away.

I’ve tried to appreciate this work in the past, but couldn’t really get started. I recently ran across the following four terms associated with the work,

  • Compensation
    -> (())
  • Cancellation
    (()) ->
  • Condensation
    ()() -> ()
  • Confirmation
    () -> ()()

Compensation and Cancellation are both considered Order, and Condensation and Confirmation are both considered Number. Number and Order are distinguished by Distinction, and the pairs of the two distinctions are distinguished by Direction.

I understand Laws of Form starts with “Draw a distinction.” Perhaps I would say “Draw a distinction, then draw a distinction of that distinction.”






For my further reading:




Compensation (+2) (Pairs of parentheses)
Cancellation (-2) (Involutory?)
Condensation (-1) (Idempotence)
Confirmation (+1)



T. S. Eliot: Four Quartets

August 12, 2016

sq_four_quartets5At the still point of the turning world. Neither flesh nor fleshless;
Neither from nor towards; at the still point, there the dance is,
But neither arrest nor movement.

— From Burnt Norton by T. S. Eliot

Time is a child playing dice.








The Four New Elements

August 8, 2016

sq_new_elementsFour new elements have been named! They are Nihonium (Nh 113), Moscovium (Mc 115), Tennessine (Ts 117), and Oganesson (Og 118).



Also see:




Timothy Williamson’s Tetralogue

August 5, 2016

sq_tetralogueA recent book of introductory philosophy is Timothy Williamson’s Tetralogue: I’m Right, You’re Wrong. Instead of using a dialogue with two viewpoints used by some classical philosophers, Williamson structures his book into a tetralogue, or a conversation with four viewpoints.

The viewpoints are portrayed by four individuals as they enjoy a lengthy train ride: Zac (Relativism), Sarah (Naturalism, Empiricism, Skepticism, Fallibilism, Materialism, Scientism), Bob (Culturalism, Traditionalism, Conservatism, Ancestralism), and Roxana (Rationalism, Logicalism).

Who’s right and who’s wrong? I haven’t read it yet but it looks interesting!

Several reviews:



A Twitter account to follow (I didn’t know it would do that):

Also see:



[*8.149, *9.146]


On Things, Thoughts, Words, and Actions

August 2, 2016

sq_ordering_autonomy_modeling_translationH. L. Ulman / Things, Thoughts, Words, and Actions: the problem of language in late Eighteenth-Century British rhetorical theory

Review at:


Consequently, he closes by proposing “four principles for analyzing the relations among systems of things, thoughts, words, and actions.” As defined by Ulman, these principles are translation (the ordering of one set of relations such that it models selected aspects of other sets of relations); modeling (the creation of new relations by systematic translation); ordering (the response of one system of relations to changes in others); and autonomy (the capacity of one system of relations to resist ordering by others).

Also see:


[*5.197, *6.106, *6.140, *7.162, *8.120, *8.121]


The Semiotic Square

July 29, 2016

sq_greimasFrom Wikipedia:

The semiotic square, also known as the Greimas square, is a tool used in structural analysis of the relationships between semiotic signs through the opposition of concepts, such as feminine-masculine or beautiful-ugly, and of extending the relevant ontology.


In an earlier post I combined an unusual representation of the semiotic square with that of the Tetralemma. Instead of using that one, please use this one instead.