Monthly Archives: May 2012

fourfolds, logic

The Square of Opposition

3 Comments

Some readers may think I’ve never met a fourfold I didn’t like. However, there are several that I haven’t presented here because they don’t seem to play well with the others. The Square of Opposition, created by Aristotle, is one such fourfold. The four logical forms of the square are relations between a subject and predicate, S and P, and supposedly exhaust the possibilities of belonging: Some S are P, Some S are not P, All S are P, and No S are P (or All S are not P).

In the diagram I have removed the S and P, and the logical forms become spare and like a Zen Koan or nursery rhyme: Some Are, Some Are Not, All Are, and None Are (or All Are Not). By doing so, they resonate more brightly with the other fourfolds and how they are presented herein. Now, the logical forms can be about existence, or the subject and predicate withdraw and become implicit to the thought.

Note:

Compare and contrast the Square of Opposition to the Tetralemma and the Semiotic Square.

The 3rd World Congress on the Square of Opposition is soon to convene. May the meeting be rewarding!

References:

http://en.wikipedia.org/wiki/Square_of_opposition

http://plato.stanford.edu/entries/square

http://www.iep.utm.edu/sqr-opp/

http://www.square-of-opposition.org/

[*4.84, *5.82, *7.70, *7.90]

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fourfolds, Physics, Science

Attraction and Repulsion

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Gravity is Love.

 — Brian Swimme

The principle of attraction and its opposite repulsion is pervasive throughout the conceptualization of modern physics. Even ancient Empedocles, of the four elements fame, thought that in all nature the force of attraction and combination was Love or Philia, and that the force of repulsion and separation was Strife or Neikos. These forces have now been depersonalized and mathematized, but still inhabit natural laws which must be obeyed. (See the Four Fundamental Forces of Physics.)

At all levels of matter and energy, from the lowest atomic interactions to the highest cosmic forces, the duality of attraction and repulsion are everywhere. In atoms, there is the strong force and the weak force that respectively pull nuclei together or push them apart. In and between atoms and molecules, covalent bonds, magnetic polarities, electric charges, hydrogen bonds, salt bridges, and hydrophobic effects gather and scatter and even make life possible. In the large-scale macro world, electromagnetism and gravity extend their influence. And in the cosmic arena, the mysterious effects of dark matter and dark energy perform without our current understanding.

In the biological world, attraction and repulsion are seen in the action of plants and animals. The plant is attracted to light and moisture, and repulsed by darkness and dryness. The animal is attracted to food and safety, and repulsed by lack and danger. Plants and animals are also attracted to their kin, and repulsed by their non-kin, because there is strength in commonality. However, too much sameness becomes toxic. It is the dynamic between attraction and repulsion that creates much of the living world and its richness.

In the human world, culture and language enable the forces of attraction and repulsion. Known culture and language is attractive; unknown culture and language is repulsive. But the human mind also craves newness. Interactions between the same and the different have been a great source of the creative drive which fuels the human spirit.

Note:

The sums of attractions are combinations. The sums of repulsions are separations.

References:

http://en.wikipedia.org/wiki/Empedocles

http://www.npr.org/blogs/13.7/2010/10/21/130724690/gravity-is-love

[*7.92]

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fourfolds

Wu Wei or Natural Action

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The sage does nothing, and yet everything is done.

— Lao Tzu from Tao te Ching

The principle of least action (or stationary action) seen in the previous entry Noether’s Theorem immediately makes me think of the Taoist concept of wu wei – literally no action or effortless action. It consists of knowing when to act and knowing when not to act (or perhaps even not knowing to act). It also means natural action, or the action of natural physical or biological systems. In Western culture, such action is considered bad and “mechanical” because physical systems are thought to be like clockwork, but in Eastern culture, it is sagelike and enlightened, harmonious. Very often intention, or conscious action, gets in the way and impedes our effort.

Another example that comes to mind is the short story “On the Marionette Theatre” by Heinrich von Kleist. In the story, one of the characters comment that marionettes possess a grace humans do not, a view which contradicts ordinary aesthetics. It is claimed that our consciousness and capacity for reflection cause us to doubt ourselves or become self-conscious, and prevent us from acting with the singlemindedness and purity of an animal or a puppet. For example, a bear in the story is able to successfully fence with the narrator, by deflecting every thrust towards him seemingly without effort. And all feints are ignored, as if the bear is reading the narrator’s mind or knowing the future before it happens.

Also note:

Philip Pullman, author of the fantasy trilogy “His Dark Materials”, was inspired by von Kleist’s story.

The character Forrest Gump, of book and movie fame, could be considered a Taoist. Be like a feather on the wind…

http://en.wikipedia.org/wiki/Wu_wei

http://www.his.com/~merkin/daoGloss.html

http://en.wikipedia.org/wiki/Heinrich_von_Kleist

Edward Slingerland / Effortless Action: Wu-wei As Conceptual Metaphor and Spiritual Ideal in Early China

[*7.91, *8.66]

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fourfolds, Mathematics, Science, Space and Time

Noether’s Theorem

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Nature is thrifty in all its actions.

    — Pierre Louis Maupertuis

From Wikipedia:

Noether’s (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proved by German mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system’s behavior can be determined by the principle of least action.

Noether’s theorem can be stated informally:

If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time.

Note:

Symmetries are transformations or exchanges in space or time that leave systems structurally or functionally equivalent to what they were before. The equivalence may or may not be an identity, but only the same in appearance or behavior.

Conservation laws are equivalences for quantitative properties of systems. A given property of matter or energy is quantitatively the same before and after, or continuously through space or time. The functional measure of this property remains constant.

So consider an analogy between Noether’s Theorem and the concept of Equivalent Exchange: for (symmetrical, differentiable) exchanges, there are properties that are equivalent (conserved)!

http://en.wikipedia.org/wiki/Noether’s_theorem

http://en.wikipedia.org/wiki/Action_%28physics%29

http://en.wikipedia.org/wiki/Lagrangian

http://en.wikipedia.org/wiki/Principle_of_least_action

http://math.ucr.edu/home/baez/noether.html

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