The Marriage of Opposites

August 29, 2015 Martin K. Jones 4 Comments

The road up and the road down are the same thing.

— Heraclitus

The Marriage of Opposites, or Chemical Wedding, or Coniunctio Oppositorum, is a term from alchemy that means combining two opposite substances, or essences, or even ideas into a unity greater than the sum of its parts. This term has also meaning in Jungian psychology as Jung showed many parallels between the processes of self-understanding and alchemy. For example, the marriage of opposites is symbolized by the union of the Animus and Anima.

Opposites are everywhere in our everyday lives and language. They are also prevalent in our social institutions such as religion, politics, philosophy, and science. There are long lists of opposites of life and language and institutions: spatial, temporal, relative, linguistic, mathematical, social, normative, philosophical, and mythological.

A + A’ = ?

What does it mean to combine two opposites into one? Does it mean that the two things are no longer extant and only the combination remains, or that the thing is its own opposite (e.g. 1 + -1 = 1)? Does it mean that a new, third thing is now created that incorporates both of the originals but they still exist as well, like Hegel’s thesis, anti-thesis, synthesis (e.g. 1 + -1 = 3)? Or does it mean that the originals annihilate each other, and nothing remains (e.g. 1 + -1 = 0)?

Usually the casual causal combination of opposites leads to an averaging of the two. For example if hot and cold liquids are combined, soon you will just get a tepid mixture. This is entropy, where the difference between the hot and the cold material is soon eliminated by the blending of the parts, and in this case actually fueled by the energy of the hot molecules.

The usual meaning of this Chemical Wedding is rather esoteric or mysterious. I propose that what the term “marriage of opposites” really means is quite different. Each “opposite” is an opposing pair itself, so that the marriage is between two pairs instead of two things. Instead of a unity, I suggest that this is the root of multiplicity. Instead of simplicity, there obtains organized complexity. Two pairs of two things yields four things in many ways: 2 + 2 = 2 * 2 = 2 ^ 2 = 4.

Let A and A’ be a pair of opposites, as well as B and B’. Then we can consider a union between those pairs to be:

(A + A’)(B + B’) = AB + AB’ + A’B + A’B’

Our individual genetic material is really a marriage of opposites in that half of it comes from each of our parents. Like Mendel’s peas, the sexual union generates the possibility of four versions of each feature. Similarly, the combination between two pairs of opposites generates a fourfold of possibilities.

How should one arrange such a union on a diagram? In Aristotle’s Square of Opposition, the true opposites are at opposite corners of a square, the “contradictories” (one is true and one is false). There are also “contraries” (cannot both be true), “subcontraries” (cannot both be false) and “subaltern” (only one implies the other) relations between corners. But the square is built from the logic of quantifiers and properties, different from this fourfold.

They can be arranged as the cycle AB + AB’ + A’B’ + A’B: One can naturally consider AB and A’B’ to be opposites, as well as AB’ and A’B. One can start with the two opposite pairs crossed, and this cycle sequence arises simply between them. Also, one nice feature is that only one of A or B needs to be changed to its opposite as we move around the cycle, even as we return to the beginning of the sequence. This is called a “gray code” in terms of binary numerals.

They can be arranged as the grid AB + AB’+ A’B + A’B’: Here the opposites fall across a diagonal that runs southwest to northeast. This doesn’t have the nice properties of the cycle above, but I have used it for many of my diagrams. Instead of a cyclic symmetry, we have a dynamic symmetry about this diagonal that runs from an imagined origin of separation towards greater mixing and combination. This is the usual binary numerical sequence.

References:

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

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

Notes:

Interestingly, while thinking about the next stage in the 2 + 2, 2 * 2, 2 ^ 2, … series, I found that the superexponential or exponential tower operation is called “tetration”. In fact, Tetration( 2, 2) = 4 as well.

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

Also, consider “Mirage of Opposites”!

[*9.36]

evolution, fourfolds, Science

Evolution and Genetics

July 29, 2015 Martin K. Jones 1 Comment

Here is a fourfold of evolutionary genetic terms to consider.

Ontogenic: related to the development or developmental history of an individual organism
Phylogenic: related to the development or evolution of a particular group of organisms
Genotypic: related to the genetic makeup of an organism or group of organisms with reference to a single trait, set of traits, or an entire complex of traits
Phenotypic: related to the observable constitution of an organism (or the appearance of an organism resulting from the interaction of the genotype and the environment)

References:

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

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

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

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

https://en.wikipedia.org/wiki/Tinbergen%27s_four_questions

Tip of the hat to:

Cesar Hidalgo / Why Information Grows: The Evolution of Order, from Atoms to Economies

[*9.22]

fourfolds, hermeneutics, religion, Science

The Book of Nature

July 26, 2015 Martin K. Jones Leave a comment

The purpose of a system is what it does.

— Stafford Beer

The natural world we find ourselves in is of sufficient wonder, beauty, pain, and terror that many insist that some demiurge had to have made it, and fashioned us as well. For centuries before the dawn of science, the notion of the “Book of Nature” was an influential concept of how knowledge about the world was to be found and understood, borrowed from ideas on how to read and interpret religious writings: exegesis or hermeneutics. Nature was a text, writ by its creator.

Back in Medieval times, there were four ‘senses’ of reading and understanding scripture:

Anagogia: the higher meaning (Invisible Invisibility*)
Allegoria: the deeper meaning (Invisible Visibility)
Historia: the literal meaning (Visible Visibility)
Tropologia: the moral meaning (Visible Invisibility)

Perhaps the meaning of these senses were more or less literal. Therefore on my diagram I have placed the higher above, the deeper below, the historical in the past, and the moral in the future. Morals inform us what we should do or what our purpose is. A heuretic of systems thinking coined by Stafford Beer is “the purpose of a system is what it does.” And remember the immortal words of Yoda: “Try not. Do or do not. There is no try.”

Fortunately or unfortunately, nature is nothing like a text. All texts are written by people, and are structured by human thought and language. Nature requires other methods for understanding its basis and processes. The so-called scientific method evolved by fits and starts to explore the workings of nature, its components, causes, structures and functions. And it continues to evolve because it is not in itself entirely mechanistic: no precise algorithm that we know of can be specified to turn the crank and do ‘science’. Does that mean it’s unscientific? Not at all.

References and Links:

* The terms Invisible Invisibility, etc. are from:

6. The four senses

The Quadralectics of Marten Kuilman

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

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

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

[*8.48, *8.52]

fourfolds, Psychology

On the Psychology of Cognition

June 11, 2015 Martin K. Jones Leave a comment

Searching for “four primary relations” led me to the work of Rev. Robert Jardine (1840-1924, Canada). His most notable (and perhaps only major) work is “The Elements of the Psychology of Cognition”.

His first fourfold consists of the “four primary relations” of consciousness: difference, resemblance, simultaneity, and succession. Each of these are relations of perception that can be informed and conditioned by other members of these four relations, or at least that is what I think he’s saying. Note that difference and resemblance have to do with information (or space), and simultaneity and succession have to do with time.

His second fourfold consists of the double dual of Internal-External and Quantitative-Qualitative, and are the relations between objects in our thought. Thus these are:

Internal Quantitative:
Relations of figure, size, shape, motion, number, and so on, of the constituent parts or elements of objects, classes or systems. These relations may be any of the four primary relations or any combination of them.
Internal Qualitative:
Relations between the qualities of objects of our knowledge, or classes of objects, these qualities being made known to us by the sensations or ideas which they produce in our minds.
External Quantitative:
Relations of any of the four primary kinds or any combinations of them between the figure, size, shape, motion, duration, number, and so on, of objects, classes or systems which are external to one another.
External Qualitative:
Relations between external objects or systems with reference to qualities made known by sense, moral or aesthetical qualities, characters, habits, conditions and any other characteristics of objects of knowledge which may be appropriately called qualitative.

Quantities he relates to Forms, and Qualities to Sensations.

Some of the material seems interesting, but before running to read, consider the beginning of the review (of the 1st edition) from Nature, by Douglas A. Spalding:

MR. JARDINE has seemingly had some personal reason for writing this treatise; for in the preface he asks the critic to bear in mind “that the book has been written with considerable haste, in order to secure its publication within a certain limited time.” It would have been wiser to ignore the critic: for this unsympathetic personage is only too certain to meet this innocent confidence with the unfeeling remark that perhaps the interests of science would not have suffered had the author taken a little more time over his work.

I could well adopt the last phrase as a tagline for my own blog! The review concludes with:

Another general criticism that must be made is, that there is not a sufficient wealth of concrete illustration, and that, though the writer has “endeavoured to express himself in as clear and simple language as possible,” his words are, nevertheless, often dark and difficult enough. What will readers “beginning their philosophical studies” make of such a sentence as this?—“It must be borne in mind that it is in their character as modes of the non-ego that objectified sensations are localised. The localising is, therefore, not so much an act of consciousness as a precept of consciousness and a form of the non-ego.”

Eh?

References and Links:

Robert Jardine / The Logical Doctrine of the Proposition. The Calcutta Review, Vol 62, No 124 (1876), 307-323.

Rev. Robert Jardine / The Elements of the Psychology of Cognition, MacMillan & Co. (2nd edition 1885)

Review of 1st edition in The Calcutta Review, Vol 60, No 120 (1875), 280-322.

Review of 1st edition from Nature 11, 422-423 (01 April 1875) | doi:10.1038/011422a0

Book available online:

https://archive.org/details/cu31924031232600

[*9.10]

fourfolds, Metaphysics

Four Primary Relations

June 9, 2015 Martin K. Jones 1 Comment

I’ve written previously about my fourfold Structure-Function (consisting of Structures, Functions, Actions, and Parts) and its association with four Modal Verbs (Must, Should, May, and Can). This resulted in the combined fourfold of Modal Things.

Here I present the next step: what it is that Structures Must do, what it is that Functions Should do, what it is that Actions May do, and what it is that Parts Can do.

Structures	Must	Maintain	=>	Maintenance
Functions	Should	Perform	=>	Performance
Actions	May	Occur	=>	Occurrence
Parts	Can	Vary	=>	Variance

The first column lists the four aspects of Structure-Function. They are loosely based on Aristotle’s Four Causes. Structures correspond to the formal cause. Functions correspond to the final cause. Actions correspond to the efficient cause. Parts correspond to the material cause.

The second column lists the Modal Verbs, the “modes” of each aspect. They are similar to deontic logic, two being more or less necessary and two being more or less contingent.

The third column lists the Actional Verbs, what it is that each aspect does in its modal way. One could also say these as mottos: “Structures must be maintained”, “Functions should be performed”, “Actions may have occurred”, and “Parts can be varied”.

The fifth column lists the four primary relations that correspond to each of the four aspects.

These four relations could inform a metaphysics, consisting of relations all the way down, all the way up, all the way back, and all the way forward.

Links:

http://plato.stanford.edu/entries/logic-deontic/

[*7.192, *8.40, *8.136]

fourfolds, Physics, Science

The Sackur-Tetrode Equation

May 18, 2015 Martin K. Jones Leave a comment

The Sackur-Tetrode Equation expresses the entropy of a monatomic classical ideal gas. Including quantum aspects of the system gives this formula a more detailed description than it would have otherwise. Above I’ve tried to represent the four uncertainties that constitute the equation in its information theoretic version: positional, momenta, quantum, and identity.

From Wikipedia:

In addition to using the thermodynamic perspective of entropy the tools of information theory can be used to provide an information perspective of entropy. The physical chemist Arieh Ben-Naim rederived the Sackur–Tetrode equation for entropy in terms of information theory, and in doing so he tied in well known concepts from modern physics. He showed the equation to consist of the sum of four entropies (missing information) due to positional uncertainty, momenta uncertainty, the quantum mechanical uncertainty principle and the indistinguishability of the particles.

http://en.wikipedia.org/wiki/Sackur%E2%80%93Tetrode_equation

http://en.wikipedia.org/wiki/Entropy_%28information_theory%29

[*9.4]

fourfolds, Philosophy

Four Philosophies

May 14, 2015 Martin K. Jones 3 Comments

If one could divide all philosophies into four groups, what would those groups be? There doesn’t seem to be a strong consensus on how to do this although several have tried.

My first inclination is to start with the Archic Philosophers, discussed by Robert McKeon and his students Walter Watson and David Dilworth. These would be the Sophists, Plato, Democritus, and Aristotle. Philosophies aren’t usally divided in this way, but pros of doing this is that all four groups emerge from classical Greek thought. One of the main cons is that many would not agree that all philosophies are decendents of these four philosophers, or even combinations of aspects from each.

Another student of McKeon, Robert S. Brumbaugh, thought the process philosophies starting from those of Heraclitus and Anaxagoras (both pre-Socratic) and ranging through Whitehead should be represented instead of the Sophists. Otherwise he choose the same three as McKeon, giving Anaxagorean, Platonic, Democritean, and Aristotelian philosophies. By doing this he can form the double dual of Materialist-Formalist (direction) and Holoscopic-Meroscopic (method).

Anaxagoras: Materialist, Holoscopic
Platonic: Formalist, Holoscopic
Democritean: Materialist, Meroscopic
Aristotelian: Formalist, Meroscopic

Two works older than Brumbaugh’s that divide philosophy into the same four groups are those of Ralph Barton Perry and James Donald Butler. Their division is Naturalism, Idealism, Pragmatism, and Realism. I believe that the Realism in these books means Platonic Realism, instead of the more recent Scientific Realism thought of today. Of course Realism has many shadings as seen below.

It might be advantageous to consider Naturalism as a group instead of Realism, since the very concept of the real has so much disagreement. Naturalism does too, but not the extent that Realism does.

Several web sites divide four philosophies of eduction into Idealism, Realism, Pragmatism, and Existentialism. To me, Existentialism is similar to the Relativism of the Sophists. But what about Phenomenalism? Is that more like Relativism or Idealism?

There is also the monumental work “The Sociology of Philosophies” by Randall Collins but I haven’t examined it yet. I suspect they are not condensed or simplified into four groups.

So for now I’ve settled on Relativism, Idealism, Pragmatism, and Naturalism.

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

Walter Watson / The Architectonics of Meaning: Foundations of the New Pluralism

David Dilworth / Philosophy in World Perspective: A Comparative Hermeneutic of the Major Theories

Robert S. Brumbaugh / Western Philosophic Systems and Their Cyclic Transformations

Ralph Barton Perry /Present Philosophical Tendencies: a critical survey of naturalism, idealism, pragmatism, and realism together with a synopsis of the philosophy of William James

James Donald Butler /Four Philosophies and Their Practice in Education and Religion

Randall Collins / The Sociology of Philosophies: a global theory of intellectual change

[*8.138, *8.151, *8.152]

alchemy, fourfolds

The Fourfold Democritus

May 4, 2015 Martin K. Jones Leave a comment

Old Democritus under a tree,
Sittes on a stone with booke on knee;
About him hang there many features,
Of Cattes Dogges, and such-like creatures,
Of which he makes Anatomy,
The seat of black choler to see.
Over his head appears the skye,
And Saturne Lord of Melancholy.

— From Robert Burton’s Anatomy of Melancholy

Truth lies at the bottom of a well.

— Democritus

References:

Christoph Luthy / The Fourfold Democritus on the Stage of Early Modern Science
Isis, Vol. 91, No. 3 (Sep., 2000), pp. 443-479
The University of Chicago Press on behalf of The History of Science Society
http://www.jstor.org/stable/237904

http://www.gutenberg.org/files/10800/10800-h/10800-h.htm

Who Was Democritus?

[*9.3]

fourfolds

Into the Woods

April 17, 2015 Martin K. Jones Leave a comment

How far can you walk into the woods?

Halfway! Because then you start walking back out!

[*8.140]

fourfolds, religion

The Religion of the Future

April 6, 2015 Martin K. Jones Leave a comment

If religion remade itself for the present and for the future, what should it be like? Robert Mangabeira Unger thinks religion is an important aspect of human existence but doesn’t serve our own needs and those to each other or to the world that we find ourselves in and are so dependent on. In “The Religion of the Future”, he continues the program that he introduced in his previous book “The Self Awakened”.

There are four major existential flaws of human existence: mortality, insatiability, groundlessness, and belittlement. Our mortality is the inevitable end of our struggle within life, although some scientists think it may be overcome someday. Our insatiability does seem to be part of human nature, a yearning for more of life and even life itself, but perhaps it could be quelled with training and resolve. Our groundlessness is due to the incompleteness of our knowledge as to the reasons of our existence and the future that we should pursue.

Unger considers belittlement to be a repairable flaw, unlike the other three. Belittlement may be different because we could learn to not reduce each others dreams and goals, but it may also be part of human nature to raise ourselves up by belittling others. We are social beings, but we are also confrontational and competitive. Even if we can learn, what is to stop the world itself from belittling us by placing physical limits on our actions and resources, or constraints on our abilities and plans?

These four flaws make us craven, clueless, needy, and terrified. Could a revolution of religion make us face up to our flaws in a mature and dignified way? Unger seems to think so and lays out his ideas. Four important principles that this religion must serve are apostasy, higher cooperation, plurality, and deep freedom. Four needful virtues that this religion must promote are self-transformation, connection, purification, and divinization.

The major religions of the past have the themes of overcoming the world, struggling with the world, and humanizing the world. What would the theme of the religion of the future be? Accepting the world? Embracing the world? Loving the world? Many religions avoid or even despise the world because it is only a means to an end, instead of an end in itself. We are indeed part of the world and must learn to accept, embrace, and love it as well as ourselves.

From the book description:

How can we live in such a way that we die only once? How can we organize a society that gives us a better chance to be fully alive? How can we reinvent religion so that it liberates us instead of consoling us?

These questions stand at the center of Roberto Mangabeira Unger’s The Religion of the Future. Both a book about religion and a religious work in its own right, it proposes the content of a religion that can survive faith in a transcendent God and in life after death. According to this religion–the religion of the future–human beings can be more human by becoming more godlike, not just later, in another life or another time, but right now, on Earth and in their own lives.

Unger begins by facing the irreparable flaws in the human condition: our mortality, groundlessness, and insatiability. He goes on to discuss the conflicting approaches to existence that have dominated the last 2,500 years of the history of religion. Turning next to the religious revolution that we now require, he explores the political ideal of this revolution, an idea of deep freedom. And he develops its moral vision, focused on a refusal to squander life.

The Religion of the Future advances Unger’s philosophical program: a philosophy for which history is open, the new can happen, and belittlement need not be our fate.

References:

Roberto Unger / The Religion of the Future

Click to access religion.pdf