Tuesday, March 10, 2020

Draft: The Quest for Totality and Its Limitations

The Pre-Socratic thinkers of ancient Greece (starting about 600 BCE) are generally accounted as marking a major advance in thinking by discarding supernatural explanations and seeking an understanding in purely secular terms.  Using the limited data available to them, they concentrated on cosmology, intended as an effort to provide a comprehensive understanding of the world.  

One way this unity could be understood is in terms of material monism. Thus Thales held that water was the primordial; while Anaximenes assigned that role to air.  Not all Greek thinkers held that through observation and reasoning one could grasp the totality of the world, as some accepted that our visible realm was suspended in a mysterious environing element known as the Apeiron, or the Boundless. 

An important adjunct to this project of understanding is the development of criteria to distinguish truth from falsehood.  

Greek concern with the issue of distinguishing truth from falsehood is documented from early times.  The gates of horn and ivory are a literary image used to distinguish true dreams (corresponding to factual occurrences) from false. The phrase originated in the Greek language, in which the word for "horn" is similar to that for "fulfill" and the word for "ivory" is similar to that for "deceive." On the basis of that play on words, true dreams are spoken of as passing through the gates of horn, false dreams as coming through those of ivory.

The earliest surviving attestation of the image is in the Odyssey, book 19, lines 560–569. There Penelope, who has had a dream that seems to signify that her husband Odysseus was about to return, expresses by a play on words her conviction that the dream is false. 

She says:  “Stranger, dreams verily are baffling and unclear of meaning, and in no wise do they find fulfillment in all things for men. For two are the gates of shadowy dreams, and one is fashioned of horn and one of ivory. Those dreams that pass through the gate of sawn ivory deceive men, bringing words that find no fulfillment. But those that come forth through the gate of polished horn bring true issues to pass, when any mortal sees them. But in my case it was not from thence, methinks, that my strange dream came.”

Homer greatly influenced Greek literature as a whole. Plato refers to the two gates in his dialogue Charmides:   Socrates: "Listen then," I said, "to my dream, to see whether it comes through horn or through ivory.”

Virgil borrowed the image of the two gates in lines 893–898 of Book 6 of his Aeneid, describing that of horn as the passageway for true shadows, and that of ivory as that through which the Manes in the underworld sends false dreams up to the living.

The gates of horn and ivory figure in the the work of many modern writers, such as T. S. Eliot, H. P. Lovecraft, Margaret Drabble, and Seamus Heaney.

One of the most challenging of the Pre-Socratics was Parmenides of Elea. The single known work by this thinker is a poem, On Nature, only fragments of which survive. In it, Parmenides stipulates two views of reality. In "the way of truth" (a part of the poem), he explains how all reality is one, and existence is timeless, uniform, and necessary. In "the way of opinion,” Parmenides characterizes the world of appearances, in which one's sensory faculties lead to conceptions which are false and deceitful.

Assuming that one can correctly identify the way of truth and follow it, an exciting prospect opens, whereby one can essay a comprehensive understanding of the world.  This prospect has, as it were, haunted Western thought ever since.  Yet is such a complete and clear understanding really possible?  The following paper seeks to explore this dilemma.

An important challenge stemmed from the world of emerging Christianity, which acknowledged that in this veil of tears only a partial understanding of reality is vouchsafed to human beings. Thus the expression “through a glass, darkly” has become an enduring metaphor for our relationship to truth.  It stems from one of the epistles of the Apostle Paul, where he alludes to the image, incomplete and possibly faulty, that we obtain from a poor mirror of the type common in his day.  “For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known.”  (1 Corinthians 13:12)

Later Christian thought described this gap in knowledge in terms of the sacred mysteries.  

Although the concept is not honored equally by all Christian traditions, many if not most basic aspects of Christian theology require a supernatural explanation. To name but a few key examples, these include the nature of the Trinity, the virgin birth of Jesus, and the resurrection of Jesus. These are mysteries in the sense that they cannot be explained or apprehended by reason alone.

The word mysterion (μυστήριον) appears 27 times in the New Testament. It denotes not so much the meaning of the modern English term mystery, but rather something that is mystical. In the biblical Greek, the term refers to "that which awaits disclosure or interpretation.”   In the Catholic church the Latin term is mysterium fidei, "mystery of faith", defined in the Catechism of the Catholic Church (1997) to mean a mystery hidden in God, which can never be known unless revealed by God.

While all the main doctrines of Christian churches have long been fully public, the loosely defined area of Christian thought called Christian mysticism often addressed the contemplation of sacred mysteries and may include the development of personal theories about them, undertaken in the knowledge that they can never be fully apprehended by man.

At this point it is appropriate to essay an excursion into the philosophical trend known as skepticism, bearing in mind that it poses the problem of knowledge broadly and not the question of totality as such.  In ancient Greece, philosophers as early as Xenophanes (c. 570 – c. 475 BCE) expressed skeptical views, as did Democritus, and a number of Sophists.  Gorgias, for example, reputedly argued that nothing exists, that even if there were something we could not know it, and that even if we could know it we could not communicate it.  The Heraclitean philosopher Cratylus refused to discuss anything and would merely wriggle his finger, claiming that communication is impossible since meanings are constantly changing. Socrates also had skeptical tendencies, claiming that he knew nothing, or at least nothing worthwhile.

Ancient skepticism faded during the late Roman Empire, particularly after Augustine (354–430 CE) attacked the skeptics in his work Against the Academics (386 CE). 

There was little knowledge of, or interest in, ancient skepticism in Christian Europe during the Middle Ages. Interest revived during the Renaissance and Reformation, particularly after the complete writings of Sextus Empiricus were translated into Latin in 1569. A number of Catholic writers, including Francisco Sánchez (c. 1550–1623), Michel de Montaigne (1533–1592), Pierre Gassendi (1592–1655), and Marin Mersenne (1588–1648) deployed ancient skeptical arguments to defend moderate forms of skepticism and to argue that faith, rather than reason, must be the primary guide to truth. Similar arguments were offered later (perhaps ironically) by the Protestant thinker Pierre Bayle in his influential Historical and Critical Dictionary (1697–1702).

The early modern period saw fundamental changes in the way the solar system is viewed, as seen in the figures of Copernicus and Kepler.  Yet these changes, brilliant as their discovery was, did not fundamentally change the issue of totality in the world.  For that a major advance was the law of gravitation credited to Sir Isaac Newton. This principle, first presented in 1687, states that two bodies exert a gravitational attraction for each other that increases as their masses increase and as the distance between them decreases.  The discovery of the law of gravitation, everywhere the same, helped to secure the sense of a single, pervasive world picture. 

In reality Newton's interests were more complex, almost bewildering from the viewpoint of later centuries. He produced many writings that would now be classified as hermetic or occult studies. These works embraced chronology, alchemy, and Biblical interpretation (especially regarding the Apocalypse).  Arguably, Newton's scientific work may have been of lesser personal importance to him, as he placed emphasis on rediscovering the occult wisdom of the ancients. 
After purchasing and studying Newton's alchemical works, Maynard Keynes, opined in 1942 at the tercentenary of his birth that "Newton was not the first of the age of reason, he was the last of the magicians."  
All the same, Newton’s fame, which was international and specific to his scientific interests, helped to secure the prestige of mathematics as the key to understanding the universe.  

In fact mathematics, as a discipline and style, was central to the work of the three greatest philosophers of the era: Spinoza, Descartes, and Hobbes.

For his part Hobbes became interested in mathematics only late in life and so was not able to make any significant contributions.  Perhaps for this reason his reverence for the discipline was intense.

Stepping away from early modern thought, a different undercurrent emerges, as there may be a theological aspect.  Apophatic theology, also known as negative theology, is a form of religious thinking and practice which attempts to approach (or non-approach) the deity by negation, essaying to speak only in terms of what may not be said about the ineffable perfection that is God. The apophatic tradition is often, though not always, allied with the approach of mysticism, which aims at the transcendent vision of God, the apprehension of the divine reality lying beyond the realm of ordinary perception.

Historically, Christian apophatic theology came to the fore with the fifth-century thinker Dionysus the Areopagite, resurfacing from time to time in later centuries. 

Another analogy, a contemporary one, is with the somewhat diffuse concept of Agnotology, defined as the study of culturally induced ignorance or doubt, including the publication of inaccurate or misleading scientific data. In 1995 Robert N. Proctor, a Stanford University professor specializing in the history of science and technology, and linguist Iain Boal, coined the neologism on the basis of the Neoclassical Greek word ἄγνωσις, agnōsis, "not knowing", and -λογία, science or discipline.  More generally, the term also highlights the complaint that some make to the effect that more knowledge of a subject leaves one more uncertain than before.  As a rule discussions of agnotology assume the undesirability of ignorance, and the need for its unmasking and refutation, while Symbolism, as interpreted herein, maintains that is is inescapable.

We turn now to the modern world.

In the nineteenth century a prominent movement in literature and painting was Symbolism.  Its key principle was that one should concentrate on the nuance rather than direct statement.  This approach by definition precluded the quest for any complete inventory of the world, which at best could only be hinted at.

In addition, there were some significant analogies in the sciences. For example, the mathematician Bernhard Riemann (1826-1866) showed that Euclidian geometry did not (as long thought) offer a comprehensive method for mapping the physical world.  To achieve this goal required the supplement of non-Euclidian geometry. Through his pioneering contributions to differential geometry, Riemann laid the foundations of the mathematics of general relativity. 

On November 8, 1895, German physics professor Wilhelm Röntgen stumbled on X-rays while experimenting with Lenard tubes and Crookes tubes and began studying them. He wrote an initial report "On a new kind of ray: A preliminary communication.”  Röntgen referred to the radiation as “X," indicating that it was an unknown type of radiation. The name stuck, although (over Röntgen's objections) many of his colleagues suggested calling them Röntgen rays. Röntgen was investigating cathode rays from a Crookes tube which he had wrapped in black cardboard so that the visible light from the tube would not interfere, using a fluorescent screen painted with barium platinocyanide. He noticed a faint green glow from the screen, about 1 meter away. Röntgen realized some invisible rays coming from the tube were passing through the cardboard to make the screen glow. He found they could also pass through books and papers on his desk. Röntgen threw himself into investigating these unknown rays systematically.  He discovered their medical use when he made a picture of his wife's hand on a photographic plate formed due to X-rays. The image of his wife's hand was the first photograph of a human body part using X-rays. When she saw the picture, she said "I have seen my death.”

The discovery of X-rays caused a veritable sensation.  This was in some respects unpredictable for reactions to the new discovery included publications linking the new kind of rays to occult and paranormal forces, such as telepathy.In due course the American architect Claude Bragdon exploited x-ray findings in his architectural theories and drawings, reflecting concern with Theosophical thought and an associated engagement with non-Euclidean geometry. Bragdon’s earlier publications, which develop concepts and representational strategies focused on ornament and space, evidence a burdensome Theosophical agenda resulting in compromised clarity.   Later he revised his earlier ideas, abandoning Theosophical notions of “x-ray vision.”

The Theosophy of Helena Petrovna Blavatsky and her associates was an early manifestation of New Age thought, which not infrequently slips into positing the power of forces that are not in fact real.

Another speculative development of the time was interest in the fourth dimension,  an extension of the three dimensions of ordinary experience.  New possibilities opened up by the concept of four-dimensional space (and the challenge posed by trying to visualize it) helped inspire many modern artists in the first half of the twentieth century.  Early Cubists, Surrealists, Futurists, and abstract artists purloined ideas from higher-dimensional mathematics, using them radically to advance their work.

Turning to the more conventionally respectable realm of modern philosophy, there is the contribution of the German thinker Edmund Husserl.  Put baldly, the essence of Husserl's philosophy is the central role he accorded to phenomenology.  He held that in some sense phenomenology could lead to the achievement of philosophical certainty and that this element of certainty could then be used to develop a completely rational worldview. But this dream was shattered, for in the judgment of many, phenomenology failed. And this finding established the fact that the quest for certainty (in the guise that many major philosophers since Descartes had attempted) is a futile quest. Husserl stood at the end of the trend that began with Descartes, namely that we can achieve clear and distinct ideas.  He concluded that, per contra, Descartes's goal was unachievable.

A major advance in twentieth-century mathematics offered a radical challenge to conventional thinking in the sciences.   Here the outstanding figure was Kurt Gödel (1906-1978).  “Kurt Gödel's incompleteness theorems” designates two propositions advanced by this mathematician in 1931.

In a formal system, there are axioms. All axioms are a true, at any rate within the bounds of the environing logic. A theorem then provides other true statements from the axioms, adhering to certain rules. A sequence of such statements is called a proof of a statement, because it shows that the statement is true, given the axioms.

Ideally, it should be possible to construct all true statements in the formal system in that manner. A system that has this property is called complete; one that does not is called incomplete. Another requisite required of a theory is that there should be no contradictions. This means that it is not possible to prove that a statement is true and false at the same time. A system that does not include theories that allow this is called consistent.

Gödel maintained that every non-trivial formal system is either incomplete or inconsistent: 

1.  For a given (non-trivial) formal system, there will be statements that are true in that system, but which cannot be proved to be true inside the system.

2.  If a system can be proved to be complete using its own logic, then there will be a theorem in the system that is contradictory.
Gödel’s findings challenged David Hilbert’s program which sought to find a complete and consistent set of axioms for all of mathematics.  It seems that this endeavor is impossible. 

In addition to the incompleteness theorems, a further scientific analogy from the realm of knowing vs. not knowing stems from recent findings regarding Dark Matter.  Dark Matter is a form of matter now thought to account for approximately 85% of the matter in the universe and about a quarter of its total energy density. Its presence has been inferred from a variety of astrophysical observations, including gravitational effects which cannot be explained by accepted theories of gravity unless more matter is present than can be seen. For this reason, most experts believe that dark matter is abundant in the universe and that it has exercised a powerful influence on its structure and evolution. Dark Matter is called dark because it does not appear to interact with observable electromagnetic radiation, such as light, and so it is undetectable by existing astronomical instruments.

Looking back over the complex windings traced above, it seems that in the cultural realm the Symbolists had made a key discovery.  In the last analysis, the gist of Symbolism is arguably that every conclusion derived from observation or thought is embedded in a larger context of the unknowable. In some cases persistence clarifies the unknown, making it known.  In other cases it is not, and perhaps never will be known.