Fibonacci, Fractals, and Inorganic Teleology

ImageAmong the most philosophically challenging scientific data of the last half century are those relating to the physical constants  of the universe (listed below) which allow it to be a cosmos instead of utterly disordered chaos. These constants were “finely tuned” to their present values when the universe came into existence out of absolutely nothing roughly 13.7 billion years ago. You cannot derive their values from something more basic; they simply occurred as “givens” from the first second of our universe’s existence. These values did not develop but were present full-blown at singularity. They did not evolve: they simply were.
Cosmologists Barrow and Tipler wondered what would happen if they were slightly different. Tinker ever so slightly with the values of any of the basic physical constants, and life would have been impossible, not just life of our kind, but life of any kind that involves complexity.

Because of their highly ordered nature, random origin of the constants has been widely conceded to be effectively zero probability (cf. physicist Donald Page has calculated the odds as 1 in 10,000,000^124. By comparison, there are 10^18 seconds since the creation of the universe and around 10^80 atoms in the observable universe).

Mathematician Emile Borel affirmed that anything with odds of happening less than one in 10^50 is impossible (Borel is best known for creating the the first effective theory of measuring sets of points beginning the modern theory of functions of a real variable). Random origin of the constants is well beyond this threshold -by orders of magnitude; selection by lottery would only overcome this statistical obstacle if there were an infinite number of unobservable universes from which ours was selected, yet a universe generating “machine” would also have to be exceptionally highly ordered too, and contemporary physicists have recently suggesting that multiple universes would be clones of one another rather than infinitely variable as the infinite unobservable multi-universes lottery selection theory requires.

Many physicists and philosophers have been attracted to similar arguments in the last thirty years (during which the ramifications of the delicately balanced physical constants first came to our attention; cf. the lecture by Dr. Francis Collins (PhD, & MD), first and long-time director of the Human Genome Project, here.  Collins’ PhD is in Quantum Mechanics, though his focus now is on genetics). It was this issue which former leading atheist and world famous philosopher Antony Flew cited as convincing him to abandon atheism for belief in God (many atheists claim it was rather because Flew must have become senile!).

Contemporary thinkers who remain atheists attempt to escape this conundrum in the only way left to them: they postulate a hypothetical infinite number of unobservable universes from which a highly ordered one could have been a random occurrence. Contemporary atheism is thus forced to argue for the actuality of an essentially zero-probability event by postulating something in principle unobservable (non-scientific/metaphysical).

“‘I can’t believe that!’ said Alice. ‘Can’t you?’ the Queen said in a pitying tone. ‘Try again: draw a long breath, and shut your eyes.’ Alice laughed. ‘There’s no use trying,’ she said: ‘one can’t believe impossible things.’ ‘I daresay you haven’t had much practice, said the Queen. ‘When I was your age, I always did it for half-an-hour a day. Why, sometimes I believed as many as six impossible things before breakfast.’” -Lewis Carroll, Through the Looking Glass

The slightest alteration of the following physical constants would result in a universe incapable of supporting life -not just life of our kind, but life of any kind that involves complexity, and in a universe that would be chaos rather than cosmos:

Gravitational Coupling Constant
Strong Nuclear Force Coupling Constant
Weak Nuclear Force Coupling Constant
Electromagnetic Coupling Constant
Ratio of Protons to Electrons
Ratio of Electron to Proton Mass
Expansion Rate of the Universe
Entropy Level of the Universe
Mass of the Universe
Uniformity of the Universe
Stability of Protons
Fine Structure Constants
Velocity of Light
Distance Between Stars
Rate of Luminosity of Stars
8Be, 12C, and 4He Nuclear Energy Levels.

An infinite number of unobservable universes -even were it the case- would not, of course, necessarily “belong” to our atheist friends who need it so badly to account for zero probability of random origin of the universe’s physical constants  at singularity; in fact it would be a perfect case scenerio of the ancient Augustinian cosmological theodicy of pleroma, which posited all possible varieties and ranges of entities might actually exist; we will leave that subject for a  possible future post; let us now move along to consider the central topic of this essay.

B. FRACTAL GEOMETRY:  ON FINDING ORDER IN UNEXPECTED PLACES

In what follows, we will explore one of the most astonishing and brilliant discoveries of the last century. Although initially a mathematical discovery, its implications can be seen to permeate our cosmos from the microsphere to the macrosphere to a degree that is nothing less than mind-boggling, in a manner that was utterly unknown just a few decades ago.

“This is how God created a system that gave us free will. It’s the most brilliant maneuver in the universe, to create something in which everything is free! How could you do that?! …exploring this set I certainly never had the feeling of invention. I had never the feeling that my imagination was rich enough to invent all the extraordinary things. I was discovering them; they were there although no one had ever seen them before. It’s marvelous! A very simple formula describes all of these very complicated things. Who could have dreamed that such an incredibly simple equation could have generated images of literally infinite complexity? We’ve all read stories of maps that revealed the location of some hidden treasure. In this case the map is the treasure!” -Benoit Mandelbrot, in Fractals: the Colors of Infinity (Arthur Clarke Documentary).


Why do certain patterns (Fibonacci/fractal patterns) constantly reappear throughout nature (organic and inorganic!) in phenomena as incredibly diverse as neuron firing patterns, trees and flowers, lightning, networks of veins in body, crystal structures, the inner structure of lungs, hearts, and other organs, hurricanes, spiral galaxies, viruses, most formations of plant life, cellular microtubules, chemical structures (e.g. platonic solids), family trees, snowflakes, even thoughts? (if you are not a mathematician or scientist, you will be able to more fully appreciate what all the things in this essay –indeed most things in our universe- have in common after you watch the video which follows

II. FRACTALS IN HUMAN PHYSIOLOGY (Yale University Biology Dept.)

“Some of the most visually striking examples of fractal forms are found in physiology: The respiratory, circulatory, and nervous systems are remarkable instances of fractal architecture, branches subdividing and subdividing and subdividing again. Nice pictures are provided in Goldberger, Rigney and West. Although no clear genetic, enzymic, or biophysical mechanism yet have been shown to be responsible for this fractal structure, few doubt this. Careful analysis of the lungs reveal fractal scaling, and it has been noted that this fractal structure makes the lungs more fault-tolerant during growth. The heart is filled with fractal networks: the coronary arteries and veins, the fibers binding the valves to the heart wall, the cardiac muscles themselves, and the His-Purkinje system, etc.

“In addition to falut-tolerance during growth, fractal branching makes available much more surface area for absorption and transfer in bronchial tubes, capallaries, intestinal lining, and bile ducts. Kalda has proposed a fractal model of the blood vessel system that achieves a homogeneous oxygen supply throughout the body. Also, the redundancy of fractal structures make them robust against injury. For example, the heart can continue to function even after the His-Purkinje system has suffered considerable damage. From his work on the ability of fractal drums to damp vibrations, Bernard Sapoval deduced another advantage of the fractal character of the circulatory system: “the fractal structure of the human circulatory system damps out the hammer blows that our heart generates.” “The heart is a very violent pump, and if there were any resonance in blood circulation, you would die.” Fractals may save our lives every minute. Here are some casts of animal lungs. Finally, we note the body exhibits dynamical fractals. For example, it is well-known that healthy heartbeats are chaotic rather than regular. A careful plot of heart rates over several time scales reveals self-similar scaling (Goldberger, Rigney and West). http://classes.yale.edu/fractals/Panorama/Biology/Physiology/Physiology.html ; On the fractal nature of the human circulatory system, see here.

III. BLOOD CELL DYNAMICS GOVERNED BY FIBONACCI RATIOS

Blood cell dynamics are also governed by Fibonacci ratios:  http://arxiv.org/abs/physics/0411169 “This paper demonstrates that the pattern of lipid spicules that emerge on the surface of red blood cells in the classic ‘Discocyte to Echinocyte’ shape change is a generative spiral, and presents a qualitative, fluid- driven mechanism for their production, compatible with the work of Douady and Couder. Implications for the dynamics of cell growth, plant cell phyllotaxy, programmed cell death and gravity sensitivity are explained in terms of a new qualitative model of cellular fluid dynamics.”

IV. LEAVES, BRANCHES, FLOWERS, AND BASIC STRUCTURES OF PLANTS

Plant Phylotaxis is the arrangement of plant elements as primordia on the shoot apex, e.g. branches, leaves, petals, stamens, sepals, florets, etc.).] The angle subtended at the apical center by two successive primordia is equal to the golden angle (137.5 degrees) in more than 90% of all plants studied worldwide. Such an arrangement allows incorporate maximum packing efficiency for fruits and seeds, maximal access to sunlight by leaves, etc. See further at http://www.math.smith.edu/phyllo//About/math.html

V. INFORMATION ENCODING IN THE BRAIN

Information encoding in the brain is also a Fibonacci process, as explained by Harald Weiss and Volkmar Weiss, “The golden mean as clock cycle of brain waves” in Chaos, Solitons & Fractals Volume 18, Issue 4, November 2003, Pages 643-652; cf. abstract and full article here; cf. also Weiss, Volkmar, “Memory Span as the Quantum of Action of Thought,” Cahiers de Psychologie Cognitive 14 (1995) 387-408 here.

VI. THE FINE STRUCTURE CONSTANT AND THE STRUCTURE OF SPACE-TIME
The fine structure constant and the structure of space are also according to Fibonacci. See Carlos Castro, “Fractal Strings as the Basis of Cantorian-Fractal Spacetime and the Fine Structure Constant,” Chaos Solitons Fractals 14 (2002) 1341-1351 here.

VII. FIBONACCI AND FRACTAL GEOMETRY: GENERAL OBSERVATIONS
All fractal self-similar structures (whereupon parts resemble the whole object in shape) incorporate in their geometrical design numbers which are functions of the golden mean.

In case the reader is unfamiliar with fractal geometry, the relationship between Fibonacci and fractals is illustrated simply in the photo above which shows phi (which represents the average of the Fibonacci series) in the Mandelbrot set. The Mandelbrot set is used to generate fractals and fractal art. As anyone knows who has viewed this type of art, amazingly complex and at the same time strikingly NATURE-LIKE and LIFE-LIKE PATTERNS (like insects, leaves, flowers, rock formations, faces, etc,) are quite common with the Mandelbrot “algorithm” (google fractal art!). Random generation is not contra “structure” given an algorithm which “guides” the unfolding; hence chance itself may be ‘governed’ in such a way as the gorgeous symphony of life may still be to a degree “orchestrated”

It is critically important to note that the “algorithm” which generates the ‘similarity in infinite diversity’ we see in nature is not a specific number (phi), but a range of Fibonacci ratios, e.g. from 1/1, 2/1, 3/2, 5/3, 8/5, 13/8, 21/13, 32/21 and so on infinitely. Phi, the average of these ratios, is not a ‘magic number,’ but merely the average of all such ratios. In nature it is not so much phi that is important as it is the SPECTRUM OR RANGE OF VALUES which phi may embody as an average. It is the fact of a Fibonacci range rather than a specific uniform value that especially allows infinite diversity within the algorithmic similarity to be maximized. Thanks to God not all flowers or faces look alike! It is the startling diversity of our universe, in spite of its unfolding within the fine-tuned confines of specific physical constants etc. that never fails to take our breath away.

VIII. MAGNETIC FIELD BORDERS AND ELECTROMAGNETISM

“Also Mandelbrot curves have been discovered in cross-sections of magnetic field borders, implying there is a 3-D mandelbrot equivalent that is closely tied to electromagnetism and therefore a deep structural and fundamental aspect of life, and physical space/time…

“…we see the Mandelbrot relationship to the period-doubling ‘chaos’ equation which is used to describe population expansion, plant growth, weather instability and a host of other physical processes. This relationship also has a habit of popping up unexpectedly in other dynamic non-linear equations (fractals made from Newtons method of deriving a cube-root being the most obvious)

“Think about that for a moment – Take any slice of the magnetic field of the earth, sun, a plant, the data on audio or video tape, and there is our old familiar Buddha looking mandelbrot! This suggests an unknown, yet-to-be-clarified fundamental importance of the Mandelbrot Set in many physical processes. Clearly this is something far more significant than a means of generating visually pleasant mathematical abstractions.

“Many things previously called chaos are now known to follow subtle fractal laws of behavior. So many things turned out to be fractal that the word “chaos” itself (in operational science) had to be formally defined as following inherently unpredictable yet generally deterministic rules based on nonlinear iterative equations. Fractals are unpredictable in specific details yet deterministic when viewed as a total pattern – in many ways this reflects what we observe in the small details & total pattern of life in all it’s physical and mental varieties, too….” -http://www.miqel.com/fractals_math_patterns/visual-math-mandelbrot-magic.html

IX. NANOTECH BOMBSHELL: RANDOM MOTION OF FERROFLUID DROPLETS ON SILICON

Physicists, Stéphane Douady and Yves Couder from the Laboratory for Statistical Physics in Paris in 1992 demonstrated tiny magnetized ferrofluid droplets in pool of silicone oil ultimately form spirals described by the golden angle (see the video here; an abstract in Physical Review (Douady, S. and Y. Couder. 2002. “Phyllotaxis as a physical self-organized growth process,” Physical Review Letters 68 (March 30):2098-2101) can be found here).

X. FIBONACCI AND THE HUMAN FORM:  ADDITIONAL OBSERVATIONS
We have already seen the amazing extent to which Fibonacci inform us about our neural structure, thought structure, organ structure, blood dynamics, circulatory system, etc. etc.; the golden ratio also explains human perceptions of beauty to the degree that standard practice for plastic surgeons and dentists is to carefully employ these ratios in reconstruction of the face and teeth, branching patterns and proportions of skeletal structure, and many other applications beyond the scope of this brief essay.


XI. A “DNA” DOUBLE HELIX NEAR THE CENTER OF THE MILKY WAY?!!

In March of 2006, an incredible news story was released about a double helix nebula found near the center of the Milky Way. “We see two intertwining strands wrapped around each other as in a DNA molecule,” said Mark Morris, a UCLA professor of physics and astronomy, and lead author. “Nobody has ever seen anything like that before in the cosmic realm. Most nebulae are either spiral galaxies full of stars or formless amorphous conglomerations of dust and gas — space weather. What we see indicates a high degree of order.” See the original article at the UCLA website here.

The double helix, mysteriously mirrored in the stars and the DNA of living creatures, is another Fibonacci structure:

XII. ANCIENT ISRAEL’S HOLY ARK OF THE COVENANT AND BRAZEN ALTAR

Intriguing also is the presence of this precise ratio in the Tabernacle of Israel. If it was only there once, it would be more reasonable to attribute its presence to chance, and we are reminded of the exhortation to Moses to ensure he adhered exactly to the heavenly pattern (cited below). This “signature literally written all across the face of the cosmos” appears in two critically important structures which have different dimensions, in the most important artifacts known to ancient Judaism: the Holy Ark of the Covenant, and the Brazen Altar where all Israel’s sacrificial offerings were brought.

2.5/1.5 = 1.6666667 (=5/3)
Exodus 25:10:”And they shall construct an ark of acacia wood two and a half cubits long, and one and a half cubits wide, and one and a half cubits high.”
5/3 = 1.6666667
Exodus 27:1: “And you shall make the altar of acacia wood, five cubits long and five cubits wide; the altar shall be square, and its height shall be three cubits”
Exodus 25:40: “And see that you make them after the pattern for them, which was shown to you on the mountain.”

If one already considers Christian theism of reasonable warrant it becomes difficult not to see the very signature of God in almost every direction one can possibly look -from the heavens to the mirror.

XIII. LARGE SCALE STRUCTURE OF THE UNIVERSE, AND NEURAL CONNECTIONS
From Constantine, David, “They Look Alike, but There’s a Little Matter of Size” (New York Times, Aug 15, 2006): “One is only micrometers wide. The other is billions of light-years across. One shows neurons in a mouse brain. The other is a simulated image of the universe. Together they suggest the surprisingly similar patterns found in vastly different natural phenomena. Mark Miller, a doctoral student at Brandeis University, is researching how particular types of neurons in the brain are connected to one another. By staining thin slices of a mouse’s brain, he can identify the connections visually. The image (below left) shows three neuron cells on the left (two red and one yellow) and their connections. An international group of astrophysicists used a computer simulation last year to recreate how the universe grew and evolved. The simulation image (below right) is a snapshot of the present universe that features a large cluster of galaxies (bright yellow) surrounded by thousands of stars, galaxies and dark matter (web).” (Source by Mark Miller, Brandeis University; Virgo Consortium for Cosmological Supercomputer Simulations; http://www.visualcomplexity.com).

How can the large scale structure of the universe and a mouse neuron have the same structure? The degree to which the Fibonacci ratio is present in both inorganic structures and the bodies of living beings suggests there is something more than genetics and selection alone involved in the latter. Despite a stunning difference in scale there a key similarity: neural networks, like the fine structure of the universe, are (and the large scale structure of the universe) are fractal (http://www.fractal.org/Life-Science-Technology/Publications/Fractal-Neural-Networks.htm)

XIV. WHAT DOES IT TAKE TO BUILD A WORLD?

“What does it take to build a world? This is the central question of my research. My overarching goal is the creation from first algorithmic principles of an entire planet, well-defined everywhere and at all scales, with visual complexity, appearance, and beauty similar to Earth, and to bring that model to real-time performance. Needless to say, this undertaking subsumes a large number of interesting and challenging elements. These include developing our capabilities in visual realism, models of natural phenomena, computational efficiency in such models, and algorithmic art. I am confident that there are enough challenges involved to keep me busy for the rest of my days.

A planet, at the scales of ordinary human experience, is defined by its landscapes. Landscapes are in turn defined by the form of the land, the lighting, the current state of the atmosphere, and by the life forms found within it. My research encompasses the first three, terrain, lighting, and atmospherics; peculiarities of taste and predilection lead me to eschew modeling life forms, leaving them to others to perfect. There is no accounting for taste, and “I love landscapes!” …All successful synthetic terrain models for computer graphics are fractal: That is, they feature complexity resulting from the repetition of form over a variety of scales. The complexity resulting from this repetition of form over many scales leads to the odd idea of fractal dimension: a spatial dimension which is intermediate between the familiar integer-valued (i.e., 1, 2, and 3) dimensions we’re used to dealing with.”

-Professor Ken Musgrave, Fall 1994 George Washington U. EECS Newsletter; http://www.wizardnet.com/musgrave/article.html Dr. Musgrave works with Benoit Mandelbrot, the discoverer of the Mandelbrot set.

XV. SEASHELL STRUCTURE, PLANETARY ORBITS, AND SPIDER WEBS?

All informed observers concede the undeniable and astonishing ubiquity of Fibonacci and fractals in nature. Even some basic natural phenomena which at first glance seem to depart from mathematization according to *phi* (an average of the ratios of the Fibonacci series) can be found, upon closer analysis to contain more Fibonacci than is first apparent to the uncritical eye. As we have emphasized, it is the Fibonacci series which is so prevalent in nature rather than *phi* (the average of said series) per se: phi is a mathematical abstraction of the range of things we see, it is but an average, a human methodological contrivance. There is an additional surprising point to consider regarding phenomena like seashells and planetary orbits, which are Fibonacci on the main, but with variations:  the manner in which variation from Fibonacci occurs in e.g. seashells and planetary orbits actually itself algorithmic according to precise Fibonacci exponents (see www.spirasolaris.ca/llight.html)

XVI. SOME SURPRISING CONCLUSIONS

There are some rather revolutionary conclusions from the recent revolution in fractal geometry stemming from Mandelbrot’s great discovery. First, “chance” itself is “governed” algorithmically to an extent entirely unsuspected just a few decades ago. Yet this algorithmic “governance” is such that infinite variety is not precluded, but rather enabled! The centuries-old philosophical presupposition that chance and governance are opposite has been effectively demolished by Mandelbrot’s amazing discovery. It is also interesting that the discovery was initially within the realm of pure mathematics, rather than the empirical (empirical, i.e. depending on sensory observation); as a video presented below emphasizes, some philosophers of science who prefer to methodologically restrict the “scientific” to the directly observable in a manner similar to that of the Logical Positivists of the early 20th century resisted acknowledging the vast extent to which nature embodies this newly discovered fractal geometry (the demarcation criterion between science and non-science is obviously of critical importance for the philosophy of science; significantly this issue has not been resolved and may be irresolvable in principle (cf. the Kuhn-Popper debate and beyond). Such skepticism, however, could not long survive decades of careful measurement.

Arthur C. Clark produced a fabulous series on fractals titled The Colors of Infinity which documents and describes all this and more, with interviews with such luminaries as Benoit Mandelbrot (who discovered fractal geometry), Stephen Hawking, and many other great pioneers of fractal mathematical applications (the videos are found below). We’ll close this brief essay with some fascinating quotations from some of these men taken from part 5:

“This is how God created a system that gave us free will. It’s the most brilliant maneuver in the universe, to create something in which everything is free! How could you do that?!”

“…Albert Einstein refused to accept the idea of a dice-playing deity. He wrote a letter to Max Borne in which he said ‘you believe in a dice-playing God; I believe in complete law and order.’ So he obviously felt that chance and deterministic laws were not compatible and he preferred the deterministic laws. Now what the Mandelbrot set and Chaos and related things have done for us is to show that you can have both at the same time. So it is not whether God plays dice that matters, it’s how God plays dice.” “I [Benoit Mandelbrot] can tell you exploring this set I certainly never had the feeling of invention. I had never the feeling that my imagination was rich enough to invent all the extraordinary things. I was discovering them, they were there although no one had ever seen them before.” It’s marvelous! A very simple formula describes all of these very complicated things…” “Who could have dreamed that such an incredibly simple equation could have generated images of literally infinite complexity? We’ve all read stories of maps that revealed the location of some hidden treasure. In this case the map is the treasure!” -from Fractals: The Colors of Infinity

© 2010 by katachriston.wordpress.com (text)

Posted in Philosophy, Science, Science and Philosophy, Theology | 7 Comments

Origin and Limitation of the Satisfaction Theory of the Atonement:

I. ORIGIN OF THE SATISFACTION THEORY OF THE ATONEMENT (from Church historian Jaroslav Pelikan):

“…the processions and the drama of the Middle Ages kept the motif of Christus Victor alive even when Latin theology was no longer able to deal with it adequately because of its preoccupation with interpreting the death of Christ as an act of satisfaction… More than any other treatise between Augustine and the Reformation on any other doctrine of the Christian faith, Anselm’s essay has shaped the outlook not only of Roman Catholics, but of most Protestants, many of whom have paid him the ultimate compliment of not even recognizing that their version of the wisdom of the cross comes from him, but attributing it to the Bible itself [see Pelikan, Christian Tradition Vol. 3, pp. 106-57; 4:23-25, 156-157, 161-163]. Anselm’s Why God Became Man belongs to a consideration of the theme of the “wisdom of the cross” for another reason as well In it he develops his argument, as he says, ‘as though Christ did not exist [remoto Christo],’ claiming to proceed through reason alone. The underlying presupposition of Anselm’s thought was the consistency of God and the universe, which God did not violate by arbitrary acts, for such acts would undermine the moral order of the universe itself. Rightness consisted in rendering to each a due measure of honor. Although created for participation in such rightness, the human race had refused to give God due honor and had fallen into sin. This God could not overlook or forgive by fiat, without thereby violating ‘rightness’ in the moral order; such was the demand of divine justice, which Anselm could have defined as ‘God taking himself seriously.’ Yet both human wisdom and divine revelation made it clear that God was a God not only of justice, but of mercy, who declared ‘I have no pleasure in the death of the wicked, but that the wicked turn from his way and live’ (Ezek 33:11).” -Jaroslav Pelikan, Jesus Through the Centuries, pp. 106-107.

II. AN UNSATISFACTORY LIMITATION OF SATISFACTION THEORY

The Westminster Confession says the crucifixion of Christ “hath fully satisfied the justice of his Father; and purchased not only reconciliation, but an everlasting inheritance in the kingdom of heaven for all those whom the Father hath given unto Him.”[1]

“Satisfaction” in the Reformed Confessions, as Reformed theologian Charles Hodge explains, represents “a perfect satisfaction, so that justice has no further demands…” the crucifixion of Christ alone as a full and absolutely comprehensive satisfaction “met and answered all the demands of God’s law and justice against the sinner… This is what is called the perfection of Christ’s satisfaction. It perfectly, from its own intrinsic worth, satisfies the demands of justice… It follows from the perfection of Christ’s satisfaction that it supersedes and renders impossible all other satisfactions for sin” (Charles Hodge, Systematic Theology, Vol II., Ch 4, “The Satisfaction of Christ”).

According to this model the cross of Christ alone “satisfies” absolutely every divine requirement for reconciliation. Nothing else, absolutely nothing else, needed. One might well expect St. Paul, on this model, should have written “If Christ has not been raised, since the cross alone is “satisfactory” to expiate your sins, you are delivered from your sins regardless.” But St. Paul affirmed the very opposite:

“If Christ has not been raised… you are still in your sins” (1 Cor 15:17). If Christ had only died, but had not been raised, His death alone would not be “satisfactory” for the expiation of sins, according to St. Paul.

This emphasis upon the absolute soteriological necessity of the resurrection is also found in Paul’s letter to the Romans: “He was delivered over to death for our sins and was raised to life for our justification” (Rom 4:25).

Joel B Green of Asbury Seminary in Kentucky observes, “because of the singular focus on penal satisfaction, Jesus’ resurrection is not really necessary according to this model” (Joel B. Green and Mark D. Baker, Recovering the Scandal of the Cross (Downers Grove: IVP, 2000), p. 148).

But why would the resurrection be such an absolute soteriological necessity, as St. Paul undeniably does present it, for the expiation of sin?

Going back before the medieval origin of the Satisfaction Theory we find the paleo-orthodox / patristic writers had a different, and fuller view of reconciliation with God “in Christ.” It involved actual mystical union, a living fellowship or communion (koinonia), with the living Christ: salvation consisted in His actual glorifying presence. It would on this view be a bizarre contradiction to suggest a dead savior was “satisfactory”; if the savior was merely dead, there would be no one to be in Union with, no glorifying presence, no theosis! (which is what the early fathers conceived salvation to be). On this model it is perfectly understandable to affirm “If Christ has not been raised… you are still in your sins” (1 Cor 15:17).  Without a living Christ there would be no living union with Christ, which is what the early fathers universally understood salvation to be.
We do not worship a dead victim, but a Living Victor, who lives and presently intercedes.

A dead vine can produce no fruit, but only a living one: I am the true vine…” Except our Savior were risen and alive it would be impossible to “Remain in me, as I also remain in you. No branch can bear fruit by itself; it must remain in the vine. Neither can you bear fruit unless you remain in me” (Jn 15:4).

_____________

[1] The Westminister Confession, Ch 8.5. [Reformed/Calvinist; other Reformed Confessions affirming the Satisfaction Theory include Second Helvetic Confession, The Heidelberg Catechism, Formula Consensus Helvetica,  The Satisfaction Theory of the Atonement is also affirmed in The Augsburg Confession and Formula of Concord (Lutheran), and in the Roman Catholic Council of Trent. Since that time many within various trajectories of Protestantism have questioned the Satisfaction Theory

See also the related article: “Propitiation or Expiation: Did Christ Change God’s Attitude?” http://katachriston.wordpress.com/2011/06/22/propitiation-or-expiation-did-christ-change-gods-attitude/

Posted in New Testament, Theology | 1 Comment

Worship and Liturgy in the Later NT and Early Fathers

The following introductory overview of recent scholarship contains selected/thematic excerpts from: I. I. R. P. Martin, “Worship and Liturgy,” in Ralph P. Martin and Peter H. Davids, eds., Dictionary of the Later New Testament and Its Developments: A Compendium of Contemporary Biblical Scholarship (1997), pp. 1224-1238; II. J. L. Wu”Liturgical Elements,” in ibid, pp. 659-665. We plan to expand this post with the addition of further related excerpts from the companion volumes DPL, DJG, and DNTBD, e.g. “Worship,” “Liturgical Elements,” “Hymns,” etc. as time permits.

I.  WORSHIP AND LITURGY
1. Encouragements and Cautions
2. Method and Approaches
3. Paul and the Pauline Legacy
4. Evidence from Syria-Palestine
5. The Rome-Asia Minor Axis
6. Johannine Patterns and their Influence
7. Some Conclusions
1. Encouragements and Cautions.
What could be said of worship as it may be understood from the evidence of the
Pauline literature (cf. “Worship,” DPL) is equally valid in reference to the non-Pauline
literature. That is, based on the traditions of belief and praxis inherited from Judaism,
Christian understanding and praise of God expressed itself in acknowledging him as Creator and Redeemer. God is still hailed as the sovereign Lord whose fiat brought the world into existence (Heb 11:3; Rev 4:11) through the mediation of the cosmic Christ (Heb 1:2; John 1:3) and by whose will the creation is sustained (Rev 4:11; cf. Col 1:15–18). The same God has acted savingly in the coming of Christ to rescue and restore the lost creation. Revelation 5:9–14 expresses this jubilation in lyric form, while the cosmic backdrop of the new age Christ has inaugurated is seen in Ignatius’s “song of the star” (Ign. Eph. 19.1-3; on this text as a Christ-hymn see Lohmeyer, 64; with further comment in Martin 1997, 10–13). In a crisp, creedal formulary, the incarnational-redemptive tag is given in 1 Peter 1:20 in a context of Christ’s sacrifice (1 Pet 1:18–19) and victory (1 Pet 3:21–22). Praise is thus directed to Israel’s God, known as the Father of Jesus Christ (1 Pet
1:3) and the Father of those whose trust is in him (1 Pet 1:17; Heb 2:10–13; 1 Jn 1:3;
2:1, 13; 3:1) and who are part of the new creation that celebrates his grace (Jas 1:18) in
hymns and in worship speech and acts (Rev 1:12–18; 19:10; 22:8–9; for such texts that
forbid worship when angelomorphic beings were regarded as rivals to the one God, see L. T. Stuckenbruch).
Just as scholars, by applying form-critical methods to the Pauline letters, have
identified several passages as liturgical (see DPL, Liturgical Elements), so by means of
these same techniques parts of 1 Peter, Hebrews, James and Revelation have been treated as embodying worship forms and fragments (see Liturgical Elements; Hymns). Indeed, theories that have tried to understand whole NT books as emanating from a liturgical setting and incorporating rudimentary service directives have been proposed. This has tended to bring the entire approach into disrepute, with accusations of “pan-liturgism,” that is, the misplaced confidence of being able to “detect reverberations of liturgy in the New Testament even where no liturgical note was originally struck” (Moule 1961, 7; cf. Dunn, 1990, §36). One notable example will illustrate the danger. Reasoning back from the Passover celebration which may underlie Hippolytus’s order in the Apostolic Tradition (c. A.D. 215, at Rome), M. H. Shepherd (1960) proposed that the parallel structure he
perceived in Revelation contained the framework of a fully developed baptismal liturgy,
made up of interrogations; preparatory fastings, leading to the initiation itself; lessons
from the Law, the Prophets and Gospel, with psalmody and a baptismal Eucharist. Aside from the debated issue of whether all these elements of worship are seen in Hippolytus, it
raises much skepticism to think that the entire Apocalypse is a virtual transcript of a
Paschal initiation rite, composed as a running commentary on what was happening
liturgically. Much the same can be said for F. L. Cross’s equally imaginative
reconstruction of the scenario behind 1 Peter as a baptismal liturgy.
To remain unconvinced by these somewhat outlandish proposals, which have not
withstood critical scrutiny, however, does not cast doubt on the more reasoned bids to
discover snatches of hymnic and confessional forms, baptismal images and reminders,
Eucharistic prayers and catechetical instructions in several places of the NT corpus (see
Liturgical Elements). Alert to the dangers of seeing liturgical data everywhere, we are
not precluded from investigating the literary, stylistic and contextual shape of the
passages under review with a view to placing them in a suitable Sitz im Leben of the
churches’ worshiping life and practice, if that placement throws light on their origin and
gives an extra dimension to their point.
Two other considerations, moreover, pose a warning as we seek to deduce what
worship was like in the congregations reflected in our texts. One is the temptation to
harmonize. In the case of the Pauline materials, the task of constructing a picture of the
worshiping life of his communities was not hampered by an impossible diversity. Churches
on the Pauline foundation, while different in cultural background and outlook and facing
several problems, were at least kept together by their common allegiance to Paul and his
colleagues and belonged together as a corpus within a manageable time frame. The biblical
books under review in this article have no such unifying thread and represent a wide
spectrum of diverse cultures, interests, compositions and challenges, to say nothing of
the multiform nature of the literature in its genre (Acts, epistles, apocalypse) we are
seeking to encompass. Given these inconcinnities, to collate the worship styles and
practices with their meanings across such a wide terrain into an intelligible picture is
almost an impossible venture; and to seek to harmonize the different features and findings
so as to yield a common pattern is to run the risk of a false harmonization which will
only distort the evidence and give a wrong impression. When we attempt a summing up, this caveat will need to be borne in mind and a question-mark will need to be reasserted
against those attempts to find in too detailed a way a basic liturgical unity within the
late apostolic period (see Cullmann, 7–36; Bradshaw 1992, 37).
The other pitfall is that mentioned in Bradshaw’s handbook, The Search for the
Origins of Christian Worship (1992), which by its title confesses to the tentative nature
of any reconstructions of early worship and the danger of reading back from the later
liturgies the evidence that all too easily we profess to find in the earlier (NT)
documents. This method was the outstanding feature of H. Lietzmann’s celebrated monograph, Mass and Lord’s Supper (ET 1953, 1978), which sought to work backward from the service books and later manuals to the more fragmentary and disputed data. As a technique this may be defended, but it exposes the readers to a false impression that Christian worship developed in a linear fashion, and that we can trace the lines of development with unbounded confidence.
2. Method and Approaches.
The merit, however, of Lietzmann’s approach was that it gave due respect to the
origins of worship patterns in the differing geographical areas from which such service
books came, using a technique that W. Bauer also employed in the same period as
Lietzmann’s work appeared (Bauer in 1934; Lietzmann’s Messe und Herrenmahl in 1926). While the Bauer-Lietzmann approach is open to criticism in several of its aspects (see Turner, T. A. Robinson), there is less criticism when a similar appreciation of geographical
spread is seen to underlie B. H. Streeter’s works. There is no denying that early
Christianity expanded across key areas of the ancient world from the Syrian Levant (see
Syria, Syrian Christianity) to centers and hinterlands of the Greco-Roman provinces,
including Rome itself (see Rome, Roman Christianity; Alexandria, Alexandrian Christianity; Centers of Christianity).
Equally it is true that the configurations of Christian life and worship, along
with the more important aspects of belief and praxis, changed according to the places that
spawned the literature emanating from such regions. Granted that in several cases the tie-in between location and literature is problematic, and we have to rest content with
informed guesswork and sometimes speculation, yet it is undeniable that the pluriformity
of expression of both teaching and expected lifestyle represented in the documents of the
later NT and its developments into the so-called apostolic fathers is an attested reality.
It provides a suitable framework for the evolution of worship styles and practices. The
close connectedness of belief and worship, incidentally, is now an obvious datum on the
principle lex orandi, lex credendi (how a person prays is an expression of that person’s
beliefs). The data will amply illustrate this linkage as we proceed to pass the evidence
under review according to hypothetical geographical stemma.
The functionality of this approach will, we hope, be clear, and its serviceability
seen in that it obviates the more simplistic way of treating the NT books seriatim and/or
in canonical sequence. An alterative approach might have been to follow the lead of
Koester and Robinson with their proposed trajectories or lines of development as we pass
each aspect of worship practices under review and observe, for example, how baptism was
understood from its chronological beginnings in the post-Pentecost church(es) to the
second-century congregations of Ignatius, Justin and the Marcionite conventicles. This
method might well have served the readers’ interests, were it not for the possible
misleading impression it would give that early liturgical observances developed in a
system of end-on evolution. The truth rather is that often the local conditions that
emerged in distinct and distinctive regions provided pressure points that shaped the
growth or malformation of worship no less than the rise of “heresy and orthodoxy.” This
was the case until what emerged as “normative Christianity” (to use Hultgren’s
nomenclature) began to be dominant and was seen to be so in light of the embryonic creedal statements embodied in the traditions and the regula fidei from the mid-second or late-second century onward. In each case the items cherished as “normative” took shape within the setting of the cultural climate of the place on the map as well as under the
constraints of local problems and their solutions.
3. The Pauline Legacy.
The contributions to the topic that stemmed from Paul’s correspondence with his
congregations have been noted elsewhere (see DPL, Worship). In summary, these distinctives were related to the need to regulate the use of spiritual gifts in a situation (such as Corinth) which had become chaotic and unbridled. Paul’s response is given in terms of a practical reiteration of the tension between the already and the not-yet elements in Christian salvation. Believers are now in God’s realm where Christ’s lordship is
acknowledged in worship (1 Cor 12:3). Yet the fullness of their redemption is set in the
future, at the Parousia when God’s final kingdom will be established (1 Cor 15:28). The
worship cry, “God is really here” (1 Cor 14:25) needs to be heard in this context, uniting
both the reality of present salvation and its necessary futurity at the end time, which
will usher in the resurrection of the dead (1 Cor 15:42). In the interim of the church’s
life “between the times,” the emphases Paul makes are in terms of an exercise of love and
thankfulness for God’s acts in Christ and the altruistic call to build up the body of
believers (1 Cor 14:3, 12, 17, 26; 1 Cor 12:7).
These same emphases, boldly remarked in his Corinthian correspondence, come over
into Paul’s later writings, whether treated as his final reflections from a Roman near the
end of his days or as the legacy he bequeathed to his followers who published letters to
churches that claimed to be on a Pauline foundation, at Colossae, Ephesus and its environs
(see Pauline Legacy/School). As might well be expected, there are fresh emphases since new situations have emerged. In particular the need to consolidate the church, now dubbed “the pillar and bulwark of the truth” (1 Tim 3:15), is evident in the face of new doctrines, and its witness needs to be safeguarded against false teachers who deny the (future) resurrection. So in baptismal confessions (2 Tim 2:11–13; Tit 3:4–7), sometimes prefaced by the formula of a “trusted word,” and in christological hymns (e.g., 1 Tim 3:16,
introduced by “we confess”) the Pauline gospel is reasserted as deserving of all
acceptance (1 Tim 1:15). This is accompanied by the cardinal teachings of one God and one
mediator (1 Tim 2:5–7), known to be Paul’s strong conviction. Jewish-Christian prayer
language is scattered through these letters (e.g., 1 Tim 1:17), partly to demonstrate the
church’s close ties with its roots and partly to restate the (Jewish) belief in the
goodness of God’s creation, which is hallowed by prayer based on Psalm 24:1 (1 Tim 4:4–5).
The baptismal teachings in Colossians-Ephesians have given rise to debate, chiefly
on the issue whether they mark a divergence from Paul’s careful distinction as we saw
between what is true now (we are being saved) and the future hope (we shall be saved—in
hope of the Parousia, Rom 5:9–10; 6:1–14). Colossians emphasizes the present possession of salvation (Col 1:12–14) and reconciliation (Col 1:21–22), with the hymn of Colossians
1:15–20 inserted to celebrate the completeness of the universe’s restoration to harmony
with the Creator’s will and the pacification of the evil powers (Col 2:15). Believers have
entered into the benefit of Christ’s cosmic triumph at baptism (Col 2:12–13) with no
explicit eschatological proviso of what still awaits completion at the Parousia. But the
eschatological hope, while it is muted, sounds in Colossians 3:3, so it may be fairly
claimed that Colossians reflects the true Pauline tradition at this point.
Less confidence is engendered, however, in the case of Ephesians. Here the implied
baptismal setting of Ephesians 1:13–14, where “the seal of the Spirit” became a shorthand
expression for a person’s baptism (Lampe), though it does look on to the future possession
of salvation, seems rather to situate the church’s hope in the present (Eph 2:1–10; 5:14)
and to reflect a fading of an imminent Parousia. The church is already raised to the
heavenly places (Eph 2:6) where the regnant Christ has begun his rule (Eph 1:22–23, a
creedal fragment, it is believed). This noble prose poem celebrates Christ’s lordship in
exalted, hieratic terms drawn from the worship idioms of the Asian churches. Such an
eclipse of the apocalyptic denouement, associated with Christ’s return from heaven, may
well be explained by the unique occasion of Ephesians, if its purpose is more doxological
than edificatory or polemical. The nuances of liturgical language have given rise to the
idea of the church as already triumphant and transcendent in its heavenly glory now and
indeed as taking its place within the creedal confession (Eph 4:4–5), as though the church
professes belief in itself—a forerunner of the sentence in the Apostles’ Creed (“I believe
in . . . one, holy, catholic, apostolic church”)—and has its place in salvation history
securely grounded on a (true) apostolic base (Eph 2:20; 3:5).
4. Evidence from Syria-Palestine.
4.1. Jerusalem. It is not easy to separate out from the data and descriptions in
the book of Acts what is objective historical reporting of church life and practice in the
holy city (see Jerusalem; Jewish Christianity) and the holy land, with extensions to the
Syrian province from Damascus to Antioch (Acts 8:1; 9:19; 11:19–29; 13:1–3), and Luke’s
conscious bid to idealize the scenes in the interests of his own theological viewpoints.
Perhaps the truth lies in a mediating position. Assuming that the writing of Luke is meant
to have an edificatory purpose (so both Haenchen, 103–110; and Marshall, 33), it would be
natural to suppose that the author recalls the early days of the church not in a nostalgic
vein but in order to point up certain lessons for the church of his own day. He tells the
story, based on reliable eyewitness testimony, he believed (Lk 1:1–4; Acts 1:1), of how it
was in the beginning when the Spirit first came on God’s new creation. He raises the cry
ad fontes: back to the fountainhead of the church’s early moments, yet he does so with a
view to recapturing the past as he retells it so as to make it speak to his present.
Luke’s successive pictures of the church at worship are arranged to drive home a single
point—that worship in his church needs to recover the emphases and features that marked
the first generation, with the Holy Spirit’s power in evidence (Acts 4:31; 13:1–3), giving
rise to great freedom and joy (Acts 2:46, 47) and fidelity to apostolic norms (Acts 2:42).
Initiation into the community life is by baptism—based on ritual baths in
distinctive Judaisms, both mainline and sectarian (Qumran, Therapeutae)—in the name of
Jesus (Acts 2:38). This was a practice that spread with the expansion of the message to
embrace disciples in Samaria (Acts 8:12), in Caesarea (Acts 10:47–48), in Damascus (Acts
9:18 and par.) as well as more remote, unspecified regions as the Gaza strip (Acts 8:36:
v. 37 mg. in the Western reading offers a fuller account of the baptismal interrogation
and response). Initiation “in the name” of Jesus (Christ) was evidently meant to confess
his messianic headship of the new community and the place individuals had in this
messianic group as a mark of the new age he brought. Little further theologizing of
baptism is found, though Acts 19:1–7 poses the problems associated with groups that had
known only John’s baptism. If Acts 10 (baptism and receiving the Spirit in the home of
Cornelius) is meant to imply a Gentile Pentecost (cf. Lampe, chap. 5, Dunn 1970, 80–82;
1975, 154–56), then the baptism of John’s disciples accompanied by the imposition of hands and gifts of tongues and prophecy may well indicate to Luke’s readers how “disciples” become full-blown believers in Jesus as Lord.
On face value the record in Acts gives cameo pictures of the worshiping/communal
life in Jerusalem (notably at Acts 2:41–47; 4:32–35) as ideal scenes, meant to challenge
and rebuke later loss of “apostolic simplicity.” Features that marked out the earliest
community fresh from its Pentecostal experience and radiating the Spirit’s joy (Acts 2:26
based on Ps 16:8–11; cf. Acts 2:46) include above all the theme of exultant praise,
whether the locale is the temple (Acts 3:1–10) or private residences (Acts 1:3; 2:46;
9:11; 9:36–43; 10:1–8, 24; 12:12). Prayers were offered for guidance (Acts 1:23–25) and
for courage in the face of threats and dangers (Acts 4:23–31), though the reference to
“the prayers” (Acts 2:42) suggests a continued adherence to the Jewish temple liturgy
(Dugmore).
The “apostles’ teaching” has been customarily regarded as a sign of early
catechetical instruction, while “fellowship” indicates either a generalized reference to
common life or, more specifically, to the material contributions expected, but not
demanded, of each member (Acts 4:32; 5:1–11, Jeremias once believed 2:42 referred to the
offering as koinonia, but changed his mind; see Cullmann, 120). The “breaking of bread” is
a Jewish expression for a meal occasion, presumably a communal social event in which food was shared and eaten as a sign of mutual love (hence the name agapeœ, see Jude 12 where intruding teachers have “defiled” such convivial gatherings; and 2 Pet 2:13 if agapais, is read in place of apatais, see Bauckham, 1983; Ign. Smyrn. 8:2, Acts of Paul and Thecla 5,25 shows how the practice persisted into later decades). If Didache 9–10 gives the text of prayers at the love-meal (see 4.2 below), how such meal occasions were understood may be revealed and the way the agape functioned as a prelude to the later solemn Eucharist of the Lord’s sacrifice (Didache 14:1) is evident, perhaps explaining the link in 1
Corinthians 11:17–22 as a preparatory rite of sharing, paving the way for the solemn
Pauline meal in 1 Corinthians 11:23–26.
Special mention should be made of the invocatory prayer, maranatha (found
untranslated in its Aramaic form in 1 Cor 16:22; Did. 10.6). It may be claimed that here
we have the oldest surviving prayer specimen, with one possible exception (an inscription
on an ossuary found in Jerusalem with the wording, “Jesus (let the one who rests here)
arise,” thereby invoking Jesus as Lord of resurrection (So B. Gustafs-son, NTS 3, 1956–57,
65–9. But this interpretation of the graffito is contested, see J. P. Kane, PEQ 1971, 103–
08). Maranatha is a composite word, almost certainly to be divided as maœranaœ} t≈aœ}
(Fitzmyer) and meaning, “Our Lord, come,” expressing a prayer call for the Lord (i.e.,
Jesus) to be present either at the Eucharist (Cullmann) or the eschaton. The evidence at
this point is finely balanced, Didache 10.6 is part of a meal liturgy while Revelation
22:20 (“even so, come, Lord Jesus”) looks to be a variant of maranatha and is
eschatological. The setting is perhaps not exclusively one or the other; what counts is
the existence of a cultus, however rudimentary, where the risen Christ is invoked in
prayer as a forerunner of later, more developed invocations and hymns.
If we are safe in including as representative of early Jewish Christianity the
letters of James and Jude, the picture may be enlarged. Jude’s epistle is notable for its
fulsome liturgical ending (Jude 24, 25). This feature provides a window into how Christian
praying matched human need in one of the earliest NT letters emanating from Palestinian
Christianity (Bauckham). The idioms in these two prayer verses correspond exactly to the
felt need of the community, exposed as it was to dangers from antinomian intruders (Jude
4) and the threat of apostasy from a common faith (Jude 3, 22; Martin 1994, 80–81). Links with Davidic heritage represented by the holy family (Jude 1; see Relatives of Jesus) and the catechetical apostolic traditions (Jude 17) show affinity with the situation mirrored in the Didache. The teaching office of prophets and leaders is the bulwark against some influences boasting of ecstatic experiences and a trust in immediate spiritual inspiration (Jude 8; Martin 1994, 83–4).
James’s letter may well embody early Judaic traditions (Davids) that go back to
Palestinian communities. Such traditions and teachings may conceivably have been carried to Antioch in Syria, where an editor fashioned them into our existing letter with its
excellent Greek and literary flourishes. Liturgical practices may reflect this dual
setting and include a heavy emphasis on prayer in faith (Jas 1:6), especially for an
individual’s healing by elders at prayer (Jas 5:13–16), once confession and forgiveness
are realized and oil applied (on the possible significance of the use of oil here, see
Martin 1993, 124–26). The church has an honored teaching office (Jas 3:1–12) with possible suggestions of ecstatic speech as causing problems (Martin 1988, 103, 123–24). The “excellent name” (Jas 2:7) is one invoked in baptism; and it is proposed that James 2:2, 3 conceals the presence of a church/synagogue “doorkeeper,” known in the later church as ostiarius (Cabaniss 1954, 29).
4.2. Antioch-Syria. The material associated with the northern part of Syro-
Palestine (see Antioch; Syria, Syrian Christianity) is more plentiful—if we are permitted
to base our conjecture of appropriate documents from this region on some recent findings,
then the NT books will include (the redacted version of) James and Matthew’s Gospel (see
Matthean Community), to which we may add Didache and Ignatius’s letters. In listing these Christian writings it is interesting that the first three are joined by at least one
shared feature: they depend on and draw from the oracles/teachings of the Lord that modern research has identified as “source strand” in the Synoptic Gospels, namely Q. Antioch has been identified (since Streeter’s time) as the most likely place where this collection of the Lord’s sayings was assembled and used. The three main documents do not belong to the same literary category. Matthew shares the genre “gospel,” or more precisely biblos (Mt 1:1). The Didache is a church order-cum- “manual of discipline” incorporating earlier and common traditions known as the “Two Ways” (Did. 1–6; Barn. 18–20). James is usually classified as paraenetic miscellany (Dibelius, 3), but it has been editorially completed to conform to the rhetorical genre of “epistle” with both a superscription(Jas 1:1) and letter-close (Jas 5:12–20). Yet all three documents do possess common elements (cf. Shepherd 1956) and each, along with the logia source (Q; see Hartin), may be justifiably located in congregations in the same geographical region, namely around Antioch on the Orontes.
For our purposes we may note the following items in the worship life of these
communities. (1) Much is made of the role of the teacher, who is to be honored (Mt 13:52;
Did. 4:1–4; 13:2; 15:2; Jas 3), with due caution that no one should aspire to the office
too hastily (Mt 23:1–12; Jas 3:1). (2) Baptism is administered in the triune name as a
distinct development from initiation in the name of the (Lord) Jesus found in Acts (see Mt
28:18–20; Did. 7:1–3; Jas 2:7 may allude to baptism in referring to the “worthy name”
called over messianic believers). (3) Prayers couched in language and idioms directly
indebted to Jewish synagogue worship (Mt 6:7–13 which incorporates the prayer “Our
Father”; see Charlesworth), given in its Matthean form in Didache 8:2–3 with instructions
to pray thus thrice daily. In James 1:13–16 the use of prayer is treated as a pastoral
issue. All documents emphasize the role of corporate praying based on God’s role as
heavenly parent (Mt 5:16; 6:9; 16:17; Did. 9:1; 10:1; Jas 1:17, 27; 5:13–18), with special
stress laid on the need for mutual forgiveness and confession leading to reconciliation
and absolution (Mt 5:21–26; 6:12, 14–15; 18:21–22, 35; Did. 1:4; 2:7; 4:3–4; 14:1–3; Jas
2:8; 4:11; 5:16, 19–20). Fasting is a token of true worship, along with almsgiving (Mt
6:1–4, 16–18; Did. 1:5–6; 4:5–8; 7:4; 8:1–3; 13:3–7; Jas 1:27; 2:15, 16 on giving to the
needy). (4) Confession of belief in the one God (a hallmark of Jewish Christianity derived
from the shema of Judaism, Deut 6:4) runs through these documents (Mt 19:17; 22:37; 23:9; Did. 6:3 against idolatry; Jas 2:19).
(5) Special attention is drawn to the observance of the eucharistic service based
on the Last Supper words in Matthew 26:26–29 (see Lord’s Supper). In the main, these
dominical statements conform to the Markan wording, with the important exceptions that the cup word is enlarged to connect the “blood of the covenant” represented in the cup with the forgiveness of sins (“which is poured out for many for the forgiveness of sins”). It
has been surmised that for theological reasons, since remission of sins was evidently a
live issue in the Matthean community, the evangelist has transferred the promise of
forgiveness from the Markan version of John the Baptist’s role (Mk 1:4; cf. however, Mt
3:4–6) to his version of the Last Supper. He did so in order to relate forgiveness more
intimately with the impending death of the Lord. The sacrificial motifs expressed in
Matthew’s upper-room account links with Didache 14.1-3, which is best taken to refer to
the church’s Sunday Eucharist in contradistinction to the teaching expressed in the
prayers of Didache 9–10, which are more suitably explained in reference to an agape meal.
They contain no allusion to the Lord’s death (unless “broken bread,” klasma, makes this
connection, but it is more likely drawn from the non-eucharistic setting of Jn 6) and are
patterned on the Jewish table prayers (birkath hammazon; see for these examples of grace
after meals in Jasper and Cuming, 9–10) in spite of the occasion being titled as
eucharistia in Didache 9.5. A  convincing datum is in Didache 10.1 (“But after you are
filled [with food]” which suggests that the meals in view in Didache 9–10 are taken to
satisfy natural hunger, not to serve as sacramental reminders.
The issue, however, is still unresolved (see Srawley, 18–25; Bradshaw 1992, 132–
37, for a conspectus of opinion). The safest conclusions are that both canonical Gospel
and the Didache are tentative data for the deep roots of the liturgy in Jewish covenantal
theology, and the patterns of table fellowship and solemn celebration have some intimate
connection with both the synagogue service and the table graces of the Jewish tradition,
into which the Matthean Jesus has injected overtones of his atoning sacrifice. Didache 14
only faintly echoes this in its allusion to sacrifice/offering (thysia, 3 times) which is
drawn from Malachi 1:11, 14.
(6) Set in the dialogical form of the prayers in Didache 10.6 is the versicle/
response:
Let grace come, and let this world pass away
Hosanna to the God of David.
If any one is holy, let that person come!
If any is not, let such repent.
Marana tha [our Lord, come!]
Amen.
The framework suggests a call to self-scrutinizing (already the table is “fenced”
in Didache 9.5, citing Matt 7:6) before the congregational meal is taken, akin to the
rubrics implied by Paul in 1 Corinthians 11:27–34; 16:22, 23 (see Bornkamm 1969; J. A. T.
Robinson). What comes through in this dialogue is the immediacy of judgment/invitation and welcome stemming from the presence of the Lord with his people. He comes to meet them and greet the penitent with offers of his grace now as a prelude to his coming at the last day (Did. 16.7, 8, noting Mt 24:30), an eschatological note sounded in both Matthew 26:29 and frequent in James 5:7–11. Yet it is the awareness of the living Lord in the midst of his own that shows how these Syrian Christians had grasped the genius of early worship as an encounter with the risen Christ who comes to meet those gathered in his name (Mt 18:20; 28:20; a variant is seen in Gos. Thom. 30, cf. 77) as their call to him is “Hosanna,” that is, “Save now!” “Blessed is he who comes in the Lord’s name. Hosanna in the highest!” (Mt 21:9).
Ignatius of Antioch picks up this last-mentioned realization exactly in his
dictum: “Wherever Jesus Christ is, there is the universal church” (Ign. Smyrn. 8.2), as if
to emphasize the unrestrictedness of the risen Lord who comes to join his people as they
sing their hymns through Christ to the Father (Ign. Eph. 4.2) and recognize that he is
dwelling in them (Ign. Eph. 15.3) as members of God’s Son (Ign. Eph. 4.2). The earlier
description (Ign. Eph. 4) offers the attractive picture of a Christian assembly in which
“by your concord and harmonious love Jesus Christ is sung,” with its suggestion that
Christ is not only the mediator but also the object of hymnic praise (so Kroll, 19; Bauer
1924, 204). Granted that Ignatius is using the features of the liturgy—notably unison,
harmony, the right key as in music (eine Tonart, so Dölger, 127)—to drive home the need
for church unanimity and a closing of ranks behind and in submission to the ecclesiastical
leaders (Ign. Eph. 5.3), it still affords some confirmation of the centrality of Christ in
his depictions of worship.
Specimens of Ignatian hymnody are seen in Ephesians 7.2 (Kroll, 20, points to the
semitic coloring, the elevated style, the antithetical sentences and their
interrelatedness to suggest a snatch of creedal-hymnic material; cf. Norden, 256–57). Thus we read:
[there is] One physician,
who is both flesh and spirit,
born and yet not born.
God in man, true life in death,
both from Mary and from God,
first, subject to suffering,
then, impassible,
Jesus Christ our Lord.
(Ign. Eph. 7.2)
This antithetical pattern occurs also in Melito’s homily and is amplified in
Ignatius’s Letter to the Ephesians 19, expounding the “silence” of Ephesians 15.2, in
which three mysteries were accomplished: the virginity of Mary, her giving birth and the
Lord’s death. He was revealed to the “Aeons” (Bultmann, 1.177) and in the appearance of
his natal star, which illumined the heavens with indescribable brightness and attracted
the veneration of the constellations, including the sun and the moon, the new age was
born. “When God appeared in human form to bring the newness of eternal life,” all the
cosmos was affected, with the ancient (demonic) astral powers overthrown and death itself
defeated.
This celebration of Christ’s victory and reign was evidently meant to be sung in
veneration as the planetary powers too join in a chorus (Ign. Eph. 19.2), once we link the
text with Ignatius’s Letter to the Romans 2.2: “You form a chorus of love in singing to
the Father in Christ Jesus.”
A similar confession-like tribute to Christ is offered as part of Ignatius’s anti-
docetic polemic (see Docetism, for example, in Trallians 9.1-2 (cf. Smyrn. 1:1–3:3), which
again may be cast in verse form (by Norden, 266). This christological text rehearses the
movements of Christ’s birth, earthly career, condemnation “under Pontius Pilate” (pointing to the Apostles’ Creed), death on the cross (attested by all the powers, heavenly and demonic, Phil 2:10 in Paul providing the exact wording) and resurrection. All these events are connected by the adverb “truly,” with the result they lay the foundation for “true” life in the church’s resurrection.
Ignatius’s recourse to creedal and hymnic forms obviously have a polemical thrust,
yet they do throw light on how he conceived of congregational worship in the centers to
which he wrote. His great fear was that of the churches’ becoming fragmented and being
dissipated by schism. Hence his call is to rally round the bishop and his officers (Ign.
Phil. 3.1-3), which leads him to lift up the central role of the Eucharist as the church’s
focal point, with the episkopos as the indispensable ministrant (Ign. Smyrn. 8.1-2; Pol.
6.1-2). Moreover, the Eucharist for Ignatius now takes on a quasi-magical significance,
seen most starkly in Ephesians 20.3, which calls it “the medicine of immortality, the
antidote that we should not die, but live forever in Jesus Christ.” Again, it is possible
the constraints of false teaching which in turn led to rebellion against “the bishop and
the presbytery” drove Ignatius to this strongly worded eucharistic teaching, since the
sentence is introduced by the renewed call to unity based on “breaking one loaf” (cf. 1
Cor 10:17 in Paul).
When Ignatius writes of worship practices, mainly of baptism, confession, creedal
formulas and the Eucharist, it is difficult to know whether he is describing traditions
current at Antioch where he was bishop or the various centers through which he passed or
to which he was headed. We may assume some common cultic practices since he makes these allusions the basis of his appeal, all set in a trinitarian frame (Ign. Magn. 13.1),
typifying the threefold clerical ministry (bishop, elder, deacon).
5. The Rome-Asia Minor Axis.
Interestingly the parameters of this section are set by two scenes that represent
an early cameo of worship in Asia Minor (Acts 20:7–12) and nearly a century later a more
detailed description of how worship was understood in Rome c. A.D. 150 (Justin Apol. I
67). While these two accounts are separated in time and by background, what is significant
is the common elements they share. (1) The time is “the first day of the week,” later to
be known as “the day called Sunday” (Justin, Dial. Tryph. 41.4; 138.1; see Lord’s Day).
Barnabas 15.3-9 gives the theological reasoning behind this shift from Sabbath to the day
following, “the eighth day,” when Jesus rose and was made manifest and ascended to heaven, thereby claiming the day of celebration as his own (Rev 1:10; Did. 14:1; Gos. Pet. 12.50) as the risen Lord who greeted his own people at a Sunday eucharistic meal, in accordance with the Gospel evidence (Jn 20:19; Lk 24:30, 41–43; cf. Acts 1:3–4; Rordorf 1992; McKay).
(2) The nature of the assembled company is understood as a “gathering” (syneœgmenoœn in Acts 20:7, a verbal form from which “synagogue” is derived; cf. Jas 2:2; Heb 10:25 for this verb/ noun) as people come together, with the emphasis
falling more on their associating than on a consecrated building or space. At this time
Christians met in house congregations. Special structures are to be dated from the third/
fourth centuries, with the earliest, best-attested example at Dura-Europos in Syria, c.
A.D. 256 (Hopkins; see Architecture, Early Church). Yet the format and ethos of synagogue worship (see Morris, with more cautious approach in McKay) carried over into the Christian synaxis (a technical term for such a gathering, as the word implied).
(3) The setting in Acts 20 suggests a two-part arrangement of public speaking (by
Paul) and a meal occasion (Acts 20:11) with some more discourse to follow. This
interrelation of sermon and sacrament provided the basis for the later development of the
liturgy of the Word followed by the liturgy of the upper room. One of the clearest
illustrations of this dual rhythm is in fact provided in Justin, who proceeds in his
description: “the memoirs of the apostles or the writings of the prophets are read. . . .
When the reader has finished, the president in a discourse urges and invites [us] to
imitate these noble things. . . . And, as we said before [Justin Apol. I 65 refers to the
presenting of bread and a cup of water-and-wine, over which prayers of thanks are offered,
regarded as consecrated, and then shared and distributed to those absent], when we have
finished the prayer, bread is brought, and wine and water,” followed by prayers and the
offering. Justin sums up: “We all hold this common gathering on Sunday.”
The stark simplicity of these details captures some of the basic ingredients of
worship in the period c. A.D. 50–150, with suitable variations that are distinctive to
each part of the Rome-Asia Minor axis.
For what developed in Asia we need to turn to the Johannine writings. Yet the
witness in the cognate epistles, Colossians-Ephesians in the Pauline corpus, must find a
place in any appreciation of how worship was practiced in the churches of Paul’s
foundation. Colossians 3:16–17 (par. Eph 5:19–20) provides evidence of congregational
assemblies who met to admonish one another in both instruction (“in all wisdom”; cf. 1 Cor 12:8 for “utterances of wisdom” as a spiritual charism) and singing of hymns (evidently christological compositions) along with psalms (perhaps drawn from the Hebrew psalter or Jewish-Christian canticles, see DPL, Hymns) and “songs of the Spirit” (cf. Odes Sol. 14:7). All such tributes were intended to express thanks to God, and so formed part of the genre hodayah/eucharistia, which Bradshaw (1981, 30–7; 1992, 44) maintains with some cogency, was more characteristic than the berakah/eulogia type in early Christianity. Expressions of praise occur in Colossians 1:3, 12–14 with the longer, more stately and measured version in Ephesians 1:3–14, which rehearses the ground-plan of salvation-history in a trinitarian frame (Martin 1992, 13–15). Indeed the first three chapters of Ephesians have been viewed as based on a transcript of praise familiar in the Asian congregations and as celebrating the characteristic themes of the success of the Pauline gospel in repelling challenges to it (cf. 1 Tim 1:15) and the pivotal role of the apostle as its chief exponent.
Hymnic specimens are clearly to be seen in these letters. Colossians 1:15–20 has
evidently been subject to authorial redaction, and it is just possible (if not likely)
that it incorporates a pre-Christian version in praise of gnostic redemption (Käsemann
1964: see critique in the commentaries). As it stands, it announces the universal
reconciliation that both rests on Christ’s redemptive work (Col 1:20) and includes his
authority as head of the ecclesial body (Col 1:18). Both these themes are important in the
polemical use made of them, as seen in Ephesians 2:11–22 (incorporating, it may be, a pre-
Pauline version) and in the teaching of true headship as Christ’s role as heavenly
bridegroom is unpacked (Eph 5:32). Moreover, Ephesians 5:14 contains one of the clearest
evidences of baptismal hymnody in the Asian churches, with its swinging, trochaic rhythm
and its motifs of paraenesis and application sounded in the wake-up call to move forward
in Christ’s light that first shone on the baptismal candidate, who is cleansed in water
(Eph 5:26).
Clearly in these twin epistles we are in touch with the vibrant worshiping life
that pulsated through these communities as the author(s) faced threats to Paul’s
apostolate and authority in Asia. The use of liturgical idioms (such as “to the praise of
his glory,” Eph 1:6, 12, 14), baptismal recall (in Col 1:12–14; 2:11–14; Eph 5:26) and
eucharistic language (eucharisteioœ, “to thank,” is a frequent idea in Eph), along with
creedal expressions (e.g., Eph 4:4–6) and samples of prayer-speech—all give indications of
the letters as steeped in a liturgical atmosphere. They were meant to be read out in
congregational assembly (Col 4:16) and passed on to neighboring churches, evidently at
worship gatherings when their pastoral and didactic appeal would be most effective in
catching the mood of praise and exultation (especially Ephesians, as in Paul’s opening
benedictions generally; see O’Brien) and bidding the hearers to participate in (and
thereby to accept) the truth claims they make.
Ignatius, also reflecting the life-setting of the Asian churches, followed in this
tradition of letter-writing habits. As we observed, many of his allusions to music, creed
and adherence to the teachings are cited to repel what he regarded as error and seem to
have the scenario of the churches at worship in view. Indeed, H. Schlier (48–49) regards
Ignatius’s Letter to the Ephesians 4 as showing his acquaintance with Paul’s
representation of the church’s gathering for worship in canonical Ephesians 5:15–21.
It could also be submitted that the ordering of church life in the Pastoral
Epistles, equally of Asian provenance, could have led to Ignatius’s view of a strictly
hierarchical government of bishop and presbyters and deacons (see 1 Tim 3:1–3; Tit 1:7–9), who are shown to be faithful in maintaining discipline and repulsing deviance from
apostolic-Pauline norms by inculcating sound teaching and promoting worship in a proper
manner (1 Tim 4:11–16). False notions must be exposed and denounced by Timothy’s recourse to the church’s confessions of faith and creedal formulas (1 Tim 3:16, whose introductory sentence is a sign of the six-line, hymnic-poetic christological tribute that follows; 2 Tim 2:11–13). Worship functions in the pastors’ congregations as a stabilizing, boundary-fixing marker (see MacDonald), whose effect is to close ranks within an inward-looking community. This body of literature evinces a trait, shared alike by Ignatius and
Ephesians, of the church’s assuming a role in salvation history centered on itself as an
article of its faith (Eph 4:4, and often in Ignatius; cf. 1 Tim 4:15). We are here on the
threshold of ecclesiastical history, where the church itself is part of God’s salvific
plan (Eph 3:10) and sees no incongruity—indeed it rejoices in this—that it professes to
believe in itself. “I believe in . . . one, holy, catholic, apostolic church” is a
sentence ready to be inserted in the creed.
If we wanted to see how the church’s liturgical acts were becoming integrated into
its understanding of its message and mission, the thrust conveyed in the letter to the
Hebrews would provide encouragement. By common consent, this sermon-like (Heb 13:22) document (see Rhetoric) reflects Roman Christianity in the post-A.D. 70 decades of the first Christian century (see Rome, Roman Christianity). The author’s purpose is stated
with clarity: it is to show the finality and superiority of the new economy brought by
Christ who is both ministrant (Heb 2:10–13; 8:2) and sacrifice (Heb 9–10) in the new
sanctuary. Repeatedly his arguments and appeals are punctuated with liturgical idioms,
often drawn from the levitical prototypes but always suffused with and corrected by
Christian overtones (e.g., Heb 13:10–16). The language of offering and sacrifice is
pressed into service in order to highlight the immeasurable greatness of the new covenant,
based on the better sacrifice of Jesus (since it was made once-for-all) and the better
effectiveness (securing a full and final forgiveness). Yet the high priestly ministry of
Jesus continues in a heavenly sanctuary (e.g., Heb 7:25; 9:24; 13:10, sometimes taken in a
eucharistic sense, see Dunnill 240–42), and the implied call is made that the church is to
share in this worship of God through him who is the perfect worshiper (Heb 2:11–12; 13:12–16).
This is an aspect of worship here receiving its emphasis in a unique way (in the
NT) but with repercussions that were later to be enlarged and felt in the decades (e.g., 1
Clem 36:1; 40:1–5) and centuries to come. Worship is both “through Christ” (Heb 13:15) and “in Christ,” making the church one with his self-offering (Heb 7:25) so that its
sacrifices of praise are joined with the one offering that is both complete (once-for-all,
eph’ hapax) and ever-renewed as it is freshly appropriated by and mediated to the
believing community. Hebrews 13:17 mentions the leaders who serve the community; 1 Clement 41–44 reflects debate over the rightful authorities in the church (at Rome?), who should succeed the apostles in presenting the church’s “sacrifices and services” (1 Clem. 40:2); namely, the credibility of other approved persons who as overseers have “offered the sacrifices” (1 Clem. 44:4).
The audience of Hebrews needs both to catch this vision of itself as an
eschatological people sharing in the heavenly host’s triumph (Heb 12:22–24; the realized
eschatology in these verses puts this part of Hebrews in touch with the “already
accomplished” emphasis in Ephesians) and equally to face the stern realities of its life
on earth as pilgrims and strangers (Heb 11:13–16; see Johnsson, Käsemann 1984). The way to win through, for this author and the readers, is to remain committed to early baptismal pledges (e.g., Heb 4:14; see Bornkamm 1963) and keep the lines of communication with God, established in corporate worship, open (Heb 4:16) and intact (Heb 10:19–25). The temptation to withdraw from public assembly is evidently strong in time of testing (Heb 10:32–39); so the author makes adherence to the assembly a focal point of resistance and renewal, thereby giving to worship its pragmatic value and socializing dimension.
A parallel side to the way worship is seen to provide identity markers for the new
Israel and to build confidence is evident in another document also associated with Rome.
In 1 Peter the addressees are facing a loss of faith but for a different set of reasons.
In Hebrews, where hope plays a key role (Heb 6:9–20; 11:1), the conflicts were domestic
and internal, and there was theological questioning about the imminent Parousia (Heb
10:37–39). The call to hope in 1 Peter (1 Pet 1:3, 13, 21; 3:5; 5:20) is couched against a
different background. Here the hostility is directed to the churches in Pontus-Bithynia (1
Pet 1:1) from outside (1 Pet 2:12; 4:1–6), and there seems to be no debate about their
final salvation at an expected appearing of the Lord (1 Pet 1:5, 13; 4:7). The root
problem faced in 1 Peter is the loss of social identity and sense of rootlessness that has
come to people who, from their pagan environment, have joined the church and accepted its mores and manners. Their (physical) sufferings are raising problems to do with theodicy as they seek to understand and make sense of life’s contrarieties and uncertainties when their new-found faith is tested (1 Pet 1:6; 2:19; 4:12).
The author’s response in this hortatory document (1 Pet 5:12) is to impart social
identity to the readers as those belonging to the “people of God,” stretching back to
Abraham and Sarah (1 Pet 3:5, 6) and onward to the complete “household of faith” soon to
be realized (1 Pet 2:4–10; 4:17–19) and to offer assurance that God’s plans do not
miscarry as the churches come to see how Christ’s victory over all his enemies is one to
be shared by his followers who walk in his steps (1 Pet 2:21; 3:18–22; see Martin 1994,
100, n. 26). Liturgical emphases play their role in enforcing these precise points,
notably in the poetically structured passage (1 Pet 2:1–10; see commentaries, esp. Selwyn)
that celebrates the church as God’s new Israel in which erstwhile strangers and alienated
people find their new home as worshipers and family; and in the christological hymn of 1
Peter 3:18–22, whose original form may well have looked like this:
Who suffered once for sins,
To bring us to God;
Put to death in the flesh,
But made alive in the spirit,
In which he went and preached to the spirits in prison,
[But] having gone into heaven he sat at the right hand of God,
Angels and authorities and powers under his control.
The intricacies of debate over this obscure passage are many (see commentaries by
Reicke, Dalton, Boismard for basic treatments—all reacting to Bultmann’s seminal work of
1947; for survey and bibliographical references, see Martin 1978, 335–44; 1994, 95, 110–
117). For our purposes it is enough to seek to inquire how the cited lines functioned as a
hymn. The key to this problem is suggestively to observe that the section encompasses a
drama of Christ’s odyssey, framed by two occurrences of the verb “to go” (represented in
italics above). He went to visit the realm of the demonic; he went after his triumph to
take his place on the universe’s throne, with all cosmic powers held in subjugation. So
the journey motif is the key, unlocking the chief problematic issue which is to know how
relevantly such a piece of christological suprahistory would affect the lives of Peter’s
readers, who are also reminded of their baptism (in turn typified in the ark by which
Noah’s family was saved in a generation Jewish thinkers regarded as the worst imaginable
and the cause of demonic influence in the world). In Christian baptism—a thought
conceivably inserted by Peter into the preformed creed-hymn—there is an appropriating of
Christ’s identification with dark powers and his subsequent victory over them.
Here baptism receives a treatment that ostensibly links it with Paul (in Rom 6;
cf. Col 2:12; 3:1). Yet it adds a dimension of considerable pictorial, even mythological,
effect. It proclaims that believers share in Christ’s achievement in both its horror and
its glory. He made himself one with human enslavement to evil and then in his triumph over it (see Martin 1994, 114–17, referring to Rev 1:18), thus connecting its kinetic-dramatic theology with other hymns, notably Philippians 2:6–11, as well as the scenario in Gospel of Peter 10.41-42 and Acts of Pilate 5.1—8.2, in the section Christ’s Descent into Hell, and of course the Apostles’ Creed statement (at Rome, c. A.D. 150, as a baptismal creed; Kelly): “crucified, dead, and buried; he descended into Hades. The third day he rose again and ascended into heaven.” The Christus victor theme reaches its zenith in the
acknowledgement and proclamation that in baptism all demonic agencies that would tyrannize over the church and hold it prey are overcome, since Christ knew both their power to hurt and their being reduced to impotence. The logical and liturgical outcome of this theologoumenon will be the use of exorcistic and renunciation formulas as a prelude to the actual baptism seen in Hippolytus’ Apostolic Tradition (Cuming).
6. Johannine Patterns and their Influence.
If we are correct in assuming the presence in the Rome-Asia axis of styles of
worship that looked to Paul’s and Peter’s deposits of teaching to inform them, with the
universally accepted practices of baptism as initiatory rite and the Lord’s Supper as
celebratory of Christ’s resurrection victory and set in a structure that tended to respect
the authority of leaders, then in the Johannine literature the emphasis falls elsewhere
(see John, Letters of).
The powerful influences seen in the Pastorals, the Didache, Ignatius and 1
Clement, with their concerns over set prayers (the permission of Did. 10:7, “allow the
prophets to give thanks at will,” needs to be read in light of Did. 15:1–2 which shows
that itinerant prophets are on the way out and are to be succeeded by “bishops and
deacons,” as in Ign. Smyrn. 8; 1 Clem. 44), regular ministries, orderly worship (1 Clem.
20) and an incipient sacramental system (Ign. Eph. 20) seem to brook no challenge. Yet
there is another strand that mirrors a reaction in the Asian churches in which the
Johannine influence is strong. This body of literature (John’s Gospel, Johannine Epistles
and to an extent the Apocalypse) speaks to a situation where there are competing emphases, partly christological, partly ecclesiological, in the “community of the beloved
disciple” (Brown). We may even postulate a threat to worship, as John’s disciples feared
it. Both the Johannine Gospel and Epistles raise a warning against the trend to over-
institutionalize. John senses the danger of suffocating the Spirit by placing too much
emphasis on creedal orthodoxy, relying too heavily on structural forms and limiting the
spontaneity that we saw to be evident in Luke’s depictions. It is a moot point whether
John’s protest may be directed to just such a situation as that envisaged in the Pastoral
Epistles, 1 Clement and later in Ignatius.
At all events, for John the way forward is to stress the believer’s individual
participation in true spirituality, as he dubbed it. (1) Worship is “in the Spirit” (1 Jn
3:24) as in reality and is largely independent of outward forms, locations and ceremonials
(Jn 4:20–24). The water of Jewish purification rituals is marvelously transformed into the
wine of the new age, where Jesus’ glory shines out as the universal logos (Jn 2:1–11).
(2) Love of God and his family members is the real test of authentic spirituality
(1 Jn 3:1–18; 4:7–21), over against creedal rigidity and a blind trust in sacraments. The
antisacramentalism alleged in the Fourth Gospel (Bultmann 1971) is a timely, if
overstressed, protest against the opposite viewpoint of Cullmann who sees baptism, unction and the Eucharist everywhere on almost every page. There is no explicit institution of the Lord’s Supper in John 13, which does, however, have an upper-room meal. But the Evangelist has incorporated a discourse set in the synagogue at Capernaum (Jn 6) as though to stress that the Eucharist has an individualized, inner meaning as nothing less than a feeding on Christ the bread of life, just as John’s earlier chapter (Jn 4) had depicted Jesus as the giver of living water to an individual woman of Samaria. The same note is struck in Revelation 3:20: “if any one hears my voice, I will . . . eat with that person.”
(3) It cannot be fortuitous that this body of literature lacks completely the term
“church” (ekkleœsia). (Revelation is the exception, and it is notable for its inclusion of
liturgical-hymnic tributes linking the old Jewish worship [Rev 4:8, 11; 7:12; 15:3–4] to
the new age of Messiah’s redemption [Rev 5:9–14] and victory [Rev 12:10–12]). Yet for John believers do form a society under the imagery of a flock (Jn 10:1–16; cf. 11:52; see
Shepherd, Flock) and the vine (Jn 15:1–11), but inevitably in such images the important
thing is the personal relationship the believer sustains to the Lord. As the sheep hear
the shepherd’s voice when he calls each by name (Jn 10:3–5; cf. Heb 13:20; 1 Pet 5:2–4 has the chief shepherd with many under-shepherds to tend the flock, and Peter will assume such a role in Jn 21), so there is no possibility of life unless the separate branches are linked to the parent stem of the vine (Jn 15:4, 5). John’s view of the church governs his
concept of worship. The church is made up of individual believers (Moule 1962) who are
joined one-by-one to the Lord by the highly personal ties of baptism and new birth (Jn
3:1–6; see New Birth). The worship they offer springs from the experience of an enriched
individualism: “the individual’s direct and complete union with Jesus Christ sets its
stamp on the ordering of the (Johannine) church” (Schweizer, 124). This is true also of
its liturgy, remarkable for its absence of set forms and a Johannine passing over of much
that other Christians elsewhere may have taken for granted.
7. Some Conclusions.
The above survey of worship materials and patterns, drawn from literature of a
wide time span and diverse geographical and cultural spread, cannot pretend to be
comprehensive. The soundings we have taken are at best, we hope, typical of the regions
mentioned. Yet the picture is still incomplete, and the settings proposed conjectural. It
is difficult therefore to plot a trajectory or suggest a developing pattern with any
convincing coherence. The bold attempt as proposed by G. J. Cuming (SL 10 [1974] 88–105), ranging from salutation (grace and peace) by way of intercessions, Scripture readings to doxology, kiss of peace and dismissal is hardly convincing (see Martin 1982, 190, n. 6). A lot of the material emerges from the socially conditioned pressures on both writers and congregational addressees. The most we can hope for is to plot certain nodal points along
the way. And as these are observed, we can submit that certain trends are visible.
7.1. Growing Systematization of Order. In the later Pauline/deutero-Pauline
literature there is a growing move to systematization based on various factors: the
squelching of charismatic fervor seems the inevitable concomitant of the growing emphasis on instruction/teaching roles (themselves in response to deviant notions that challenged the legacy of Paul’s doctrine, e.g., in the Pastorals and Colossian-Ephesians). The rise of churchly concerns over order and fixity put a brake on immediacy and spontaneity in worship that we see at Corinth. Paul had sounded the caution, “let all things (in the worshiping assembly) be done in seemly fashion and in good order” (1 Cor 14:40, a phrase evidently picked up in 1 Clem. 40, panta taxei poiein opheilomen); and the growing
strength and authority accorded to duly appointed leaders (in the Pastorals and Eph 4:11–
16; see commentaries; Martin 1992) tended to focus the spotlight on the hierarchical
controls required to ensure that unity was promoted (Ign. Smyrn. 8, for instance) and the
episcopal office maintained (1 Clem. 44). Along the way from the picture of congregational
egalitarianism to the recognition of a settled ministry (a transition point seen in Did.
9–15), we may note the recourse made to apostolic teaching (Acts 2:42; Jude 17; Did.
incipit; Heb 13:7; cf. Heb 2:3; the Johannine letters, 1 Clem. 42) to repel false ideas
that began to rear their head.
7.2. Emerging Trinitarian Focus. The occasional nature of much of the liturgical
language, called out by the contingencies of congregational problems and challenges,
should not blind us to some well-attested constants. Among these we may include: (1) the
appreciation of God as the holy object of Christian adoration and praise. The legacy of
the OT-Judaic traditions is not overlooked but carried forward and enriched by an emerging trinitarian faith, for example, the “thrice holy” of Isaiah 6:3 is heard in Revelation 4:8, though the history of the Sanctus in the eucharistic liturgy is still a complex issue (cf. 1 Clem. 34:6; Spinks, especially 46–54). All the documents in our period highlight the transcendence and worthiness of God, without which worship (as classically understood) fails.
(2) As a counterbalance, God is praised as intimately near in Christ his Son,
whose true incarnation, death for sinners and resurrection victory over all evil forces
are pivotal events in salvation history (cf. creedal-hymnic forms in 1 Pet, Heb 1:1–4; 1
John 4:1–6; 5:20; Rev 5:1–14; Ign. Eph. 19). This prepares the ground for a doctrine of
the priestly office of the exalted Christ as intercessor and participant in the church’s
offices (Heb 7:25; 1 Clem. 40; 59—62.3; 1 Clem 61.3 is an interesting specimen of prayer
speech with nine pairs of parallel lines [in 1 Clem. 59.3]consisting of divine
predications and hymnic sentences [Robinson 1964] offered through “Jesus Christ the high priest and guardian of our souls through whom be glory and majesty”). The Pauline verse (Eph 2:18) is sometimes hailed as encapsulating the essence of early worship in its
trinitarian format (Crichton, 18, 19) and as offering a “basic morphology that cannot be
violated if liturgical theology is to be Christian” (Hoon, 115). The data that begin with
Paul’s borrowing of formulas like 2 Corinthians 13:13 (14) take on this shape in Matthew
28:19, 20; Acts 2:33; Hebrews 9:14; 1 Peter 1:2; Didache 7:1–4; and Ignatius’s Letter to
the Trallians (incipit) on the road to full-blown trinitarian creeds (in Irenaeus and
beyond; see Wainwright).
7.3. Placing the Risen Lord Alongside the Father. The place of the risen Lord in
early Christian worship is still hotly debated (see representative positions held in
Jungmann, Harris, Bauckham, France, Hurtado, Casey). From allusions that are at best
inferential (Jn 14:14 RSV mg.; cf. Jn 16:23) or incidental (Acts 7:59; 1 Clem. 21:6) to
others that precisely speak of invoking the living Christ (1 Cor 16:22; Rev 22:20; Did.
10:6) or else set the exalted one at the center of a cultus on a par with Israel’s
covenant God (Rev 5:12–14; cf. 3:21; see Guthrie, Thompson), the line moves inexorably to
a placing of Jesus alongside the Father as worthy of worship and the co-author of
salvation blessings for the church and the world. The title “God,” so reticently applied
to Jesus in the NT literature (though see Harris for the maximum value to be extracted
from such verses as Heb 1:8; 2 Pet 1:1; 1 Jn 5:20), may well have received fresh impetus
from the role cast for him in the Christians’ assembly when as Christians met on an
appointed day (i.e., Sunday, so called in Justin Apol I 67 as the day after Saturday
before daybreak [stato die ante lucem]) hymns were sung antiphonally “to Christ as to God” carmen quasi Deo (Pliny Ep. 10.96.7 for this text, c. A.D. 112; see Cabaniss 1989, 11–18).
See also Baptism, Baptismal Rites; Centers of Christianity; God; Hymns, Songs;
Liturgical Elements; Lord’S Day; Lord’S Supper, Love Feast; Prayer; Synagogue; Temple.
Bibliography. R. J. Bauckham, Jude, 2 Peter (WBC; Waco: Word, 1983); idem, “The
Worship of Jesus” NTS 27 (1981) 323–31; W. Bauer, Orthodoxy and Heresy in Earliest
Christianity (Philadelphia: Fortress 1971 [1924]); idem, Die apostolischen Väter II
(Tübingen: J. C. B. Mohr, 1924) 204; G. Bornkamm, Early Christian Experience (London: SCM, 1969); idem, “Das Bekenntnis im Hebräerbrief” in Studien zu Antike und Urchristentum (2d ed.; Munich: Kaiser, 1963) 188–203; P. F. Bradshaw, The Search for the Origins of Christian Worship (New York: Oxford University Press, 1992); idem, Daily Prayer in the Early Church (New York: Oxford University Press, 1982); R. E. Brown, The Community of the Beloved Disciple (New York: Paulist, 1979); R. Bultmann, Theology of the New Testament (2 vols.; New York: Scribner’s, 1952, 1955); idem, The Gospel of John (Philadelphia: Fortress, 1971); A. Cabaniss, “The Epistle of Saint James,” JBR 22 (1954) 27–9; idem, Pattern in Early Christian Worship (Macon, GA: Mercer University Press, 1989); M. Casey, From Jewish Prophet to Gentile God (Louisville: Westinster/John Knox, 1991); J. H. Charlesworth, ed., The Lord’s Prayer and Other Prayer Texts from the Greco-Roman Era (Valley Forge: Trinity Press International, 1994); J. D. Crichton, “A Theology of Worship” in The Study of Liturgy, ed. C. Jones, G. Wainwright and E. Yarnold (2d. ed.; New York: Oxford University Press, 1992), 3–29; F. L. Cross, 1 Peter: A  Paschal Liturgy (London: Mowbray, 1964); O. Cullmann, Early Christian Worship (SBT 10; London: SCM, 1953) 7–36; P. H. Davids, Commentary on James (NIGTC; Grand Rapids: Eerdmans, 1982); M. Dibelius, James (Herm; Philadelphia: Fortress, 1976); F-J. Dölger, Sol salutis: Gebet und Gesang im christlichen Altertum (2d ed.; Münster: Aschendorff, 1925); C. W. Dugmore, The Influence of the Synagogue on the Divine Office (London: Oxford University Press, 1944); J. D. G. Dunn, Baptism in the Holy Spirit (Philadelphia: Westminster, 1970); idem, Jesus and the Spirit (Philadelphia: Westminster, 1975); idem, Unity and Diversity in the New Testament (2d ed.; Louisville: Westminster, 1990); J. Dunnill, Covenant and Sacrifice in the Letters to the Hebrews (SNTSMS 75: Cambridge: Cambridge University Press, 1992); J. A. Fitzmyer, “The Aramaic Language and the Study of the New Testament,” JBL 99 (1980) 5–21; R. T. France, “The Worship of Jesus” in Christ the Lord, ed. H. H. Rowdon (Leicester/Downers Grove: InterVarsity, 1982) 17–36; D. Guthrie, “Aspects of Worship in the Book of Revelation” in Worship, Theology and Ministry in the Early Church, ed. M. J. Wilkins and T. Paige (Sheffield: Academic Press, 1992) 70–83; E. Haenchen, The Acts of the Apostles (Philadelphia: Westminster, 1971); M. J. Harris, Jesus as God: The New Testament Use of Theos in Reference to Jesus (Grand Rapids: Baker, 1992); P. J. Hartin, James and the Sayings of Jesus (Sheffield: JSOT Press, 1991); P. W. Hoon, The Integrity of Worship (Nashville: Abingdon, 1971); C. Hopkins, The Discovery of Dura-Europos (New Haven: Yale University Press, 1979); A. J. Hultgren, The Rise of Normative Christianity (Minneapolis: Augsburg/ Fortress, 1994); L. W. Hurtado, One God, One Lord (Philadelphia: Fortress, 1988); R. D. Jasper and G. J. Cuming, Prayers of the Eucharist: Early and Reformed (London: Collins, 1975); J. Jeremias, The Eucharistic Words of Jesus (3d ed.; Philadelphia: Fortress, 1977); W. G. Johnsson, “The Pilgrimge Motif in the Book of Hebrews” JBL 97 (1978) 239–51; J. A. Jungmann, The Place of Christ in Liturgical Prayer (New York: Alba, 1965); E. Käsemann, “A Primitive Christian Baptismal Liturgy” in Essays on New Testament Themes (Philadelphia: Fortress, 1982 [1964]); idem, The Wandering People of God (Minneapolis: Fortress, 1984); J. N. D. Kelly, Early Christian Creeds (5th rev. ed.; London: A. C. Black, 1977); H. Koester and J. M. Robinson, Trajectories through Early Christianity (Philadelphia: Fortress, 1971); J. Kroll, Die christliche Hymnodik bis zu Klemens von Alexandreia (Darmstadt: Wissenschaftliche Buchgesellschaft, 1968 repr. ); G. W. H. Lampe, The Seal of the Spirit (2d ed.; London: SPCK, 1967); H. Lietzmann, Mass and Lord’s Supper: A  Study in the History of the Liturgy (Leiden: E. J. Brill, 1953–1978); E. Lohmeyer, Kyrios Jesus: eine Untersuchung zu Phil 2.5-11 (2nd ed.; Heidelberg: Winter, 1961 [1928]); M. Y. MacDonald, The Pauline Churches (SNTSMS 60; Cambridge: Cambridge University Press, 1988); I. H. Marshall, Acts (TNTC; Grand Rapids: Eerdmans, 1980); R. P. Martin, A Hymn of Christ (Downers Grove, IL: InterVarsity Press, 1997 [1967, 1983]); idem and A. Chester, The Theology of the Letters of James, Peter and Jude (NTT, Cambridge: Cambridge University Press, 1994); idem, James (WBC; Waco: Word, 1988); idem, Ephesians, Colossians, Philemon (Int; Louisville: Westminster, 1992); idem, “New Testament Worship:
Some Puzzling Practices” AUSS (1993) 119–26; H. A. McKay, Sabbath and Synagogue: The
Question of Sabbath in Ancient Judaism (RGRW 122; Leiden: E. J. Brill, 1994); L. Morris,
“The Saints and the Synagogue” in Worship, Theology and Ministry in the Early Church, ed. T. Paige and M. J. Wilkins (Sheffield: Academic Press, 1992) 39–52; C. F. D. Moule,
Worship in the New Testament (London: Lutterworth, 1961); idem, “The Individualism of the Fourth Gospel” NovT 5 (1962) 171–90; E. Norden, Agnostos Theos (Stuttgart: Teubner, 1956); P. T. O’Brien, Introductory Thanksgivings in the Letters of Paul (NovTSup 49: Leiden: E. J. Brill, 1977); J. A. T. Robinson, Twelve New Testament Studies (SBT 34; London: 1962) 154–57; J. M. Robinson, “Die Hodajot-Formel im Gebet und Hymnus des Frühchristentums” in Apophoreta: Festschrift für Ernst Haenchen, ed. W. Eltester (Berlin: Töpelmann, 1964) 194–235; T. A. Robinson, The Bauer Thesis Examined: The Geography of Heresy in the Early Christian Community (Lewiston, NY: Mellen, 1988); W. Rordorf, Sunday (London: SCM, 1968); idem, “Sunday” in Encyclopedia of the Early Church, ed. A  de Berardino (New York: Oxford University Press, 1992) 2.800-801; H. Schlier, Die Verkündigung im Gottesdienst der Kirche (Würzburg: Werkbung-Verlag, 1953); E. Schweizer, Church Order in the New Testament (SBT 32; London: SCM, 1961); E. G. Selwyn, The First Epistle of St. Peter (London: Macmillan, 1947); M. H. Shepherd, “The Epistle of James and the Gospel of Matthew,” JBL 75 (1956) 40–51; idem, The Paschal Liturgy and the Apocalypse (Richmond: John Knox, 1960); B. D. Spinks, The Sanctus in the Eucharistic Prayer (Cambridge: Cambridge University Press, 1991); J. H. Srawley, Early History of the Eucharist (2d ed.; Cambridge: Cambridge University Press, 1947); B. H. Streeter, The Primitive Church (London: Macmillan, 1929); L. T. Stuckenbruch, “A Refusal of Worship of an Angel: The Tradition and its Function in the Apocalypse of John,” SBLSP (1994); M. M. Thompson, “Worship in the Book of Revelation”, Ex Auditu 8 (1992) 45–54; H. E. W. Turner, The Pattern of Christian Truth (London: Mowbray, 1954); A. W. Wainwright, The Trinity in the New Testament (London: SPCK, 1962).

II. LITURGICAL ELEMENTS IN THE LATER NT AND EARLY FATHERS
The notion that “the New Testament was, in a sense, a liturgical book” (Cabaniss 1989, 44–45) is a growing trend among NT interpreters. This suggestion is based on the observations that the letters or books of the NT were first read during public worship (1
Thess 5:27; Col 4:16) and that liturgical elements are richly embedded in these writings.
Some scholars have even proposed that certain NT letters are essentially liturgical
documents written for religious rites such as the baptismal service or the Eucharist
(Cabaniss 1989, 44). Frequent allusions to liturgical elements, however, may not imply
that being “a liturgical book” was the original intent for their composition (Bradshaw,
30–37). Especially when one recalls how the presence of the Holy Spirit had enacted a new
dimension in Christian worship (cf. 1 Cor 14:26; van Unnik 1959, 294), it is unconvincing
to conclude that Christian worship had already developed fixed liturgical forms with fixed
sequences in the early decades when the NT letters were written (Delling, 76; Cullmann,
27, 32; Williams, 451).
In fact most of these documents or letters were responses to various needs within
scattered Christian communities (e.g., 1 Pet, Jude and Heb). A  close examination of the
Pauline corpus shows that although liturgical elements (e.g., creedal confessions,
benedictions, doxologies, hymnic fragments and prayer acclamations such as “amen,” “Abba,” “maranatha”) appear in many letters, they are not always uniform in expression or placed in locations in line with the order of worship. Rather, liturgical elements are often
tailored to highlight relevant contents and placed in strategic contexts to clarify or
underscore the writer’s messages to his readers (see DPL, Liturgical Elements). In this
study of the liturgical elements found in the later canonical writings and in the writings
of the early apostolic fathers we further explore what types of liturgical elements are
alluded to most often, whether they are uniform in expression and why are they mentioned in their contexts.
1. Liturgical Elements in the Later Canonical Writings
2. Liturgical Elements in the Apostolic Fathers
3. Conclusions
1. Liturgical Elements in the Later Canonical Writings.
As in the Pauline corpus, liturgical elements such as benedictions, doxologies,
hymnic fragments (see Hymns), creedal confessions and some acclamations such as amen, Ter Sanctus, hallelujah and maranatha are incorporated in Acts, Hebrews, the General Epistles and the Apocalypse (see Revelation, Book of) by different writers in their addresses to different groups of readers at scattered locations.
1.1. Benedictions. The inclusion of benedictions in a letter to express the
writer’s wish-prayers for the readers may have been derived from Jewish worship, in which benediction was a common practice. In the Pauline corpus each letter commenced and ended with a benediction. In the group of writings we are considering, however, there are some distinctive features: not every letter includes a benediction (e.g., Jas and 1 Jn) and, except for 1 Peter, each letter includes only one benediction, either at the beginning (1
Pet 1:2; 2 Pet 1:2; 2 Jn 3; Jude 2; Rev 1:4) or at the end (Heb 13:20–21, 25; 1 Pet 5:14;
3 Jn 15; Rev 22:21). Even though benediction is frequently included in a letter, it is not
a necessary element. The Johannine epistles provide strong evidence: there is no
benediction in 1 John, one introductory benediction in 2 John and only a brief closing
benediction in 3 John (see John, Letters of). Here the same writer does not follow a
stereotyped format in his letters.
Benedictions are essentially wishes of grace and/or peace: “Grace be with you
[all]” (Heb 13:25; Rev 22:21) or “Peace be with [or to] you” (1 Pet 5:14; 3 Jn 15). In
some letters benedictions are elaborated with additional features such as mercy (2 Jn 3)
or love (Jude 2) or with a closing “Amen” (Heb 13:25; Rev 22:21). In Hebrews 13:20–21 and Revelation 1:4, both letters include lengthy introductions about God, the source of the
benefaction, with epithets that coincide with the major motifs of the letters (Lane, 560).
The Pauline formula “The grace of the Lord Jesus Christ be with you” and the so-called
Dominus Vobiscum (“The Lord be with you”; see Lk 1:28; van Unnik 1959), are not shared by these writings. Thus we see the contents of benedictions are also subject to modification
by each writer according to personal choice or the needs of the recipients (Delling, 76).
1.2. Doxologies. Out of gratitude for God’s redeeming grace, early Christians were
constantly offering praise (see Acts 2:46; 4:24). Just as in the Pauline letters, two
doxological formulae are found in this group of writings. One is expressed by the formula
“Blessed [be] God” (also known as the Berakhah, or Eulogy; 1 Pet 1:3; cf. 2 Cor 1:3; Eph
1:3), which is a common expression in OT worship and also resembles the Shemoneh Esreh, the Eighteen Benedictions used in the synagogue. The other is expressed by the phrase “to him be glory [and dominion] for ever and ever,” which is less formal in structure but more commonly used (e.g., Heb 13:21b; 1 Pet 4:11; 5:11; 2 Pet 3:18; Jude 24–25; Rev 1:6; 5:13; 7:12). The former type often occurs at the beginning of a letter and the latter at the end of a letter or a section (e.g., 1 Pet 4:11), sometimes with a liturgical “amen” attached to it. But exceptions are also found in the Apocalypse, where doxological expressions are placed in various contexts to maximize the tone of worship. Some follow the common formula “to God be glory for ever and ever” (Rev 1:6; 5:13; 7:12), and some begin with the expression axios ei/estin (“worthy art thou”/“is he”; Rev 4:11; 5:9, 11).
Although most of the doxologies in this group of writings follow the formulaic
expressions, they may also be modified with motifs that bring out meanings relevant to the
readers (Lane, 565). For example, the doxology in Jude has been considered as one of the
most fulsome doxologies in the NT (Martin, 66). It contains a declarative praise for God’s
specific deeds (“to keep you from falling and to present you without blemish,” Jude 24)
and a descriptive praise for who God is (“the only God, our Savior,” Jude 25; in
Westermann’s definitions, 31), and it is expressed with motifs evidently tailored to meet
the subjective needs of the readers whose faith was endangered by the false teachings of
the intruders (Martin, 80–81). Many doxologies in the Apocalypse are also more elaborate
in content (cf. Rev 4:11; 5:12, 13). Some of them are directed to Christ (Rev 5:9, 12, 13)
with similar wordings as those directed to God (cf. Rev 4:11; 7:12). The purpose is to
emphasize his deity, thereby comforting the suffering readers during the imperial
persecution. Doxologies are not confined to a limited range of thought or stereotyped
expression (Delling, 65; cf. Piper, 17).
1.3. Creedal Confessions. Creed, in its modern sense as an article of the
Christian faith, is not discernible in the NT (see DPL, Creed). Yet fragments of creedal
confessions are traceable. Among this group of writings, Acts provides us with a window on one of the earliest forms of creedal confessions in the Christian communities, namely,
“Jesus is the Lord [and/or Christ]” (Acts 2:36; 8:35–38 [the Western text]; 10:36; 16:31;
cf. Rom 10:9; Phil 2:11, where homologeoœ, “confess,” is directly connected with the
formulaic expression). This is possibly a baptismal confession, for it is consistently
connected with baptism in various geographical locations: Jerusalem, Samaria, Caesarea and Philippi. And since the document is written partly with a polemic objective, it is
probably the writer’s intention to show his recipients (Theophilus and eventually the
Romans) that Christian communities as outlined in Acts 1:8 are founded on the same faith, “Jesus is the Lord/Christ.” They are not political rebels against the Roman government (see Hymns, for similar usage of hymnic materials in Acts; see Civil Authority; Roman Empire). The creedal confessions found in 1 John such as “Jesus is the Christ” (1 Jn 2:22), “Jesus Christ is come in the flesh” (1 Jn 4:2) and “Jesus Christ is the Son of
God” (1 Jn 4:15; cf. Heb 4:14), however, are mentioned as criteria for discerning one’s
faith and are most likely introduced for apologetic purposes.
In Hebrews the writer refers to the homologia three times (Heb 3:1; 4:14; 10:23;
also the verb form in Heb 11:13; 13:15) and exhorts his readers to hold fast to it. This
repeated allusion has been generally acknowledged (e.g., Bornkamm; Michel; and more
recently Lane, with some modifications; contra Delling, 79–80) as evidence for the
existence of certain fixed forms of creedal confession in the latter part of the first
century (see 1 Tim 3:16; 4:6; 6:20; 2 Tim 1:13, 14; 2:11–13; 4:3; Tit 1:9, 13; Jude 3;
“the faith,” “the deposit” and “sound teaching/doctrine” all clearly support this notion).
In the case of Hebrews, Christ’s sonship (Heb 4:14) and high priesthood (Heb 3:1) are the
key confessions acknowledged by the members of the community. The reason for exhortation is also directly related to the urgent needs of the readers. Being Jewish converts in the Diaspora, the readers have been attracted by a form of heretical and gnosticizing Judaism and are at the stage of returning to their former beliefs. Thus the writer’s allusions to the homologia that spells out the supremacy of Christ are intended to serve as powerful reminders to the readers of the belief they once confessed (Lane, 103–4). They should “hold fast” to it and not fall back (Heb 10:39). Creedal confessions in early Christian communities are all christocentric and are designed for the presentation, identification and defense of this new faith.
1.4. Prayer Acclamations. The most familiar prayer acclamation found in this group
of writings is “aœmeœn,” a transliteration of the Hebrew word ’amen, meaning “firmness,
certainty.” This word is frequently used in the OT and the intertestamental period as a
vocal expression signifying a person’s agreement to or endorsement or affirmation of
another person’s words or prayers (e.g., 1 Chron 16:36; Neh 8:6; Ps 41:13; Tob 8:8; 1 Esdr
9:47). In the Jewish synagogue, “amen” became a liturgical term attached to various forms
of prayer. When early Christians began their worship they readily adopted this usage.
Evidences are found in the General Epistles, where “amen” is consistently added to the end of doxologies (Heb 13:21; 1 Pet 4:11; 5:11; 2 Pet 3:18; Jude 25) and benediction (Heb
12:25). This is not done perfunctorily by the writers. By adding an “amen” at the end of
doxologies, the readers are given an opportunity to make the message of praise their own
(Delling, 64) as well as to unite with one another through their simultaneous utterance of
this liturgical acclamation. The unified “amen” is a means for promoting the corporate
spirit of worship (MacDonald, 109).
In the Apocalypse, however, “amen” has richer connotations besides being added to
the end of various doxologies (Rev 1:6; 7:12b) and the final benediction (Rev 22:21). It
is seen as an expression of affirmation of another person’s prayer (Rev 5:14; 19:4) or
serves as an emphatic yes (Rev 1:7; 7:12a; 22:20). But a more significant use of “amen” is
found in Revelation 3:14. There it is identified as a christological title, and the
meaning of “amen” is clearly spelled out in the following phrase, “the faithful and true
witness” (RSV), serving as a double emphasis of Christ’s faithfulness. It must be noted
that the choice of epithets for Christ in this context, just as in Revelation 2:1, 8, 12,
18; 3:1, 7, is directly related to the specific needs of the church. In the case of the
Laodicean church (Rev 3:15), believers have failed to follow the One who was faithful in
carrying out God’s promise of salvation and made it possible for them to utter the “amen”
together in corporate worship. Here we see another example of using “amen” as a
christological title to convey the writer’s message to his readers (cf. Paul’s similar use
of “amen” in 2 Cor 1:20 for underlining his argument; see DPL, Liturgical Elements, §5.1).
The use of “amen” may be more than just a formal consent or endorsement.
There are two other liturgical acclamations in the Apocalypse: Ter Sanctus (the
“Thrice Holy,” Rev 4:8) and “hallelujah” (Rev 19:1, 3, 4, 6). Both acclamations are also
found in the OT (Is 6:3; Pss 104–06, 111–13, 115–17, 135, 146–50, the so-called Alleluia
Psalms) and are not alluded to in other parts of the NT.
The origin of Ter Sanctus is a song of praise sung by celestial beings, the
seraphim, in the presence of God (Is 6:1–3; there, probably the triune God or Yahweh, in
contrast to Brock’s view, which suggests that Ter Sanctus is directed to Christ),
proclaiming his holiness and his sovereignty, which eventually led Isaiah to an awareness
of his own unworthiness (Brock, 32). Although this acclamation is not found elsewhere in
the NT, its presence in Revelation 4:8 indicates its continual usage in Jewish worship
(possibly as a liturgical element used in the Jewish synagogue; see Spinks, 46–54, 194,
cf. van Unnik 1951, 213). It was adopted by Jewish Christians in the Diaspora to be cited
on occasions such as the Eucharist (Brock, 31–32; van Unnik, 205; contra Moule, 64).
Notably the Ter Sanctus is the first song of praise that commences the heavenly worship in
the book of Revelation.
Since Revelation 4:8 is the only place in the NT where Ter Sanctus is mentioned,
the writer’s purpose must not be overlooked. As in Isaiah 6:3, Ter Sanctus is also sung by
celestial beings, the four living creatures, in the presence of God (Rev 4:6–8). The
similarities between these two passages strongly suggest that the writer’s intention is to
stress the holiness of God. The writer uses this acclamation to highlight God’s holiness
as the foundation of universal worship. The acclamation is followed by the description of
God as one “who was, who is and who is to come” (Rev 4:8)—a theme repeated throughout the book (Rev 1:4, 8, 14, 17, 18; 2:8). God’s eternal character implies his sovereign control
in human history. This twofold message of God’s holiness and sovereignty, laid out side by
side through the acclamation Ter Sanctus in a worship setting, helps to remind as well as
comfort the suffering readers who were undergoing persecution.
The other acclamation, “hallelujah,” is a Greek transliteration from the Hebrew
word halelu®a®h, meaning “praise [ye] the Lord.” In the OT it is found frequently in the
Psalter (e.g., Ps 104–6, 111–13, 115–17, 135, 146–50). The plural imperative form of the
verb indicates that the term was a directive to the worshiping congregation in the temple
and was meant to evoke a response. In the course of time it became an independent
exclamation of joy, so that the Greek-speaking Jews simply transliterated it (see LXX)
instead of translating it (Cabaniss 1970, 116). Although it is not found in other NT
writings, its presence in Revelation 19 testifies to its continual usage in the Jewish
communities and its adoption by Jewish Christians in the Diaspora as a joyful chant. Since
“hallelujah” is mentioned only here, the writer’s intention is also evident. In Revelation
19 “hallelujah” is placed at the last song of praise, shared by both celestial and human
beings in exuberant response to God’s sovereign judgment upon the evil (Rev 19:1, 3, 4)
and his final victory (Rev 19:6). Just as the Hebrew Psalter closes with God’s chosen
people singing “hallelujah” (Ps 150 ends with this word), the Apocalypse also closes with
the “hallelujah chorus,” inviting the readers to join. The book closes on a high note.
While reminding his readers to focus on God’s power and sovereignty, the writer skillfully
incorporates the familiar acclamation hallelujah to achieve his goal more effectively.
The frequent references to liturgical language in Revelation do not make it a
liturgical book, as some have overstated (e.g., Shepherd, Cabaniss, Piper, Vanni). Prayer
acclamations (Ter Sanctus and hallelujah) are selected and incorporated in strategic
locations to bring out a cohesive picture of victory and hope for the comfort and
encouragement of the readers as they are reminded of God’s holiness and sovereignty. Their presence in the book goes far beyond serving merely liturgical purposes.
2. Liturgical Elements in the Apostolic Fathers.
Around the turn of the first century of the Christian era, liturgical elements
were still a common literary element in letters. For example, benedictions were found
either at the beginning of a letter (1 Clem. 1; Pol. Phil.; Ign. Trall.; Ign. Rom.) or at
the close of a letter (1 Clem. 58, 59; Barn. 21; Ign. Eph. 21; Ign. Pol.; Ign. Smyrn. 12).
The expression of benediction as a wish-prayer for readers, however, is very flexible in
wording (esp. in Ignatius’s letters) and in length (e.g., 1 Clem. 58). Doxology is a more
fixed expression (mostly following the popular formula “to God be glory for ever and ever,
amen”; Diogn. 12; 1 Clem. 20, 32, 38; [except in Ign. Eph. 1, where the formula “blessed
be God” is employed]) and less restricted in location (e.g., 1 Clem.; doxologies are found
throughout the letter: 20, 32, 38, 43, 45, 50, 58 and 59). Therefore, while fixed formats
provide guidelines for expression, flexibility in wordings and usages is always allowed
and accepted.
Besides benediction and doxology, prayer acclamations such as “amen,” Ter Sanctus,
“hosanna” and “maranatha” are also attested in some of the early fathers’ writings,
indicating a continual usage of these acclamations in the later and postapostolic era. The
acclamation amen is always attached to the end of a doxology (1 Clem. 20, 32, 38, 58, 59)
or a letter (see Ign. Eph.; Ign. Pol.; also Ignatius’s letters to St. John and the Virgin
Mary) as a symbol of confirmation of the blessing uttered. In Didache 10.6 and Justin
Martyr’s Apology I 65, “amen” is explicitly an acclamation of consent to the leader’s
prayer at the eucharist. In other words, the liturgical usage of “amen” is quite fixed by
the end of the first century. The second acclamation, Ter Sanctus, is found in 1 Clement
34 and is considered a loose quotation of Isaiah 6:3 (van Unnik 1951, 247), warning the
readers against laziness and calling them to follow the example of angels in submitting to
God’s will. The emphasis there evidently is not directly related to God’s holiness as in
Revelation 4:8. Nevertheless, its allusion may reflect its regular usage in early church
worship (van Unnik 1951, 248).
A more significant use of prayer acclamations is found in Didache 10.6:
Let grace come and let this world pass away
Hosanna to the God of David
If any man is holy, let him come
If any be not, let him repent
Maranatha
Amen
The Sitz im Leben of this paragraph is generally acknowledged to be the Eucharist
(Audet, Jungmann, Cabaniss). It was recited antiphonally by the leaders and the
congregation. Apparently these three words were already familiar liturgical acclamations
employed in early church worship; thus no translation is deemed necessary. “Hosanna”
derives from two Hebrew elements: ho®sha{ and naœ}, meaning “save, please” and thus
signifying a cry for help (Ps 118:25). In the NT this word is only found in the Gospels in
the context of the triumphal entry (Mt 21:9; Mk 11:9, 10; Jn 12:13). Although the original
meaning of this word may have been familiar to the Jewish people in the Christian era, it
seems more likely that this acclamation had developed into an expression of exuberant joy
(Hart, Hawthorne, Brown, contra Werner, Pope), as indicated by the occasion and the manner in which this cry was expressed (also see Luke’s use of doxa in place of “hosanna” in Lk 19:38). In Didache 10.6 the utterance of “hosanna” in connection with God as the God of David (similar to the expression directed to Jesus at his triumphal entry) also supports the idea that it was understood by Jews and Gentiles in the Christian era to be an
expression of joy rather than a call for help or deliverance.
“Maranatha” is a Greek transliteration of an Aramaic word, marana} ta}, probably
denoting an imperative cry (“Our Lord, come!”) rather than a statement (“Our Lord has
come”; see DPL, Liturgical Elements, §5.3). It is most likely the earliest Christian
prayer (Cullmann, 13) and originated among Jewish Christians in Palestine or Syria as a
plea for the fulfillment of Christ’s eschatological Parousia (cf. Rev 22:20) as well as
for his immediate presence at the Lord’s table. This prayer is quickly and widely adopted
by Gentile Christians in the Diaspora (1 Cor 16:22) as a part of the eucharistic liturgy.
In Didache 10.6 “maranatha” is placed at the end of the antiphonal recitation followed by
the close of the eucharistic meal. It represents the congregation’s climactic hope. And by
adding the liturgical “amen” to it, the congregation is provided an opportunity to adopt
the prayer to themselves. Thus the order of arrangement of these three words in Didache
10.6 reflects the beliefs and practices of early Christians in their worship.
3. Conclusions.
The above study provides us some clearer understandings of the forms and functions
of liturgical elements in later canonical writings and the writings of early apostolic
fathers.
The presence of some liturgical elements in various NT writings and the allusion
to prayer acclamations such as “amen,” “hallelujah,” Ter Sanctus and “hosanna” without
translation or explanation testifies to the existence of certain fixed expressions and
worship formats (e.g., to commence a letter with introductory benediction and/or doxology and to close with benediction and/or doxology) that had already been adopted by scattered Christian communities in their corporate worship.
The inclusion of these liturgical elements, however, is selective according to the
genre of the letters and/or the themes of the writers. The absence of “Abba” in this group
of writings does not mean that “Abba” is not used or known outside the Pauline communities (Delling, 71). Similarly the inclusion of Ter Sanctus and “hallelujah” in the Apocalypse (Rev 4:8; 19:1, 3, 6) does not imply that these are elements unique to the Johannine circles.
In the light of diverse motifs or themes that were often added to the somewhat
fixed formulas, it is also clear that liturgical elements were still in the stage of
development. Doxologies and benedictions, while generally following similar formats, are
occasionally tailored to motifs in order to meet the specific needs of the readers or to
coincide with the overall message of the writers (see Jude 24–25 versus 2 Pet 3:18; Heb
13:20–21 versus 1 Pet 1:2). In this respect there is a solidarity between Paul and other
NT writers in their use of liturgical elements.
Liturgical language is still employed by early apostolic fathers in their writings
as a literary style and occasionally for didactic or polemic purpose. Nevertheless, the
forms and usages are comparatively fixed despite the fact that varieties are still
attested.
NT writers’ use of liturgical elements witnesses to a blend of form and freedom in
early church worship as well as literary works. Freedom must operate within the accepted
framework to ensure orderliness, whereas formality must also allow flexibility of
expression to guarantee meaningful practice—this is the essence of NT worship.
See also Baptism; Hymns, Songs; Lord’S Supper, Love Feast; Worship and Liturgy.
Bibliography. J.-P. Audet, La Didaché: Instructions des Apôtres (Paris: Gabalda,
1958); G. Bornkamm, “Das Bekenntnis im Hebräerbrief,” TBl 21 (1942) 56–66; P. F. Bradshaw, The Search for the Origins of Christian Worship (New York: Oxford University Press, 1992); S. P. Brock, “The Thrice-holy Hymn in the Liturgy,” Sobornost 7 (1985) 24–34; R. E. Brown, The Gospel of John (AB; Garden City, NY: Doubleday, 1970); A. Cabaniss, “Alleluia: A  Word and Its Effect” in Liturgy and Literature (Tuscaloosa, AL: University of Alabama Press, 1970) 114–21; idem, “A Note on the Liturgy of the Apocalypse,” Int 7 (1953) 78–85; idem, Pattern in Early Christian Worship (Macon, GA: Mercer University Press, 1989); J. D. Charles, Literary Strategy in the Epistle of Jude (London: Associated University Presses, 1993); A. Chester and R. P. Martin, The Theology of the Letters of James, Peter, and Jude (NTT; Cambridge: Cambridge University Press, 1994); O. Cullmann, Early Christian Worship (London: SCM, 1953); G. Delling, Worship in the New Testament (Philadelphia: Westminster, 1962); P. Fiedler, “Neues Testament und Liturgie,” Archiv für Liturgiewissenschaft 25 (1983) 207–32; H. Hart, “Hosanna in the Highest,” SJT 45 (1992) 283–301; G. F. Hawthorne, “Hosanna,” ISBE 2:761; J. A. Jungmann, The Mass (Collegeville, MN: Liturgical Press, 1976); W. Lane, Hebrews (WBC; Dallas: Word, 1991); H. Lietzmann, Mass and Lord’s Supper: A Study in the History of the Liturgy (Leiden: E. J. Brill, 1979); A. MacDonald, Christian Worship in the Primitive Church (Edinburgh: T & T Clark, 1934); O. Michel, “(,” TDNT 5:199–220; C. F. D. Moule, Worship in the New Testament (London: Lutterworth, 1961); O. A. Piper, “The Apocalypse of John and the Liturgy of the Ancient Church,” CH 20 (1951) 10–22; M. H. Pope, “Hosanna: What It Really Means,” Bible Review (1988) 16–25; J. M. Ross, “Amen,” ExpT 102 (1991) 166–71; B. D. Spinks, The Sanctus in the Eucharistic Prayer (Cambridge: Cambridge University Press, 1991); S. Schulz, “Maranatha und Kyrios Jesus,” ZNW 53 (1962) 138; D. E. Smith and N. H. Tauffig, Many Tables: The Eucharist in New Testament and Liturgy Today (London: SCM, 1990); K. Trudinger, “Amen, Rev. 3:14 . . . ,” NovT 14 (1972) 277–79; W. C. van Unnik, “1 Clement and the ‘Sanctus,’” VC 5 (1951): 204–48; idem, “Dominus Vobiscum: The Background of A Liturgical Formula” in New Testament
Essays: Studies in Memory of Thomas Walter Manson, ed. A. J. B. Higgins (Manchester:
Manchester University Press, 1959) 270–305; U. Vanni, “Liturgical Dialogue as a Literary
Form in the Book of Revelation,” NTS 37 (1991) 348–72; G. Wainwright, “The Praise of God in the Theological Reflection of the Church,” Int 39 (1985) 34–45; N. Walker, “The Origin of the ‘Thrice-holy’,” NTS 5 (1958–59) 132–33; E. Werner, “‘Hosanna’ in the Gospels,” JBL 65 (1946) 97–122; C. Westermann, Praise and Lament in the Psalms (Atlanta: John Knox, 1981); R. B. Williams, “Liturgy and the New Testament,” Worship 42 (1968) 450–65.

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Excerpts from “Confessions of a Doe” by St. Justin Popovich

I have heard there are demons. Can those be worse than men?

…Between you, men, and us there gapes a broad abyss, and neither can we ever come to you, nor you to us. You do not have a sense for our worlds. If we, does, were to come over to your side with our heart, it would be as if we entered hell. Time ago, we used to be in paradise. But you, humans, turned that into hell for us. What for you the demons are, you, the humans, are the same for us. The birch-trees told us: “we saw where Satan fell from heaven onto earth; he fell among men, and he has remained there. He, the outcast of heaven, proclaimed: the pleasantest place for me is among men, and I too have my paradise, and this is them: the humans…

You men knowingly and voluntarily embrace sin, evil, and death, and in so doing drag us, without our consent, into them through your vileness and malice, for you had power over us, and so you shall account for us: for all our anguish, misfortunes, sufferings and death.

…I listened to the azure sky whispering to the black earth this eternal truth: on Judgment Day men shall have account for all anguish, for all sufferings, for all miseries, for all deaths of the earthly beings and creatures. All animals, all birds, all plants shall stand up and charge against the human race all pains, all insults, all evil, and every death men have inflicted on them in their proud love of sin. Because, coming along with the human race -both in front and after it -are sin, death, and hell.

Were I to choose from among all creatures, I would prefer a tiger to man, for not being as bloodthirsty as man; I would also prefer a lion to man, for not being as ferocious as man; and also I would prefer a hyena to man, for being less disgusting than man; I would prefer the lynx, too, to man, for not being as fierce as man; would prefer a snake, too, to man, for not being as cunning as man. I would rather prefer any monster to man, for even the most terrible monster is not as scary as man… O, I do speak the truth, and I speak from the bottom of my heart. Was it not man who invented and created sin, death, and hell? And that is far worse than the worst, more monstrous by far than the most monstrous, and more terrible than the most terrible thing ever in all my worlds.

I overheard the brook of tears warbling: “People boast of intelligence, their reason. I judge them for their major deeds: sin, evil, and death. And here is the conclusion I reach: if their creation of sin, evil, and death, is a function of their intelligence then that is no gift but a curse. Intelligence that lives and expresses itself through sin evil and death is a punishment from God. A great intelligence is also a great punishment. They would insult me were they to tell me I had reason as man. If reason is the only distinction of man then I not only renounce it but also damn it. Were my paradise and my immortality dependent on it then unto the ages I would have renounced both paradise and immortality. Without goodness intelligence is a punishment of God. And the great reasoning power without great goodness is an unbearable damnation. With intelligence, but without goodness and tenderness, man is a perfect devil. From the angels of heaven I have heard -while they were washing their wings in my tears, the devil is a great intelligence without a drop of goodness and love. Man too, is the same, if there is no goodness and love in him. An intelligent man -but one without goodness and compassion, is hell for my tender soul, hell for may sad heart, hell for my good-natured eyes, hell for my meek nature. My soul strives after one single yearning: that I would never live in this world or in the next, side by side with a man intelligent, but deprived of goodness and of compassionate tenderness. Otherwise, destroy me, O God, and convert me to non-being! -St. Justin Popovich, “A Doe in Paradise Lost: Confession of a Doe.”

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The Laws of Thought: A Short Historiography of a Paradigm in Transition

From James Danaher, “The Laws of Thought,” The Philosopher, Volume LXXXXII No. 1.

Western philosophy to a very large extent has been founded upon laws of thought. We believe that our thinking should strive to eliminate ideas that are vague, contradictory, or ambiguous, and the best way to accomplish this, and thereby ground our thinking in clear and distinct ideas, is to strictly follow laws of thought. Ones like:

The law of identity (A=A),
The law of non-contradiction (A does not equal ~A), and
The law of the excluded middle (either A or not A but not both A and ~A).

In spite of how dominant these laws of thought have been, they have not been without their critics, and philosophers from Heraclitus to Hegel have leveled powerful arguments against them. But the issue does not seem to be whether the laws are applicable or not, but where and when are they applicable? Certainly, the laws of thought have a place, but what is that place?

Both the laws, as well as opposition to them, can be traced to the Pre-Socratic philosophers. It was Parmenides who first formulated the law of non-contradiction. “Never will this prevail, that what is not is.”

Plato also refers to this in the Sophist: “The great Parmenides from beginning to end testified . . . “Never shall this be proved – that things that are not are.”” (Plato, Sophist, 237A)

It may seem strange that the principle of non-contradiction was not part of a natural way of thinking that had its origins deep in our prehistory, but rather was introduced by Parmenides in the 5th century B.C. Even more surprising is the fact that Parmenides’ law of non-contradiction represented a radical break from the Ionian philosophy of nature which preceded it. The Ionian philosophy was based on observation or experience in the ordinary sense. On the basis of such experience, Heraclitus argued that contradictions not only existed but were essential and the basis of a thing’s identity:

“Not only could it be stated that identity is the strife of oppositions but that there could be no identity without such strife within the entity.”

Heraclitus argued that since things changed, they had to contain what they were not. Only such contradictions could account for change. As Heraclitus says, “Cold things grow warm; warm grows cold; wet grows dry; parched grows moist.”

In direct opposition to Heraclitus, Parmenides claimed that identity involved the idea of non-contradiction. What made for the difference between Heraclitus and Parmenides was what they respectively believed were the proper objects of thought. For Parmenides, the things we encounter in our experience make for poor objects upon which to fix our thoughts. Indeed, the things we experience are not suited to provide the kind of knowledge that Parmenides, and so many others who were to follow him, wanted. The kind of knowledge they desired was a knowledge that was fixed and certain. Such knowledge would require objects of thought that were equally fixed and certain. Thus, Parmenides settled on the idea of being itself into which all change would collapse.

The Pythagoreans too desired objects of thought that were fixed and certain. For them, mathematics provided those kinds of objects. Plato too sought similar objects of thought and settled on otherworldly forms that were eternal and immutable. With the Platonic forms, as with Pythagorian numbers and Parmenidian being, the laws of thought are certainly applicable. Thus, Plato endorsed the laws of non-contradiction and excluded middle in the Republic when he has Socrates say,

“It is obvious that the same thing will never do or suffer opposites in the same respect in relation to the same thing and at the same time.” (4:436b)

Of course, Plato was well aware that in order for the laws of thought to work they needed to be restricted, for if left unrestricted they could lead to absurd conclusions. In the Euthydemus, Euthydemus’ brother Dionysodorus argues that Socrates must be the father of a dog, since the dog had a father, and Socrates has admitted that he is a father (298d-299). Since one cannot be a father and not be a father at the same time, Socrates must be the father of the dog. Although Socrates is obviously not the father of the dog, it was not so obvious in Socrates’ day where Dionysidorus’ thinking went wrong. Thus, Plato attempts to sort out where and when the laws of thought apply and where and when they do not apply.

The restrictions Plato places on the laws of thought (i.e., “in the same respect,” and “at the same time,”) are an attempt to isolate the object of thought by removing it from all other time but the present and all respects but one. Thus, although we are involved in many relationships, when we think about ourselves relationally, we must restrict our thinking to one relationship, at one time, in order for the laws of thought to be applicable. Thus, it is not only the Platonic forms that are abstract and apart from the world of experience, but any idea to which the laws of thought are to be applied must also be abstracted from the reality of our experience which is multi-relational and multi-temporal.

Like Plato, Aristotle also believed that the laws of thought, in spite of being controversial, were cornerstones of all right thinking. He argues for them in several places (Metaphysics G, 3&4; De Interpretatione 11, 21a32-33; Topics IV 1, 121a22-4; Sophistical Refutations 5, 167a1-6). It is, however, not so much that he argues for them as he sets them in a proper light. That is, he shows were they are appropriate and where they are not appropriate. Basically, what he says is little different from Plato. He argues that such laws apply only to attributes and attributes at a particular time and in a particular respect.

“The same attribute cannot at the same time belong and not belong to the same subject and in the same respect” (Metaphysics G, 3,1005b18-20).

By limiting the laws of thought in this way, Aristotle overcomes Heraclitus’ claim that identity contains contradictions because the attributes of a thing change over time. By isolating identity in one moment of time, Aristotle abstracts the objects of thought just as Plato had done. Thus, identity is set in a different light than it had been for Heraclitus who understood identity as dynamic and thus involving change and equally contradictions.

But Aristotle also introduces another element to further support the laws of thought. The principle he introduces concerns the way we formulate our concepts or ideas of kinds. According to Aristotle, our idea of a kind or species is best conceptualized by uniting the genus of a species with its differentia or the characteristic that differentiates that species from the other members of the genus (Metaphysics VII. 12. 8-40 and Post. Analytics II. 13). To establish a clear concept of the species “man,” we combine the genus “animal” and the differentia or that characteristic which distinguishes man from other animals * for example, that he is rational. Thus, the species “man” is conceptualized as, “rational animal.” It may be true that our clearest concepts are those which proceed from, and are members of, a single genus. Our desire for clear and distinct concepts has made Aristotle’s model for conceptualizing species enormously influential in Western thinking. In biology we classify and understand species under a single lineage whereby each concept or idea of a species belongs to only one genus. Every family of living things belongs to only one order, and every order belongs to only one class, and every class to only one phylum and kingdom. Such ordering gives us neat and clear concepts and satisfies our desire to conceptualize things in as simple and clear a way as possible. But the platypus does not fit neatly into a single genus or more precisely into the class designated as “mammal.” In fact, many species do not seem to fit such a neat Aristotelian model, and might better be conceived if we understood them to belong to more than a single genus.

This Aristotelian model for conceptualizing species has not only been applied to biological species, but we attempt to organize all of our experience in a similar fashion. In spite of the fact that many of our concepts might be better conceived if we understood them as descending from multiple genuses, the Aristotelian model of concepts which descend from a single genus is deeply entrenched in our thinking. One of the reasons behind its entrenchment is that such a principle allows the laws of thought to work consistently and appear universal. On another model in which concepts are thought to descend from multiple genuses, the laws of thought are not as applicable because, as a member of more than a single genus, a concept could contain contradictory attributes.

MATERIALISM AND THE CORPUSCULAR PHILOSOPHY
With the modern era, a mechanical view of the universe replaced Aristotle’s biological paradigm. With such a model, things were no longer organic wholes but composites of parts and, as such, more compatible with an analytic way of thinking that broke things down into ever smaller parts until all contradictions disappear, and the laws of thought prevailed. Basic to this mechanical view known as the corpuscular philosophy, was an apparent distinction between the kinds of qualities that we attribute to physical entities. Qualities such as shape, extension, motion, etc. were thought to exist within the objects themselves, while tastes, smells, colors, etc. were said to exist within us. The former kind were referred to as ‘primary’ and the latter kind ‘secondary’ (Essay Concerning Human Understanding, II. viii. 17).

The explanation the corpuscularians offered was that these secondary qualities were produced in us by the arrangement and motion of the insensible corpuscles which were made up of primary qualities and constituted the internal structure of a thing. So a physical thing like a strawberry, while not actually possessing anything that resembles the taste or smell of the strawberry, does have the power to produce those sensations within us because of the arrangement and motion of the insensible corpuscles that make up the strawberry’s internal structure. By contrast, when we perceive that the strawberry is extended, we are perceiving a quality that represents the thing itself, since the strawberry is made up of corpuscles and corpuscles are extended.

Thus, the claim of the corpuscularians was that primary qualities were more real than secondary qualities. Of course, what is meant by “more real” is that primary qualities seem to be more objective than the subjective, secondary qualities. But why should we privilege the objective over the subjective? One reason, perhaps the most important reason, is that the laws of thought are more applicable when subjectivity is removed. Subjectivity certainly undermines the laws of thought. While a thing can be sweet and not sweet at the same time, it cannot not be square and round nor in motion and at rest at the same time. Consequently, primary qualities make better objects of thought in the sense that the laws of thought better apply with them than with secondary qualities. What has in fact taken place, however, is that the objects of thought have been made ever more abstract and removed from the reality of the world we actually experience.

The idea of primary qualities, like the objects of mathematics, Plato’s otherworldly forms, or Aristotle’s idea of species that are members of single genuses, are enormously abstract and artificial notions and not like anything we actually experience. The pure objectivity of primary qualities is something we create rather than experience and we create it for the sake of having clear and distinct objects of thought to which the laws of thought might be consistently applicable. By the 18th and 19th centuries, such abstract notions of objectivity would come under attack from a phenomenological perspective which would take up the Herclitian theme and argue that the phenomenal world of experience is more real than the abstract world we have come to think about.

PHENOMENALISM
Berkeley’s phenomenalism privileged the world of experience over the abstract world of objective matter which the corpuscularians had introduced. Berkeley thought that abstract ideas of any kind were inconceivable (Principles of Human Knowledge, sect. 5), and that primary and secondary qualities were inseparably joined in the phenomenal world and could not be separated even in thought.

“I desire anyone to reflect and try, whether he can by any abstraction of thought, conceive the extension and motion of a body, without all other sensible qualities. . . extension, figure, and motion, abstracted from all other qualities, are inconceivable.”

(Principles of Human Knowledge, sect. 10)

For whatever reason, Berkeley did not explore the consequence of his phenomenalism upon the laws of thought. Hegel, however, certainly did. Like Berkeley, Hegel’s phenomenalism attacks the idea of abstraction, but Hegel seems to have had more of an understanding of how much the idea of abstraction was at the very base of traditional logic and metaphysics. Hegel seems to understand that the focus of traditional logic was to make “abstract identity its principle and to try to apprehend the objects of reason by the abstract and finite categories of the understanding.”

By so doing, traditional logic secured a realm over which the laws of thought could sovereignly rule. Once proper objects of thought have been created through abstraction, the laws of thought certainly apply. Hegel would argue, however, that these laws of thought do not apply when the objects of thought are not such abstract entities. Thus, the laws of thought do not universally rule over all thinking but are only universal when the objects of thought are abstracted from the reality of the phenomenal world. If we turn our attention upon the world of experience, “everything is inherently contradictory.” Thus, Hegel posits the law of contradiction, rather than the law of non-contradiction.

As it was for Heraclitus, reality for Hegel is something that moves, thus making any fixed, abstract identity impossible. Things are always becoming and so they must contain within themselves that which they are not. Contradiction is the root of all movement and vitality; it is only in so far as something has a contradiction within it that it moves, has an urge and activity.

A little later, he says something that is even more shocking to those who strictly adhere to the traditional laws of thought and imagine them to be the basis of all right thinking. “Something moves, not because at one moment it is here and at another there, but because at one and the same moment it is here and not here, because in this “here”, it at once is and is not.” This is an obvious contradiction, and the laws of thought would say that something cannot be here and not here at the same time. Of course, what is behind Hegel’s statement is the matter of how we conceive of time. If we think of time and motion analytically, and the continuum of time moves from one fixed, analyzable point to another (i.e., t1, t2, t3 . . . ), thus constituting a present or here, then Hegel is certainly wrong. If that is the case, then something is here (e.g., t4) and not any other place. If, however, there are no fixed points on the continuum that is time, and time is continually moving, then it cannot be stopped and analyzed without making it something other than what it is. If the nature of time, like motion, defies arrest, then Hegel is right and analytic thinking is not suited to understand such things. To think of time as an ongoing continuum forces us to think contrary to the laws of non-contradiction and excluded middle, and understand that something is both here and not here at the same moment.

If motion defies the traditional laws of thought, then all living things violate the laws of thought in so far as they are in constant motion * not in the sense that they experience constant local motion but in the sense that all living things experience perpetual internal motion. This internal motion of all living things prevents them from having any fixed, analyzable point of identity.

“Abstract self-identity is not as yet a livingness…. Something is therefore alive only in so far as it contains contradictions within it.”

Hegel even attacks the law of identity and claims that the law of identity says very little in itself. The fact that A = A is no more than a tautology and has little meaning. It tells us almost nothing about the identity of a thing. The only way a thing truly takes on identity is through its otherness or what it is not. What a thing is not is as necessary to the identity of a thing as what it is in that what it is not is what gives boundaries, definition, and meaning to a thing. Thus, its otherness must be contained within the very identity of the thing.

What is at the base of all that Hegel has to say is a logic that is synthetic rather than analytic. With a synthetic logic which joins things into ever greater wholes rather than analyzing them into ever smaller parts, the laws of thought are not the universal principles they are with analytic thinking. With a synthetic logic that examines wholes rather than parts, contradictions are natural and to be expected. The way to eliminate contradictions is to employ an analytic logic which divides things into ever smaller parts until the contradiction disappears. When Plato and Aristotle qualify the law of non-contradiction and say “in the same respect,” and “at the same time,” what they are doing is breaking a thing down into its parts. If we focus on ever smaller parts, we can eventually eliminate all contradictions and thus preserve the law of non-contradiction and the law of the excluded middle. When, however, we deal with the whole, rather than the parts, we are treating all the respects or parts together and then we certainly may encounter contradictions and the truth is often both/and rather than either/or.

When we say that life is full of joy and sorrow, we can eliminate that contradiction, or any such contradiction, by analyzing life and dividing it into joyous parts and sorrowful parts. That is, in one respect, it is joyous and in another respect it is sorrowful. If, however, we leave life (or anything else) whole and do not analyze it into this respect or that respect, we see myriads of contradictions because that is the nature of the reality in which we live. We have been taught to think analytically about abstracted parts of our experience in order that the laws of thought can be neatly applied, but that is only one way of thinking. We can also think about wholes rather than parts and when we do, the laws of thought do not always apply.

This does not mean that there is no place for analytic thinking and the laws of thought. Analytic thinking is a mode of thought we use all the time. The problem lies in the fact that Western intellectual history has been intent upon creating an understanding that is founded upon universal laws, and, in order to create such universal laws, we have attempted to eliminate all objects of thought to which such laws do not universally apply. This, however, is irrational since there obviously are dynamic and holistic objects of thought to which the laws of thought do not universally apply.

Twentieth century science has discovered the bicameral nature of the human brain, and although pop psychology might be too quick to draw hard and fast lines between the two hemispheres of the brain and assigns analytic thought to the one and synthetic thought to the other, there certainly is something to the fact that the physiology of our brains allow us to think in different ways. Analytic thinking, based upon one hemisphere of the brain, has dominated in the West. Thus, it is no wonder that the laws of thought seem so absolute to so many.

But to strictly apply the laws of thought to all of our thinking is perhaps to use only half our wits.   James Danaher, “The Laws of Thought,” The Philosopher, Volume LXXXXII

Illustrations are by M. C. Escher.

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The Paradoxical Justice of God (St. Isaac the Syrian, Homily 60)

“The watchfulness of discernment is superior to every discipline of men accomplished in any way to any degree. Do not hate the sinner. For we are all laden with guilt. If for the sake of God you are moved to oppose him, weep over him. Why do you hate him? Hate his sins and pray for him, that you may imitate Christ Who was not wroth with sinners, but interceded for them. Do you not see how He wept over Jerusalem? We are mocked by the devil in many instances, so why should we hate the man who is mocked by him who mocks us also? Why, O man, do you hate the sinner? Could it be because he is not so righteous as you? But where is your righteousness when you have no love? Why do you not shed tears over him? But you persecute him. In ignorance some are moved with anger, presuming themselves to be discerners of the works of sinners.

“Be a herald of God’s goodness, for God rules over you, unworthy though you are; for although your debt to Him is so great, yet He is not seen exacting payment from you, and from the small works you do, He bestows great rewards upon you. Do not call God just, for His justice is not manifest in the things concerning you. And if David calls Him just and upright (cf. Ps. 24:8, 144:17), His Son revealed to us that He is good and kind. ‘He is good,’ He says, ‘to the evil and to the impious’ (cf. Luke 6:35). How can you call God just when you come across the Scriptural passage on the wage given to the workers? ‘Friend, I do thee no wrong: I will give unto this last even as unto thee. Is thine eye evil because I am good?’ (Matt. 20:12-15). How can a man call God just when he comes across the passage on the prodigal son who wasted his wealth with riotous living, how for the compunction alone which he showed, the father ran and fell upon his neck and gave him authority over all his wealth? (Luke 15:11 ff.). None other but His very Son said these things concerning Him, lest we doubt it; and thus He bare witness concerning Him. Where, then, is God’s justice, for whilst we are sinners Christ died for us! (cf. Rom. 5:8). But if here He is merciful, we may believe that He will not change.

“Far be it that we should ever think such an iniquity that God could become unmerciful! For the property of Divinity does not change as do mortals. God does not acquire something which He does not have, nor lose what He has, nor supplement what He does have, as do created beings. But what God has from the beginning, He will have and has until the end, as the blest Cyril wrote in his commentary on Genesis. Fear God, he says, out of love for Him, and not for the austere name that He has been given. Love Him as you ought to love Him; not for what He will give you in the future, but for what we have received, and for this world alone which He has created for us. Who is the man that can repay Him? Where is His repayment to be found in our works? Who persuaded Him in the beginning to bring us into being Who intercedes for us before Him, when we shall possess no  memory, as though we never existed? Who will awake this our body for that life? Again, whence descends the notion of knowledge into dust? O the wondrous mercy of God! O the astonishment at the bounty of our God and Creator! O might for which all is possible! O the immeasurable goodness that brings our nature again, sinners though we be, to His regeneration and rest! Who is sufficient to glorify Him? He raises up the transgressor and blasphemer, he renews dust unendowed with reason, making it rational and comprehending and the scattered and insensible dust and the scattered senses He makes a rational nature worthy of thought. The sinner is unable to comprehend the grace of His resurrection. Where is gehenna, that can afflict us? Where is perdition, that terrifies us in many ways and quenches the joy of His love? And what is gehenna as compared with the grace of His resurrection, when He will raise us from Hades and cause our corruptible nature to be clad in incorruption, and raise up in glory him that has fallen into Hades?

“Come, men of discernment, and be filled with wonder! Whose mind is sufficiently wise and marvelous to wonder worthily at the bounty of our Creator? His recompense of sinners is, that instead of a just recompense, He rewards them with resurrection, and instead of those bodies with which they trampled upon His law, He enrobes them with perfect glory and incorruption. That grace whereby we are resurrected after we have sinned is greater than the grace which brought us into being when we were not. Glory be to Thine immeasurable grace, O Lord! Behold, Lord, the waves of Thy grace close my mouth with silence, and there is not a thought left in me before the face of Thy thanksgiving. What mouths can confess Thy praise, O good King, Thou Who lovest our life? Glory be to Thee for the two worlds which Thou hast created for our growth and delight, leading us by all things which Thou didst fashion to the knowledge of Thy glory, from now and unto the ages. Amen.

-St. Isaac the Syrian, Homily 60.

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Freud’s Critique of Religion

Sigmund Freud

The thesis of God as a “father-wish” originated with the publication of Sigmund Freud’s main critique of religion, The Future of an Illusion (1927). This thesis has been widely discussed and analyzed; only some highlights will be reproduced here.

1. It is impossible to deny that “wishing for God” is a perennially recurrent phenomenon; even atheist Friedrich Nietzsche displayed this tendency: “I hold up before myself the images of Dante and Spinoza, who were better at accepting the lot of solitude… [and] all those who somehow still had a “God” for company… My life now consists in the wish that it might be otherwise… and that somebody might make my “truths” appear incredible to me” (Kaufmann, trans., The Portable Nietzsche, p. 441).

2. The deductive argument for atheism from Freudian Illusion Theory may be pronounced effectively dead, reduced in current thought to an instance of the genetic fallacy (the claim something is false merely by virtue of its ostensible origin). Something is not ipso facto illusory merely because it is wished for, but only if it is a mere wish. As Hans Kung observes:

“…is a faith bad and its truth dubious simply because –like psychoanalysis itself– it also involves all possible instinctual inclinations, lustful inclinations, psychodynamic mechanisms, conscious and unconscious wishes? …Perhaps this being of our longing and dreams does actually exist… the psychological interpretation of belief in God is possible and also legitimate. But is the psychic aspect itself the whole of religion? It should be observed that Freud has not in fact destroyed or refuted religious ideas in principle, and neither atheists nor theologians should ever have read this into his critique of religion. For, by its very nature, psychological interpretation alone cannot penetrate to the absolutely final or first reality: on this point it must remain neutral in principle. From the psychological standpoint, then, the question of the existence of God –and even the positive force of the argument must not be exaggerated- must remain open.” -Hans Kung, Does God Exist, p. 302

3. The God of Judaism and Christianity is as much an *anti-wish* as he is a wish. If it were not so there would be no human sin. Frequently God is precisely what no one wanted, or would be likely to want; he frequently demanded, and does demand, precisely the opposite of what any sane person would have placed on their wish list. It is not hard to imagine Abraham saying “You want me to cut off what part of my body?!” “You want me to kill my son Isaac?! The one you promised to bless the whole world through?!” Jeremiah had absolutely no desire to preach. Jeremiah’s audience had absolutely no desire to hear. God was not what anyone wanted; he was what everyone didn’t want. If Dietrich Bonhoeffer was correct in saying “When Christ calls a man, he bids him come and die” (Bonhoeffer, The Cost of Discipleship), that is precisely what no one wants unreservedly. C. S. Lewis was mortified when he became a Christian; it was the last thing he ever wanted to be; he describes himself as having entered the kingdom of God “kicking and screaming.” Similarly once upon a time the last thing I ever wanted was to become a Christian. It seemed silly and false to me. Yet I have found it to be a pearl of great price…

4. Not only the existence of God, but also the rejection of God, or the rejection of a particular kind of God, can have a psychological origin in wishes. Mircea Eliade brilliantly articulated the nature of Freudian ideology as a cultural fashion:

“…a cultural fashion is immensely significant, no matter what its objective value may be; the success of certain ideas or ideologies reveals to us the spiritual and existential situation of all those for whom these ideas or ideologies constitute a kind of soteriology” (Mircea Eliade, Occultism, Witchcraft, and Cultural Fashions: Essays in Comparative Religion, p. 5).

Thomas Paine’s opposition to the ancien régime in France, for example, undoubtedly gave additional impetus to his desire to assault the Christian faith so virulently. Professor Eliade’s observation clearly suggests the alternate possibility, from a Christian point of view, of:

5. A Christian Psychology of Atheism. Fr. Andrew Angiorus presents a Christian view of this whole question:

“‘Therefore God gave them over in the sinful desires of their hearts’ (Rom 1:24). Generally, atheists and agnostics are talking about themselves when they talk about the absence of God. They simply express their personal subjective truth (that their souls are empty) in an objective way and try to generalize their experience. In other words, there is no theology, or even philosophy here, it is just their own ill or deficient psychology, which is what atheism is… In the Scriptures Christ says clearly that only the pure in heart will see God. In other words, intellectuals, examiners and professors will never understand God, if their minds are not pure… How do we know if someone has a pure heart? The pure heart is evidenced by the way we live. As Peter says, a person devoted to the Lord “does not live the rest of his earthly life for evil human desires, but rather for the will of God” (1 Peter 4:2); “Who may ascend the hill of the LORD? Who may stand in his holy place? He who has clean hands and a pure heart, who does not lift up his soul to an idol or swear by what is false. He will receive blessing from the LORD and vindication from God his Savior” (Ps 24:3-5).” +Fr. Andrew Anglorus

Cf. also the extensive documentation by Paul Vitz of New York University of socio-psychological correlates to affirmation of atheism in Vitz, Paul, The Faith of the Fatherless.

© 2011 by katachriston.wordpress.com (text)

Posted in Philosophy, Philosophy of Religion, Psychology, Psychology of Religion, Theology | Tagged , , , , , | 3 Comments

Prof. Danny Shectman Receives Nobel Prize for New “Impossible” Form of Matter: Infinitely Variegated Quasicrystals

the image

Quasicrystals (cornell.edu)

He was fired by two time Nobel Prize winner Linus Pauling. As of today he is the recipient of his own Nobel Prize for defending the very “impossible” form of matter he was fired over. His story of ridicule, ostracism, hostility, and rejection by the mainstream scientific community for affirming something anomalous/discordant to the predominant scientific paradigm reads like something straight out of Thomas Kuhn’s The Structure of Scientific Revolutions. But he was right! The scientifically impossible in this case was not only possible, it was actual.

“For a couple of years I was alone, I was ridiculed, I was treated badly by my peers and my colleagues, and the head of my laboratory [two-time Nobel Prize recipient Linus Pauling] came to me smiling sheepishly and he put a book on my desk and said ‘Danny, why don’t you read this and see that it is impossible, what you are saying.’ And I said, ‘I teach this book… I know what it says, and I know it’s impossible, but here it is! This is something new!’ That person expelled me from his group  He said ‘you are a disgrace to our group; I cannot bear this disgrace,’ and he asked me to leave the group. So I left the group. And he was a good friend of mine! But he could not stand that people would say ‘this nonsense came from your group!’ This was the atmosphere. People not only did not believe in what I said: people were hostile! The community of non-believers was very large in the beginning. In fact it included everybody! The leader of the group was Linus Pauling, a two-time Nobel laureate. He was a very important figure, and the idol of the American Chemical Society, and to his last day he was standing on stages and publishing papers saying that Danny Shechtman is talking nonsense.

the image

Hologram of a Quasicrystal (esrf.edu)

“Two years later I came back to Technion, and here I met professor Ilan Blech who was the first person to believe in my observations, and we linked forces and he proposed a physical model that explains how these crystals could form. And the two of us for publication in a journal, the Journal of Applied Physics, and the paper was rejected on the grounds that it would not interest the community of physicists. And so that summer of 1984 I went back to NBS and met another colleague of mind, John Cahn who was the chief scientist there. Then he invited another scientist, from France named Denny Gratius, and the four of us published another paper (D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “A Metallic Phase with Long Ranged Orientational Order and No Translational Symmetry”), which was published very quickly, and then hell broke loose, because it did interest the community, and many scientists around the world started to work on these materials, and they called me from around the world: ‘I have it! I have it! I have it too!’” And so the community of believers grew, slowly; the community of unbelievers shrunk. The new form of matter which had different symmetries than known before, which is called quasi-periodic crystals, or in short quasicrystals, is accepted into the community of crystal. So the definition of crystals was broadened to include crystals which were not known before.” -Dan Shechtman

Penrose Tiling

Penrose Tiling (geom.uiuc.edu)

The Geometric pattern of Penrose tiling which occurs physically in quasicrystals was completely unknown even to mathematicians until the 1970s when it was presented as a mathematical model by Roger Penrose. As the tiling pattern expands over larger ratios it converges to the ever present Fibonacci/Golden Ratio known as phi[1] intrinsic to a vast swath of diverse yet similar structures including spiral galaxies, snowflakes, neural connections, flowers, electromagnetic field borders, circulatory and pulmonary structure, basic chemical arrangements (tetrahedron, icosahedron, etc.), and so on (see my article Fibonacci, Fractals, and Inorganic Teleology for further details and implications).

Decagonal Quasicrystal

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[1] “For icosahedral quasicrystals [see image below], each approximant may be characterized by a rational approximant T,, = Fn,+1/Fn (Fn is a Fibonacci number) to the golden mean T. As TnT the lattice constants and the number of atoms contained in a lmit cell tend to infinity. The lattice constant of an nth order cubic approximant to an icosahedral quasicrystal may be expressed where aqc is a quasilattice constant – the edge of the golden rhombohedral tile. Each next approximant therefore has a lattice constant that is approximately 1.62 times larger. The volume of the next approximant, and correspondingly also the number of atoms in the unit cell, increase by a factor of T^3 = approximately 4.24. In practice, a third or fourth generation approximant is essentially indistinguishable from the infinite quasicrystal” (J. B. Suck, Michael Schreiber, Peter Häussler, Quasicrystals: An Introduction to Structure, Physical Properties, and Applications, p. 397).

Icosahedral Quasicrystal

http://i.imgur.com/RltGJ.png

Continue to Fibonacci, Fractals, and Inorganic Teleology

Posted in Philosophy of Science, Science | 2 Comments