Complete Incompleteness

The materialists hold to the opinion that the world of nature is complete. The divine philosophers declare that the world of nature is incomplete. There is a wide difference between the two. The materialists call attention to the perfection of nature, the sun, moon and stars, the trees in their adornment, the whole earth and the sea—even unimportant phenomena revealing the most perfect symmetry. The divine philosophers deny this seeming perfection and completeness in nature's kingdom, even though admitting the beauty of its scenes and aspects and acknowledging the irresistible cosmic forces which control the colossal suns and planets. They hold that while nature seems perfect, it is, nevertheless, imperfect because it has need of intelligence and education. In proof of this they say that man, though he be a very god in the realm of material creation, is himself in need of an educator. Man undeveloped by education is savage, animalistic, brutal.  Laws and regulations, schools, colleges and universities have for their purpose the training of man and his uplift from the dark borderland of the animal kingdom.

    (Abdu'l-Baha, The Promulgation of Universal Peace, p. 329)

The whole or transcendent is immanent in every part.  Thus formal cause, which is environmental cause, when it is glimpsed through the interstices of being and thought, is the appearance of the whole behind the flux of its moving parts, a quick perception of the coordinating principle itself, the one organizing its manifold appearances.  Because the whole is immanent in all the parts, in any closed, formal, finite system, everything is both self-referential and each element refers to all others.  The universe is like a hologram, each part of it, no matter how small, reflects every other part simultaneously. For, the basic substance of the universe is the qualities of God and these are everywhere and in everything, each with its own frequency, each diffused throughout the entire creation.  There are the particle/wave states of the subatomic energy packets, each individualized particle holds all the qualities of the universe but its defining character, what makes each particle itself and not any other, is one of these qualities.  Wave and the particle are complementary states of the photon, both its focal point and the energy pulsing in waves out from it: wave and particle are the same yet different, neither is separate from its medium but, rather, different manifestations of it.  

Said another way, all the qualities of the higher, which is the same as the essential, are diffused throughout the lower, so that the lower is the generalized version of what is altogether in the higher order reality—all the qualities of God are in each of His Manifestations and in all of Them; all the qualities of the Manifestations are in every soul and in humanity; all the qualities of man are in Nature, for each is made in the image and likeness but not the nature of the higher order reality.  But a part of the essence of the higher reality is within the lower order reality.  Baha’u’llah, speaking of the creation of man, writes: “With the hands of power I made thee and with the fingers of strength I created thee; and within thee have I placed the essence of My light.” (The Arabic Hidden Words #12)

 The higher aspect within a lower system is its essence, center and pivot.  It is what completes the lower order reality as a structure of being, and what drives it toward ever more complex manifestations of its qualities for it brings higher order energy and intelligence into the lower order system.  The Yin/Yang symbol is a useful but not quite accurate picture of what I mean.

The whole of the spiritual world surrounding the creational world manifests in a focal point, a Manifestation, Who appears at its “mid-most heart” and radiates out via His Words the powers of that spiritual world to transform this lower one.  This relationship is a universal law: “When ye consider this matter with care, it will become apparent that this is according to a universal law, which one can find at work in all things: the whole attracteth the part, and in the circle, the centre is the pivot of the compasses.  Ponder thou upon the Spirit: because He was the focal centre of spiritual power, the wellspring of divine bounties…” (Selections from the Writings of Abdu'l-Baha:62)  Thus, the whole manifests in the center; rather, it manifests as the center of a lower order, coordinating its actions, organizing its powers, driving its development.  It completes the lower order by linking it with a higher order, and its influence radiates out over the entire lower order, diffusing simultaneously throughout the entire lower order because the whole is within every part.

How does the lower order develop toward greater complexity?  We can use Godel’s proof to speak on this point.  It rests on the principle of mapping.  That is, Godel proved incompleteness when he gave metaarithmetical statements themselves—i.e. statements about arithmetic—numbers.  By doing this he showed that arithmetic can encode metaarithmetical statements and higher order metaarithmetical statements can be mapped into the language of arithmetic.  But, though encoded and expressed arithmetically, the truth or falsity of these metaarithmetical statements can’t be proved

Now, logically, it is impossible for infinite Mind to communicate its knowledge to finite minds.  Human thought can never capture the truths of Revelation, or prove by our standards of rational thought the truth or falsity of many of them.  Nevertheless, communication does occur.  His Truths are analogies of truths that we can grasp.  Some of the truths of revelation can be “mapped” via figurative language, metaphors, similes, analogies, etc. into human language and thereby expressed to test their truth.  But their truth or falsity often cannot be proved logically.  This requires faith and action and in this way transform human thought into a higher kind of human thought and, then, we may then “see” their truth. 

This communication can occur in some measure because, again, we are made after His image and in His likeness—not His nature--so He may communicate with us and we understand something of what He says—i.e. the image and likeness of His thought and meaning in our own world of understanding.  The Creative Word is just this process of mapping higher, more complex meanings into human thought so that greater complexity of understanding and better coordinated action can be released.  New meanings are encoded into our life, and this leads to breakdown and breakthrough.  Baha’u’llah warned, “the world’s equilibrium hath been upset” and this occurs from trying to assimilate higher truths into our current level of understanding.

From my point of view, every Revelation is a mental field, or expression of the universal Mind.  Each revelation patterns into a unique configuration the essential properties—the qualities of God—inherent in the realities of things.  These configurations are logically-related to each other and over vast cycles of time these grow in complexity because Revelation Itself is progressive.  In other words, no Manifestation reveals the whole of reality, but reality as a whole, each whole more complex than the one before, all approaching but never reaching the complexity of the whole of Reality. 

Within the realm of human knowledge we also strive for consistency, because that is the basis of rational thought.  Every science has its own consistency, i.e. its approved methods of inquiry and verification; its shared assumptions and paradigms.  Each of the sciences is a kind of language that yields particular knowledge of creation.  By putting the yield of these sciences together into a sort of cross-correlation a more comprehensive picture of reality is obtained.  Science is the revelation of nature and of all objective reality.  Human intelligence and knowledge completes nature.

‘Abdu’l-Baha says: “It is evident, therefore, that the world of nature is incomplete, imperfect until awakened and illumined by the light and stimulus of education.” (The Promulgation of Universal Peace:309)  It may seem strange that human education is necessary for nature to be complete, but, as the opening quote said, without intelligence nature is incomplete.  “If the world of nature were perfect and complete in itself, there would be no need of such training and cultivation in the human world—no need of teachers, schools and universities, arts and crafts. The revelations of the Prophets of God would not have been necessary, and the heavenly Books would have been superfluous.  If the world of nature were perfect and sufficient for mankind, we would have no need of God and our belief in Him. Therefore, the bestowal of all these great helps and accessories to the attainment of divine life is because the world of nature is incomplete and imperfect.” (The Promulgation of Universal Peace:310)

Inherently Incomplete

It has now been proved by rational arguments that the world of existence is in the utmost need of an educator, and that its education must be achieved by divine power. There is no doubt that this holy power is revelation, and that the world must be educated through this power which is above human power.

            (Abdu'l-Baha, Some Answered Questions, p. 11)

This series of posts are attempting to bring together insights from science and religion to show how they ultimately point to the same higher truth.  Last post presented the thesis that Godel’s proof provides a logical foundation from which to argue the inherent incompleteness of all formal systems of thought.  There is something within every formal system that is not “of itself’ but is the representation of a higher entity in the system.  Paradoxically, this something else is what makes the system a system, for it stands in opposition to it.  Consistency is not within any system, but only as part of a richer system, which is also only fully consistent within yet another, higher system.  Yet consistency is essential, especially in thought.  For, once one accepts a logical contradiction, one can prove anything, and that is the end of rational thought.  The key point of this concerns self-referencing statements which cannot be proved within any formal system of thought. 

So, what possible conclusions and implications can be drawn from Godel’s work in support of the lead quote above?

The first conclusion we can draw is something like this: The whole is complete, consistent and perfect by itself.  Any part of that whole, by itself, is not complete or perfect, though it may be consistent in itself.  But its consistency cannot be proved or known by itself.  It can only be known as it is part of the whole. 

An implication of this conclusion is that: many seem to think that the humanity is a kind self-enclosed, self-referencing system, sufficient unto itself, with no higher authority to appeal to.  This is a modern-day hubris described by sociologist Daniel Bell as the belief that ‘I come out of myself.”  But in thinking this way we sacrifice a sense of completeness and when a creative advance is required, for challenges always occur, we often prove inadequate and become lost.  We get away from our real nature when we try to define ourselves, as the Biblical story of the Tower of Babel shows (Book of Genesis 10:10), for we have no objective standpoint from which to do this.  Hence in all cases self-referring becomes self-subverting.  How?

Because humanity is not a self-contained system, the truth or falsity of our self-referential statements—i.e. statements we make about our essential nature—are often unprovable, remaining purely matters of belief.  However, in matters of belief, such as fundamental moral principles or interpretations of reality, the process of knowing their truth is highly problematic, because they cannot be proved logically or rationally in a way that can not be subverted by a logical or rational proof of a belief that is contrary.  Moral intuitions are highly subjective and hard to generalize to others, and interpretations of reality are almost as many as people.  Too, some problems seem intractable. 

Human thought can be consistent when formalized, as in a syllogism.  Consistency is the basis of rational thought.  But even wrong ideas and interpretations can be grounded on rational assumptions and “proved” using logical arguments.  Hence sound logic and consistent rational thought do not, by themselves, enable us to avoid dangers and pitfalls, like racism, sexism, and all those other isms that divide humanity and which help create a toxic moral and intellectual environment.  We are not the final arbiter of most matters of conscience and reason, and human thought should not be closed upon itself, no matter how rational and firmly based upon “reason.”  Rather, we, each individual and all humanity, are open systems, having access to richer thought than human because the Manifestation and His Words can teach us what is right and wrong about our self-understanding.  He makes humanity complete.  His Revelation completes human thought.  He and His Message bring forth from us powers and capacities which we can not bring forth from ourselves.

 Human thought, then, is inherently incomplete and must appeal to higher thought to advance beyond the conundrums that thought brings forth in its movement over problems.  This is what Einstein meant when he remarked that problems can’t be solved using the level of thought that generated them.  Some believe that humanity’s creative powers will bring forth those insights, inspirations and creative leaps that solve the problems. That is true for many problems.  But this is still to keep human thought within the bounds of human thought, and, as I have argued, human thinking is inherently incomplete and inconsistent.  So some problems may be forever beyond our ability to solve using only our own thinking. 

Baha’is believe that we can turn to the richer thought of divine Revelation to solve our problems.  But even here the same cautions about completeness and inconsistency hold.  There are no absolutes, even within Revelation.  I mean that, as Shoghi Effendi stated: “The fundamental principle enunciated by Bahá'u'lláh ... is that religious truth is not absolute but relative, that Divine Revelation is a continuous and progressive process, that all the great religions of the world are divine in origin, that their basic principles are in complete harmony, that their aims and purposes are one and the same, that their teachings are but facets of one truth, that their functions are complementary, that they differ only in the nonessential aspects of their doctrines, and that their missions represent successive stages in the spiritual evolution of human society.” (The Promised Day is Come: Preface)

The messages of the great Spiritual Luminaries are the fundamental truths of the human reality, the basis of all moral intuitions, and the most complete and accurate interpretation of Reality.  But, as Shoghi Effendi statement points out, each divine Message is neither final nor complete in Itself, but must be completed by another and more comprehensive Message to come after It. Together They are the unfoldment in more complete and complex form of a single divine Impulse.  The most recent Message is the most comprehensive and complete. It represents not the whole of Reality, for that can never be communicated, but is, rather, reality as a whole, adequate and comprehensive, complete and perfect, for its time, but not for all time.  But these Divine Revelations are the source of human development, of new sciences and of new stages and kinds of civilization.  I will discuss some of these implications in the next post. 

Mapping Truth: Godel and Incompleteness Part I

Yet one can’t do any mathematics at all, not even basic arithmetic, without referring implicitly to the infinite.

(Rebecca Goldstein, Incompleteness: 186)

In 1931 a young logician, Kurt Godel, transformed the study of logic, especially mathematical logic, and epistemology, by proving that all formal systems of human thought are inherently incomplete.  His groundbreaking, paradigm-busting, work was titled: On Formally Undecidable Propositions of Principia Mathematica and Related Systems. It yielded two famous theorems, called Godel’s incompleteness theorems.

The Principia Mathematica was a work of mathematical logic by Bertrand Russell and Alfred North Whitehead that attempted to set forth a complete and consistent formal, logical foundation and the essential principles of mathematics.  They claimed that they had done so, but upon closer examination it was found that to achieve consistency Russell and Whitehead had introduced some ad hoc principles.  A formal system, in mathematics at least, is one that is divested of all appeals to intuition.  It is a closed, axiomatic system of reasoning with primitive givens, stipulated rules of inference and proved theorems.  Because it is closed, it is finite.  There can be nothing ad hoc about it.

An axiomatic system is consistent when employing the rules of the system generates no contradictions, and consistency itself is one of the propositions of the system.  Thus, every axiom, or true statement, must be derived from the basic principles and rules of the system.  Too, no statement can be both true and false at the same time.  It is a real left-brainer construct.  Godel discovered and proved that neither the truth nor the falsity of some propositions of any formal system of thought can be proved.  That is, a proposition may be true, contextually, but it can’t be proved to be true.  It can only be proved to be unprovable.  Thus, to prove the truth of these formally undecidable propositions requires another, richer kind of thought-structure.  Thus the formal system is incomplete.  

Mind can never embrace the totality, because as Hamlet told Horatio: “There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy.” (Hamlet 1:5)  If any contradiction arises, or if a true proposition or statement cannot be proven using only the rules of the system, then the system is inconsistent (a bad thing for formalists) and incomplete (that’s OK, so long as a higher system of thought can complete it).  How to get out of this?  Think—go right-brained.  The problem comes with self-referential statements.  These operate at the limits of formal systems, defining their boundaries of truth, sort of like the complexity or chaos sciences.     

For example take the famous liar’s paradox: This statement is untrue.  Taken by itself, with no reference to anything else, if it is true, then it is a contradiction, because it says that it is untrue.  If it is untrue, then it is also a contradiction because that would mean that it is true.  Consistency is broken, and the only way out is to introduce something new into the system of thought, or to refer outside to the system to a context.  Godel proved that no axiomatic system can be sufficiently rich to formally capture even arithmetic. All formal systems are incomplete, deriving their consistency from appealing to a richer formal system. 

He proved this for all formal systems by showing how the truth or falsity of some propositions is not formally decidable using the rules of the system.  That is, the question, can a particular proposition be proved within the system sometimes yields the answer that it can’t be proved.  How? 

A particular proposition (A) is unprovable in the system if the negation of A is another proposition: A is provable in the system.  But if A were provable then its negation—which says that A is provable—would be true.  But if the negation of a proposition is true, then the proposition itself is false.  So if A is provable then it is false.  But if A is provable, then it is also true.  So, assuming the consistency of the system, if A is provable then it is both true and false—a contradiction—which means that A is not provable.  But that is exactly what A said in the first place: that it is not provable.  So A is true.  Therefore, A is both unprovable and true and this is expressible within the system.  The final conclusion is that the formal system is either inconsistent or incomplete, which are the two-sides of one coin.  The proof rests on the method of assigning a number to statements so that a blending of voices—arithmetical and metaarithmetical—is accomplished such that arithmetical statements are also making metaarithmetical statements: i.e. statements about arithmetic made in numbers, each statement assigned a number.  This is possible because language and number are both symbol systems--i.e. numbers can be assigned letters and letters numbers, as in numerology.

In using the same language of arithmetic, i.e. the map, to express both meanings and metameanings, two different sorts of descriptions will be collapsed into one another.  It is introducing an element of the organization of events on the level of events itself, as if the thoughts organizing your physical behavior were themselves part of your physical behavior.  In arithmetic, arithmetical descriptions setting forth relationships between numbers are, of course, expressible within the formal system e.g. 2+2=4.  But if, as Godel did, you assign a number to a metastatement about arithmetic (e.g. the rule that the sum of two integers is another integer could be given the number 5) then metadescriptions about the logical relationships holding between numbers (i.e. the syntax of the language) can be described within the formal system itself.  Metastatements are purely syntactic, i.e. rules about rules.  They can not be proved to be true or false using the rules of the system.  They are simply unproveable.  That is, it is not about the truth or falsity of any statement, but about its proveability to be one or the other.  Rebecca Goldstein sums up the results: “Godel’s first incompleteness theorem tells us that any consistent formal system adequate for the expression of arithmetic must leave out much of mathematical reality, and his second theorem tells us that no such formal system can even prove itself to be self-consistent.” (Incompleteness: 192)

That is, the syntactic features of formal mathematical systems (e.g. the rules of combining numbers in arithmetic) can’t capture all the truths about the system, including the truth of its own consistency.  Consistency, which defines the system, transcends the grasp of the system itself: consistency is not completeness.  Completeness is something else.  There is something within all formal system that is not “of itself’ but is the representation of a higher entity to the system: paradoxically, what makes the system a system by being something else.    This "something else" completes the system, or, at least, is the means of its completeness.  Consistency is not within any system, but only as part of a richer system, which is also only fully consistent within yet another, higher system. 

In any universe of discourse, whether language or number, this kind of confusion of realms that arises with self-referencing—where the metasyntactic and the syntactic statements collapse into one another, so that the logical relations that hold between units of meaning (e.g. numbers and their relations) in the formal system themselves become relations expressible in the language of the system—is the mechanism of encoding complexity, for it allows an entity of a higher level of reality to exist in some form in a lower level of reality.  Potentially, infinite meanings can then be expressed in finite language if they become self-referential in a higher sense.  OK, so what?  

The implications are terrific. But that is for next post.

The Purpose of Creation: Final Cause

Know thou, moreover, that the Word of God…hath never been withheld from the world of being.

(Tablets of Baha'u'llah:140-141)

Francis Bacon pointed out that true knowledge is knowledge of causes.  Creation is causality.   Cause, as the correlative of effect, is understood as being that which in any way gives existence to, or contributes towards the existence of, any thing.  This description of cause is wrong, of course, for, strictly speaking, cause, being a transcendental, cannot be captured in a logical definition. Aristotle was the first thinker to systematically investigate the nature and anatomy of causality and he came up with four: formal cause, material cause, efficient cause, and final cause. But what Aristotle undertook was the analysis of essences in such wise as to perceive and classify those principles which, in conspiring to bring the essence of any effect, object or event, actually into existence, flow into it, as it were. For the real idea of cause pertains to that which in any way influences the production of an effect as an essence.

‘Abdu’l-Baha accepts Aristotle’s formulation and explains the interaction of the four causes: “Essential preexistence is an existence which is not preceded by a cause, but essential phenomena are preceded by causes. Preexistence of time is without beginning, but the phenomena of time have beginnings and endings; for the existence of everything depends upon four causes—the efficient cause, the matter, the form and the final cause. For example, this chair has a maker who is a carpenter, a substance which is wood, a form which is that of a chair, and a purpose which is that it is to be used as a seat. Therefore, this chair is essentially phenomenal, for it is preceded by a cause, and its existence depends upon causes. This is called the essential and really phenomenal.” (Some Answered Questions: 280)

But I am adding a fifth cause, the spiritual cause of creation.  Creation is the sequential unfolding of an inner spiritual structure of unity into an outer structured organic union of being that mirrors it and reflects back to it. This unity in diversity, this movement of a diverse spiritual whole that is reconstructed into a differentiated organic whole in another and smaller plane is summed up in Aristotle’s four causes: the formal cause finding its mirror-form in the destined final cause through the interaction of the efficient cause upon the material cause.  Then, via symmetry, there is a reply of the final cause back to the formal and drawing the efficient to itself in development of the material at every stage and level, so that interaction and interrelation occur, so that not just a one-way relation dominates but a creative relationship is formed. 

We must distinguish the causes.  Spiritual or first cause is all four causes operating simultaneously as the “Be and it is” creative power of the Manifestation of God.  As the defining form, formal causality is often called something like the image of the thing to be created conceived by the maker, inventor or artist.  Some say that it is like a blueprint showing how the final cause, the purpose of the thing, can be realized through the efficient cause working upon the material cause.  But it is a mistake to identify the blueprint with the formal cause, just because it seems to be what the builder works from.  The blueprint itself causes nothing.  It is rather the final result of many prior causes and actions.  Hence the blueprint idea is actually much closer to the final cause, what draws the efficient causes toward it.  The final cause, like the efficient, is extrinsic to the effect, the latter being the cause of the existence of the former, and the former causing the latter, not in its existence, but as to its activity. 

However, it would be still be wrong to say that final cause, the purpose, is just the outcome, the end result of the effort of efficient cause acting upon the material cause under the guidance of the formal cause.  It is wrong to say this because final cause is not a result but a cause.  Therefore, it is present from the beginning in spiritual and formal cause. The Master says that the universe has no beginning and no ending, but final denotes an ending.  But final cause means only as part of a complete structure of being, not Creation as the eternal and complete Thing but Creation the eternal, unending action. 

This mix-up stems from confusing the final form, which is a creation, with the purpose of that form, which started the creative process.  That is, the final cause of a chair is not the form of the chair, which is the final form or end result of creative work.  Rather the final cause is when someone sits in the chair.  Sitting is the cause (purpose) of making the chair. 

Final cause suggests the future influencing the present in the sense that it is what a thing is to become that helps determine its present stage of development i.e. keeping the goal in mind while working.  Thus final cause is, too, a spiritual cause.  Spiritual first cause is all four causes simultaneously and eternally present and creative.  In relation to the whole creation, then, the final and the formal causes that together make up the world are not just created, but more properly, eternally co-created and co-create.  Baha’u’llah wrote: “There can be no doubt whatever that if for one moment the tide of His mercy and grace were to be withheld from the world, it would completely perish. For this reason, from the beginning that hath no beginning the portals of Divine mercy have been flung open to the face of all created things, and the clouds of Truth will continue to the end that hath no end to rain on the soil of human capacity, reality and personality their favors and bounties. Such hath been God's method continued from everlasting to everlasting.” (Gleanings from the Writings of Baha'u'llah:68)

So what does this have to do with me, you ask?  Quite a bit actually.  After complete and perfect Creation, there is creation as creating.  Though the final cause of the cosmos is open-ended in itself, yet every created thing within it has a final cause, a purpose, and the final cause of creation is humanity.  Thus: “Having created the world and all that liveth and moveth therein, He, through the direct operation of His unconstrained and sovereign Will, chose to confer upon man the unique distinction and capacity to know Him and to love Him—a capacity that must needs be regarded as the generating impulse and the primary purpose underlying the whole of creation. (Gleanings: 65)

        The capacity to know and to love the Creator is both “the generating impulse” (formal cause) and “primary purpose” (final cause) of all creation. Baha’is state this purpose in their daily obligatory prayer: "I bear witness, O my God, that Thou has created me to know Thee and to worship Thee..."

          Does this mean that this impulse and purpose were in effect from the beginning of the world, even when no people peopled it?  Yes.  The Master says: “Therefore, it cannot be said there was a time when man was not. All that we can say is that this terrestrial globe at one time did not exist, and at its beginning man did not appear upon it. But from the beginning which has no beginning, to the end which has no end, a Perfect Manifestation always exists.” (Some Answered Questions:196-197)

          And if a Manifestation exists, then there must exist beings for Him to manifest before.  Thus even when man did not appear on earth, the purpose of creation remains the same eternal purpose: “Briefly, there were many universal cycles preceding this one in which we are living. They were consummated, completed and their traces obliterated. The divine and creative purpose in them was the evolution of spiritual man, just as it is in this cycle. The circle of existence is the same circle; it returns. The tree of life has ever borne the same heavenly fruit.” (The Promulgation of Universal Peace: 220)