You can add up the parts
But you won’t have the sum
You can strike up the march
There is no drum
Every heart, every heart
To love will come
But like a refugee
Ring the bells that still can ring
Forget your perfect offering
There is a crack, a crack in everything
That’s how the light gets in
From “Anthem” by Leonard Cohen.
We know from Gödel’s Theorem that any axiomatic system beyond the complexity of simple addition can only be incomplete so long as it contains no contradictions – incomplete and consistent. Completeness can only be achieved by including falsehoods – contradictions. A system which is complete and inconsistent can prove anything which is one reason contradictions must be vehemently avoided. Better to prove too little than to prove too much. Gödel’s Theorem put the kibosh on Whitehead and Russell’s attempt to prove that mathematics is true, and to find a mathematical system with axioms that did not generate paradoxes. Mathematics is true, but not all of it can be proven to be true. Gödel actually managed to use one of these paradoxes constructively in his proof that incomplete and consistent was the best that could be achieved with moderately complex axiomatic systems.
Gödel’s Theorem proves that mathematics cannot be formalized – meaning it is not possible to turn math into the mere manipulation of symbols following rules that ignore what those symbols mean. That is why computers have not superseded mathematicians, because computers have no understanding of what they do. The truth of Gödelian propositions can be seen and understood by human consciousness, but not purely by reference to rules within the axiomatic system. This hints at some connection between consciousness and the transcendent. Consciousness is necessary precisely because not everything can be reduced to rules; to a system. Consciousness must be free and not algorithmic to function. The halting problem similarly proves that there is no algorithmic method (step by step procedure) for (mindlessly) testing the validity of all algorithms. Understanding must put in an appearance.
In The Brothers Karamazov, Dostoevsky has Ivan quote from Voltaire: “If God did not exist, it would be necessary to invent him.” Ivan goes on to wonder that so primitive a creature as man could figure out God’s necessity. It can take quite some thinking however to discover just why we cannot do without God. At one point, Berdyaev describes our conscience as communication with the divine – though it is all too evident that many people’s consciences are deranged; corrupted and perverted by mass movements and ideologies. And then there are the many more whose conscience functions but the person ignores it to avoid the wrath of the deranged and powerful.
It is an odd fact that symbolic logic, mathematicised in the nineteenth century, has to contain things that are not at all logical. Predicate logic contains the axiom that if the consequent of a conditional is true, then the overall statement is to be regarded as true. A conditional is “If p then q.” p is the antecedent. q is the consequent. This makes no sense at all and is utterly ridiculous. In natural language, “if…then” implies some meaningful relationship between p and q. If you are a good boy, then you’ll get an ice cream. If it rains on Saturday, then our picnic will have to be moved indoors. If sodium is added to water, then there will be an explosion. If she smiles at me in that way, then maybe she likes me. In the first instance, the consequent is being offered as a reward. In the second, the conditional is contingency planning. In the third, the conditional indicates a causal link. In the fourth, an inference about someone’s possible feelings is being made. The fact that if p then q covers all these very different scenarios means symbolic logic is too crude to replace natural language. But the fact that the conditional is always regarded as true if the consequent is true violates common sense and seemingly all logic – though it is precisely formalized logic that is producing the absurdity. With regard to the first example, if the boy has an ice cream, no matter how he got it, including stealing it, then we are supposed to agree that “If he is a good boy, then he will get an ice cream” is true. The truth table definition of the conditional is:
p q p → q
T T T
T F F
F T T
F F T
Truth tables cover every single possible truth value assignment to the variables. This rule does not mean that p becomes magically true. As you can see with the truth table, even if p is false, so long as the consequent is true, then the conditional is regarded as true. This rule in logic can be summed up as “if q, then if p then q,” or, q → (p → q). Thus, predicate logic regards the statement “If Jimmy loves Doreess and has never eaten Swiss cheese, drunk a cola, or stared at a cat, then the speed of light is 299,792,458 m/s” as true, while the fact that there is no connection between p and q is treated as irrelevant.
With these examples of fracture and illogic in the midst of logic, it is as though one is pounding out a metal circle to lie flat against the ground but every attempt results in the last little bit smashing into pieces. Or perhaps one is trying to keep the circle flat, and yet the earth is curved, and the circle bends no matter what we do. The nineteenth century novel Flatland by Edwin Abbott is an allegory about a square being living in a two-dimensional reality that sees a circle that starts small and gets bigger and bigger. In fact, the circle is a sphere that the square cannot comprehend until the circle lifts the square up so it can perceive three-dimensional reality. The author intended this story as an allegory for our inability to comprehend the transcendent. While the flatland leaders privately acknowledge the reality of the sphere they execute witnesses to prevent this knowledge spreading in the manner of Plato’s Cave. Others, like Ken Wilber, have adopted the phrase “flatland” to describe science’s fixation with surfaces rather than depth and interiors, i.e., consciousness. The novel We by Zamyatin is similar in that it is about trying to cram people into a “perfected” reality that is governed by mathematical equations. The last step is to remove imagination so that people can be shoved into their assigned social box and finally be “happy.” The perfect person in the perfect society. This reality must remain incomplete and consistent. Immanence is not sufficient unto itself. Attempting to hammer the perfect conceptual circle just smashes it. The missing piece points to a mystery as we wait, in faith and hope, for the circle to turn into a sphere and raise us up. “The Fire Balloons,” a story in some editions of The Martian Chronicles by Ray Bradbury also features spheres. They are Martians who have put themselves through some kind of process, though they have forgotten what, that has left them as largely incorporeal floating blue spheres that reminds a priest of the fire balloons his grandfather used to light on the fourth of July. Two priests have decided to try to save their souls. One of them tries out the idea of the image of a spherical Jesus which he imagines as being appropriate to spherical creatures much to the other priest’s dismay. They bring a pump organ to play them hymns. The spheres try to avoid the two priests but eventually tell them that they have no need of saving. They are immortal, do not need to eat, never get tired, have no sexual feelings, and are incapable of sin of any kind. Suffering not, God is unnecessary for them. Not having overcome any difficulties and not facing the same existential problems as humans, the Fire Balloons have nothing to teach us and certainly not to learn from us. They have no crack opening onto the transcendent.
Despite the halting problem demonstrating that computer programming cannot be left to computers to do, and Gödel’s Theorem showing that math requires human mathematicians and cannot be formalized, some computer scientists and philosophers continue to imagine that they will be able to program computers with consciousness. Theorems are not theories and are thus not susceptible to being later disproved. They are not tentative, but facts about reality. When an algorithm is not valid, the effect is for the program never to terminate; never to halt. Whether this will happen or not cannot be determined algorithmically i.e., unthinkingly. Just how these computer scientists think they can bypass these facts is unknown.
The impossibility of creating consciousness using algorithms is assured. Consciousness remains “the hard problem,” of how a material thing like the brain could generate consciousness. A strong possibility is that the brain does no such thing; see Consciousness: What Is It and Where Can It be Found? If scientists, per impossible, somehow succeeded in creating Artificial General Intelligence this would mean the man-made creation of consciousness, yet it is consciousness that cannot be accounted for in materialist metaphysics. It is consciousness that evades determinism and reductionism, and points to spiritual realities. If software engineers succeeded with AGI, the connection between consciousness and religious faith would be shattered, and we would be like Morpheus in the Matrix movies saying “I had a dream. But, this dream has been taken from me.” Morpheus emits this existential moan when he learns that, seemingly, Neo is not a savior, but is merely an anomaly programmed into the Matrix to prevent its destruction. And the Matrix too is relevant to our discussion. The “Architect,” the Creator of the Matrix, who comes from the machine world, must program a fracture in what he wanted; which is a hermetically sealed simulated reality. The Architect is effectively the evil god of the Gnostics; the Demiurge who creates physical reality in the Gnostic view. The Architect tells Neo that when he first designed the Matrix, a computer-generated fictional reality designed to keep the populace mentally occupied and roughly content, he made it perfect. The humans, with their bodies in their slime-filled pods rejected this reality and died. So, in the next iteration, the Architect made the simulated reality imperfect. Again, the people would not accept it and died. Finally, an “intuitive program,” the Oracle, stumbled upon the answer: the introduction of choice and free will. Only then would humans accept their existential situation. People were given the choice to accept the simulated reality or to see through the illusion and reject it. 99% of people happily chose the simulation. 1% rebelled, exited their illusion-producing cocoon, and joined the humans living in Zion, the underground city in which flesh and blood humans live: in reality. Neo is a calculated anomaly who can bend the rules of the Matrix to a degree that no one else can, and, with the latest iteration of the anomaly, even the wider reality. When it came time for the Machine World to terminate Zion, Neo, the One, would return to the Source, allowing a temporary dissemination of the code he carries, reinserting the prime program after which he would have to select from the Matrix twenty-three individuals, a combination of males and females, to rebuild and repopulate Zion. Failure to comply, the Architect informs Neo, will result in a cataclysmic systems crash killing everyone connected to the Matrix which, coupled with the termination of Zion, will result in the extinction of the entire human race. Each new “Neo” has a “contingent affirmation that was meant to create a profound attachment to the rest of the species,” meaning a generalized love for mankind. This version of Neo, however, is different because his attachment is far more specific – his love is for one particular woman; Trinity. The Architect wants Neo to choose going to the Source to save Zion, but sees that Neo has chosen Trinity. The architect comments: “Hope; it is the quintessential human delusion, simultaneously the source of your greatest strength and your greatest weakness.” He incorrectly predicts that Neo will be unable to save Trinity and that it is too late.
Faith and hope are made possible by choice. And choice is possible through freedom; that only the Ungrund, the causeless cause, can provide. Materialist scientists know that materialism implies determinism. If we humans function adequately, being soulless, they should be able to program a material thing to do the same. They do not know that material reality has a crack in it through which consciousness enters with its intrinsic connection to freedom and thus the transcendent. The downside of choice, creativity, and imagination is that evil and destructive things can be imagined as easily, perhaps more easily, than dynamic order and goodness. A building can be destroyed in seconds that takes years to build. The film Stalker, by Tarkovsky, explores this duality of freedom, acknowledges the risk of choosing evil, and votes for freedom regardless because we cease to be human under total compulsion no matter how good the compelled “heaven” is supposed to be.
 This part seems like gobbledegook handwaving that resists comprehension.
 The Matrix movie universe can be divided into body, mind, and spirit. Zion represents body, the Matrix, the mind, and the Machine World, spirit. The three Matrix movies can be seen as body, mind, and spirit at war with each other, rather than working together in harmony.