Modern science uses a model of knowledge based on axioms, logic, objectivity, mathematics, and mechanism. Axioms are the basic truth. From it, other truths are derived by logic. To test these against reality, each thing must be exactly one thing, called objectivity. To avoid subjective opinion, objects must be reduced to numbers through a measurement, called mathematization. Objects can be divided into smaller objects and their interaction constitutes a mechanism or the working of a machine.
Each of these assumptions in modern science is false. Ideas do not have an independent existence. They always exist in a person. Logic doesn’t create new ideas. A person creates new ideas from previous ideas but the creative process is not always logical. A person is not just one thing. He can be many things, some of which are observed at one time, place, and situation. Ideas don’t govern objects. Persons create and impart ideas to other persons who may accept and be governed by them or reject and be punished by persons. A measurement tells us what the effect is, not what the cause is. Even the effect is not constant because it is one of the many possible things that something can be at a given time, place, and situation. Persons try to guess causes based on effects but those guesses are not guaranteed to be true. Thus, measurements do not guarantee objectivity. Machines have no self-knowledge, self-correction, or self-replication. Persons are necessary even to create, replicate, monitor, and improve machines.
Since every assumption in modern science is false, therefore, it should not surprise us if these flaws are exposed over time. This would have been obvious even at the beginning of modern science if its creators had done some critical thinking. Since that is water under the bridge now, we can only examine these imminent failures to show why modern science is an imaginary pie in the sky with no foundation.
Table of Contents
- 1 Comprehensive Failure of Mathematics
- 2 Comprehensive Failure of Mechanism
- 3 Comprehensive Failure of Objectification
- 4 Comprehensive Failure of Logicization
- 5 Comprehensive Failure of Axiomatization
Comprehensive Failure of Mathematics
Gödel’s Incompleteness Theorem
There are so many different formulations of Gödel’s Incompleteness that those who read just one of those formulations but don’t investigate its full implications, don’t understand what it is saying.
In one such formulation, that I often use, the theorem says that no theory of numbers can be consistent and complete. We have to ask: What is a theory of numbers? The answer is that it is a generative system that can generate all kinds of numbers from some simple axioms, such as Peano’s Axioms on Arithmetic. If we have a generative system of numbers, we can use it to generate an entire universe based on those axioms, because space, time, matter, and motion can all be reduced to numbers. Hence, a generative system of numbers is equivalent to a Theory of Everything. Conversely, the absence of a generative system of numbers is equivalent to the absence of a Theory of Everything. This doesn’t mean that no Theory of Everything can ever exist. It just means that such a theory cannot involve numbers.
In another formulation, that I generally do not use but most people love to use uncritically, the theorem says that we cannot prove all the theorems about numbers. This seems very benign because nobody is able to state precisely what we cannot prove. You have to list all the individual claims that cannot be proven (or disproven) and until we have made a very long list of such claims, it seems that those claims are rare, if not irrelevant. Not being able to prove all theorems about numbers seems so benign to most people because we continue to assume that reality is mathematical and that we can continue modeling reality through numbers, although there may be rare problems that we may not solve. Unless we can prove that we cannot solve those very problems, for all practical purposes, nothing has changed.
There is a lesson to be learned here, namely, how you describe a problem has tremendous ramifications. For instance, if you say that the temperature of the earth may rise by 20C due to global warming, then most people may say: It’s going to be a little hotter, and we will sweat more, but we can address that issue by using more deodorant. You can also state the same problem differently: If the temperature rises by 20C, there will be severe droughts and floods, most coastal areas would be submerged under water, millions of people may die due to droughts and floods, and the world as we know it would cease to exist.
The latter phrasing will get you a lot of attention than the former when they are just different faces of the same problem. There is a root cause that has numerous effects. Some of those effects—such as sweating due to global warming—may be benign, while the other effects—such as floods, droughts, and extinction—may be drastic. Our perception of the problem is based on which of the faces of the problem we see. If you see the benign effects, then you might think the problem is not serious. If you see the serious effects, then you are more likely to think that the same problem is far more serious.
The serious implications of Gödel’s Incompleteness have been obscured by showing its benign faces. These include: (a) Consciousness cannot be reduced to mathematical computation, (b) we cannot prove all theorems about numbers, and (c) some mathematical problems may be unsolvable. All these are effects of a problem, not the cause. The cause has millions of effects, some of which are benign but others are drastic. If we do not state the drastic effects—such as the incompleteness vs. inconsistency issue, which destroys the possibility of a mathematical theory of everything, and indicates that all our mechanistic models of reality (even if somewhat useful) are false—we don’t realize the problem.
Objectification is the Root Problem
The real problem, if we understand Vedic philosophy, is that reality is like persons but we model it as objects in binary logic and mathematics. Many differences result due to this one simple difference:
- Aspect Reality
- A person has six aspects called self, cognition, emotion, relation, conation, and intention, which underdetermine other aspects. Specifying one aspect only entails what the other aspects cannot be, however, it does not fix what the other aspects must be.
- An object has one aspect—its physical properties—which are independent such that the presence of one property does not interfere with other properties. The position and momentum of a classical particle are non-interfering properties of the particle.
- Tiered Reality
- Each of these six aspects of a person has many tiers. The cognition of a person includes many tiers—body, senses, mind, intellect, ego, moral sense, and many layers of the unconscious. Each of these tiers also in turn comprises multiple tiers within them.
- An object is one tier of reality. If we restrict reality to just one tier, then the description is obviously incomplete. You can assume that what we see with our senses is all the reality there is, but you cannot explain what you see without what you can’t see.
- Inseparable Reality
- The aspects of a person cannot be separated into independent parts because each part affects others. The artistic ability in a person influences their philosophy and their philosophy influences their art. Their social bonds change their art and philosophy.
- Objects can be divided into smaller objects, like cutting an apple into pieces. But a cut apple rots faster than an uncut apple. Parts after separation are different than before it. The reduction of the whole into parts does not give us the same parts as before.
- Non-Reducible Reality
- By modeling an uncut apple as the assembly of cut pieces, reductionism creates object thinking in which parts are a priori independent. That is false because separated parts are not the same as unseparated parts, just like a cut or uncut apple.
- Reality is non-reducible in which there are distinct wholes and parts, but because they affect each other, therefore, they cannot be called independent of each other. We don’t merge parts into a whole, don’t equate them, and don’t call them independent.
- Qualitative Reality
- We cannot quantify deeper levels of reality (e.g., thoughts, emotions, intentions, etc.) but we can partially quantify some of the effects of the deeper levels of reality (e.g., quantifying anxiety as blood pressure) when it actually has many other effects.
- Quantification ensures that we never understand the full implications of a deeper cause because it has many effects of which we measure a few, if not just one. We can never explain all effects of a cause if those theories employ quantification.
- Moral Reality
- In object thinking, all causality—e.g., motion—must be explained based on one tier of reality. However, the same causality—e.g., motion—can be explained based on many different tiers of reality—such as the existence of a mind—that governs bodily motion.
- The laws of causality—e.g., the motion—must be based on the measurement of a single tier of reality in object thinking. But the laws of causality must be based on multiple tiers of reality in person thinking, including the level of a personal choice.
Once we grasp this fundamental difference between object and person thinking, then we can understand the meaning of Gödel’s Incompleteness in a much more nuanced way than before:
- There are many tiers of reality, but mathematical sciences can only capture the shallowest tier because they are measuring the effects rather than the many tiers of reality that cause it.
- There are many effects in the shallowest tier, but mathematics cannot explain them using a single theory with single causation, making the theory of the shallowest tier incomplete.
In simple words: (a) there are many tiers of reality, but mathematics can only capture one tier, (b) there are many effects in the shallowest tier produced by the same cause, (c) mathematics cannot explain all these effects using a single cause theory without producing a contradiction, (d) to remain consistent, some of the effects must be disregarded while forming a theory, which makes the theory incomplete. Single-tier reality is the result of objectification. Multiple-tier reality is the result of personification.
A person has a body, senses, mind, judgments (or true, right, and good), and a self. This five-tier minimal conception of a person is called pañca-kośa in some Vedic texts identified as anna-maya (body), prāṇa-maya (senses), mano-maya (mind), vijñāna-maya (judgment), and ānanda-maya (self). We can only perceive the last tier called the body. The next four tiers are not sense perceivable. Objectification of reality eliminates the deeper four tiers of reality. Then it is quantified by instrument measurement making it impossible to think of deeper levels of reality because numbers have no levels; they exist in a straight line. If deeper levels of reality are inconceivable, then all surface modeling is incomplete.
Quantification of reality is an illusion in a quality system because quantities are applied to separate things while qualities are always entangled. I can count five fingers on my hand but those fingers are not independent things. Injecting poison into one finger will poison all fingers. This never happens with objects—putting poison in one object doesn’t poison all objects because those objects are independent.
Thus, when reality is a single body—called a Virāta-Rupa or Cosmic Form—then every so-called object is actually part of a single body such that changing one part of the body affects all other parts. Deeper levels of reality establish progressively greater unity in parts until we get one thing—the Puruṣa. If we substitute a body with mutually independent parts, then we get no unity. Since unified behavior differs from independent behavior, therefore, the modeling of a body as independent particles fails.
The fact is that the five tiers of reality constitute different meanings of numbers. At the level of the body, we can say that numbers denote “things”. But at the level of senses, they denote “actions”. At the level of mind, they denote “concepts”. At the level of judgments, they denote “truth values” (such as true and false, along with right and wrong, and good and bad). At the level of the self, they denote six different meanings—thing, activity, concept, truth, right, and good—simultaneously. We can’t get rid of meanings because number does not mean one thing. In a computer, 1 and 0 can be a thing (value), a concept (character, array, integer, long, or decimal), an instruction (activity), or a judgment (true or false).
The minimum ontology in Vaiśeṣika is dravya (concept), kriya (activity), and guna (value). The minimum ontology in Nyāya is true, right, and good. The minimum ontology in Sañkhyā is sattva (concept), rajas (activity), and tamas (value). The minimum ontology in Yoga is body, mind, and soul. The minimum ontology in Mīmāṃsā is word, meaning, and grammar. The minimum ontology in Vedanta is sat, chit, and ānanda. If these ontologies are combined, then the minimum ontology is six-aspect personhood.
Therefore, we can reduce all problems to one contrast—objects vs. persons. Mathematics models reality as objects, when that reality is persons. The smallest observable reality is a trisarenu with six aspects. It cannot be quantified because a number has one face while a trisarenu has six faces. The body we see with our senses is one of the six faces. The same body is an activity such as speaking, a concept such as human, a role such as a father, a judgment such as truth, right, and good, and a judge who makes that judgment. We can never reduce the six-fold ontology to anything simpler. Mathematics tries that and becomes incomplete. The simple conclusion is that a person cannot be reduced to an object.
We cannot call a person a six-dimensional reality because changing something on one dimension does not change anything on the other dimensions, contrary to a person, where changing the body, activity, type, role, judgment, or judge affects everything. Six aspects of a person are not independent. This fundamental property is only conceivable in terms of qualities and never in terms of quantities.
Using the Inverted Tree Illustration
To understand Gödel’s Incompleteness, imagine a tree with roots, trunks, branches, twigs, and leaves. We cannot capture the nature of the root, trunks, branches, and twigs using mathematics—this is the first form of incompleteness. Similarly, we cannot explain all the leaves of the tree, namely, the observable effects of the deeper reality using a single theory—which is the second form of incompleteness.
Whatever we can explain using mathematics always comes at the cost of ignoring something else. For instance, no two leaves on a tree are exactly identical. But if we ignore the differences between the leaves, then we can approximate the behavior of some leaves with a common theory. That theory will always deviate from reality, so we have to use probabilities—reality is many different kinds of leaves, but to explain with a single theory, we have to assign various kinds of leaves different probabilities. For instance, some leaves are smaller while others are larger—we need a probability for that. Some leaves are darker while others are lighter—we need a probability for that. Some leaves are older while others are newer—we need a probability for that. If we want to explain more leaves, then we must have more probabilities for different types to subsume many different kinds of things within a single theory.
Finally, if we want absolute precision, then we can measure one of the leaves accurately—i.e., whether it is dark or light, old or new, smaller or bigger, etc. But that precision comes at the cost of not knowing anything else. If we deploy many people to study different leaves, the result will be five blind men who cannot agree with anyone else. Thus, precise measurement of one leaf excludes all the other leaves, along with branches, trunks, and the root. Since we cannot know the branches, trunks, and the root, hence, we cannot predict or explain the result of measuring one leaf. This is incompleteness. Precision in science can only be obtained by restricting inexplicable data collection to just one leaf.
Many Formulations of the Problem
We can formulate the same problem in many ways: (a) we can never measure the root, trunks, and branches, because they are not directly observable, (b) we can try to know the entire tree while sitting on one leaf, but everything other than that leaf will be known inaccurately, (c) while we can precisely measure one leaf, we cannot explain or predict its behaviors, (d) we can deploy many people to know different leaves, but what they learn can never be reconciled quite like the five blind men, (e) we can probabilistically predict a bunch of leaves, but we will never precisely predict any individual leaf, and (f) the different paths through these different formulations of “incompleteness” constitute varied but unpredictable trajectories because each such trajectory can be replaced by another over time.
Because there are six different canonical formulations of incompleteness, and we can change one formulation into another, therefore, we might think that we have solved the previous problem when we have only substituted one problem with another. Incompleteness is therefore not just an unsolvable problem. It also has the power to create the illusion of solving an unsolvable problem. Since we can draw infinite trajectories through the six canonical forms of the problem, hence, someone can cycle through the six canonical forms of the problem thinking that he is continuously progressing.
Likewise, even if someone accepts incompleteness as a fundamental feature of mathematical modeling, they don’t understand how incomplete mathematics is, unless they know how massive the inverted tree is, and absolute precision in data (without any prediction and explanation of that data) can only be achieved for one leaf. It is only if we understand that the tree has infinite leaves, branches, and trunks, all emanating from one root, that we realize that the ability to measure just one leaf (without the ability to predict or explain even that leaf) out of infinite possible alternatives is almost as good as nothing.
Comprehensive Failure of Mechanism
Mathematics is Itself Mechanism
A few decades after Gödel proved mathematical incompleteness, Alan Turing proved the equivalence of mathematics and machines. It was already well-known that every machine can be described using a mathematical formula. But it was not clear if every formula could be converted into a machine. Turing proved the equivalence of mathematics and machines such that after his proof, every mathematical formula represents some machine and every machine realizes a mathematical formula. We call these machines “computers” today because (a) they are machines, and (b) they compute some formula.
But as a corollary of the equivalence between machines and mathematics, all the inherent limitations of mathematics must also be the limitations of machines. If we cannot fully represent reality using a mathematical formula, then we cannot fully model reality as a machine. Again, we can present this as a benign problem—Everything may not be a machine, but many things may be. What goes unsaid in this claim is that nothing can be completely modeled as a machine. There are infinite different mathematical models that can approximate something at some time, place, and situation, but none of these infinite models will capture the nature of the same thing for all times, places, and situations. Thus, we need infinite mathematical models to describe one thing—at different times, places, and situations.
This problem is gravely obscured if we use probabilities to describe reality because it creates the illusion of predicting something while predicting nothing. For instance, saying that an economy will grow and decline with a 70-30 probability seems like a positive scientific claim. But it is totally useless because even if we observe a declining economy for the next 140 years, it could continuously grow for the next 60 years, to give us exactly 70-30 likelihood of growth and decline. A 70-30 probability can be confirmed over one day, one week, one month, one year, one century, one millennium, and so on. We can never falsify this claim because the time needed for falsification is not given by probability. All possible event sequences that concord with such probabilities need infinite unique predictive models. Hence, the uncertainty in any probability is infinite. Probability rebrands “infinite ignorance” as “knowledge”.
We can state the probabilities of the occurrence of letters in a book. Some letters occur more frequently than others. But knowing letter occurrence probabilities tells us nothing about the sequence of letters in a book. The same occurrence probabilities are compatible with infinite other books in which the letters occur in a different order. Letter probabilities exclude infinite books with different probabilities. And yet, despite excluding infinite other books, there are still infinite possible books with a given probability.
Basic Flaws of Mechanistic Thinking
The parts of a machine are separable. We can dissemble a machine into its parts and assemble them again. After that assembly, the machine will work just as before. But we cannot cut a living body into pieces and then put those parts again and expect it to work just as before. If an apple is cut into pieces, the parts of the apple rot faster. But the parts of a dissembled machine do not wear out faster. Even a simple thing like an apple is not a machine because the properties of parts within the apple are different from the properties of parts outside the apple. The properties of machine parts remain the same.
Mathematics and machines are inadequate models of reality because one thing becomes a different thing in a different ensemble. To recover the objectivity of the parts, we must say that each part is many potentials, and some of those are realized in one collection. For instance, a person who joins another team may be the same person but he behaves differently. Through his presence, the behaviors of other team members can also change. The marriage of a person in a different family can bring out previously hidden traits. If a body part is transplanted into another body, it can cause other body parts to behave in previously unseen ways. Some drugs can evoke abnormal reactions in some bodies than in others.
Thus, we can never say what something is, until we have tested it in every collection. Each collection may have latent properties that are revealed only upon the addition of a new thing. Likewise, each thing may have latent properties that are revealed only in a new collection. Thus, objectivity undergoes a radical change when we talk about entangled parts. The parts of a machine are objects with fixed properties. The parts of an organism are potentials that may or may not be exhibited in a collection. Object modeling is deterministic. The modeling of potentials in an organism is not deterministic. This non-deterministic potential can be described probabilistically, which is the same as infinite ignorance.
Factually, nothing is an object. Everything is a collection of potentials. But we can restrict the exhibition of potentials by combining objects in fewer ways. The determinism we observe is the result of restricting the exhibition of potentials. That determinism always comes with incomplete knowledge. For instance, we restrict our knowledge of a person to his bodily dimensions. The person is so much more than the bodily dimensions. But as we discover more about the person, modeling him will require contradictory mathematical models. Incomplete knowledge is consistent and complete knowledge is contradictory.
Just like the six canonical expressions of the incompleteness of mathematics, we can provide six canonical expressions of indeterminism of machines—(a) change of each part on removal or addition or other parts, (b) exhibition of different properties in the same part in different collections, (c) non-deterministic behavior of each part in every collection, (d) incomplete description of each part in every collection, (e) complete description requires testing each part in infinite other collections, and (f) to reconcile all these myriad descriptions, we need a new conception of objectivity as a collection of varied potentials.
Failure of Mechanism in Quantum Theory
The separability of parts is an assumption in the mathematical modeling of reality. A whole must be the sum of its parts for it to be modeled mathematically. But the whole is not a simple sum of parts of living things. The property of inseparability is seen in quantum mechanics because a quantum particle in an ensemble changes the properties of all other quantum particles. Removing a quantum particle from an ensemble is like removing the brain, heart, lungs, or kidneys from a body. Or, like removing a family member from a family. Or, like removing a member of a team from the team. Every member of a team, member of a family, or member of a body changes as a result of removing other members.
Quantum mechanics also describes the property of quanta using various terms such as wave-particle duality, entanglement, collapse, probabilities, indeterminism, and irreversibility. These are not separate problems. They are different canonical expressions of the same problem in quantum theory. Since the problem can be described in many ways, hence, each interpretation of quantum theory can try to fix one canonical version of the problem to create the illusion of progress while the problem has simply changed form. For instance, we can substitute the problem of quantum collapse with the interaction of two systems called decoherence. It just leads to a new question—Which two systems are interacting? The choice of interacting systems is as big a problem of choice as the choice of quantum state during a collapse. But reformulation of a problem in a new canonical form creates the illusion of progress.
The problem of quantum mechanics remains unsolved because science has defined objective truth as one thing, rather than inseparable perspectives on the same thing. Our consciousness moves from one sense to the other, to gather different sensations. One person emphasizes smell over taste and another person emphasizes color over touch. Those varying emphases are varying probabilities of seeing the same thing to varying extents as taste, touch, smell, sound, and sight. These probabilities are not objective truths because another person can deemphasize one sensation over another. And yet, there is objective truth because everything is some taste, touch, smell, sound, and sight, although observation is not going to give us precisely that objective truth if we are biased differently than the thing we observe. This is deeply problematic for Western thinking where objective truth means everyone should see the same thing in the same way and any variance between observers means they are under illusion.
Complete Neglect of Contextuality
Modern science is constructed from logic and mathematics and they assume that one thing is only one thing. It must remain the same thing inside and outside a collection. There should not be a contextual variation in the properties of that thing. That unchanging nature of things is modeling reality as objects rather than as persons. But that modeling is flawed because every sense percept has a different contextual effect. We can never universalize the effects of sounds, touches, sights, tastes, or smells.
Even the act of instrument measurement involves one of the infinite possible contexts—in which some sound, touch, sight, taste, or smell is measured by an instrument—and different instruments will never measure precisely the same result due to contextual activation of the infinite potentials within anything. Even the idea that we can measure the objective quantitative value of some “object” is false. Factually, we can never replicate an experiment precisely which means that idea of repeatability of experiments in science is itself founded on a false object notion of reality. The result of observation varies with every repletion. The so-called crisis of reproducibility in science is a feature of nature, not a human bug.
Every mathematical model is at best an approximation and at worst a falsehood. Every claim that stipulates “X is Y” where X is an object and Y is a property is at best an approximation and at worst a falsehood. This is because X is not an object, but a person, and Y is a trait of the person which may not always be exhibited, but even if it is exhibited, there may be a different set of reasons—understood only by understanding the deeper levels of reality—for exhibiting it. Thus, neither can we predict that Y will always be exhibited using a mathematical formula, nor can we explain the exhibition of Y always in the same way. That inability to predict and explain reality using mathematics is incompleteness.
This problem is minimized, marginalized, and misrepresented by using the mathematical model when it reasonably approximates reality and not using that model when it starts deviating from reality. The fact is that even when the model approximates reality, it is not the nature of reality, just as much when it deviates from reality. But those with vested interests in building such models don’t highlight the basic problem with mathematical models because that would rapidly diminish their importance. They instead say: Reality is mathematical, but we just haven’t found the correct model of reality yet. Give us more money, more projects, more people, and more power, so that we can develop a better model.
Comprehensive Failure of Objectification
Christian Roots of Scientific Materialism
There is an ideology underlying this conviction that goes back to Christianity under which matter is inert, rather than a person. We have to remember that monotheistic religions came out of pagan predecessors where nature was personalized. There were gods of wind, fire, and water. Nature was a mother. Pagan religions had many demigods, and this was hugely problematic to people who wanted to assert their rule over others because you could not get people under one ruler without a common religion.
Monotheistic religions were created for political purposes—replace many religions with one religion. Pagan religions were the hurdle and the solution was the depersonalization of nature, the rejection of gods governing nature, to say God made nature to be used and exploited for human purposes. Thus, new religions were created in which God created the material world but did not interfere in its working. The world was not animate or living. It was inert but moving. God made man with choice and God made nature without choice. Thereby, rivers, mountains, seas, and land are not persons. There are no gods of wind, fire, and water. Animals, plants, fishes, and birds are not living things. They are just mathematical machines that exist for man to use just as he wishes. This is the religious origin of objectification.
This ideology has been ingrained in Western society for thousands of years to the point that people cannot imagine the personalization of nature. It doesn’t matter how many mathematical models fail because the logical and mathematical modeling of matter is a religious dogma impervious to reason. Even if you read about Gödel’s Incompleteness, you must conclude that the effects must be minor and benign. Maybe we cannot solve all mathematical problems, maybe we cannot model everything using logic and mathematics, but it is our limitation in knowing reality mathematically but reality is still mathematical. This is the surprising conclusion that Gödel came to after presenting incompleteness theorems.
The chain of events from the rejection of demigods, the destruction of pagan religions, the depersonalization of nature, and the birth of mathematical science, to mechanistic models of nature are part of a continuum of falsehoods. That falsehood began with the Christian desire to replace pagan religions with monotheism. Since pagan religions personalized nature, their destruction necessitated nature’s objectification.
Christian Roots of Mathematization
Today we find many people talking about how consciousness cannot be reduced to a mathematical computation. What they are really saying is this: Don’t reduce me to a mathematical equation but you can reduce nature to an equation. Nobody ever says that mathematics is a false ideology even for nature. Nobody says that nature is also a person. Nobody wants to accept that rivers, mountains, seas, and forests are also persons. According to Christianity, the human soul is a person and God is a person but everything else is impersonal. This naturally results in mind-body or spirit-matter dualism. Nobody has been able to solve this dualism for two thousand years, and nobody will ever solve it.
The claim that consciousness cannot be reduced to a mathematical computation is only half the truth. The full truth is that nothing can be reduced to a mathematical equation because everything is a person. The failure of mathematics and mechanism does not deter Christians. They advance new claims such as the Fine-Tuning Design Argument, to say that nature is governed by mathematical equations and God uses His intelligence to tune these mathematical laws. When mathematics is itself incomplete, and all mechanistic theories have failed, what is the value in attributing that failure to God’s intelligence?
The fact is that nobody is able to even explain how mathematics governs nature. The mathematical laws of nature have to be computed. It requires a universal computer. Where is that computer? The complexity of natural laws created by modern science is so immense that the computer that calculates these laws for all material particles will have to be bigger than the universe. God cannot just tune the laws of nature. He also needs to create a gigantic computer to perpetually compute these laws.
Even that gigantic computer itself has to be governed by some laws, which have to be calculated by an even bigger computer. The bigger and bigger computers need more and more energy. Hence, for one universe to exist, infinite universes—bigger than the previous universe—must exist. Therefore, God created a mathematical universe is not the real proposition. The real proposition is that God must have created infinite universes, each bigger than the previous one, to compute laws for the next one.
Christian Roots of Modern Atheism
Christianity is the cause of rampant atheism today because if mathematical equations can run the world, then they can surely create it. If God is not necessary to run the world, then God is not necessary to create it. Atheism began when Christianity depersonalized nature. Modern science took that atheism a step further to say that if the world runs by equations, then it was created by equations. The running of the world is billions of years long and the creation is just a blip in that time. When we can study and describe the material world through equations, there is no reason to create it any differently.
We cannot separate Christianity from objectification, mechanization, and mathematization because Christianity depersonalized nature in its ambition to replace pagan religions that personalized nature. Any separation of objectification, mechanization, and the mathematization of reality from Christianity will only obscure the historical fact and ensure that a solution to the problem will never be found because if we don’t know what the causes and origins of a problem are, then we can never have a solution.
There is no hiding the fact that Christian societies claim that nature works like a clock. There is no hiding the fact that Christian societies began the rampant exploitation of nature. There is no hiding the fact that Christian societies relentlessly pushed materialism through their education system. There is no hiding the fact that Christian societies call everyone who personalizes nature Satanic.
The criticism of modern science cannot be separated from that of Christianity because all the false ideas of modern science are coming from Christianity. Christians do not oppose the mathematization of nature. They coopt it to claim that God fine-tunes mathematical equations. Christians do not say that nature is not a machine. They happily advance the mechanization of the universe.
Self-Inflicted Wounds of Christianity
My criticism of a religion that depersonalizes nature is not just the criticism of one faith by another. It is the criticism of faith based on scientific evidence that points to the irrevocable refutation of all ideas that Western civilization has produced since antiquity. The West produced those ideas and the West produced the evidence that refutes those ideas. Religion and science are the self-inflicted wounds of the West. The initial wound was religions that depersonalized nature. The next wound was the creation of science based on the ideology of depersonalization of nature. The final wound is the falsification of the depersonalized ideology of nature by rational and empirical evidence. This last wound is fatal because it kills the foundation of both science and religion. Now the West has no foundation for a civilization.
It is this civilizational crisis that explains why all the evidence against mathematization, mechanization, and materialism is obscured, marginalized, and minimized. The fact that the evidence has been sidelined doesn’t mean that it is irrelevant. The importance attached to the evidence is not objective truth. It is sidelined to preserve the Abrahamic depersonalization of nature. Without depersonalization, one has to go back to pagan religions, undoing over two millennia of Western civilization. It will destroy not only the monotheistic religions but also modern science. The West will have nothing to claim superiority. Therefore, the evidence against Western civilization is hidden by the Western civilization.
The correct foundation was pagan religions because they personalized nature. We could rise from that foundation to say that persons governing nature are governed by a superior person. The conflict among pagan gods is like the conflict between water, fire, and air. Each is opposed to the others, but they allow the other to dominate alternately because they are ruled by a superior person. Harmony is established by the superior person. He is the elder in the family who maintains peace in a family of fighting children. Abrahamic religions removed the conflicting pagan gods and the superior person who maintains peace between them to conjure a self-consistent mathematical reality. That conjecture is false. Of course, nobody in the West will talk about it because the conclusion will be going back to pagan religions.
Comprehensive Failure of Logicization
The Fundamental Problem of Logic
The problem of Aristotelian logic arises due to the soul-body distinction. When we say A is A, and call it the Principle of Identity, the first A is the soul and the second A is the body. When we say “Arjuna is a father”, Arjuna refers to a soul and father refers to the body. If the body is temporary, then A is A is false. Since the body is always temporary in the material world, therefore, A is A is always false.
Similarly, bodily distinctions are defined in relation to other bodies. If we say “Arjuna is a father”, Arjuna refers to a soul, and father refers to a relationship with a child, such as Abhimanyu. If Abhimanyu dies, then Arjuna ceases to be a father. The death of Abhimanyu affects other claims such as “Arjuna is a husband” because the husband may not be the same after the child’s death. Changes to one thing are changes to many things because they are mutually entangled. We cannot separate them as independent things although they are individual things. Individuality is interdependence rather than independence. Finally, as the child grows up, gets married, and becomes a father, the same person is both a child and a father. “Abhimanyu is father” and “Abhimanyu is child” are both true, destroying the mutual exclusion of something either being a father or a child, which was previously true for Arjuna and Abhimanyu.
Change is the refutation of Aristotelian logic. Since change is a constant in this world, hence Aristotelian logic is always false. To use logic, we have to redefine the meaning of “is” and “is not”. They have to refer to what is possible and impossible. Even if “Arjuna is a father” is true, it is not the only truth, since “Arjuna is a warrior” is also true. It doesn’t mean “A father is a warrior”, as it would under Aristotelian logic (if one thing is equivalent to two things then they are equivalent to each other). Likewise, being a father and being a son are not mutually exclusive or logically contradictory to each other although for a given time, place, context, and person they are mutually exclusive and logically contradictory.
Description of Motion and Change
It is now possible to speak of two kinds of evolutions, that we can call change and motion. Change refers to making the possible impossible or vice versa. When Abhimanyu dies, the possibility of Arjuna acting as the father of Abhimanyu ceases but he can be a father again in relation to someone else. Motion refers to the realization of possibilities one after another, such as Arjuna being a father and a warrior. If we go to the spiritual world, then change stops—as birth, death, old age, and disease are terminated—but motion continues. What is possible today doesn’t become impossible tomorrow, or vice versa. However, all that is possible today may not always be realized today. It may as well be realized tomorrow.
Thus, we have to define two kinds of “is” and “is not”—one that refers to change and another that refers to motion, or one that refers to possibility, and the other that refers to actuality. In the present world, both possibility and actuality are changing and Aristotelian logic is therefore continuously falsified. But an alternative logic that relies on the notion of change and motion will never be falsified. It will allow the possibility of change with motion (present world) and motion without change (another world).
Impersonalism equates the denial of change to the denial of motion. The personalist does not. He says: Yes, the change can end, but motion can go on. The materialist has no idea of the distinction between change and motion. He only talks about motion but his “is” and “is not” are continuously falsified. Whatever axioms he begins with invoke some “A is X” where A is a soul and X is a body but because the body changes continuously, therefore, “A is X” is continuously falsified. The failure of logic is not the failure of rationality. It is only the failure of the idea that reality is actuality instead of potentiality.
Linguistic Versions of Logical Problems
The linguistic counterpart of logic is that each word can have only one meaning. For example, the word “apple” cannot sometimes be a class of things and sometimes an individual thing. If we use the word “apple” to refer to a class of things, then we can never say “This is an apple” because doing so involves equating the class of things to an individual thing. Then, what are we going to call “this thing” if not an apple? We cannot call it an orange or a banana because these are also classes, and moreover, “this thing” is not even a member of the class called orange or banana. The result of all these problems is that we cannot call “this thing” anything because every word can denote both a class and a thing.
The reality is that a word is just like a person—i.e., a set of potentialities. In one context, we see some of the potentials of a person activated. In another context, we see a different set of potentials activated. For instance, the word Hari can mean the Supreme Lord, a monkey, a thief, or a lion. All these meanings are hidden potentials within the word Hari. However, context reveals one of those meanings. In one context, only one of those meanings would be used, although we could use a different meaning and arrive at a funny or ridiculous outcome. For instance, we could say “Hari is eating an apple”. If we interpret Hari as a lion, it would mean that the lion is eating an apple, which would be false.
The complexity in a single word is as big as the complexity in a person because we need to invoke all the six aspects of personhood in talking about a word—self, cognition, conation, emotion, intention, and relation. There is a word—the self. It has many possible meanings—cognition. It can have many different effects—conation. It can be uttered with different purposes—intention. It can trigger different feelings in us—emotions. And it can be joined in many different ways with other words—relation. Modeling the properties of a single word requires the same complexity as modeling the properties of a person. Since a person cannot be emulated by a machine, therefore, even a word cannot be so emulated.
We can extend this problem with words—which we call “sounds”—to every other sensation. For instance, the parent touching a child is not the same as a stranger touching a child. The effect of color or shape is not the same on everyone, or even at all times, places, and situations. The same can be said of tastes and smells. The fact that everything is a collection of potentials, some of which are activated at one time, place, or situation, in different ways for different things (because they too are a collection of potentials), means that no universalist model of reality can ever be accurate. A mathematical law is just a universalist model of reality that supposes that one thing always exhibits the same behavior. It can never be true if everything is a collection of potentials selectively activated in different contexts.
Complete Failure of Universalism
It is not well-known, but Western Liberalism is rooted in the failure of Western Universalism to find any truth. Hence, liberalism says: Everyone can choose their truth. This initially meant a democratic society where the truth is whatever the majority says it is. But since there is no way to know the truth, hence, even the consensus of the majority is no better than the opinion of the minority. In fact, foisting the consensus of the majority on the minority is also the “oppression” of minorities. Therefore, democracy is also a problem for liberalism. Liberalism can be realized only by giving equality to every opinion.
Thus, the new thrust of liberalism is not democracy. It is rather the equalization of every class, race, gender, religion, ethnicity, culture, and so on. You no longer look for a democracy enforcing the views of the majority over the minority. You rather look to undermine all majorities to lift the minorities. Gone are the days when the most meritorious would determine what the truth is. Now, the truth cannot even be known by the meritorious. In fact, meritocracy is also a tyranny of institutions ruled by a meritocracy setting arbitrary self-serving standards of merit, denying power to others on grounds of merit. To the extent that societies are still democratic—and the majority is “oppressing” the minority—the solution lies in increasing the vote share of minorities as the pathway to end the tyranny of the majority.
Western Universalism was the ideology of “one truth”. Western Liberalism is the ideology of “no truth”. We can say that “no truth” is also universalism but it is fundamentally opposed to the “one truth” universalism. This is now a conflict between the “one truth” conservatives and “no truth” liberals. All the Marxist paradigms of class conflict can now be applied to the conflagration between conservatives and liberals. Conservative conflicts existed between societies upholding different universal truths. Liberal conflicts are now embedded in each society trying to destroy the “tyranny” of any truth claim.
If we reverse this trajectory to separate people into different societies holding “one truth”, then we will go back to the clash between “one truth” universalist societies. If we continue on the present trajectory, then we will exacerbate the clash between “one truth” and “no truth” forms of universality. The fact is that those affirming their faith in “one truth” have no foundation for their truth claims either because universalism is false for logic and language. The alternative is contextual truth but a society that has espoused universalism for 2,500 years is not going to retract it. It will replace the “one truth” universal with the “no truth” universal and still call it a Universal Truth.
This is also a self-inflicted wound. If someone insists on “one truth”, they will end up with “no truth”. It takes a while to cross over from universalism to nihilism. But the destiny is predetermined at the outset. From the ashes of this nihilism may arise authoritarian dictators to re-enforce universalism. A society can oscillate between universalism and nihilism endlessly repeating the mistakes of their past.
Universalism is the denial of choice and the rejection of individuality. This is why in Vedic philosophy, it is called nirviśeṣa or impersonalism due to the rejection of individuality, choice, and multiplicity. Its opposite, nihilism, is called śūnyavāda or voidism. The West is called nirviśeśa and śūnyavāda because it oscillates between the universals of “one truth” and “no truth”. Impersonalists say that Brahman is one truth and everything else is false. They arrive at the oneness of all individuals by denying the choice of truth. If everyone believes in exactly the same thing, then they cannot be called separate individuals. The Voidists say that there is no truth. They reject all “one truth” claims.
Due to the prevalence of radical individualism, the West considers itself the antithesis of impersonalism and voidism. But every individualist disagrees with other individualists on what the truth is. They get no consensus, which is liberalism. As individualism increases, it leads to “no truth” which is nihilism. But if some society insists on “one truth” then there can be no choice of truth, ideological differences must disappear and all the minds must merge into one mind.
If we observe a universalist society, we find vast swaths of uniformity. But in India, it was said that the taste of water changes every two miles and the language changes every eight miles. Even when I was a child, I would sometimes walk a few miles in my hometown and find people whose words I did not understand but I liked the sounds of their voices. Some of them smelled like freshly tilled earth, others like a forest, some like freshly cut wood, and others like a mix of seasonal flowers. British colonialism brought some uniformity to India but otherwise, there was sheer diversity. Still, nobody said I am the only truth or there is no truth. Thus, universalism cycles between “one truth” (impersonalism) and “no truth” (voidisim) but personalism remains diverse and united.
Universalists think that the existence of many truths is confusion, disagreement, and dissent. They think that the existence of many classical traditions in India means that nobody agrees with anyone. This is a result of their universalism. They don’t know that infinite truths join to form a body of truth. The term viśeṣa denotes a unique truth. There are infinite viśeṣa that unite to construct a body of truths. Unity among viśeṣa makes all of them true, with the soul of the body being the supreme truth from whom infinite truths have expanded as the soul’s body and its complete expression. Cutting off one part of the body limits the soul. Hence, all the eternal body parts are called eternal truths.
The diversity of truths is not dissent. It is unity in diversity. But in impersonalism, all these truths merge into one; the body dies and we are just left with the soul. In voidism, the body dies, many truths separate into dissenting claims, and we get no truth. Western Universalism cycles between impersonalism and voidism. We never get many truths united into a body of truth. We either get one truth or no truth. It is either nirviśeṣa or śūnyavāda. One truth is forced on everyone through a central power. As liberty dawns, we move toward no truth.
Comprehensive Failure of Axiomatization
The Irrationality of Axiomatic Choices
The logic that Aristotle created, and the West upheld for 2,500 years, is an illusion because it operates on axioms but there is no logical way to choose axioms. Everyone can choose their axioms, create their private universe of personal truths and falsehoods, and logic will never disprove any of their claims because Aristotelian logic is always self-consistent. So, every rationalist can disagree with every other rationalist on their axioms and their conclusions, and no one could ever call anything truth.
The West escaped this relativism of rationality by using institutional power to define axioms. These axioms are called “commandments”, “laws”, “values”, “covenants”, “standards”, and so on. Truth is always established by fiat because the axioms are selected by some coercive institutional power.
Generally, the axiom-makers make different axioms for themselves and others. Euclid’s axioms of geometry don’t apply to Euclid. They only apply to geometrical shapes. The commandments of religion don’t apply to priests and emperors. They just apply to ordinary people. The laws of a nation don’t apply to the rulers. They just apply to the ruled. When these discrepancies are noticed, all axioms, commandments, covenants, rules, and values are discarded. Everyone makes their own assumptions and there are no universals. So, who is going to fix bad axioms and assumptions? Shouldn’t logic be responsible for the self-correction of axioms and assumptions?
Aristotelian logic has no capacity for self-correction. It can derive truths from axioms. But it cannot say if the axioms are true or false. When the Aristotelian system of logic is universalized, then all self-corrective mechanisms are lost. Now truth either depends on what powerful institutions define as axioms or whatever each individual believes in.
Open and Closed Logical Systems
Gödel proved that logic can never produce self-contradiction. This means that bad axioms can never be falsified. But he also proved that mathematics is incomplete, which means that any mathematical system will never capture the whole truth. He did not explore the possibility that a complete system can generate a self-contradiction, in the act of falsifying bad axioms to ensure that they are corrected.
Aristotelian logic is an open system. We can never talk about the whole in an open system because the whole includes the system that is talking about it. Aristotelian logic is an illusion. The logical system has to be closed so that we can talk of the whole, complete the knowledge, and enable the falsification of false claims. Any logical system that doesn’t enable the self-correction of false axioms is false.
A machine infers axioms into conclusions. But a machine can never self-correct. The defining trait of a person is self-correction. This is always achieved by applying the conclusions of some axioms to the person who created those axioms. If the person says: Everything is an object, then he must be objectified to see if he can accept that axiom. If he says: Everything can be exploited, then he must be exploited to check if he can accept his assumptions. If he says: Everything is working deterministically, then he must be deprived of his freedom to check if he truly believes in it. If he insists: Everything is random, then he must be put into a world devoid of order to check if we can accept his claim. Whenever we make a universal claim, it has to be applied back to us, because we are part of that universe. No universe means no universal claims. So, we can either exit all universes to stop making universal claims or we have to abide by our claims.
When a Cretan says “All Cretans are liars” then he falsifies himself. The contradiction would also not arise if he said “All Cretans are truthful”. Thus, universal claims are self-negated when we cannot accept them. The same universal claims are self-affirmed when we can accept them. There is no objectivity, and yet, there is truth. Truth is whatever we can accept. Falsity is what we cannot.
Completing mathematics simply means that when we make a universal claim, it must apply to us too because we are part of the universe. Now we must only make those claims that we can accept being applied to us. This always results in a self-correcting axiomatic system because most axiomatized truths are rejected when they are applied to us. A complete rational system is a closed rational system. It must reflect every claim such that the claims about the universe are applied to every part of the universe.
In a closed system, there is no axiomatic or a priori truth. Truth is whatever you can accept to be true. If you can accept depersonalization, then depersonalization is truth. But if you cannot accept that, and yet you make that claim about others, then your claim will be falsified in a self-contradiction, by applying that claim to you. Mathematics is impersonal. It models everything as a machine. By its application, every human is depersonalized. Since persons produced depersonalization, they created a Frankenstein to devour themselves. Self-contradiction is the possibility of a falsehood being universalized and then refuted by application to itself. I once stood at the edge of a cliff and shouted: “You are a fool”. After just a moment, the sound echoed back: “You are a fool”. This is the result of a closed system. It echoes back every claim.
The Necessity of Infinite Universes
Thus, in Vedic philosophy, there are infinite closed universes. In some universe, we can shout “You are a fool” and the sound will be echoed. If we can accept the echo, perhaps laughing loudly at it, then there is no problem. We will be that Cretan who can accept that “All Cretans are liars” to falsify all his claims. But in another universe, we can smile and say “You are nice” because we can accept the echoes of our claims.
This is a closed system because we can choose whatever axioms we like, and logic will put us in a world governed by our axioms. What people call the law of karma is just closed system logic. It echoes the same sounds that we utter. The birds of the same feather are flocked together. Everyone can choose their feathers and they will be flocked with the birds of their kind. If they happen to not like the feathers of others, then they have to change their feathers first. Truth is whatever we want it to be, provided we can accept that truth being applied to ourselves. Truth is a free choice and what we can like eternally. If our axioms, assumptions, values, and preferences keep changing repeatedly, then they are false. They are not false because someone else says so. They are false because the person who makes those claims is going to reject them.
There is no universal truth. But there are better and worse truths. The universe where we smile at the echo of “You are nice” is better than where we laugh at “You are a fool”. This is because everyone will eventually get bored of laughing at “You are a fool” and seek a universe that echoes “You are nice”. Free choice doesn’t mean an irrational choice. Rationality simply means what I like. We just have to give enough time for the echo to come back. Thus, the philosophy of karma also becomes the philosophy of reincarnation and eternal life. I cannot shout “You are a fool” and then disappear. I have to stick around to listen to the echo. Abrahamic religions take away that possibility by talking of one-life existence. The problem of Aristotelian logic is also the problem of Abrahamic religions. We cannot criticize one without the other. We cannot accept either because neither self-corrects axioms.
The Falsification of Logical Axioms
Due to the possibility of refutation of false axioms, rationality is not self-consistent. I cannot assume whatever I want and expect to never run into a contradiction, as would happen in Aristotelian logic. The logic that is consistent is not complete. The complete logic allows for the possibility of refutation of false axioms, hence it cannot be self-consistent. Of course, truth is self-consistent. We cannot equate the self-consistency of truth to the self-consistency of logic. This is because each person can choose their axioms. Axioms are not universals. They are individual choices. By pairing together bad choices, the axioms are falsified and therefore corrected. Likewise, by pairing together good choices the axioms are verified and therefore continuously reinforced.
Hence, when I talk about the flaws of Gödel’s Incompleteness and Aristotelian logic, I am talking about a closed system of reasoning that self-corrects axioms by falsifying the false axioms without denying the freedom to choose our axioms. Incompleteness, indeterminism, uncertainty, and probability are thrown as falsifying data to whoever wants to follow the mathematical modeling of nature. This is the natural outcome in closed-system reasoning but it is totally unexpected in open-system reasoning.
The failure of axiomatization is not simple. It is the failure of mathematics, mechanism, materialism, and logic. It is falsely assumed that even if materialism is refuted, logic will be preserved, and those who criticize materialism can keep using logic. It is also falsely assumed that even if materialism is false, mathematics is true, and those who criticize materialism can keep using mathematics.
The problem is not recognized because the failure of logic is not recognized. Logic is false because it allows everyone to choose arbitrary axioms and never run into a contradiction. By assuming that we will never run into contradictions, mathematics becomes incomplete, because completeness means the ability to falsify false axioms, including the false assumptions of Aristotelian logic that logic can never be self-contradictory. With incompleteness, mechanism fails because everything theory becomes indeterministic. With indeterminism, materialism fails because there is no conception of objective reality and causality when the theory is indeterministic.
The problems of modernity began in antiquity. Since logic is false, therefore, mathematics, mechanism, and materialism are false. Christianity that came between antiquity and modernity was not true. It was also false because it claimed that instead of nature punishing us for bad assumptions, God forgives all our sins. Thereby, everyone can assume whatever they like and just add “God’s forgiveness” to it. By adding “God’s forgiveness” to an axiomatic framework, Christianity justified every false axiom created by institutional power.
Therefore, from the Vedic perspective, science and religion are parts of the same problem. Science makes bad assumptions, and religion forgives those sins. Religion makes its own false assumptions and self-forgives its sins. Forgiveness of sins is the root of all problems. What if those sins are not forgiven? What if every choice comes with responsibility? What if bad assumptions are falsified by pairing people with the same bad assumptions? That would be a marriage made in heaven, solemnized on earth, and lived in hell.
Heaven means logic that pairs people with the same assumptions. Earth and hell also mean the same. Hence, heaven, hell, and earth are simply logic. The difference is simply that everyone can choose their axioms, be paired with people with the same choice, suffer or enjoy, change or remain unchanged, and then be transported (or not) to the commensurate heaven, hell, or earth. When we enjoy, we call that heaven. When we suffer, we call that hell. When both are mixed, we call that earth. But they are all logic. In fact, they are the same logic. But they are not one truth. Earth is a better truth than Hell, and Heaven is a better truth than Earth, so there is a ladder of truths. We can summarize it: Complete logic gives us a ladder of truths with infinite rungs on it.