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There are many ways to demonstrate the problems of logic, set theory, and Gödel’s incompleteness. They are all different ways to look at the problem, to become convinced that there is a problem. One such problem is the statement that “God has many names”. These names are not synonymous. By assigning various names to God, we describe Him in many non-synonymous ways. We don’t equate one name to another, and we don’t reject any of the names. That is contrary to logic, in which one thing can be only one thing. To preserve logic, we can throw away all except one name, and then, we will know God incompletely. To keep all the names, and know God completely, we have to throw away logic. Thus, “God has many names” leads to the same problem—inconsistency vs. incompleteness. In this post, I will do a summary of the paradoxes that arise in logic, set theory, and number theory, before discussing how the same problem of contradictions appears when God is called by many names. We will then discuss the solution to the problem, and how that solution applies to everything.

Three Formulations of Incompleteness

Gödel proved two incompleteness theorems. We can call them 1T and 2T for brevity. 1T states: “All systems of arithmetic are incomplete—i.e., they cannot prove or disprove all the statements within the purview of that arithmetic system”. 2T states: “No system of arithmetic can prove its consistency”. These two statements are constructed cleverly by using the phrase “cannot prove or disprove”. How do you prove that you cannot prove or disprove? The answer is—”the method of contradiction”. You assume that you can prove or disprove, and show that the assumption leads to a contradiction.

There are objections to the proof by contradiction. Some say: Proof by contradiction isn’t proof. To prove something, we must construct a step-by-step procedure to prove it. These objections suppose that there is something wrong with logic—the principle of excluded middle—X must either be true or false, not neither. Hence, on the off chance that someone might say: You haven’t proved anything by constructing a proof by contradiction, Gödel’s theorems are phrased as “you cannot prove or disprove” rather than “the arithmetic system, if complete, is inconsistent”. But before incompleteness, Gödel had proved the consistency and completeness of formal logic—that logical statements are true by virtue of their structure rather than meaning. Thereby, objections to proof by contradiction are rejected.

Hence, if we combine two facts—(a) logic is consistent and complete, (b) assuming consistency and completeness for arithmetic leads to a contradiction—then we can say “an arithmetic system is either inconsistent or incomplete”. This simpler statement combines three theorems—logic’s consistency and completeness, 1T, and 2T—and is generally used, although it is not a theorem that Gödel “proved” in the historical and academic sense of published papers. Let’s call this theorem 3T. We can rephrase it as follows: “Assuming that logic isn’t broken, arithmetic is either inconsistent or incomplete”.

The Fundamental Problem of Logic

We have to remember what logic is—statements true by virtue of structure rather than meaning. For instance, “A is A” must be true for all A. It cannot be true for some A and false for other A, depending on what the word A means. It also entails that we have to distinguish between A and its meaning.

For instance, “A is A” can be “God is God”, a useless tautology. To make the identity principle useful in logic, we have to say “God is omnipotent” and identity will imply that “Omnipotent is God”. If we now say that “God is omniscient”, then by identity, we will conclude “Omniscience is Omnipotence” because we are relying on the truth conclusion by virtue of sentence structure rather than word-meaning.

To eliminate such outcomes, Aristotle limited logic to those words that either have only one meaning or all alternative meanings are synonymous. Thereby, “God is omnipotent” and “God is omniscient” are not permissible in logic because God has two non-synonymous meanings—omniscient and omnipotent.

Hence, when we say that logic is consistent and complete, we are relying on one word with one meaning. Since one of the above two statements about God is forbidden by logic, therefore, one of these statements—”God is omnipotent” or “God is omniscient”—must be rejected within logic.

The Fundamental Problem of Set Theory

20th-century philosophers and mathematicians tried to solve this problem by set theory and ran into paradoxes. For instance, we can form two sets—Omniscient := {God} and Omnipotent := {God}—and then we have a well-defined notion of “is”: X is Y if X is a member of Y. However, with set theory, a new problem concerning “is not” is created. For instance, by the above definition of “is”, the definition of “is not” would be that something is not a member of a set. Then, “Omniscience is not Omnipotence” must mean that some member of either of these sets is not a member of the other set. Since there is only one member in both sets, therefore, to sustain the difference between Omniscient and Omnipotent, we must remove God from one of the two sets. Thereby, God cannot be Omniscient and Omnipotent, due to set theory!

If we insist that God is both Omniscient and Omnipotent, then we get the same problem of logical contradiction. As a result, the system of reasoning is either inconsistent (God is a member of mutually exclusive sets creating a logical contradiction) or incomplete (God cannot be both omnipotent or omniscient, so one of the above two claims must be rejected). Anyone who claims that God is both Omnipotent and Omniscient can now be called irrational because he has broken the cardinal principles of logic and set theory.

Multiple Forms of the Problem

The problem of logic, the problem of set theory, and the problem of Gödel’s incompleteness are the same problem in different forms. Incompleteness simply means that logic will not allow multiple meanings of the same word—e.g., “God is omniscient” and “God is omnipotent”. If we try to evade that problem by redefining “is” as membership of a set, then we will get a problem with “is not”. We can state the problem in many different ways—(a) one word has only one meaning, (b) sentences that use different meanings of the same word must be rejected, (c) any system that tries to include words with multiple meanings leads to contradictions, thereby rendering the logical system self-inconsistent.

It takes a while to get convinced about this problem. You have to try to avoid the problem in different ways, and you will find that each way leads to a new problem. For instance, let’s suppose we try to define God as a set {Omniscient, Omnipotent}. Since we are using a set-theoretic language, hence, we must define the members of the above set as follows—Omniscient:= {God}, and Omnipotent:= {God}. By substitution, God := {{God}, {God}}, which means that I must assume God to define God.

Let’s now try to define “is not God”. We can have two definitions—(a) some of the attributes of God are missing, or (b) all of the attributes of God are absent. By the first, we can remove either Omniscient or Omnipotent, and get not-God := {{God}}, which means “God is not God”. By the second, not-God := {}, which means nothing is not God (since not-God is an empty set). Hence, either God is a self-contradictory concept (God is not God) or everyone is God. Depending on your creativity, you can create infinite additional problems.

The Theological Form of the Problem

The Vedic tradition says—nāmnām akāri bahudhā—or that God has infinite names. God is Svarāt or independent. God is infallible or Acyuta. God is the supreme truth or Satyam-Param. God is endless or Ananta. God’s stomach is bound by a rope; hence one of His infinite names is Dāmodar. These names do not refer to different gods. They refer to one God with many names. However, those names are not synonymous. Viṣṇu Sahastranāma notes one thousand non-synonymous names of Lord Viṣṇu.

We cannot use these infinite non-synonymous names of God within logic, because we will always end up with contradictions—e.g., “the endless is bound by a rope”. To remain logically consistent, we have to remove either “endless” or “bound by a rope” from our conversation. Thereby, what is permitted by logic must also become an incomplete truth by eliminating some truth about God. Thus, we get a theological form of Gödel’s Incompleteness: The use of infinite non-synonymous names of God is inconsistent; however, if we restrict ourselves to only one name of God, then it is incomplete.

This is why religion is logically contradictory: The word “God” has many non-synonymous meanings. In Christianity, God is omnipotent, omniscient, and omnibenevolent. The mere use of three words leads to a contradiction in the form of the problem of evil (since I’m suffering, therefore, either God doesn’t know that I’m suffering, or He isn’t powerful enough to cure my suffering, or He doesn’t love me to cure my suffering). But if limit God to only one of the three words, then He is described incompletely.

My Realization of Incompleteness

I struggled for 15 years with this problem. Every subject I studied revealed the same problem, namely, that “one thing is not one thing”. It is actually many things. One word doesn’t have one meaning. It actually has many meanings. I traced this problem back to Aristotle, and then the historical legacies of Socrates and Plato. Socratic debates were conducted on the principle that any word with one definition is flawed. If you say that man is a two-legged animal, then a man who lost one leg in a war is no longer a man. Similarly, the definition of man as a two-legged animal includes penguins. Whatever definition we use, is either too broad or too narrow. But if we permit many definitions then we also get contradictions.

Plato then misled many generations of Greeks into believing that our inability to provide one complete definition is our flaw. In reality, there is an ideal world in which everything has one definition. Obviously, to be logically consistent, that ideal thing in the ideal world must not have contradictory definitions. For instance, the ideal man in the ideal world must either be kind or cruel. He cannot be sometimes kind and sometimes cruel. Platonic eternity meant everything was fixed, static, unmoving, and unchanging.

Aristotle then misled hundreds of generations by saying that we can restrict ourselves to those words which have one meaning. He thought that numbers are such words that have only one meaning. But Gödel disproved Aristotle when he showed that even numbers can be used in many ways—e.g., as names and things—and all such ways are necessary to complete mathematics.

At the end of this struggle, I wrote Gödel’s Mistake—The Role of Meaning in Mathematics, where I traced the origins of the paradoxes in set theory, number, theory, and computational theory. Digits like 1 and 0, for example, are used in three distinct ways in computers—(a) data, (b) instruction, and (c) truth values. A program is 1s and 0s—because a program is instructions. A picture file is 1s and 0s—because a file is data. And you can pass a data file to a program to print a truth value—true or false. However, since we cannot reconcile these three different meanings of 1 and 0, therefore, we have to compartmentalize them into three separate memories—data memory, instruction memory, and truth value memory. A computer compartmentalizes these three types of number interpretations.

The result of compartmentalization is incompleteness. For example, when you pass a program file to a compiler, the compiler treats it as data rather than instructions. It can at most check if the program has a correct syntax and not what the program does on being executed because it is parsing data rather than instructions. The compiler cannot know if the program is malicious. All problems of computer security are rooted in the inability to interpret numbers alternately as data and instruction.

Origins of the Problem in Reality

Identifying the problem is quite different from solving the problem, although part of identifying it is knowing that “one thing is not one thing”. The solution is found in Vedic philosophy—one thing is many things. Everything originates in one thing—God—who is infinite things at once. This is why there are infinite names of God that describe the various things that He is. Those infinite things include mutually opposite things—e.g., that He is endless, and yet He is bound by a rope.

The things that originate from God are fewer things at once. So, it is possible to look at the simplest thing around us—which has progressively expanded from more complex things to be fewer things at once—and claim that “one thing is only one thing”. This is a gross oversimplification of reality but if it works in some contexts, then people get addicted to oversimplifying everything in order to study it. Logic, or “one thing is only one thing” is the embodiment of that tendency to oversimplify things.

The solution to the problem requires aspects. The opposite things that God is are His aspects. We can liken these crudely to the six faces of a cube. Left and right, top and bottom, front and back, are logical opposites, but they are aspects of the cube. When you see one aspect, you don’t see the others. Hence, all the aspects are potentials that can be realized by a choice, and at the point of realizing that potential, the whole can be equated to the aspect by using the connector is. In another context, however, we can equate the whole to the opposite aspect by using the connector is. Contexts are not simultaneous. Thus, the left side and right side, the top side and the bottom side, and the front side and the back side, are the cube, but not simultaneously. The problem of logic is universalizing the mutually opposite claims.

Realizing the Problem in Reality

This problem reached its pinnacle in quantum mechanics where one macroscopic thing is many orthogonal microscopic things—like the faces of an infinite-faced dice—but you can never measure them simultaneously, which is why Einstein claimed that “God does not play dice”. The problem went further to say that the properties of a particle—e.g., position and momentum—cannot be measured simultaneously. Niels Bohr then devised the term “complementarity” to describe atomic reality.

However, nobody had the insight or foresight to rethink what “complementarity” meant in the case of the “simplest” things—if the simplest thing is not one thing, but many things, then logic fails because logic was formulated based on the assumption that at least the simplest things are just one thing.

If atomic particles are the “faces” of an object, then table and chair are the multiple faces of a room; the many rooms are the many faces of a house; the house is one of the many faces of the city, and each citizen of a country is one of the many faces of the country. If someone changes their citizenship, they change to become the face of another country. Thereby, “motion” is not uniform because the moving thing changes in the very process of becoming the face of something else. If a chair is moved from the kitchen to the bedroom, it changes imperceptibly because it is now a face of the bedroom instead of the kitchen. If we go to a holy place, we change because we are now the face of the holy place. To go to another planet, we must have the capacity to become the face of something that we are currently not. This would construct an inverted tree that converges from many things to many faces of one thing.

Nobody wants to go down that path, because they want to think of many things rather than many faces of one thing. The many things are separate from each other. The many faces of a thing are inseparable. So, the problem of quantum entanglement would be trivially easy if we said that many particles are just many faces of one thing, and hence while they seem distinct, they are actually inseparable. To avoid these conclusions, quantum physicists created a “measurement problem”—a “collapse” by which one thing which is actually many things, “collapses” into one thing—just to preserve the idea that one thing is only one thing as far as our everyday world is concerned and atomic reality is an exception.

The problem of quantum mechanics is also the problem of logic—the false idea that “one thing is only one thing”. If empirical evidence shows that one thing is many things, scientists create interpretations of that evidence that helps them preserve the false idea that “one thing is only one thing” because that is the lens through which science sees everything. They cannot think in any other way because rejecting that false idea requires them to start from scratch from the time that Aristotle had gone wrong.

The Absolute Necessity of Semanticism

This idea of aspectism—as seen through the six faces of a cube—however, proves inadequate when we realize that we are talking about a “cube” separate from its “faces”. In quantum mechanical language, there is something called a “wavefunction” akin to a cube, which collapses into the observation of one of the faces. When it collapses, you can say “this face is the cube”, but otherwise, “the cube is not just the face”. This is also a violation of logic, because sometimes “X is Y” but at other times “Y is not X”.

Therefore, aspectism alone doesn’t solve the problem, because there is a deeper problem of logic. We cannot superimpose the ideology that “one thing is many things” upon the logic that claims “one thing is only one thing”. We also need to be able to say that when we see one of the faces, we are seeing the cube. However, the cube is distinct from each of these faces. In simple words, “seeing one of the faces of the cube is also seeing the cube”, however, “the cube is not any of those faces being seen”.

This problem can only be solved by semanticism, in which “cube” is a concept and the six faces are conceptual aspects of that concept. As an example, “black is color” but “color is not black”. We have to treat the “cube” just as we treat “color”, and each of its “faces” just as we treat the various “shades”. Set theory does the opposite—it treats “color” as a set of “shades”, and reduces a cube to its faces. If we cannot see all the faces, or if one face is logically non-synonymous to others, or if one non-synonymous face is logically opposed to another face (e.g., top and bottom) then we run into many problems.

Intension and Extension

This problem is discussed in the philosophy of language by using two terms—intension and extension. The word “color” means something, which is its intension. The set of various “shades” is the extension of that intension. We cannot equate the intension to the extension, which means “color” has two non-synonymous meanings. These two meanings, while distinct from each other, cannot be separated from one another because the extension is a part of the intension, and intension is a part of extension. For instance, when we say that “black is a color”, the intension (color) is a part of extension (black). But since color includes black, therefore, the extension (black) is a part of intension (color). Thus, we cannot separate the intension and extension and we cannot equate these non-synonymous meanings.

This complicated problem of non-synonymous meanings of a word being inseparable from one another is called Bhedābheda in Vedic philosophy. We can extend this to a cube. The six faces of a cube are non-synonymous meanings of the word “cube”, not separable from the cube, and hence each other. Now, we can talk about how the same thing is many things without creating logical contradictions.

The simple statement is—nāmnām akāri bahudhā—or that God has infinite names. But this is not so simple, because the names are non-synonymous, and when the same thing is two different things, then logically speaking those two different things must be synonymous, giving us a contradiction. All the extra complexity comes from trying to resolve that contradiction to say how one thing is many things. We need to say that each thing has many aspects, and that thing and its aspects are meanings.

The Philosophy of Word and Meaning

This problem is seen in two distinct uses of the Sanskrit term pada. A pada is a word. But because that word has many meanings, therefore, those meanings are various aspects of the word. Hence, the term sampada means “along with the aspects”. But the term padārtha represents the “meaning of a word”. Thereby, when the five elements of Sāñkhya, namely, earth, water, fire, air, and ether are called padārtha, we have to ask: What is the pada? That pada is the concept in the mind (such as a table) and it is expanded in five ways as sound, touch, sight, taste, and smell into a sense-perceivable object. Thus, what is within the mind can be called sampada—“along with the aspects”. But what is perceived by the senses is called padārtha—the “sense-perceivable meaning of the concept residing in the mind”.

The “word” in the mind is not the sound we hear. But if we think of the concept, its presence in the mind has an effect on the sense of hearing, due to which the sound is triggered by the thought. Hence, the thought “table” and the sound “table” are not identical and not separable. The thought “table” can be called by another name, but since it is called in a particular linguistic context by one specific name, therefore, in that context, the name is one of the faces of the concept. We can strip all these faces from the concept and add a different set of faces because the thing is distinct from the faces, and yet, in a certain context, that thing is identified by using one of its many faces.

Therefore, we have to talk about the cube and its six faces as concepts. The cube is the sampada or intension, while its six faces are the padārtha or the extension. The sampada and padārtha are non-synonymous meanings of the word “cube”—because sometimes the word refers to my thought and at other times to the thing being seen. Both meanings are required but they are non-synonymous.

The additional problem is that just as thought gives rise to the object, similarly, the object gives rise to the thought. Thereby, the thought of “cube” is sampada with the padārtha of five sense-perceivable properties of the six distinct faces, and the five sense-perceivable properties of the six different faces are the sampada with the padārtha of the thought “cube”. This problem is called inside and outside. The cube is inside all the faces, and the faces are inside the cube. This problem is noted succinctly by stating that the five elements of Sāñkhya are inside and outside each other. For instance, everything is in ether and comes out of it. And everything that comes out of ether has ether within it.

Since the mental concept is present in the sense-perceivable reality, therefore, we can acquire the concept by observing that reality, provided we also use the mind along with the senses. When the mind is used along with the senses, the mind is called the “sixth sense”. It is that sense which perceives the concept in the sense-perceivable reality. However, the sense-perceivable reality is produced from the mental reality. Thus, we can produce a world out of thought, and we can perceive the world to know the thought that produced it. Thereby, the world is in the thought, and the thought is in the world. They are non-synonymous, inseparable, and necessary aspects of each other.

We can apply this principle to mind and body. The mind is in the body, and the body is in the mind. If the mind wasn’t in the body, then hurting the body would not hurt the mind. If the mind wasn’t outside the body, then the death of the body would mean the death of the mind. Therefore, we need two opposite claims for life and death. The materialist gets away by saying “the mind is in the body” because he is only talking about life. He needs the opposite claim while talking about death. Given the contradiction between the two claims, we can never solve the mind-body problem logically. Instead, we need a semantic way of thinking in which the cube is in the faces and faces are in the cube.

This philosophy is essential to explain how we can know God by chanting His names. That is because all the names of God are in God and God is in all His names. This is because those names of God are His many faces, and when we see one face, we are seeing Him. The ability to know God through many names entails that each name is one face of God, and He can be known through all the faces. Similarly, God has many forms—which are partial aspects of God akin to His faces—and God can be known from those many forms.

Implications for Theology

The many forms and faces of God are not monotheism in the classical sense—because one thing is many things. The many forms and faces of God are not polytheism in the classical sense—because those many things are one thing. This is not just the philosophy of God. Rather, it is the philosophy of everything. God just happens to be that thing with the greatest number of faces. But even a quantum particle has multiple faces. By increasing or decreasing the number of faces, we don’t change the fundamental principles of reality.

This idea was first articulated by Sri Ramanujāchārya through the Viśiṣṭādvaita philosophy. The “Advaita” is that one thing called the cube, and the many faces of the cube are the details, specifics, or Viśiṣṭa of the cube. The problem is that in this cube-face philosophy, the cube was not separate from the faces. Hence, if the soul was one of the faces of the cube, then when the soul suffers, then God must be suffering. To fix this problem, Sri Mādhavāchārya revised the philosophy into Dvaita where the cube and the faces are separate. This then led to the problem of how God could be the cause of the soul—and indeed the cause of all causes—if the soul was eternally separate from God. Then the philosophy of Śuddhādvaita was created by Viṣṇu Swami to say that soul and God are just like a drop and an ocean—same in quality and different in quantity. But this led to the new problem that if the drop is removed from the ocean, then the ocean must reduce. Finally, Nimbārkachārya created the philosophy called Bhedābheda in which the ocean and the drop are one and different such that the part is in the whole and the whole is in the part. However, we could not visualize how these contradictory claims could be reconciled in logic, hence Sri Chaitanya formulated the term Achintya Bhedābheda to say that all these things might be inconceivable but they are true.

The problem is that Vedānta applies not just to God, but to everything. The cube-face philosophy is a truth about God—as the thing with the greatest number of faces. And it is a truth about the quantum particle—the thing with the least number of faces. So, if the doctrine of God is inconceivable then the doctrine of atomic particles is also inconceivable. That—of course—is a fact now: Nobody can conceive how an atomic object can be in many places at the same time, be an individual thing and yet remain inseparable from other things, or how it can be described both as a wave or particle alternately. So, it is wrong to say that religion is inconceivable and science is conceivable. Both are equally inconceivable. In fact, if we understand the nature of the two problems, they are inconceivable in the same way.

However, if we can solve the problem of quantum objects—or any subject that is inconceivable due to each word having many meanings—then we have solved the problem caused by Achintya in the philosophy of Bhedābheda. This is the beauty of Vedānta or the “conclusion of knowledge”. It gives us one word, that summarizes everything from God to atoms. This one word—Bhedābheda—is the theory of everything, if we can explain what it means. What it means is simple—a cube-face philosophy of aspects with everything defined as meaning.

When we talk about the many names of God, such as infallible, independent, or endless, we are talking about the extension rather than the intension. These different extensions are like the many faces of a cube, but the cube is the intension. One face is not the other face, hence, infallible is non-synonymous with endless. And yet, because there is an intension, hence, they are all different names of God. The simple statement that “God has many names” is a very complicated problem of logic, set theory, Gödel’s Incompleteness, and linguistics—”one thing is factually many things”. If we don’t understand why the problem is this complicated, then we also don’t understand the statement.

When that one thing expands into many things, the intension expands into extension. However, by that expansion, the intension doesn’t cease to exist. It exists like a cube distinct from its six faces. If we cannot distinguish between the extension and the intension, or the intension being many extensions, then we will run into contradictions. Those contradictions are not unique to religion; they exist in all subjects because each word or sampada has many expansions called its padārtha. The same contradictions appear within religion when God is called by many non-synonymous names. Therefore, the problems associated with religion can be found in every other subject.

Four Causes of Incompleteness

Now we are in a position to talk about the four ways in which incompleteness manifests—(a) the whole is not reducible to its aspects, (b) each aspect is not equivalent or identical to the other aspects, (c) the parts are not separable from the whole although the whole can be spoken of separately from the parts, and (d) the various aspects of the whole, while distinct, cannot be separated from each other.

The Whole is Not Reducible to Its Parts

This problem is encountered in physical theories when the properties of macroscopic objects are not reducible to the properties of the microscopic. The microscopic properties are the various extensions of the macroscopic intension. However, they are organized in a specific manner, rather than randomly, just like the six faces of the cube have to be organized in a specific manner to construct a cubic structure.

In principle, we can cut the six faces of a cube and align them into a rectangle. We cannot reduce the cube to its six faces because those faces can also be organized into a rectangle. The cubic nature of the whole is responsible for organizing the faces into a specific structure, which means that the presence of the cube—the whole—gives rise to additional properties (i.e., the cubeness) absent from its parts.

Each Part is Not Equivalent to Other Parts

The six faces of the cube may seem indistinguishable from each other, but they are not identical. If we could color these faces by different shades, then we can also make them distinguishable. Even otherwise, if we examined these faces microscopically, we will find them non-equivalent. That non-equivalence of the faces also involves a distinction between “face” and its “parts”. All the parts are not identical and hence the face is organized as a square instead of being aligned in a straight line.

The thing that we consider “invisible” as a whole, has a visible effect, namely, that it organizes the parts in one way instead of another. The parts themselves cannot determine that organization. Hence, there is an observable effect, and yet, we don’t seem to perceive the cause that causes that effect. This is because that effect is akin to the concept in the mind different from sense perceivable effects. The thing we call a “cube” or “rectangle” is due to a mental perception rather than sense perception.

Parts Cannot be Separated from the Whole

In principle, we can break the cube into smaller pieces. However, all those pieces will be different from when they were part of the cube. This is just like we can cut an elephant into pieces and all the pieces would then be “dead”—i.e., they will lack the property of being leg, trunk, tail, ear, and stomach.

Reductionism is predicated on the premise that joining two things keeps those things unchanged. That is contradicted by what we now call “quantum entanglement” of the parts. The parts get entangled and acquire properties that they would not if they were non-entangled. The entanglement requires the concept of an “ensemble”—the whole that combines the parts into an entangled structure. If you try to remove the “ensemble”, then the entanglement breaks, and the parts are also mutually different. Hence, while the parts are in the ensemble, we cannot talk about them as if the ensemble doesn’t exist.

Parts Cannot be Separated from Each Other

The nature of entanglement is that we cannot define the parts independently of each other. Something would not be a tail unless there was also a trunk, ear, stomach, and leg. Every part requires the other parts to be defined as that part. Hence, we can only define all the parts collectively and mutually or not at all. Given the problem of circularity arising from this mutual definition, we define the parts in relation to the whole rather than in relation to other parts. This requires the whole to exist logically prior to the parts—i.e., as the intension that precedes the expansion of that intension into its extension.

Each extended part bears a different but unique relation to the intension. By this relation between intension and extension, the different extensions are also mutually defined and inseparable. Thereby we can say that the parts are not separable from the whole, and cannot be separable from other parts.

The Nature of Vedic Philosophy

Vedic philosophy can be summarized in one word—Bhedābheda. The simple requirement is cube-face philosophy with cube and faces being meanings. The rest of the discussion is simply what the different kinds of meanings are and how one meaning is the cube and other meanings are faces, and how those faces then become cubes to expand more faces.

There are many non-synonymous expressions of this philosophy:

  • Holism instead of individualism or reductionism
  • Unification instead of fragmentation
  • Aspects instead of “one thing is only one thing”
  • Personhood instead of objectivity
  • Semanticism instead of physicalism
  • Qualities instead of quantities
  • Completeness and consistency instead of either/or
  • Hierarchical reality instead of one-tier reality
  • Non-binary logic instead of binary logic
  • Higher and lower truth instead of true vs. false

Non-synonymous doesn’t mean a different thing. It just means a different face of the same thing. Every non-synonymous description is simply turning the cube to seeing a different face, just like the ideology of “one thing is only one thing” is a cube that produces many different problems of logic, set theory, number theory, computational theory, causal indeterminism, and probabilistic descriptions.

When we formulate Bhedābheda in the context of modern scientific problems or describe it in ways that it might not have been described before, we are motivating the same philosophy in the way that even those who don’t like to discuss God but would like to discuss the material world can learn about God. The doctor sometimes gives a sweet-tasting medicine so that children will accept them like candies.