The Truth is Infinite

First- and Second-Order Logics

Suppose I show you an apple, and ask you: Is it one truth, or is it many? What will you answer? Here are some facts to consider. The taste, smell, color, shape, size, and weight are many truths about the apple. So, obviously, there are many truths. But the collection of these truths is one thing—the apple—so it is also one truth. Therefore, the correct answer to the question would be: It is one truth and it is many truths. It is one truth as an apple and it is many truths as taste, smell, color, shape, size, and weight.

However, you cannot reconcile the statements “it is one truth” and “it is many truths” within Aristotelian logic because one and many are mutually contradictory positions in logic. Therefore, you have to choose one of those contradictory positions—i.e., either “it is one truth” or “it is many truths”. Both positions will deny you some truths. Either you have to say that that there is an apple without taste, smell, color, shape, size, and weight. Or, there is taste, smell, color, shape, size, and weight without an apple.

Both positions constitute incomplete knowledge. In modern terminology, “it is an apple” is called a first-order claim because “order” is defined relative to the object and the object is first relative to itself. The statements “it is taste”, “it is smell”, “it is color”, “it is shape”, “it is size”, “it is weight” are called second-order claims because they pertain to properties that are second relative to the object. A rational system that deals with first-order claims is complete and consistent (because truth is one) but one that deals with second-order claims is either incomplete or inconsistent (because there are many truths).

The Problem of Incompleteness

This problem is called Godel’s Incompleteness. It arises because logic cannot admit that the same thing is one truth and many truths. If something has just one property, then the property and the object become identical—e.g., this is an apple. The problem arises if the same thing has many properties—e.g., having taste, smell, color, shape, size, and weight. If there are many properties, then is becomes has. But when each of these properties is given a value (such as by saying that the color is red), then has again becomes is. For instance, we say: The apple is red.

Thus, we go through the phases of “this is apple”, “this has color”, and “this is red”. Since “this” is also round, therefore, we get the one truth of apple and many truths of red, round, and sweet. Then we have to choose between “it is one truth” or “it is many truths”. The inconsistency is choosing both options “it is one truth” and “it is many truths”. The conversion of “has” to “is” arises because the relation between apple and its properties is not the same in different directions. We can say that the “apple is red” but we cannot say “red is apple”. This is a non-binary condition.

The non-binary condition arises becasue at the point of observation, we see only one property while the other properties are excluded. For example, while seeing the color, the taste and smell are excluded. At that juncture, the whole apple has been reduced to just its color. Therefore, we have to say that the apple is red, at this juncture, because the whole apple is just reduced to red at the point of observation. However, this is a truth that depends on the time, place, context, and person observing the apple. This is not a universal truth. For another time, place, situation, and person, the apple will be sweet. Red and sweet are potentials of the apple, and the apple is reduced to one potential at the point of observation, although it can be reduced to another potential for another observation.

Thus, first-order logic pertains to truths that are independent of time, place, situation, and person. But second-, third-, fourth-, and other higher-order logics pertain to truths dependent on time, place, situation, and person. The former is universal truth and the latter is contextual truth (based on time, place, and situation) and individual truth (based on the person). There is one universal truth for each thing and infinite contextual and individual truths. If we limit oursevles to universal truth, then the knowledge system is incomplete. But if we try to universalize contextual and individual truths, then the system is inconsistent. A complete logical system requires us to reconcile universal, contextual, and individual truths.

The Failure of Set Theory Too

Mathematicians tried to solve this problem using set theory. The solution said that we will make a set whose members are taste, smell, color, shape, size, and weight. Let’s try to do that with two apples.

A1: {sweet taste, fruity smell, red color, round shape, 6 inches size, 200 grams weight}

A2: {sour taste, fruity smell, green color, oblong shape, 4 inches size, 120 grams weight}

Since A1 and A2 have different members, therefore, they cannot both be called “apple”. The set theory construction applies only to one thing and cannot be applied to multiple things because each thing is a different set. Thus, if we try to solve the problem of one truth vs. many truths using set theory, we do get one thing (the set) and many things (the members) but that one thing is not the same thing (apple).

Whatever definition of the concept apple you come up with, will always exclude some apples. For example, if apples are defined as red color, then the green apples will be excluded from being apples. As a result, we can use set theory to talk about individual things, but never to talk about general concepts. No general definition of an apple will admit all the things that we would like to call apples. In fact, any sufficiently precise definition of an apple will only admit one thing as apple and exclude all other things. Thereby, knowledge cannot use concepts, types, or classes. It can only talk about individual things.

The Reason Why Mathematics Fails

Despite the generic failure of logic and set theory (the foundations for the rest of science), there are scenarios in which both of them work. This is the scenario where each set has only one definition.

Natural Number Set N: {1, 2, 3, 4, …}

Rational Number Set R: {1/1, 2/1, 1/2, 1/3, 2/2, 3/1, …}

Note how N and R are not like apples. There are many apple variations. But there is only one set of all natural numbers. Therefore, natural number is not a class of things. It is one set. A set is not a class. A class allows variations such as in the shape, size, and color of an apple. A set allows no variation. Hence, sets and classes are different ideas. But everywhere in textbooks, we find the words set and class being used interchangeably. This is highly misleading. There is no theory of classes. There is just a theory of sets. Nobody can define an apple using set theory because an apple is a concept and not a set.

Similarly, numbers can denote both things and names. When the thing and the name are identical, then there is no problem. It is just like calling a barber Mr. Barber. But sometimes they are not the same, like calling a carpenter Mr. Barber. When names and things are misaligned then we have to use numbers in two different ways. But mathematics cannot use numbers in two ways without creating contradictions. That contradiction is just like calling a carpenter Mr. Barber and interpreting it to mean that he is a barber, then finding that a carpenter doesn’t work like a barber.

The existence of knowledge requires the existence of language, and the existence of language requires the existence of names and concepts, different from things. A word in a language is a thing, but it can also be a name and a concept. Hence, words need to exist in three modes—name, concept, and thing. But in mathematics, words can only exist in one mode—e.g., as a thing. In a world governed by mathematics, a language that uses names and concepts cannot exist. Without language, knowledge cannot exist. The failure of mathematics is the result that knowledge and languages can exist. The failure of mathematics is a good thing. The alternative would leave us without language and knowledge.

Plato, Aristotle, and Modern Science

In Platonism, there is a world of pure forms called the Platonic world. A perfect apple exists in this world. All real apples are imperfect imitations of the perfect apple. But Plato had no explanation of how the perfect apple becomes many imperfect apples. Who is inserting the imperfection in the perfect apple? How are we going to study the imperfection when we don’t even know what the perfection looks like? Platonism is therefore a useless idea because it creates more questions than it gives answers to.

Hence Aristotle junked Platonism. He limited rational thinking to only those things that are precisely definable within the logic he created—namely arithmetic and geometry—and not bother with all other concepts such as the concept of an apple. Science was restricted to arithmetic and geometry, but the rest of the world was not reducible to science. Science was a very limited mathematical endeavor.

However, during Enlightenment in Europe, scientists created a new religious dogma that said that God thinks mathematically and He made a mathematical world. There was no foundation for this claim. It was just one of many fictitious claims that Christianity had been making for centuries. They had gotten so comfortable with fictitious claims that they accepted a new religious dogma in which God made the world and God is a mathematical thinker hence everything in the world had to be mathematical. The Aristotelian definition of science was rejected. Now mathematics applied to the whole world.

Fanaticism of the Religious Dogmas

We can see that an apple is one truth and its taste, smell, color, shape, size, and weight are many truths. We can also see that logic cannot reconcile how the same thing is one truth and many truths. Despite this failure, Aristotelian logic is not abandoned in science. We can see that set theory cannot explain classes. We can also see that without classes, our minds are not reducible to science. Despite this failure, set theory is not abandoned as a model for reality. We can see that the ordinary world rests on ordinary language. We can also see that ordinary language uses words as things, names, and concepts. Hence, language cannot be reduced to mathematics because numbers are always used in one way. Despite this failure, mathematics is not discarded as a model for reality.

This problem perplexes many people. They don’t know that science is based on a fictious Christian dogma that God is a mathematical thinker. Atheists may abandon God, but they don’t abandon the religious dogma that nature is mathematical. Their rejection of religion is superficial when they keep believing in the religious dogmas. Since modern science is rooted in a religious dogma, and all religious dogmas are impervious to reason, hence, even science is impervious to reason. The failure of its dogmas doesn’t end those dogmas. Science sticks to its religious dogmas just like other religious dogmas are carried forward despite evidence against them.

A more appropriate word for modern science is “Christian Science” because it came out of Christian assumptions. No other religion in the world has said that God is a mathematical thinker. Nobody has ever claimed that nature is reducible to mathematics. That is a uniquely Christian claim. Factually, Christianity took exclusive credit for creating science. It should now take the exclusive blame for the fundamental problems of modern science too. Therefore, I don’t see any essential difference between science and religion; to me, both are just Christianity.

The Necessity of Mind and Body

Returning to the example of an apple, the apple is a concept that resides in our mind and the apple’s taste, smell, color, shape, size, and weight are the percepts that reside in our body. If we have to talk about a real apple (apart from our senses and the mind), then the apple is a mind and the apple’s taste, smell, color, shape, size, and weight are the apple’s body. The one truth pertains to the mind and the many truths pertain to the body. If we study the many truths, then we are studying the body without the mind. If we study the one truth, then we are studying the mind without the body. The apple is the whole and its properties are its parts. The whole without parts or the parts without the whole are incomplete.

To understand the apple, we have to say that there is one thing with many faces. We can compare the apple to a cube with six faces. The cube is the whole and its six faces are parts of the cube. The faces of the cube are many truths and the cube is one truth. The same thing is one truth and many truths. However, the one truth and many truths are also distinct as concepts (mind) and percepts (body). We can never perceive the cube as a whole. We can only conceptualize a cube. We can perceive the faces of the cube one by one. The cube conceptualization allows us to unify six faces into one single thing.

The Coordinate Reference Frame

The one truth and many truths are reconciled in mathematics by the use of two separate constructs—algebra provides a definition of the mental concept and geometry provides the bodily incarnation of the mental concept. The mental concept is compatible with many bodily incarnations—i.e., many cubes. The mental concept and the bodily percept are mapped together using a coordinate reference frame. This reference frame is something in between algebra and geometry or mind and body and joins them.

This coordinate reference frame is called ākāśa in Sāñkhya philosophy. We loosely translate it as space. But it is not universal space. It is a personal coordinate frame that connects the body and the mind. Each person can use a different coordinate frame to connect the mental and bodily realities. Therefore, even if we want to call it a space, it is still a private and personal space that connects algebra to geometry.

Algebra uses variables such as x, y, and z. However, there is always a fixed numerical relation between these variables. For example, in the Pythagorean Theorem, x² = y² + z². Variables can be varied in numerical values provided a numerical identity is preserved. The numerical identity doesn’t exist for a concept such as an apple. Thus, an apple cannot be reduced to an algebraic equation or geometry. Nevertheless, we can talk about the concept apple and the percepts of taste, smell, color, shape, size, and weight.

We can still visualize a multi-dimensional space with taste, smell, color, shape, size, and weight as its dimensions in which the properties of the apple will be given a unique location. But where will we place the concept apple that unifies all these properties into a single entity? It cannot be a dimension like taste, smell, color, shape, size, and weight because it is not a percept. It cannot be a location along these dimensions because it is not a value. It has to be something that binds these dimensions together.

Thus, Sāñkhya philosophy talks about the mind as the origin of ākāśa. The concept apple is the origin, the properties of taste, smell, color, shape, size, and weight are dimensions of space and the values along these dimensions are the percepts of the apple. Since there are many percepts, therefore, the apple is simultaneously in many dimensions that are united into a single origin. The many percepts are the many truths of the apple and the origin or concept apple is the single truth. The same thing is a single truth and multiple truths. The mental reality is singular and the bodily reality is plural.

An Alternative Conception of Space

This alternative type of space is described as an inverted tree in which the root is the origin, the branches are emanated from the origin, so they are part of the origin, and yet they become distinct truths. The distinct truth is not a separate truth. It is part of the truth. The concept is the whole truth, the percepts are the partial truths, and hence the whole is singular whereas the parts are plural.

The immediate casualty of this type of space is logic. The Law of Identity is broken because the apple is red but red is not apple. The Law of Non-Contradiction is broken because the apple can be either red or green. The Law of Excluded Middle is broken because the apple can be both sweet and sour. The body of the apple (percepts) has been produced from the mind (concept) hence one thing is many things.

In modern science, space is distinct from its material contents. The contents are plural and the space is singular. But since space and matter are distinct, therefore, the same thing is not singular and plural. Logic applies to this space because one thing is identical to itself (the law of identity), one thing is either itself or something else (the law of excluded middle) and nothing it both itself and something else (the law of non-contradiction). These three-fold logical laws apply when mind and body are separated. But if we attempt to unify mind and body—as in concepts and percepts—then logic is immediately broken.

Dualistic vs. Non-Dualistic Logic

Western thinking is built upon dualisms of concept and percept, mind and body. This thinking operates on first-order claims in which each object has just one property such that we can equate the object to the property. For example, “bachelors are unmarried men” works in first-order logic because the property of being unmarried men is the only property of the bachelor object. Even if we try to separate this sentence into “bachelors are unmarried” and “bachelors are men” the first-order logical system is broken because by the law of identity, all men must be unmarried. In first-order logic, we cannot separate man and unmarried into separate properties. They have to be just one property. A dualistic logic works only when the two sides of a dualism (e.g., object and property) are semantically identical.

A non-dualistic logic doesn’t require identity. Apples can be either green or red, both sweet and sour, and the apple is red but red is not apple. A non-dualistic logic integrates percepts and concepts, mind and body. There are multiple things bound into one thing without being semantically identical.

In the dualistic system, there is a single truth about everything. In a non-dualistic system, there are infinite truths about one thing. These truths are like the different faces of the same thing. When seeing a different face, we neither separate the face from the thing nor do we equate the face to the thing. This makes non-dualistic logic non-binary. Two things are neither identical nor different. They are non-different. The non-different category is not semantically identical to the not-different category.

The Inevitable Collapse of Universalism

Plato and Aristotle were both trying to create universalism. Plato applied universalism to the whole world and Aristotle restricted it to mathematics. Christianity then took Platonic universalism and applied it to religion and God, although the application was restricted to the mind. Christian Science then married Plato and Aristotle and universalized mathematics as the model of the whole material world.

The fact is that universalism is a false ideology because it insists that there is only one truth about everything when the fact is that there are infinite truths about everything. Universalism works by separating mind and body and under first-order logic. Therefore, the entire chain of events from Plato to Aristotle to Christianity to Christian Science are a series of horrible mistakes because the universalism that they were trying to apply to study reality is itself a false idea about reality.

Reality is not just one thing. It is also many things. The many things are not separate things each with its own nature. They are rather imbued with the nature of one thing from which they have expanded like the percepts of a concept, or the body of a mind. The separation of body and mind, the separation of various parts of the body, and the reduction of reality to separate parts is how universalism came to treat “truth is one”. This is a false theme because reality cannot be separated into parts in this way. Therefore, universalism is also a false theme for science and religion.

The Meaning of Truth is Infinite

By saying that “the truth is infinite”, I don’t mean that there are infinite separate truths, each of which is just one truth. What I mean is that there are infinite truths that are mutually inseparable such that we cannot discount the presence of other things in knowing anything. This is a common theme in atomic physics where the problem is called entanglement. Its importance has been minimized by the false assumption that quantum physics might eventually reduce to classical physics, where we would be able to separate the entangled parts into individual parts. The ontological assumptions of separability are so deep in science that even when entanglement is seen, it is hoped that it will eventually disappear.

To think of an entangled reality, we have to visualize reality as a single body or an organism. In contrast, modern science visualizes reality as comprising many independent parts, which is called mechanism. We cannot know any part of the body without understanding the body as a whole. The grasp of the whole assists the grasp of the parts and vice versa. By “the truth is infinite” therefore I mean that each truth is infinite, rather than there are infinite truths. Everyone can accept that there are infinite truths. But reducing that infinity to individual things that are one truth each is the method of modern science. This method has deep roots in Christianity where all individuals are things-in-themselves. Each individual is then just one truth unrelated to the other individuals that are separate truths. The reductionism of modern science is also a Christian theme.

Thus we see a continuity from Greek antiquity to modern times in terms of fundamental principles of reductionism, individualism, and separationism. The superficial ideas have changed, but the deep underlying themes have remained unchanged. It is these themes that lead to incompleteness, because reality is entangled. Entanglement is not just an ontological claim, but an epistemological, and logical one too because it changes our idea of knowing (i.e., one thing cannot be known in isolation) and logic (three principles of Aristotelian logic don’t hold). If we persist on treating entanglement as merely an ontological problem, and try to grasp this ontology within the traditional Western epistemology and logic, then we get incompleteness in which either the unity or the diversity are unknowable.