Computing,  Logic,  Mathematics,  Philosophy

Sāńkhya, Reductionism, and New Science

Many people believe modern science is reductionist and an alternative anti-reductionist science must replace it. This post discusses why Sāńkhya is reductionist—because it reduces everything to only three modes of nature (sattva, rajas, and tamas). It also discusses why Sāńkhya is anti-reductionist—because the first mode of nature in this reductionist theory (sattva) represents the whole, which precedes the contradictory parts (rajas and tamas). Sāńkhya becomes anti-reductionist because the whole precedes the parts. And yet it remains reductionist because there are only three states in nature. The post discusses Gödel’s Incompleteness and how incompleteness arises from the problem of opposites. It then argues why the Sāńkhya anti-reductionist model of reduction can be made to work—because the opposition between rajas and tamas is a feature of the logical system, not a bug. In the process, we can see how a shift from bi-stable to tri-stable logic changes science so fundamentally. This shift (in logic itself) constitutes the essence of what we might call “Vedic science”: it is not pseudo-science, and it is not just philosophy; it is science in every sense of the word, just based on a different kind of logic. Just as binary logic is the basis of all modern science (because any law of modern science can be computed on a binary digit computer), “Vedic science” is based on a ternary logic computation.

The Five Blind Men and the Elephant

Five blind men are having a fight. One  says “this is a rope”. Another says “this is a tree trunk”. And a third says “this is a giant football”. They think they are talking about the same thing, but actually they are talking about different parts of a thing. The wise man informs them about the whole—the elephant—which reconciles the contradiction of parts. The problem is that you cannot see this whole. So you are likely going to reject it.

British philosopher Gilbert Ryle gives an example of this rejection in his book The Concept of Mind. He cites a visitor being shown around Oxford University, which—quite curiously—has no campus. The visitor is shown numerous colleges, libraries, laboratories, which in turn are comprised of bricks, the cement, the ground, the doors, the chairs, and classrooms. The visitor can obviously see all of these things. But if the visitor, after going around Oxford, asks “Where is the Oxford University?” then the answer to that would be that there isn’t such a thing as “Oxford University” aside from the bricks and mortar that make up the various buildings. What we mean by “Oxford University” is just the sum-total of all those bricks, wood, mortar, glass, and steel. Ryle’s critique of concepts is important because, in the case of an elephant, we can see a rope, a tree trunk, a giant football, but we cannot see an elephant. So, you might conclude that there are parts but the whole is nothing but the sum of the parts.

Ryle made a mistake, which is that whether or not the whole is recognized, the parts superficially appear to be the same but they are described differently. For instance, before you know about the elephant, you call something a “rope”. The same thing, after you know about the elephant, becomes a “tail”. The recognition of the whole does not change the sensations but it changes the concepts by which these sensations are described. The “tree trunk” becomes the “leg”, the “giant football” becomes the “stomach”, the “flat pan” becomes “ear”, and so forth.

Gödel’s Incompleteness Theorem

The problem of the five blind men is that they exchange information about their individual perceptions but they cannot reconcile them. If each blind man kept their knowledge to themselves, they would not experience the contradiction. Thus, individually, each blind man is consistent with observations. But between the different blind men, they are inconsistent, because they are dealing with different parts of a whole. This problem is currently faced in all areas of science where narrowly focused theories do successfully describe some phenomena but they cannot be extended to other phenomena. Thus, we have many contradictory descriptions—like the claims of the five blind men.

This problem is formally enshrined in the famous Gödel’s Incompleteness Theorem according to which a mathematical theory (one that deals with numbers) can be either consistent or complete, but not both. If you remain narrowly focused, the world seems consistent but incomplete. If you become broad-minded, and incorporate a wide variety of phenomena, then you can find completeness but you will now face contradictions.

We have to both understand this problem and solve it. Understanding the problem means realizing that the world is indeed built from opposites. Solving the problem means to find a way to reconcile the opposites—without merging, without dissolving, and without destroying them. Both seem futile if you think that the world is consistent. In other words, to solve Gödel’s problem, you have to give up logic as currently conceived—i.e. a domain in which only truth exists, and falsities cannot exist. We have to instead discover a logic in which both truth and false exist and we have to choose one.

A world in which only truth exists has no role for choice. Why would you need choice if there was no room for mistakes? A logic that begins in the idea that falsity doesn’t exist (because the world is logical) ends in the denial of free will. This is how modern science works: it replaces free will with mathematical laws. The law is logically and empirically proven, and once the law is known, there is no room for mistakes because everything is the outcome of that truthful law. And yet, as we have seen above, such mathematical laws are confined to narrow domains of material phenomena. If you try to cover a broader set of phenomena you run into logical contradictions between laws.

Mathematics tells us something very profound—namely that the world is comprised of opposites—which we cannot fit into a single theory (if we think that only truth exists). To describe the world, we must admit to the existence of falsities too. This logical system (in which both false and true exist) can be the basis of a new way of thinking in which the world is hot and cold, bitter and sweet. The duality of the world becomes the stepping stone to a completely different kind of logical thinking.

The Three Modes of Nature

Sāńkhya describes nature as built from the three modes of nature—sattva, rajas, and tamas. In the example of the five blind men, the elephant is sattva, while his trunk and tail are rajas and tamas. We normally see the world as built from opposites—e.g. front and back, left and right, inside and outside, and these opposites exist in everything—e.g. your body has a front and a back. But the mind also sees how these opposites are reconciled within a whole. That unity is sattva, which precedes the duality. It is the wise man who sees the unity to reconcile the opposites—e.g. by calling the tail and trunk parts of the elephant.

The elephant is the abstract idea, while the tail and trunk are the details inside elephant. The tail and trunk appear to be mutually opposed, if we do not include the idea of the elephant. But if the elephant is included, then the tail and trunk are not opposed. The resolution of the conflict requires a deeper perception by the mind, because the perception of the senses remains contradictory. This “mind” is the first mode of nature called sattva-guna which constitutes the “whole”. Within this whole, rajo-guna and tamo-guna create contradictory parts. In that sense, if you see the separate parts without prior seeing the whole, then you will find contradictions (as Gödel’s Incompleteness illustrates). The trick is to see the whole first, and then perceive the parts, because through such an approach, you can see that the parts are like two sides of the same coin. The sides are contradictory, but within a whole.

The problem is that you cannot perceive the whole by the senses. Your senses can only see one side of the coin at a time—and they cannot therefore see the coin itself. To see the coin, you have to take the two opposite sides and then reconcile them in your mind (rather than in your senses). Through such reconciliation, the coin becomes a pure concept—it exists in the mind, but not in the senses. “Oxford University” is thus a mental or subtle object, not a sensual object. You can see the different bricks in the buildings, but you cannot see the university because it exists only in the mind. If you reject this existence, then you would be faced with logical opposites—i.e. contradictions.

Since senses cannot see the abstraction, Western philosophy claims that it is unreal. Thus, I can see your brain, and your brain is real. But I can’t see your mind or ideas, so ideas must be unreal. When everything is reduced to sense perception, then all ideas disappear. Only a material reality—which cannot be given any meaning (because meanings are not visible)—remains. And now you cannot remain satisfied with this material reality, because it is full of logical contradictions. No matter what you think, your idea would be refuted by another observation. Since you trust your senses to arrive at truth, you will forever be tossed between opposite beliefs—because nature indeed is contradictions.

The Necessity for a Third Logical State

The problems of logical contradiction are addressed by recognizing a third category—the whole. Of course, simply recognizing that there is a third category doesn’t solve the problem unless we see it as a new logical category. This is owing to the Gödel’s Incompleteness problem where we cannot fit a third logical category into the current form of logic. This is important enough to deserve a discussion.

In computers, all data and programs are represented using two digits—1 and 0. To the naive person, 1 and 0 appear to be numbers, but they are actually not numbers. If we understand Boolean Logic and Binary Arithmetic then we can see that 1 and 0 are logical states because Boolean Arithmetic treats 1 as TRUE and 0 as FALSE. Therefore, if for whatever reason you think that the world is logically consistent, then think again—1 and 0 are logical states denoting TRUE and FALSE, and they exist simultaneously! Boolean Arithmetic already violates fundamental philosophical assumptions in Aristotelian logic, but unless we admit a third logical category, we are resigned to maintaining the semblance of continuity with classical logic.

Using the two bits 1 and 0 we can encode the value for any kind of property—e.g. color, form, size, distance, tone, pitch, and so forth, but we cannot encode their types. There is no way to say that a number represents color and not distance. Computers have no understanding of concepts. A computer is like the five blind men who touch the skin of the elephant and try to derive some concepts based on previous training—i.e. mapping percepts to concepts (now called Machine Learning).

This mapping doesn’t actually make the computer a “thinking machine” because it cannot represent concepts since a concept is not 1s and 0s. A concept is a third logical state, and owing to Gödel’s Incompleteness unless we admit that state, the machine remains one of the five blind men.

Historical Struggles with Concepts in Logic

To address this problem, we have to explicitly bring concepts into logic. Those of you who are familiar with the development of modern mathematics, would know that Bertrand Russell and A. N. Whitehead made such an attempt in early 20th century producing Principia Mathematica. However, they did not actually revise logic; instead they added concepts to logic, calling these concepts “sets”, resulting in Set Theory. This theory is now known to be riddled with paradoxes and incapable of dealing with some concepts such as “self” (for more on the problems related to the concept of “self” see a previous post).

The fundamental mistake in Set Theory is that a concept is reduced to its extension (i.e. members) rather than to its intension (i.e. meaning). When we try to use such a theory to describe concepts, we quickly arrive into a situation of opposites—because concepts are defined through oppositions (hot vs. cold, black vs. white, bitter vs. sweet). Since we already reduced the set to its members, we don’t have a “higher” construct that can “resolve” this contradiction. That now leads to paradoxes.

In Sāńkhya, a concept is that which is logically prior to the parts, because the universe is constructed as an inverted tree in which the more abstract precedes the more detailed. As a useful contrast, Bertrand Russell also constructed a hierarchy of types—but bottoms-up rather than top-down. To be doubly sure that nobody mistook it for a top-down hierarchy, he added an Axiom of Reducibility which essentially says that I must be able to reduce the higher concept to a collection of lower concepts!

Three Modes of Nature as Logical States

Sāńkhya is a truly top-down hierarchy in which the abstraction precedes the details. Since the parts are described as opposites within the logically prior whole, the concept of “whole” must be described as neither of these opposites. This in turn means that we have to expand the logical states in computation. As I described earlier, we have to add a new logical state—“Neither TRUE nor FALSE”—in a new kind of logic, which replaces the Square of Opposites in Aristotelian logic with Chatuskoti.

This logical system is created from the three modes of nature. While there are four categories, only three modes are involved because the “both” category mixes the two opposite modes (rajo-guna and tamo-guna) while the “neither” category is the original mode (sattva-guna) that precedes the opposites. These three modes construct the tree of material nature, in which sattva-guna is the higher node, while rajo-guna and tamo-guna are two opposite branches. In this logical system, it is possible to not just talk about the parts of an elephant (e.g. the tail and the trunk) but also the whole elephant prior to the parts. Clearly, since this “elephant” exists in a disembodied state, we have to say that the mind of the elephant precedes the elephant’s body parts.

Modes of Nature and the Logic of Nature

For the last two thousand years, Western philosophy has pursued an onerous dream of reducing matter to numbers, and then reducing numbers to logic. This dream was shattered in the early part of the 20th century due to Gödel’s Incompleteness Theorem which said that even if we are successful in reducing all matter to numbers (i.e. in formulating a complete mathematical theory of material nature) we would still fail in reducing mathematics to logic. Quite separately, each field of physics has found that it is unable to reduce matter to numbers which goes by various names such as uncertainty, unpredictability, probability, or incompleteness. Essentially, we cannot predict what will happen, which means nature is doing something but that causality we are not able to capture in a mathematical theory.

The dream of Western philosophy lies shattered because of the twin problems above. First, we are not able to reduce matter to numbers. Second, we are not able to reduce numbers to logic.

Sāńkhya has the potential to address these problems. Matter, in this theory, is numbers. Your senses, sense perceptions, ideas, beliefs, intentions, and morals, are all numbers. There are two numbering schemes—absolute and relative—owing to which everything has a universal and local number. The absolute numbering is how the nodes of a semantic tree are counted from root to leaf. The relative number is how an arbitrary node becomes the root of my personal counting system. Sāńkhya enables us to see how everything in the material world is numbers—i.e. matter is reduced to numbers.

Just like binary opposites 1 and 0 create all numbers, and these numbers then become text or language, and this language is then used to encode physical states (but not concepts), similarly, in Sāńkhya, there are three categories which create a new kind of logic, which is used to construct numbers, which exist as sounds, and represent morals, intentions, beliefs, thoughts, sensations, and sense objects. This is the ultimate dream of knowledge—reduce all matter to language, language to numbers, and numbers to logic. Sāńkhya represents the fulfilment of that dream that the world has pursued for millennia.

Sāńkhya and Reductionism

Owing to this property, Sāńkhya is also reductionist. The difference is that all Western thinking tries to reduce the world to two states—TRUE and FALSE—while Sāńkhya reduces everything to the three modes of nature (TRUE, FALSE, and neither TRUE or FALSE). In comparison to Aristotelian logic, Sāńkhya adds a new logical category—“neither”—which produces a hierarchical tree of numbers, which becomes the tree of nature when we choose some node as the root of all our personal meanings. The difference is miniscule, and yet this small change in logic drastically and fundamentally alters the world.

We know that the reduction of nature to the binary logical states (TRUE and FALSE) cannot work due to Gödel’s Incompleteness Theorem, and the project of materialist reduction has already failed. We have to now understand how the reduction to three logical states can work. This is, in essence, the sum and substance of “Vedic science”. It involves showing how everything reduces to the three modes of nature. At the most superficial level, this science is about how the material world reduces to perception and cognition. At a deeper level, it involves a space constructed like a tree, and nodes on that tree are absolute and relative positions counted using numbers. At an even deeper level, it involves the understanding that these numbers are produced from the three modes of nature—i.e. logical states.

Therefore, understanding Sāńkhya means we first reduce matter to perception. Then we reduce perception to concepts. Then we reduce concepts to numbers. And finally we reduce all numbers to logic. This is the fundamental promise of knowledge—the world is real because it is logical. You don’t need anything more than logic to understand the world, but of course you need to get to the root of the question: Why is the world logical? What underlies the idea that nature is rational?

Transcending the Material World

Rationality has far more profound foundations than we have thought so far. I will discuss in a subsequent post why the material world “depends” on a transcendental world: the reason is that a tri-stable logical rationality (a system of reasoning) is based on properties of consciousness. The three modes of material nature are actually reflections of three properties of consciousness—sat, chit, and ananda. They provide the justification for why the material logic is tri-stable.

If we agree that the material world is tri-stable or the three modes of nature, then we can understand the nature of the world beyond matter. If we insist that the world is bi-stable, and only one state (truth) actually exists (and falsity doesn’t), then there is no need for a world beyond the present world.

In that sense, a new science of the material world points towards a transcendental world, simply by seeking the logical foundations of the material world. This is unlike the current material science which concludes that there isn’t a world beyond the present world because some truth exists in the current world (the world is real) and if we can find that truth in the world then anything incompatible with this truth (i.e. science) must not exist.

The conclusion emerging from modern science—namely that since this world exists, anything else incompatible with this world cannot exist—is based on a flawed bi-stable logical thinking in which only truth exists. Once we recognize that even in this world contradictions exist, and a new science that reconciles these contradictions requires us to induct both contradictions and their reconciliation into the same logical system, then one is compelled to ask: Why does the world have three states, rather than one? Clearly, one is better than three. Therefore, a description that says there are three states is not final, and we must seek how three states can be reduced to just one.

That reduction is outside the material world, and we have to transcend the material world—after we have reached the depths of material logic. In short, the study of matter ends in material logic, but if you want to know why we have this logic, then you must transcend the material world. Whether or not you transcend, simply by acquiring a new way of thinking you can see that there is a necessity for a justification for matter outside matter. We can know how the world works, but we cannot explain why it works this way without transcendence. This justification serves as the foundation of the present world.