This article simply attempts to marry vedantic philosophy with mathematical logic. Before you start reading I should provide a disclaimer that I am not formally trained in Philosophy, and what follows should be considered as musings of a dilettante.

The article has been primarily divided into three segments. In the first segment, I try to elucidate some basic definitions and tenets (of the *Taitereya Upanishad*), which supposedly form the backbone of the *Advaita* framework and is subject to usual contention from the rationalists.

In the next two segments I try to draw logical inferences, and pose arguments and counter arguments, using the work of the two most iconic logicians, western academia has seen in the last couple of centuries, namely Bertrand Russel and Kurt Godel. The last section attempts to use Godel’s incompleteness theorems and *Drik Drishya Vivek* (from the *Mandukya Upanishad*) to counter the rationalist argument.

**What is ‘Brahman’? (Taitereya Upanishad: Second Chapter – Brahmananda valli))**

What is Brahman? The definition provided is as follows:

*“Tadeshabhyukta satyam gyanam anantam brahma*

*Yogada nihitam guhayam parameteoman*

*Suashnute sarvankyaman brahmana sahavipashchiteti”*

*Brahman is existence (Satyam), Knowledge (gyanam), infinite (anantam).*

Brahman literally means that expands without limit and it is impersonal. It simply means vast. There is no “it” qualifying it. Let’s dissect the three parts of the definition and unravel them.

*Anantam & Satyam*

*Anantam* literally means no limit. What do you mean by limit? In Vedanta there are three kinds of limit

- “Limit in Space”,
- “Limit in time”,
- “Limit in object”

__Limit in Space__: Spatial boundary. If something has no limit in space it implies, there is no point in space where it is not. So Brahman is omnipresent.

__Limit in time__: Periodic boundary. Not limited by time implies Perennial or eternal. Birth and death are limits in time. Creation and destruction are limits in time. Krishna says “whatever is created is bound to die”.

__Limit in Object__: This refers to identity. For example, if an object is a bowl it cannot be a cup or another bowl. Now not limited in object implies its complement is null or in other words what it is ‘Not’ is nothing. That’s confounding. What it actually means is “everything”. But then any “thing” is necessarily limited in object. Thus, the only alternative is searching for a commonality in all “things” or “objects”. Now that sounds like an insurmountable task, right?

But let’s delve a bit further. Let’s look at a logical truism. If there is an object ‘A’ it “EXISTS”. Thus, for any object (from sub-nuclear particles to galaxies), it must “EXIST”. So “EXISTENCE” is common for all objects if real.

Okay, makes sense! Does this satisfy the first two conditions too? The answer is yes. “Existence” is an abstraction and is certainly not limited by time and space. Infact, time and space too exist.

*Satyam* in Sanskrit literally translates to truth. And if true, existence follows from an obvious logical truism (because if it does not exist, non-existent truth would be a self-contradiction).

*Gyanam*

*Gyanam* quite literally translates into knowledge. Now this “knowledge” too needs to satisfy the first property i.e *Anantam*. Now what would this imply?

Let’s say an economics graduate knows about Keynes’ theory, whereas a Physics graduate would know about Einstein’s relativity. So knowledge of this kind is certainly limited in space and object. Also did you know about Pythagoras’ Theorem when you were born? No, you learnt it in high school. So the knowledge about Pythagoras’ theorem is certainly time-dependent or limited by time. Now we seem stuck.

What is that “knowledge” which satisfies the three conditions mentioned in the definition of ‘Brahman’? Certainly not anything acquired through intellect. The solution methodology used in solving this problem is “guessing a solution and proving it’s right” (an often used strategy in Mathematics).

Let’s look at ‘consciousness’ which actually enables the intellect to function. Now every individual has ‘consciousness’. You have and had consciousness right from your first second of existence. So clearly it is not limited in space or time. Infact, the Upanishads claim that even if the universe is absent, consciousness is still there, in an unmanifested form.

A synonym for “existence” in Sanskrit is *“Sat”,* and that for “knowledge” it is *“Chit”.* Thus “Brahman” is often referred to as “*Sat Chit Anantam*”.

So far so good. Seem perfectly logically coherent. Right? Well now comes the two mystic *Mahavakyas* from the *Mandukya Upanishad*, which will make all Vedanta – followers lock horns with the rationalist. What are they? Here you go:

(“You are that”): It simply and bluntly says “You (the reader) are Brahman”*Tat Tvama Asee*: “I am Brahman.”*Aham Brahmasmi*

Now the question is how do we prove this? Experientially we don’t feel like “Brahman”. We feel like the body mind combo. Well a believer might say, one cannot disprove it. But that’s not a philosophically sufficient defense. Why? Keep reading!

### Bertrand Russel’s Teapot

Let’s say if I make the statement “A little tea – pot is revolving around Pluto”. Are you bound to accept it? I might say that since it is impossible for you to disprove it, you ought to accept it as “true”. Russel says no. You as the listener need not bear the burden of disproving it. The “burden of proof” lies on me, the one would made the statement.

This, in turn implies that the “burden of proof” of the two *Mahavakyas* lies on the one(s) making the statements i.e the *Upanishad*.

Now the contest is turning interesting, isn’t it?

Well, before we wonder what the proof can be or whether there is actually a proof, there is a loophole which needs your attention. Is it necessary that anything which is “true” can be proved? The famous mathematician Hilbert in the early 1900s said “Anything which is true ought to be proved”. But this notion was turned around by two revolutionary ideas. Entered the legendary Austrian logician Kurt Godel in the 1930s with what is famously called the “incompleteness Theorems”.

### Gödel’s Incompleteness Theorems

Gödel’s incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert’s program to find a complete and consistent set of axioms for all mathematical/ logical systems or frameworks is impossible.

The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths. For any such consistent formal system, **there will always be statements that are true, but that are unprovable within the system.** The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.

Employing a diagonal argument, Gödel’s incompleteness theorems were the first of several closely related theorems on the limitations of formal systems**. They were followed by ****Tarski’s undefinability theorem**** on the formal undefinability of truth**.

**Tarski’s undefinability theorem**, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics. Informally, the theorem states that *arithmetical truth cannot be defined in arithmetic*.

### Drik Drishya Vivek

The fundamental tenet of the “*Drik Drishya Vivek*” is that the observer/ analyser is certainly different from the observed/ analysed. This fundamental distinction between the subject and the object is further used to argue that we aren’t the mind – body complex. Let us see how?

It starts with the eye and an object we see. Well, of course they are different. Infact, the only thing our eyes can’t see are the eyes themselves. The eye can see a reflection of itself in the mirror, but not the eye itself. Let’s go ahead.

What we see, forms an inverted virtual image on your retina. Then the electrical impulses carry the information to the brain, which then interprets it. Now, here the retina is the observed or analysed and the brain is the observer. And ofcourse they are different.

Let’s move further ahead. Whatever we see evokes a reaction for certain. If I see a beautiful garden, I feel pleasant. If I see an unfettered tiger in front of me I will be scared. Now both pleasant and scared are states of the mind, which are nothing but a complex state determined by varying degrees of secretion of hormones. But the point is can we observe the state of our minds?

The answer is ofcourse yes! I can feel the pleasantness which a beautiful garden will evoke. This is where *Drik Drishya Vivek* argues that since the observer and the observed are fundamentally different and the state of the brain can be observed, what we consider “I” should be different from the brain or the intellect. Which in turn leads us to the two above *Mahavakyas.*

Given the* Drik Drishya Vivek*, it is easy to observe that what is being termed as “I” (which in turn is Brahman) is apart from the intellect, which would imply that fathoming it with the axioms of the intellect should not be trivially possible.

Does it mean that it not having a proof in the framework of our intellectual framework makes it ‘false’? The answer lies in Godel’s incompleteness theorems. A perfect retort to the imbecile obsession with “proof”.

**-by Dripto Bakshi**

*(Featured image source)*

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