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What is truth? Some people say that truth means existence. If a tree exists, then it is true. But it also means that if you think that the tree doesn’t exist, that thought is also true, because your thought exists. To allow for the distinction between truth and existence, we have to invoke meanings. The thought that the tree doesn’t exist exists, but it is not true, because truth pertains to the meaning rather than existence. Once truths are tied to meanings, and not to existence, then we can consider the fact that the bigger meanings are truer than the smaller ones, and consistency with the bigger meaning is a greater criterion for truth than the consistency with the smaller meanings. Thereby, we can say that if the tree’s existence is inconsistent with the bigger truth, then even if the tree exists, thoughts about the tree are not true. Similarly, if God is the bigger truth, and the world is inconsistent with God’s nature, then we must say that the world exists, but is false—like a dream or false thought. Then, there is no contradiction between the claims—(a) the world exists, and (b) the world is false. The world’s existence is like that of a false sentence. This is one of the many examples of non-binary truths, and this post discusses their nature.

The Problem of Fundamental Truth

One of the central problems with binary truths is that all truths are equally true, and all falsities are equally false. For example, if God is true, and a table is true, then God and table are equally true. The nature of equal truths is that you can derive one truth from another. Thus, if God and table are equally true, then, we can derive the table from God, and God from the table.

The ability to derive one truth from the other means that no truth is fundamental. God may be an axiom for one person, and the table may be an axiom for another person. Since both are equally true, therefore, simply by changing the axioms, we can alter what we consider fundamental. Thereby, someone can say that tables are fundamental truths, and God is a derived truth.

In Vedic philosophy, we can derive God from the table, and the table from God. And yet, God is the fundamental truth. This is because God is pervasively true, while a table is contextually true. The pervasive truth is also immanent in the contextual truth; hence, it is possible to derive God from the table. But since God is transcendent to all other truths, hence, it is possible to derive everything from God. Thus, we arrive at a nuanced position in which there is a fundamental truth, which can also be derived from the non-fundamental truths, and yet, the ability to derive the fundamental truth from the non-fundamental truth doesn’t mean all truths are equal.

The fundamental and non-fundamental truths are reconciled by a hierarchy of truths, which are organized like the root, trunks, branches, twigs, and leaves in an inverted tree. The properties of the root, trunk, branch, and twig are immanent in the leaf. Hence, by knowing the leaf fully, we can know everything. If the soul is the leaf, then by fully knowing itself, it can know everything else. Likewise, by fully knowing the table everything else can be known perfectly. And yet, that doesn’t make the soul or the table fundamental truths, because they are not pervasively true.

Qualities Break Classical Logic

This system of hierarchically organized truths depends on qualities. The deeper quality—e.g., color—is embedded in the shallower quality—e.g., red. And yet, because color is more pervasive than red, hence, it is a more fundamental truth. Likewise, sight is more pervasive than color (because of colorless shapes), hence it is even more fundamental than color. The system in which all truths are equally true, and no truth is fundamental (as a result of which, we can arbitrarily switch the axioms, changing the definition of the fundamental truth), depends on quantities.

The system of qualities, however, leads to serious issues in binary notions of truth. For example, if red is color, but color is not red, then the principle of identity (one thing is itself) in logic is broken. Since both red and blue are colors, but color is neither red nor blue, therefore, the principle of mutual-exclusion (either red or blue) is broken. Likewise, since color includes both red and blue, therefore, the principle of non-contradiction (not both red and blue) is broken.

When all the principles of binary logic are broken, then the doctrine of oneness-and-difference is employed, because binary logic means oneness-or-difference. This is called Bhedābheda.

Equivalent Ways of Describing Qualities

We can see an intimate connection between (a) hierarchy, (b) non-binary logic, (c) qualities, (d) immanence and transcendence, (e) oneness and difference, and (f) more or less true.

If we emphasize that two things are separate, we would be partially correct because even if we emphasized that two things are identical, we would be partially correct. This partial correctness is the result of things being more or less true. Other than the Absolute Truth or God, everything is less true, because it is less pervasively true. But that doesn’t mean it is false. When certain truths are widely true, but not pervasively true, we can call them contextual truths. But when certain truths are true only for an individual, then they are individual truths. In contrast, the Absolute Truth or God is universally true. Hence, the above principles are also equivalent to the distinction between universal, contextual, and individual truths as grades of more or less true.

As we divide the qualities into smaller parts, we arrive at something that is initially contextually true and then individually true. For example, ‘man’ and ‘woman’ have several contextual definitions in different societies, and then, each person carries a unique idea of what it means to be a ‘man’ or ‘woman’, which will not be identical to the views of other men and women.

However, there is still an ideal man and woman, partially represented in each contextual and individual definition, which constitute the universal truth. Thereby, we can connect all the above ideas to degrees of ideality. The universal truth is most ideal, but contextual and individual truths are less ideal. And yet, those may be the most ideal things needed in a given context.

The most ideal truth is also the most complete, and the less ideal truth is less complete. For example, the most ideal man is the most complete man, and the less ideal man is a less complete man. Therefore, we can connect ideality to most true to the completeness of the truth. The path to that completeness goes through non-binary logic involving qualities through a hierarchy of steps that are progressively more ideal and complete, and end in the most complete and ideal.

The most ideal and complete is self-justified, hence it becomes the fundamental truth because it doesn’t need anything else for its justification. A table is not self-justified. But God is self-justified because He is the ideal and complete truth. Every other non-ideal and incomplete truth is a partial truth, less true relative to the complete truth, and a part of the complete truth.

Since the understanding of this complete truth passes through qualities, hierarchy, non-binary logic, immanence and transcendence, oneness and difference, recognizing less and more true truths, that are successively more ideal, therefore, whenever we try to describe the complete truth using a system of linearity (all truths are equally true), binary logic (identity, mutual exclusion, and non-contradiction), quantities (that are either one or different), and objects (that are either inside or outside, never immanent and transcendent), then we get many contradictions.

The Cause of Gödel’s Incompleteness

These contradictions are noted in Gödel’s Incompleteness as “no system of arithmetic can be both consistent and complete”. The simple reason is that complete truth can only be obtained in a system of non-binary logic, using hierarchies, less and more true truths, that are successively more ideal and complete, with oneness and difference, immanence and transcendence.

Modern thinking is flawed not in the narrow sense that some of the formulae do not fully account for the data, or there are too many formulae, or some formulae contradict other formulae. It is flawed in a much more serious sense that it employs binary logic, quantities, treats all truths as being equally true, and objects which can never be inside and outside another object. Objects, quantities, and formulae also lack the notions of ideality, and hence self-justification.

Thereby, even if there were a complete formula that described all reality, we would still ask: Why this formula and not another one? Of course, contradictions in the path to that formula entail that such a formula would never be attained. There can, of course, be millions of formulae that are selectively useful in different contexts, but those cannot be called universal truths. At best, we can call them contextual truths, and as the contexts become more complex (requiring more additions to the formula) each formula would simply become an individual truth—i.e., it seems true to one person, in one situation, for one kind of problem, at one place and time.

Implications of Quantity Thinking

When quantity thinking is extended to all reality, then God must be quantitatively bigger. Then, He cannot be a person with a form, because all these forms are quantitatively finite. How can God appear within the universe as an incarnation if He is bigger than all universes? How can anyone ever see God, if they are not able to see all the universes at once? How can God fit within the arms of a mother, when the mother is just like us? The conclusion is always that God cannot be known, except as an infinity. That infinity is imperceptible because we are finite. The only way to know the infinite is to become infinite ourselves. Therefore, either the word ‘infinity’ is meaningless (the word ‘infinity’ is not like the word ‘table’ because we can point to something finite called a table, but the word ‘infinity’ doesn’t refer to anything finite) or it is meaningful only if we become infinite. The former is materialism and the latter impersonalism.

Once you designate ‘infinity’ as a meaningless word, then you can start eliminating all other words that cannot be reduced to something finite and measurable in terms of something you can point to as a thing. For instance, either ‘love’ is a certain number of particles or it is meaningless. Similarly, either ‘beauty’ is a certain number of particles, or it must be meaningless. Now, a ‘bigger person’ is simply one who is taller and bulkier. The definition of ‘big’ is simply a larger quantity, and what cannot be measured in terms of a smaller quantity is meaningless. Due to the equality of all truths, you can define each thing in terms of interchangeable axioms. For example, you can say that something is either 1 kilogram or 0.001 tons. Thereby, neither kilogram nor ton is fundamental truth; they are equally arbitrary because either of these can be used to measure, hence, whatever we call fundamental truth is an arbitrary choice of a measuring standard.

Now, the ‘soul’ must be either all the particles in the body, or it is a meaningless word. Thereby, if you urinate or defecate, then the ‘soul’ must be reduced in proportion. When you eat, then the soul must expand. And when the body disintegrates, then the soul has ceased to exist.

Theism Necessitates Non-Binary Logic

When quantities, binary logic, inside vs. outside, and all truths are equally true, take hold of our worldview, then atheism is inescapable. That atheism can come in the form of materialism or the sense that there is no soul or God. Or, it can come in the form of impersonalism, namely, that there is an infinite truth, but it can never be known by the finite unless the finite dissolves into the infinite. Therefore, anyone who thinks that they can reconcile theism with modern science hasn’t actually worked out the nature of the problem before they seek the solution.

The solution is non-binary thinking based on qualities, that involves a hierarchy of more and less true truths, some of the things that exist are not true, the truth is immanent even in falsities, which make the falsity simultaneously one and different from the truth. Yes, the world is false, the world exists, God is immanent in the world, so it is neither true nor non-existent. By knowing the false, we can know the truth, because the truth is within the falsity. This solution is incredibly difficult and seemingly inconceivable, but it is the only possible solution. When all that is impossible has been eliminated, then whatever remains, however difficult, must be accepted.