Reasoning vs. Arguments

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If we make a claim, its rationality can be judged by checking its consistency against our assumptions. Reasoning is the connection between my claim and my assumptions. If my claim is consistent with my assumptions, then it is well-reasoned. It may still not be true. To establish the truth, we must prove that my assumptions can explain all the available evidence. This process to arrive at the truth is useful.

Arguments instead are clashes between two sets of assumptions. You prejudge something to be false because you believe in the opposite idea. You attack their position from the premise of your truth and their falsity. You compel them to counterattack your position, from the same type of prejudgment. This process is endless and futile. It can never lead one to the truth. But it can be theatrical entertainment.

This distinction between reasoning and arguments is important for any debate. Reasoning is necessary to establish how something follows given a set of assumptions. Evidence is necessary to establish that the assumptions completely explain the evidence. Arguments are unnecessary once we have established that one set of assumptions is complete while the other is incomplete. Arguments are useless if they point out differences in sets of assumptions without showing why one set of assumptions is better than another. However, it is these useless arguments that most people indulge in most of the time.

The Nature of Reasoning

Reasoning always involves a set of assumptions and a method of inference. If something can be inferred from the assumptions, following the prescribed rules or methods of inference, then it is well-reasoned. However, it may still not be true. To establish the truth, we have to check if the assumptions are correct.

We cannot establish the correctness of assumptions just by the internal consistency of assumptions and inferences. This is why reasoning is not itself a method of knowledge unless its assumptions can be validated. To prove those assumptions, we have to test their completeness against the available evidence.

If a set of assumptions can explain all the available evidence, then it has been tested against the evidence, and it can be called true. However, if a set of assumptions cannot explain all the evidence, then it must be considered falsified by the evidence, and we must look for other assumptions.

Thus, we can provide some simple and precise definitions of useful terms for our future use.

• Reasoning: Checking if the claim can be inferred from the assumptions.
• Completeness: Checking if the assumptions explain all the available evidence.
• Truth: Those assumptions that completely explain all the available evidence.

The Nature of Mathematical Reasoning

In mathematics, reasoning is defined as logical consistency with axioms. That is, given a set of assumptions, we must be able to show that inferences follow those assumptions using rules of logic. By logic, we mean binary logic, that uses principles of identity, non-contradiction, and mutual exclusion.

In mathematics, checking if all randomly constructed statements can be proven or disproven, by checking their consistency against a given set of assumptions, is called completeness. Consistency check uses binary logic. By this logic, we must be able to prove or disprove any arbitrary statement. If we can do that, then the assumptions are complete with respect to some specific domain of statements.

For example, if there is a set of assumptions that can be used to logically prove or disprove any arbitrary statement about numbers, then it will be called a complete set of assumptions for numbers. If there is a set of assumptions that can be used to logically prove or disprove any arbitrary statement about geometrical shapes, then it will be called a complete set of assumptions for geometry.

Thereby, consistency is a weak requirement for reasoning, and completeness is a strong requirement. If the strong requirement is satisfied without violating the weak requirement, then the assumptions along with the associated logic used for reasoning are collectively called the rational truth. If we can satisfy the weak but not the strong requirement, then reasoning is incomplete consistency and not truth.

Based on this definition of rational truth, we could expand our vocabulary to include rational truth.

• Reasoning: Checking if the claim can be inferred from the assumptions.
• Completeness: Checking if the assumptions explain all the available evidence.
• Truth: Those assumptions that completely explain all the available evidence.
• Rational Truth: Assumptions that either prove or disprove all arbitrary statements.

Rational truth is a stronger claim than truth because truth is only required to explain all the available evidence, but rational truth must prove the impossibility of all that is not evidence.

Logical Falsities in Mathematics

It may surprise people to know that mathematics is false—by the above self-appointed idea of rational truth—because of Gödel’s Incompleteness Theorems that show no system of {axioms, logic} can be complete. If we can prove or disprove some arbitrary statements, but not others, then {axioms, logic} are not complete, and hence not rational truth. If no system of {axiom, logic} can prove all the arbitrary statements about numbers, then we have established that no arithmetic system is rational truth.

This problem perplexed Gödel so much that he became a Platonist. A mathematical Platonist says: There is obviously mathematical truth, but we may not be able to prove all the truths. Even those things that we cannot prove or disprove must either be true or false. The limitation of proofs cannot limit their truth. But we are entitled (whatever it means) to personal beliefs, even if we cannot prove them.

Mathematical Platonism is religion in disguise. It says: Even if I cannot prove or disprove something, I can believe in it because the proposition must be either true or false. Let’s apply mathematical Platonism to God’s existence. We cannot be ambivalent about God’s existence because the statement “God exists” is either true or false. We cannot be rationally an atheist, because we haven’t disproven the statement “God exists”. And we cannot call “God exists” rational truth because His existence is not proven. You can still believe in God, and reject ambivalence and atheism, although it cannot be called rational truth.

Gödel reinvented Christianity in mathematics via Platonism, by allowing people to have whatever beliefs they liked because they could not be logically proven or disproven, but they had to be true or false. Protestant Christianity had asserted that idea earlier: We cannot prove God’s existence by reason. Therefore, the belief in God’s existence had to be based on faith alone (Sola Fide). A rationalist would argue that we cannot believe in anything unless there is proof for it because everything is either provably true or false. Gödel demonstrated that everything cannot be proven but it can be true.

Based on Gödel’s mathematical Platonism, we can expand our vocabulary to include faith in it.

• Reasoning: Checking if the claim can be inferred from the assumptions.
• Completeness: Checking if the assumptions explain all the available evidence.
• Truth: Those assumptions that completely explain all the available evidence.
• Rational Truth: Assumptions that either prove or disprove all arbitrary statements.
• Faith: The thing that I believe in despite my inability to prove or disprove it.

The Advent of Indeterministic Theories

There are a wide variety of belief systems, which do not predict or explain all the evidence. They are called indeterministic theories. Indeterminism in physics corresponds to Gödel’s Incompleteness in mathematics. Like mathematics can construct arbitrary sentences which cannot be proven or disproven, likewise, nature can give us arbitrary facts which cannot be predicted or explained by physical theories.

Indeterminism pervades every single physical theory. These theories explain or refute some of the evidence (like some arbitrary mathematical claim), but not every single one of them. The theories allow many possibilities, some of which are observed sometimes, but we cannot say when, where, why, how, or what will be observed by who. Indeterminism can be divided into two parts: (a) you can provide some probability of something happening, and (b) you remain totally silent even on probabilities.

Classical mechanics, for example, is indeterministic on inelastic collisions (where particles split or merge), and you cannot even give probabilities of which outcome is more or less likely. If we add constraints on classical mechanics (e.g., that the total number of particles is constant), then we get Statistical mechanics, where the possibility that can be achieved in more ways is also more likely. Quantum mechanics, similarly, is indeterministic but it gives probabilities on the likelihood of outcomes.

Based on a survey of such prominent physical theories, we can further expand our vocabulary.

• Reasoning: Checking if the claim can be inferred from the assumptions.
• Completeness: Checking if the assumptions explain all the available evidence.
• Truth: Those assumptions that completely explain all the available evidence.
• Rational Truth: Assumptions that either prove or disprove all arbitrary statements.
• Faith: The thing that I believe in despite my inability to prove or disprove it.
• Indeterminism: Ability to explain and predict some but not all the evidence.

The Discovery of Propaganda

There are many things that are programmatically outside a set of axioms because the axioms were framed after rejecting those possibilities. An example is the Cartesian mind-body divide. The “mind” in question includes thought, feeling, intention, values, and choices. They are also called qualities and were designated secondary properties by Locke. Due to Lockean and Cartesian distinctions, the abovesaid phenomena of the mind cannot be modeled using numbers, binary logic, or physical properties.

However, you can still run the propaganda that someday these phenomena will be explained by physical properties. A lie repeated often enough convinces people that it must be the truth. This lie takes many forms: (a) the mind is an epiphenomenon of physical properties without a step-by-step explanation of how the mind arises from physical properties, (b) the mind may not be fully understood today, but it would be eventually reduced to physical properties even though it is logically impossible to do so, and (c) because mind-body dualism has proven to be intractable and science has been successful, therefore, we must conclude that the body is governed by science, and the mind must be reduced to the body.

Based on the prominence of such dogmas at present, we can further expand our vocabulary.

• Reasoning: Checking if the claim can be inferred from the assumptions.
• Completeness: Checking if the assumptions explain all the available evidence.
• Truth: Those assumptions that completely explain all the available evidence.
• Rational Truth: Assumptions that either prove or disprove all arbitrary statements.
• Faith: The thing that I believe in despite my inability to prove or disprove it.
• Indeterminism: Ability to explain and predict some but not all the evidence.
• Propaganda: The thing I believe to be true despite all the contrary evidence.

The State of Science Today

In current science, we know that reasoning (using binary logic) is possible, but reasoning doesn’t guarantee the truth, because its assumptions are unproven. We also know that there is no completeness in any theory because no theory explains all the evidence that lies within the scope of the theory; this is due to indeterminism. Therefore, we cannot assert the truth of any theory. We know that rational truth is impossible due to Gödel’s Incompleteness Theorems. We can still hold onto our faiths, due to mathematical Platonism, although we can neither prove nor disprove it. Finally, to proclaim progress despite unresolvable issues, there must be propaganda to assert the impossible despite the contrary evidence. If that lie can be repeated enough times, it will be considered true.

Based on these considerations, we can now pass a verdict on the above vocabulary:

• Reasoning: Possible and widespread.
• Completeness: Not attained thus far.
• Truth: Not attained thus far.
• Rational Truth: Logically impossible.
• Faith: Possible and widespread.
• Indeterminism: Pervasive in all theories.
• Propaganda: Possible and widespread.

What do you see? I see that science has failed in getting to the truth. Every theory is indeterministic. No theory explains all that data that lies within its scope, due to indeterminism. It is logically impossible to attain completeness using mathematics due to Gödel’s Incompleteness. Therefore, you can:

• Use indeterministic theories to create gadgets with limited scopes,
• Hold onto religion-like beliefs because they cannot be disproved,
• Employ propaganda to claim things contrary to all the evidence.

The Landscape of Arguments

In this environment, where the best-case scenario is a probability, the worse case is strongly held beliefs because they cannot be disproved, and the worst case is propaganda despite contrary evidence, arguments amount to debates between (a) probabilistic likelihood, (b) unproven beliefs, and (c) outright lies. These arguments constitute battles between different assumptive worldviews.

The worldview that has led to probabilistic likelihood uses binary logic, numbers, and physical properties. The worldview of unproven beliefs uses scripture and freely invented dogmas by myriad gurus and priests. The worldview of propaganda uses television, media, and theatrics to deceive the ignorant public.

The fact is that none of these three are founded on truth, per the definition of truth above: Those assumptions that completely explain all the available evidence. People are arguing based on their arbitrarily chosen hypotheses, that (a) either incompletely explain evidence (i.e., they explain as much as they neglect), or (b) are neither supported by nor contrary to evidence (evidence is totally irrelevant to their claims), or (c) contrary to evidence (disproven by evidence but forcefully asserted anyway).

Rationality Does Not Imply Truth

You can see all these people arguing rationally, which is checking if the claim can be inferred from the assumptions. But there is no truth in them because the assumptions themselves are not validated. Their arguments amount to a clash of cultures, ideologies, and dogmas: Each argument makes different assumptions, without establishing prior that their assumptions are true by completeness.

Many people invest a lot of time and energy in listening to these arguments and hope that they will find the truth by someone else critically examining each position for them during a debate. This is a lazy and hopeless approach to the problem of truth because you can never find the truth through arguments between contradictory ideologies, worldviews, or dogmas unless you can prove that one of them is complete. There is no other definition of truth, or at least, nobody has been able to give one thus far that soundly and consistently distinguishes between verifiably true, unverifiable faith, and verifiably false.

Therefore, arguments are useless, even though they are rational—i.e., they can be logically derived from some assumptions—because through the argument we do not validate the assumptions. We are simply demonstrating that the worldviews are contradictory, which we knew even before those arguments.

How Do We Know the Truth?

Therefore, in any useful system of knowledge, there is absolutely no room for arguments. But there is ample room for reasoning, stating the assumptions, testing those assumptions against evidence, and disproving a system of thought by showing how the assumptions are either internally inconsistent or contrary to the evidence. This rational and evidential process is not argumentative because we always enter the worldview of the person we are trying to refute, accept all their assumptions, and then show that there is a problem in their worldview, without bringing in any extraneous assumptions.

Once we comprehensively refute that worldview, then we come out of that worldview and enter a new worldview, and we can reemploy evidentiary reasoning to prove that there is no problem. Again, there is no argument, because we are not trying to pit one worldview against the other. We are instead subjecting each worldview to the same evidence and the same standards of reasoning.

This is how we know the truth. It is not a debate between two sets of unverified assumptions. It must be the independent verification of each worldview to show that it is either true or false. As long as the definitions of truth, evidence, and reasoning are shared and agreed upon, this is achievable.

But that is not what happens most of the time. Most of the time it is a clash of unproven ideologies, using one ideology’s assumptions to critique another ideology’s assumptions, with no attempt to apply the same standards of reasoning, evidence, and truth to each ideology separately and individually. This is because people are interested in winning the argument, rather than in knowing the truth.

The Format of Classical Indian Debates

Debates between positions have been a long-standing Indian tradition. But they were quite different from modern debates. In a classical Indian debate, two parties—let’s call them A and B—would sit opposite each other. One of the two parties—let’s say A—will make a claim. B will then ask A some questions, without making any assertions. As A answers the previous question, B will ask them new questions. B will try to establish an inconsistency or incompleteness in A’s worldview, based purely and entirely on A’s assumptions (i.e., without introducing his worldview’s assumptions). If that is achieved, then A’s worldview has been falsified and will be rejected, although A hasn’t yet lost the debate.

After this, the process reverses: B makes a claim, and A will then ask them some questions, without making any assertions. As B answers the previous question, A will ask them new questions. A will now try to establish an inconsistency or incompleteness in B’s worldview. If that is achieved, then B’s worldview has been falsified and will be rejected, although B hasn’t yet lost the debate.

The decision of who won the debate is based on who withstood the test of scrutiny throughout. If both parties failed the mutual scrutiny, then nobody won the debate. If one of them stood the test of scrutiny, while the other did not, then their worldview is accepted and they won the debate. Winning a debate amounts to withstanding another person’s scrutiny of your worldview based on your worldview. It doesn’t matter what your assumptions are, as long as they are internally consistent and explain the evidence. It was never a clash of worldviews.

This process of debate allowed the emergence of radical ideas in Indian society because nobody was prejudging a worldview based upon their current worldview. It is impossible to arrive at new radical ideas in today’s environment because everything is prejudged by people’s current worldviews. People are unable to enter another person’s worldview to see reality differently from their perspective.

Present-day debates begin with two parties making their “opening statements” where they outline their worldviews, while subsequent arguments between these parties constitute a comparison between apples and oranges. They never see the world from another viewpoint and find its flaws. Even if such flaws are identified, the debaters do not abjure their ideas. They remain stubbornly resilient, employing phrases like “I believe” and “I think” while judging the other person from their unsubstantiated worldview.

Debates in Nyāya Philosophy

The system of Nyāya philosophy models our worldly existence as a debate between us and Nature. You can choose whatever assumptions you like, and Nature will ask you questions. Based on your responses to those questions, there will be further questions. This process continues until you hit a dead-end, and cannot answer Nature’s questions. Now you have lost. You must change your assumptions and restart.

You can change your assumptions infinite times but Nature will not release you until you can fully answer all of Nature’s questions consistently and satisfactorily. Once you have validated to Nature that you have the correct understanding of reality, then Nature will release you. You have not won the debate and Nature hasn’t lost. But you have graduated from Nature’s examination system. Nature has validated that you have the correct understanding of the truth. And the truth will set you free.

The point is that debates are natural, but arguments are not. If you have the wrong understanding of reality, then Nature will simply present you with contrary evidence to disprove your understanding. If you have a somewhat better understanding, then Nature will smile at you, take you down a garden path, and spring a surprise on you that you were not expecting. Nature is perfect at debating.

Science-Religion Debate Example

Let’s apply this idea to a science-religion debate. The scientist should not bring his assumptions to debate a religionist. Rather, he must enter the religionist’s worldview and point out inconsistencies or the inability to explain the available evidence. Then, the religionist can enter the scientist’s worldview, and point out either internal inconsistencies or the inability to explain available evidence.

But this never happens. The scientist says: We have built useful technology and hence religion is false. And the religionist says: You have made society immoral, hence, your ideas are false. After some time, both assert their “freedoms” to practice and propagate their respective belief systems.

There is nothing wrong with assuming the existence of God, provided we can explain all the evidence based on that assumption. The existence of God, at this stage, is an axiom. It can be used to reason—i.e., establish its conclusions, which have to be tested against evidence of this world. Likewise, there is nothing wrong with assuming materialism as an axiom. But it has to be used to reason—i.e., establish their conclusions, which have to be validated against the available evidence. If either religion or science fails to explain the available evidence, or there are internal inconsistencies in their explanations, then both have lost and both must be rejected.

However, this never happens, because scientists don’t know enough about religion, and religionists almost as a rule know very little about science. To have a rational debate, one must enter the other worldview and refute it on the grounds of inconsistency or incompleteness. But nobody wants to do that, because they simply cannot hold a viewpoint different from theirs, even for the purposes of a debate. But neither side will acknowledge it as their shortcoming. They will instead use a debate to assert the superiority of their viewpoint, trying to invalidate the other party. It also cannot happen because both debating sides are either inconsistent or incomplete or both. If they accepted the correct standard for a rational debate, both would lose.

Given the problematic nature of these debates, most scientists and religionists evade them by insisting that they will not entertain criticism from outsiders although criticism from insiders is acceptable because they know that the insiders will not question most of their assumptions. They have a firm faith that their worldview will outgrow and outlast everyone else’s, so the opposing party will die and disappear from the face of the earth, eventually. By escaping the scrutiny, they create their private echo chambers which can neither be improved nor rejected. The repetitious and self-affirming echo chamber constitutes propaganda and not truth.

Rational Debates are Not Arguments

Debates were not always useless. They can still be useful if the rules of the debate are changed. For example, no party should be allowed to make assertions while countering the other party. They can only ask the other party questions and show that their claims result in incompleteness or inconsistency. This is a logically precise version of a debate in which you begin with some axioms—the original claims of a debater—and derive conclusions from them to prove that they are either inconsistent or incomplete. That is, they either contradict themselves, or other evidence, or fail to account for the evidence.

The definition of rationality is that we are free to choose our assumptions. The definition of truth is that we must validate the completeness of our assumptions against all the provided evidence. Hence, by a debate, carried out rationally and based on the abovesaid methodology of debates, we can arrive at the truth. However, if we break this method, then we convert a debate into an argument. Such arguments are not meant to elicit the truth. They are meant to be theatrical entertainment for the audience.