Sometimes, we instinctively feel something is right but struggle to articulate it logically and coherently.
In such cases, we are forced to express it directly using intuitive language. While this might resonate with those who strongly share the same intuition, it fails to convince those who are skeptical or hold opposing views.
Then, we have no choice but to try and explain it logically and systematically. If we give up, we would have to either ignore the other party or exclude skeptics from the discussion. From a societal perspective, this could lead to division and a form of social violence.
Furthermore, the problem here is that if something feels right intuitively but cannot be explained verbally, it risks being labeled as subjective, arbitrary, or idealistic in a fanciful sense. If it involves uncertainty, it might be labeled as optimistic or pessimistic.
On the other hand, there are cases where skeptics or those with opposing views can logically explain their opinions verbally. This puts the intuitive side at an even greater disadvantage. If they are labeled with the aforementioned terms, any third party observing the discussion will perceive it as a weak, labeled opinion versus a strong, logical one.
This is compounded by the bias of assuming a gap between intuition and logic—a deeply rooted belief that logic is always correct and intuition is unreliable.
However, things that are intuitively perceived as correct should, in most cases, also be explainable logically. Intuition and logic are not contradictory. It merely means we haven't yet found a way to connect them.
The reason why opposing views can be logically explained is often due to differences in underlying assumptions, objectives, or hypotheses regarding uncertainty. Therefore, logically explaining something that feels intuitively right under different assumptions, objectives, and hypotheses is not a contradiction.
Once both opinions can be logically explained, the discussion's focus can then shift to what to do with the assumptions, objectives, and hypotheses. This allows third parties observing the discussion to express their will based on whether they agree with the assumptions, objectives, and hypotheses, rather than being swayed by labels or the perceived strength of the arguments.
What we must discover to logically explain in words what we intuitively feel is correct is what I call intellectual crystallization.
The Psychological Captivity of National Interest
Here, I'd like to present an example of intellectual crystallization: a logical explanation concerning the ideal of world peace and the counter-argument of national interest.
World peace is generally intuitively desirable, but in the face of the realism of national interest in actual international society, it tends to be dismissed as an unattainable ideal.
Simply put, national interest refers to a situation advantageous for a country's survival and prosperity.
Given two options, choosing the one that offers greater advantage constitutes a decision that aligns with national interest.
However, when we say a certain option is advantageous for a country's survival or prosperity, to what point in time does this advantage refer?
Historically, losing a certain war has sometimes led to a country's long-term survival.
Conversely, a country's prosperity could also, in some cases, ultimately lead to its downfall.
This implies the unpredictability of national interest.
Furthermore, the term "national interest" is often used by those who seek to steer decision-making towards military expansion or hardline policies against other nations.
Considering the unpredictability of national interest, it must be said that it is a rhetoric used to force decisions for war—a highly uncertain choice that people typically would not willingly make.
And if one truly desires the long-term survival and prosperity of a country, focusing on "national interest" as an indicator is meaningless.
What should be focused on are permanent peace, governance, economic prosperity, and risk management.
If permanent peace is achieved, domestic governance functions appropriately, the economy is sufficiently prosperous, and uncertainties can be controlled to a manageable level, then a country can easily achieve survival and prosperity.
Moreover, the pursuit of national interest is not something that progressively accumulates. It is speculative: it increases if successful, and decreases if not.
Therefore, it is not rational to use national interest—which is unpredictable, used as rhetoric for war, and lacks progressive accumulation—as an indicator.
Instead, we should consider methods to make permanent peace, governance, economic prosperity, and risk management progressively accumulable, and pursue those methods.
This does not mean creating indicators to measure and manage the degree of these things.
It means we should accumulate knowledge and technologies to achieve them. And if other countries utilize this knowledge and technology, it will function even more advantageously.
Thus, the accumulation of this knowledge and technology becomes a progressive accumulation.
In contrast, knowledge and technology aimed at pursuing national interest do not possess this nature. This is because if other countries utilize them, one's own country becomes disadvantaged.
In other words, knowledge and technology for national interest cannot be progressively accumulated.
Considering it this way, the pursuit of national interest actually proves to be detrimental to a country's long-term survival and prosperity. Of course, there may be situations where short-term realities force decisions based on national interest.
However, at least, a long-term strategy for national interest is an illusion and an irrational idea. In the long term, a strategy of ensuring survival and prosperity through progressive accumulation is rational.
National interest is like holding a country's long-term survival and prosperity hostage.
It resembles the phenomenon known as Stockholm Syndrome, where a hostage psychologically defends their captor for survival.
It seems we can fall into such a state of psychological captivity by convincing ourselves that there is no other way.
Natural Mathematics
This analysis is not merely a way of thinking to affirm world peace or a correct argument to refute opposing views.
It is an objective logical model, similar to mathematics. Therefore, it does not claim that world peace is rational in all situations. In the short term, it acknowledges that a concept like national interest is useful in many contexts.
This is because the effect of cumulative differences grows larger over longer periods, but is smaller in the short term.
On the other hand, in the long term, there will always be a point where the concept of national interest inevitably becomes irrational. That is a mathematical fact based on logic.
There are challenges in expressing this formally in mathematical terms. However, even if it cannot be expressed formally, the strength of its logical structure remains unchanged.
I call the expression of such mathematically robust logic in natural language "natural mathematics."
The previous example is powerful precisely because it discusses within a structure based on this natural mathematics.
In this way, by discovering intellectual crystallizations with mathematical structures, we can logically explain what we intuitively feel is correct.
In Conclusion
Of course, intuition is not always correct.
However, the idea that intuition is inherently fallible or irrational misinterprets its true nature.
Where intuition and existing logical explanations clash, there is a high probability that an intellectual crystallization lies dormant.
And by revealing the mathematical structures that can express intuitive evaluations through logical reasoning using language, we unearth this crystallization.
If successful, we can present opinions that are not only intuitively appealing but also logically rational.
And that, indeed, becomes a step in our intellectual progress, allowing us to move forward.