Sometimes, we instinctively feel something is right but struggle to articulate it logically.
In such cases, we are forced to express our intuition in straightforward, intuitive terms. While those who strongly share that intuition may agree, we cannot gain agreement from those who are not convinced or hold opposing views.
If we cannot articulate it logically, we must find a way to do so. Otherwise, we would be forced to ignore dissenting opinions or exclude skeptics from the discussion, which could lead to societal division and a form of social violence.
Furthermore, a problem arises when something we intuitively feel is correct cannot be adequately explained in words: it risks being labeled as subjective, arbitrary, or idealistic in a purely imaginative sense. If it involves uncertainty, it might be labeled as optimistic or pessimistic.
Conversely, there are cases where those with skeptical or opposing views can explain their positions logically. This puts us in an even more disadvantageous position. If they label our views as described above, any third party observing the discussion will perceive our labeled, weaker argument against their logical, stronger one.
This is compounded by the bias of assuming a gap between intuition and logic—a deeply ingrained belief that logic is correct and intuition cannot be trusted.
However, things that are instinctively felt to be correct should, in most cases, be explainable as logically correct. Intuition and logic are not contradictory; we simply haven't yet discovered the method to connect them.
The reason opposing views can be explained logically is due to differences in their underlying premises, objectives, or assumptions about uncertainty. Therefore, logically explaining something that feels intuitively correct under different premises, objectives, and assumptions is not a contradiction.
Once both sides can explain their views logically, the discussion can then focus on what to do about the premises, objectives, and assumptions. This allows third parties observing the debate to express their opinions based on agreement with these premises, objectives, and assumptions, rather than being swayed by labels or the perceived strength of arguments.
To logically explain in words what we intuitively feel is correct, we must uncover what I call "intellectual crystals."
The Psychological Captivity of National Interest
Here, I'd like to present an example of an intellectual crystal. It concerns the ideal of world peace and the logical explanation surrounding national interest as a counter-argument.
Typically, world peace is intuitively seen as desirable, but in the face of the realism of national interest within the actual international community, it is often dismissed as an unattainable ideal.
Simply put, national interest is a situation advantageous for a nation's survival and prosperity.
Given two options, choosing the more advantageous one is considered a decision aligned with national interest.
However, when we say a choice is advantageous for a nation's survival and prosperity, at what point in time are we referring to this advantage?
Historically, there have been cases where losing a war led to a nation's long-term survival.
Also, a nation's prosperity could, in turn, lead to its collapse.
This signifies the unpredictability of national interest.
Furthermore, the term "national interest" is often used by those who seek to guide decision-making towards military expansion or hardline policies against other nations.
Given the unpredictability of national interest, it can only be seen as a rhetoric used to force decisions for war—a highly uncertain choice that people usually wish to avoid.
Therefore, if one genuinely desires the long-term survival and prosperity of a nation, focusing on national interest as an indicator is meaningless.
What should be focused on is permanent peace, governance, economic prosperity, and risk management.
If permanent peace is achieved, domestic governance functions properly, the economy is sufficiently prosperous, and uncertainty can be kept to a manageable level, then a nation can easily attain survival and prosperity.
Moreover, the pursuit of national interest is not a progressive accumulation. It is speculative, increasing when successful and decreasing when it fails.
Therefore, it is not rational to use national interest—an unpredictable concept used as rhetoric for war, with no progressive accumulation—as an indicator.
Instead, we should consider and pursue methods to make permanent peace, governance, economic prosperity, and risk management amenable to progressive accumulation.
This does not mean creating indicators to measure and manage the degree of these aspects.
It means accumulating the knowledge and technology to achieve these goals. And this knowledge and technology, if utilized by other nations, will function even more advantageously.
For this reason, the accumulation of such knowledge and technology becomes a progressive accumulation.
Conversely, the knowledge and technology pursued for national interest do not possess this quality. This is because if other nations utilize them, one's own nation becomes disadvantaged.
In other words, knowledge and technology for national interest cannot be progressively accumulated.
Considering this, the pursuit of national interest can actually be detrimental to a nation's long-term survival and prosperity. Of course, there will be situations in the short-term where decisions must be made based on national interest as a reality.
However, at the very least, a long-term strategy for national interest is an illusion and an irrational idea. In the long term, a strategy of securing survival and prosperity through progressive accumulation is rational.
National interest is like holding the long-term survival and prosperity of a nation hostage.
It appears similar to the phenomenon known as Stockholm Syndrome, where a hostage psychologically defends their captor for their own survival.
It seems we can sometimes fall into such a state of psychological captivity by convincing ourselves that there is no other way.
Natural Mathematics
This analysis is not merely an argument to affirm world peace or to refute opposing views.
It is an objective logical model, similar to mathematics. Therefore, it does not assert that world peace is rational in all situations. In the short term, it acknowledges that concepts like national interest can be 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 inevitably be a point where the concept of national interest becomes irrational. This is a mathematical fact based on logic.
While it can be challenging to express this in formal mathematical notation, the strength of its logical structure remains unchanged even if it cannot be formally expressed.
I call the expression of such mathematically strong logic in natural language natural mathematics.
The previous example is powerful because it is argued on a structure based on this natural mathematics.
By discovering such intellectual crystals with mathematical structures, we can logically explain what we intuitively feel is correct.
Conclusion
Of course, intuition is not always correct.
However, the idea that intuition is inherently prone to error or irrational misinterprets its true nature.
Where intuition clashes with existing logical explanations, there is a high probability that intellectual crystals lie dormant.
By uncovering the mathematical structures that can express intuitive evaluations through verbal logic, we excavate these crystals.
If successful, we can present arguments that are not only intuitively appealing but also logically rational.
And that, indeed, will be a step forward in our intellectual progress, enabling us to advance.