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The $2 Trillion Logic Error
In 2021, the world watched in disbelief as the most sophisticated military machine in history collapsed in weeks against an adversary with no air force, no tanks, and a GDP smaller than a mid-sized US city. The world witnessed a humiliating defeat in real-time: the greatest empire lost a 20-year war to a guerrilla force. The footage of the US military fleeing the Kabul airport, abandoning tens of billions of dollars’ worth of weaponry, circled the globe.
More than four years have passed, yet it seems no one has seriously attempted to make sense of what happened. How is it possible that after spending $2 trillion over twenty years fighting a guerrilla group, the United States still lost?
Modern political science and philosophy are incapable of answering this question. All they can offer are excuses about a "lack of will," "errors by politicians and generals," or "betrayal by allies."
But what if victory and defeat can be predicted even before the battle begins? What if victory or defeat is strictly deterministic and does not depend on how politicians behave in their offices or generals in their headquarters?
I contend that there is an ideal metric that allows us to evaluate the prospects of any actor decades in advance. I argue that all political analysts and philosophers are simply looking in the wrong place. True understanding of the nature of a "Subject" lies not in evaluating GDP, the number of tanks and missiles, or military budgets. In a way, it is much simpler. Victory or defeat lies in the plane of logical necessity, not subjective variability.
Moreover, by knowing the answers to these questions, we can design ideal Subjects ourselves. I am offering you an instruction manual for creating the ultimate weapon.
Welcome to Axiomatic Theory—a manual for hacking reality.
The Foundations: Set Theory
Let’s start from the beginning. My theory was born from mathematical Set Theory. This system was created to formally describe how we organize and categorize reality. Its fundamental concept is simple: a set is a collection or a pack of definite and distinguishable objects that are thought of as a single whole.
The simplest example is an ordinary grocery store. Imagine a shelf with vegetables. A tomato, a cucumber, and a pepper are different items. But our brain instantly unites them into a set called "Vegetables." We draw an invisible boundary in space that separates these items from "Fruits" or the "Meat Department."
Set theory is, in essence, a story about how we draw boundaries. We take the chaos of billions of individual atoms and objects and "package" them into mental boxes: "my family," "citizens of the country," "democratic values." Each such name is a label on a box containing a set of objects we have agreed to consider a single entity.
Historically, this theory, devised by Georg Cantor, relied on intuitive understanding and a single but powerful rule: for any property P(x) that can be expressed in mathematical language, there exists a set A consisting exactly of all objects x that possess this property P(x). Simply put, a set is defined by the property of its elements. Any property we can formulate creates a set.
Political Cantorianism
Now, let’s take the liberal American empire and project Cantor’s rule onto it. We get the following: any imperative that we are able to formulate based on the premises of its own ideology is an integral part of that ideology—its subset. Moreover, in our world, the more such imperatives we can formulate within an ideology, the better and more "universal" it is considered.
But this is precisely where the Subject—the carrier of "ideology-as-a-set-of-all-subsets-of-its-imperatives"—begins its fall.
Political Cantorianism is a mode of operation where an ideology feels compelled to formulate as many moral imperatives as it possibly can. Modern liberal institutions, such as the UN, act as Cantorian Machines.
Take the UN as an example. Its ideology is liberalism. We have the Palestinian-Israeli conflict. "Political Cantorianism" requires us to formulate as many moral imperatives regarding this conflict as we are capable of expressing. We get a vast number of liberal imperatives: the security of Israel, the rights of Palestinians, the necessity of a Palestinian state, Israel's right to self-defense, zero tolerance for anti-semitism.
We see a huge number of imperatives, each of which is "good" on its own, but together they lead to a paralysis of will for whoever formulates this set of axioms—simply because they are all in mutual conflict with one another.
The Russell Trap
Cantor's idea was noble. He wanted to create a closed, self-sufficient system that was as clear, logical, and attractive as possible. His idea failed and was subsequently dubbed "Naive Set Theory."
What happened? Its vulnerability was exposed by Bertrand Russell, who formulated his famous paradox. He divided all conceivable sets into two types:
Normal sets, which do not contain themselves. For example, the set of all apples is not an apple; it is a list. A box labeled "Vegetables" is cardboard, not a vegetable. Most objects in the world are like this.
Abnormal sets, which include themselves. Imagine the "Set of all abstract ideas." The concept of this set is itself an abstract idea, so it must lie inside the box. Or the "List of all lists": it is a list itself, so it must be mentioned within itself.
Now for the interesting part. Imagine we decide to create a "Registry of all Normal Sets." We start one giant folder and write down the names of only those sets that do not contain themselves.
And here a question arises that makes the "engine" of logic overheat: Should this Registry include itself in the list?
If we DO include it: The Registry will contain itself. But according to the rules we established, it can only contain "normal" sets (those that don't contain themselves). Therefore, it doesn't belong there. Error.
If we DO NOT include it: Then our Registry is a set that does not contain itself. By definition, it must be included in the list! Но as soon as we include it, we return to the previous point. Another error.
This is Russell's Paradox. As soon as we try to draw a boundary around "everything that has no boundaries," logic collapses.
This paradox is not a fun riddle. It is the moment when the "program" of our thinking throws a critical error. In mathematics, this led to a massive crisis; in life, this is exactly what happens to political actors. When international law tries to create "rules of universal equality that satisfy everyone," it falls into the same trap. The system tries to eat its own tail, and at that moment, its will is paralyzed.
The Zermelo Filter
The mathematical world emerged from this crisis in 1908 thanks to Ernst Zermelo. His solution: Zermelo prohibited creating sets "out of nowhere" based on a simple description. He introduced a rule: you cannot just create a "set of all objects possessing property X." You can only take an already existing set and "filter" a subset of elements from it that you need.
Zermelo effectively established a "ceiling" for systems, forbidding them from being infinitely all-encompassing.
For the world of international politics, the conclusion is this: you cannot simply proclaim "noble goals." Modern liberal actors strive to be "the set of all good things," thereby planting a logical landmine under themselves. To formulate goals and imperatives, one needs a clear filter; otherwise, the Subject's internal logic will begin to explode from internal contradictions, much like it did during Russell's thought experiment.
And we have this filter…
End of Part One. If anyone is interested, I am ready to continue
The $2 Trillion Logic Error
In 2021, the world watched in disbelief as the most sophisticated military machine in history collapsed in weeks against an adversary with no air force, no tanks, and a GDP smaller than a mid-sized US city. The world witnessed a humiliating defeat in real-time: the greatest empire lost a 20-year war to a guerrilla force. The footage of the US military fleeing the Kabul airport, abandoning tens of billions of dollars’ worth of weaponry, circled the globe.
More than four years have passed, yet it seems no one has seriously attempted to make sense of what happened. How is it possible that after spending $2 trillion over twenty years fighting a guerrilla group, the United States still lost?
Modern political science and philosophy are incapable of answering this question. All they can offer are excuses about a "lack of will," "errors by politicians and generals," or "betrayal by allies."
But what if victory and defeat can be predicted even before the battle begins? What if victory or defeat is strictly deterministic and does not depend on how politicians behave in their offices or generals in their headquarters?
I contend that there is an ideal metric that allows us to evaluate the prospects of any actor decades in advance. I argue that all political analysts and philosophers are simply looking in the wrong place. True understanding of the nature of a "Subject" lies not in evaluating GDP, the number of tanks and missiles, or military budgets. In a way, it is much simpler. Victory or defeat lies in the plane of logical necessity, not subjective variability.
Moreover, by knowing the answers to these questions, we can design ideal Subjects ourselves. I am offering you an instruction manual for creating the ultimate weapon.
Welcome to Axiomatic Theory—a manual for hacking reality.
The Foundations: Set Theory
Let’s start from the beginning. My theory was born from mathematical Set Theory. This system was created to formally describe how we organize and categorize reality. Its fundamental concept is simple: a set is a collection or a pack of definite and distinguishable objects that are thought of as a single whole.
The simplest example is an ordinary grocery store. Imagine a shelf with vegetables. A tomato, a cucumber, and a pepper are different items. But our brain instantly unites them into a set called "Vegetables." We draw an invisible boundary in space that separates these items from "Fruits" or the "Meat Department."
Set theory is, in essence, a story about how we draw boundaries. We take the chaos of billions of individual atoms and objects and "package" them into mental boxes: "my family," "citizens of the country," "democratic values." Each such name is a label on a box containing a set of objects we have agreed to consider a single entity.
Historically, this theory, devised by Georg Cantor, relied on intuitive understanding and a single but powerful rule: for any property P(x) that can be expressed in mathematical language, there exists a set A consisting exactly of all objects x that possess this property P(x). Simply put, a set is defined by the property of its elements. Any property we can formulate creates a set.
Political Cantorianism
Now, let’s take the liberal American empire and project Cantor’s rule onto it. We get the following: any imperative that we are able to formulate based on the premises of its own ideology is an integral part of that ideology—its subset. Moreover, in our world, the more such imperatives we can formulate within an ideology, the better and more "universal" it is considered.
But this is precisely where the Subject—the carrier of "ideology-as-a-set-of-all-subsets-of-its-imperatives"—begins its fall.
Political Cantorianism is a mode of operation where an ideology feels compelled to formulate as many moral imperatives as it possibly can. Modern liberal institutions, such as the UN, act as Cantorian Machines.
Take the UN as an example. Its ideology is liberalism. We have the Palestinian-Israeli conflict. "Political Cantorianism" requires us to formulate as many moral imperatives regarding this conflict as we are capable of expressing. We get a vast number of liberal imperatives: the security of Israel, the rights of Palestinians, the necessity of a Palestinian state, Israel's right to self-defense, zero tolerance for anti-semitism.
We see a huge number of imperatives, each of which is "good" on its own, but together they lead to a paralysis of will for whoever formulates this set of axioms—simply because they are all in mutual conflict with one another.
The Russell Trap
Cantor's idea was noble. He wanted to create a closed, self-sufficient system that was as clear, logical, and attractive as possible. His idea failed and was subsequently dubbed "Naive Set Theory."
What happened? Its vulnerability was exposed by Bertrand Russell, who formulated his famous paradox. He divided all conceivable sets into two types:
Normal sets, which do not contain themselves. For example, the set of all apples is not an apple; it is a list. A box labeled "Vegetables" is cardboard, not a vegetable. Most objects in the world are like this.
Abnormal sets, which include themselves. Imagine the "Set of all abstract ideas." The concept of this set is itself an abstract idea, so it must lie inside the box. Or the "List of all lists": it is a list itself, so it must be mentioned within itself.
Now for the interesting part. Imagine we decide to create a "Registry of all Normal Sets." We start one giant folder and write down the names of only those sets that do not contain themselves.
And here a question arises that makes the "engine" of logic overheat: Should this Registry include itself in the list?
If we DO include it: The Registry will contain itself. But according to the rules we established, it can only contain "normal" sets (those that don't contain themselves). Therefore, it doesn't belong there. Error.
If we DO NOT include it: Then our Registry is a set that does not contain itself. By definition, it must be included in the list! Но as soon as we include it, we return to the previous point. Another error.
This is Russell's Paradox. As soon as we try to draw a boundary around "everything that has no boundaries," logic collapses.
This paradox is not a fun riddle. It is the moment when the "program" of our thinking throws a critical error. In mathematics, this led to a massive crisis; in life, this is exactly what happens to political actors. When international law tries to create "rules of universal equality that satisfy everyone," it falls into the same trap. The system tries to eat its own tail, and at that moment, its will is paralyzed.
The Zermelo Filter
The mathematical world emerged from this crisis in 1908 thanks to Ernst Zermelo. His solution: Zermelo prohibited creating sets "out of nowhere" based on a simple description. He introduced a rule: you cannot just create a "set of all objects possessing property X." You can only take an already existing set and "filter" a subset of elements from it that you need.
Zermelo effectively established a "ceiling" for systems, forbidding them from being infinitely all-encompassing.
For the world of international politics, the conclusion is this: you cannot simply proclaim "noble goals." Modern liberal actors strive to be "the set of all good things," thereby planting a logical landmine under themselves. To formulate goals and imperatives, one needs a clear filter; otherwise, the Subject's internal logic will begin to explode from internal contradictions, much like it did during Russell's thought experiment.
And we have this filter…
End of Part One. If anyone is interested, I am ready to continue