Jocaxian Theorems
João Carlos Holland de Barcellos
translated by Debora Policastro

Jocaxian Theorems
João Carlos Holland de Barcellos

Jocaxian Theorem of First Cause (JTFC)

The Jocaxian theorem of First Cause establishes that:
The first cause of all events that took place in a closed system (one that is not influenced by events external to the system) is the randomization.


Let’s use the concept of time in which time is defined as a relationship between events. An event is a change of state in the system. Therefore, time is not independent from whatever happens. If, for example, no event takes place, that is, the state of the system remains unaltered, time then disappears. Change is necessary so that time can exist. If there is no change, there is no time.

Randomization is the word we use to say that there is unpredictability or that there are no causes. There are two types of randomization: objective and subjective. In the subjective randomization there are causes for the phenomenon, but they are either unknown or we cannot describe them. In the objective randomization, which we will talk about, the phenomenon occurs with no real causes, that is, its causes are inexistent.

The objective randomization exists in our nature, in our universe. As an example, we can cite the moment of decay of an electron in an atom: the electron can decay from a more energetic orbit to a lower-energy one by liberating a photon. Such phenomenon is not regulated by any physical law: it is considered by the quantum mechanics to be an objectively random phenomenon. There is nothing, no rule that can determine when the electron will decay from its orbit. Another example would be the creation and destruction of virtual particles in the vacuum.

First, in order to demonstrate the theorem, we will prove that there is no infinite time in past, that is, we cannot take the causes of the events to the infinite past and then say that there has always been a cause that preceded a given effect. Thus, we will use the Kalam’s Theorem.

The Kalam’s Theorem establishes that there is no infinite time in past. If, absurdly, there had been any event occurred in an infinite time in past, then our current present would take an infinite time to come, starting from that past. But what does “an infinite time to occur” mean? An infinite time for something to occur means that this thing will never occur. Thus, events occurred in an infinite time in past imply that we cannot have our present, but this is an absurd thinking once we are in the present! Then we can conclude that there has not been any event in an infinite time in past. That means we can deduce another important corollary: time had to have a beginning, necessarily.

As there is no infinite time in past and time had to have a beginning, the first occurring event had no previous cause, that is, it was a random event. And the theorem is proved.

Time Leakage Jocaxian Theorem (TLJT)

The Time Leakage Jocaxian Theorem establishes that:
If two systems are not isolated from each other and time exists in one of them, then time will exist in the other as well.

Time is the relationship between events. If time occurs in one of the systems and they are not isolated from each other, then these events can be also correlated from the other system. Therefore, the first system, in which time exists, can be a time counter for the second system. Thus, there will be time in the second system too.

We can use both theorems to argue against the existence of God: God cannot be timeless as this would violate the Time Leakage Jocaxian theorem. If there is time in our universe and it is not isolated from God, then time also exists to God. Besides that, by the JTFC there is no necessity for God to generate the first phenomenon. This refutes Saint Thomas Aquinas’ argument, which says that the movement requires a first engine that would be God. Also, it refutes the idea of a forever existent God, once it would contradict the corollary of the beginning of time.


The Existence Theorem

We will prove that there is an ultimate reality, a reality that does not depend on any interpretation of any being to exist.
In this text, we define reality – real existence – as events and/or facts that do not depend on interpretation (=thought, imagination, dream or processing) of any being to exist.


We will begin our proofing with “something 1”, that can be any object being observed e.g. an apple, or even the thinking itself: consciousness.
I observe something 1.
If this something 1 is the reality, the proofing finishes.
If Not:
This something 1 is just an interpretation (or imagination) of a being 1 and, in fact, does not exist in the reality. But this interpretation in itself of something 1, done by the supposed being 1, is also something 2.
If this something 2 is reality, then our proofing finishes.
If Not:
Something 2 is just an interpretation of a being 2 whose interpretation, in itself, is something 3.
If something 3 exists as a reality, the proofing finishes.
If Not:
This something 3 is just an interpretation of a being 3, which we call something 4.
Thus, in a generic way, we have:
If something (i) exists as reality, the proofing finishes.
If not:
Something (i) is only an interpretation (or imagination) of a being (i) whose interpretation in itself we call something (i+1).
If something (i+1) exists in reality the proofing finishes.

And so on. This way, if the interpretation never corresponds to a real existence, we would have an infinite recursion, which would be illogical. It would be something like a dream of a dream of a dream of a dream… infinitely. So, in order not to have this infinite cycle, we must have, at some point, an end to this recursion. That means that some of the “something (i)” have a real existence, that is, it is not an interpretation. And then we prove our theorem: “I think, therefore, something exists!”


I see a red crow. The “red crow” can be real, and if it is not, my interpretation of it can. Otherwise, a being can be imagining (or dreaming) that “I” am imagining that I see a “red crow”.

Another example would be a virtual universe: there are beings that do not really exist; they are simulated in a computer. These beings observe something. What they observe is not real either: it is virtual. Also, the beings themselves and their dreams do not exist: they are virtual. Therefore, their interpretations do not exist.
However, the computer which interprets them in this example is real, and its “imagination” (= its processing) is real, once it is what generates the virtual universe, the virtual beings and its imagination. That is:
What the virtual being observes is not real; it is a simulation of the computer.
The virtual being is not real either; it is simulated and depends on the processing of a computer.
The interpretation of the virtual being is not real either, once it depends on the processing of a computer.
The interpretation of the computer (= its processing) which produces the virtual being and what it imagines, in this example, would be real.

Refuting Descartes

That means that “I think, therefore I exist” (“Cogito, ergo sum”) from Descartes can be untrue once the thinking being, as demonstrated in the example above, can be unreal. However, as proved before, there must be some level of interpretation in which at least the interpretation itself is real.

By the “Occam’s razor”, as long there is no contrary evidence, we have consider the lower interpretative level a reality. If I observe something 1, this something 1 may exist.

Corollary: There is a real being.

As a corollary of the system we can also claim that if I observe something, there must be some “being” that has a real existence, i.e. this being itself is not an interpretation.
As we proved that there is an interpretation that is real, that is, an interpretation that does not depend on the interpretation of another being to exist, then the being that interprets must exist as well. If this “being” which does the real interpretation did not exist, that is, if it was the interpretation of another being, then its interpretation would not be real, as it would depend on this other being. Therefore, the real existence of a being is necessary so that a real interpretation can exist.

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