In reality, it fails to construct a sentence that can be interpreted as self-referential. When attempting self-reference, it enters a loop, because the substitution leaves another substitution pending, in a return to infinity. But since the trick of arithmetization is in the middle, it makes this failure unprovable in the formal system. But that does not make it a "true" statement in any scientifically important sense. If instead of arithmetization we use the English translation from Spanish, we would have:

La auto sustitución de { The self-substitution of x it is not demonstrable } no es demostrable

We have an unresolved self-substitution, so the statement is incomplete. But if the system does not have rules for interpreting English, it remains unproven, but it is still a mere malformation due to infinite regression.

In reality, Gödel fails to construct a sentence that can be interpreted as self-referential. When attempting self-reference, it enters a loop, because the substitution leaves another substitution pending, in a return to infinity. But since the trick of arithmetization is in the middle, it makes this failure unprovable in the formal system. But that does not make it a "true" statement in any scientifically important sense. If instead of arithmetization we use the English translation from Spanish, we would have:

La auto sustitución de { The self-substitution of x it is not demonstrable } no es demostrable

We have an unresolved self-substitution, so the statement is incomplete. But if the system does not have rules for interpreting English, it remains unproven, but it is still a mere malformation due to infinite regression.

In reality, it fails to construct a sentence that can be interpreted as self-referential. When attempting self-reference, it enters a loop, because the substitution leaves another substitution pending, in a return to infinity. But since the trick of arithmetization is in the middle, it makes this failure unprovable in the formal system. But that does not make it a "true" statement in any scientifically important sense. If instead of arithmetization we use the English translation from Spanish, we would have:

La auto sustitución de The self-substitution of x it is not demonstrable no es demostrable

We have an unresolved self-substitution, so the statement is incomplete. But if the system does not have rules for interpreting English, it remains unproven, but it is still a mere malformation due to infinite regression.

In reality, it fails to construct a sentence that can be interpreted as self-referential. When attempting self-reference, it enters a loop, because the substitution leaves another substitution pending, in a return to infinity. But since the trick of arithmetization is in the middle, it makes this failure unprovable in the formal system. But that does not make it a "true" statement in any scientifically important sense. If instead of arithmetization we use the English translation from Spanish, we would have:

La auto sustitución de { The self-substitution of x it is not demonstrable } no es demostrable

We have an unresolved self-substitution, so the statement is incomplete. But if the system does not have rules for interpreting English, it remains unproven, but it is still a mere malformation due to infinite regression.