Definition [entity]: A form of existence which is conceiveable and has four essential properties: limitedness, nature, abstractness and observability. (e.g. a rock is an entity which is limited in space and time, physical in nature, concrete and observable, whereas a word is non-physical, but it is limited, concrete and observable, a theory is abstract and non physical, while still being limited and observable; one would have to go into the mystical field to find some entity which is unlimited, abstract, non-observable and non-physical – the soul can be assumed to be such an entity).
Postulate [essential non-changing]: There exist entities which do not change their essential properties.
Postulate [irreversible changing]: The change of an essential property is irreversible.
Postulate [secondary selection]: There is no secondary property of an entity which cannot be bound to at least one essential property, such that it becomes void as soon as the essential property to which it is bound changes. Further on, a secondary property cannot exist in two different states of an essential property to which it is bound. (e.g. color can be bound to nature and observability; once either of the essential properties changes, color disappears)
Theorem [non-changing]: There exist entities which do not change their essential or secondary properties, regardless on the number of secondary properties.
Demonstration (1): Assume the Universe, as a collection of entities. Assume these entities as having a dynamic collection of secondary properties (i.e. they can create, alter or destroy such properties during their existence).
Therefore, a secondary property can be destroyed either by direct interraction of the owning entity, or the environment, or by the alteration of one of its essential properties. We have knowledge and proof of the existence of secondary properties bound to all states of all essential properties. For simplicity, let us suppose that secondary properties can only be destroyed by the change of an essential property to which they are bound and they can only be created once during the lifetime of an entity.
Having finished the exposition, we will continue by an induction inference.
The basis of the induction is the trivial case, plus the case where an entity can have only one secondary property. The trivial case consists of zero secondary properties. This is covered by the [essential non-changing] postulate. If an entity has one secondary property, it can either keep it, thus becoming a class one non changing entity, or dismiss it, thus becoming a trivial non-changing entity. In both cases, the existence of such entities is certain. Note: there is need for two elements in the basis of the induction, because there is a clear logical difference between them.
The induction step states as follows: If there exists a class n non changing entity, then there exists also a class n+k non changing entity, for any k finite. Suppose there is an ontological root with n secondary properties, non changing (such as the regnum „animals”). Further, suppose that all n properties are bound to only 3 of the essential properties of the entity (which, for the regnum „animals” is close to the truth, because this is an abstract entity, so no concrete-bound secondary properties can be inferred). Then, take the particularization of such an ontological root, having exactly k secondary properties, bound to the fourth essential property. Because of our supposition at the beginning, once these k properties are created, they can only be dismissed when the essential property (in our example abstractness) changes state. Hence, just as in the basis of the induction, the class n+k non changing entity can either exists per se or roll back to a class n non-changing entity, both cases being equally possible. q.e.d.
Demonstration (2): There is love. 🙂