Theorems Derived from the Open Ontology Framework for Fantasy

Introduction

This article summarises several propositions derived by applying the axioms defined in the “Open Ontology Framework for Fantasy”, published yesterday.

This article is also licensed under CC BY-SA 4.0.

Theorems Directly Derived from the Framework

The following propositions can be derived from the system of axioms and are defined here as theorems.

Theorem 1: Life Has a Natural Direction

Without external interference, entropy monotonically increases.

Therefore, life has a natural direction of state history:

S_0 \rightarrow S_1 \rightarrow S_2 \rightarrow \cdots

This makes it possible for concepts such as age and lifespan to exist.

The specific mechanisms of ageing and lifespan are work-dependent.

Theorem 2: Stopping Entropy Requires External Interference

Since entropy monotonically increases without external interference, external interference is required to keep entropy at the same value.

Theorem 3: Identity of Life

As long as its state history does not end, a life continues as the same life even if its state, circumstances, or form of existence changes.

Conversely, once its state history ends, that life ends. Even if a new history begins afterwards, it constitutes a different life.

Theorem 4: Physical / Logical Disappearance Is Not Equivalent to the End of Life

Under Axiom 4, merely ceasing to exist physically or logically does not mean that a life has ended.

The criterion for determining the end of life is the end of the recording of its state history.

This provides room for the implementation of ghosts, souls, reincarnation into another world, and similar concepts, but the existence of such concepts themselves is not mandatory.

Theorem 5: Reincarnation and Continuity of Life

Even if the body, world, or form of existence changes through reincarnation or similar means, if the state history continues as:

S_0, S_1, \ldots, S_n, S_{n+1}, \ldots

it constitutes the same life.

On the other hand, if:

S_n \rightarrow \text{End of Recording}

is followed by:

S'_0 \rightarrow S'_1 \rightarrow \cdots

it constitutes a different life.

Therefore, the inheritance of memories and the continuity of life are not equivalent.

Theorem 6: Reality Is Entity-Dependent

Under Axiom 5, for different entities a and b,

R_a \neq R_b

is permitted.

Therefore, something that cannot be cognised by one entity is not excluded from being part of reality for another entity.

Theorem 7: Absence of Degrees of Freedom in a Lower Dimension

If a lower dimension does not share a particular degree of freedom with the base dimension, phenomena that presuppose that degree of freedom do not occur in that lower dimension.

For example, if:

t_1 \notin L

then the passage of time that depends on t₁ does not occur.

This is a different phenomenon from time being stopped, as in:

t_1 \in L,\ \Delta t_1 = 0

In other words, “time does not exist” and “time exists but does not pass” are different phenomena.