Fix two distinct groups $g_1, g_2 \in \text{G}$, the set of all groups under the equivalence classes of identities. If $\text{Behavior}(g_1) \not = \text{Behavior}(g_2)$, then $\text{Causes}(\text{Behavior}(g_k)) \not = \text{Soul}(g_k)$ for some $k \in \Set{1, 2}$.

If Determinism or Materialism is true, this theory is a direct result. Therefore, we can assume our universal system is not deterministic or material.

^{For the purposes of these proofs, let $\text{Tabula Rasa}$ refer not to exactly the empiricist view, but rather the idea that the core of every agent has the same propensities. This view is necessary for the common view of transcendent morality, that is, a critical moral character, since the inverse implicates “good” and “evil” souls without any part which is void of such differences, as a part which does not have these differences would satisfy the core agent with indistinguishable propensities. Or limpidly, there is a part of humans which, among all, is a pure agent.}

Proof by contradiction:

Let souls $s_k = \text{Soul}(g_k)$ for each $k \in \Set{1,2}$.

Define $\rho$:

$\rho \colonequals \text{minimum probability for claim to be accepted as fact}$

$\text{Causes}(\text{Behavior}(g_k)) = \text{Soul}(g_k) \forall k \in \Set{1, 2}\implies$

$\text{Probability}(\text{Behavior}(g_1) \not = \text{Behavior}(g_2)) \llless \rho \implies \neg (\text{Tabula Rasa})$

$\therefore$ $\rho$ and $\text{Tabula Rasa}$ is not compatible with $\text{Causes}(\text{Behavior}(g_k)) = \text{Soul}(g_k) \forall k \in \Set{1, 2}\implies \text{Causes}(\text{Behavior}(g_k)) \not = \text{Soul}(g_k) \forall k \in \Set{1, 2}$ giving the result as desired.

Proof by alternativity:

Let souls $s_k = \text{Soul}(g_k)$ for each $k \in \Set{1,2}$.

Define $\rho$:

$\rho \colonequals \text{minimum probability for claim to be accepted as fact}$

Create copies for each group and the corresponding souls $g_{k_{i}}$ and $s_{k_{i}}$.

Switch the copied souls and groups so that no group contains its original souls, adjusting for size as needed.

$\text{Probability}(\text{Behavior}(g_k) \not = \text{Behavior}(g_{k_{i}})) \llless \rho \implies$

$\text{Temperament}(s_1) \not = \text{Temperament}(s_2) \implies \neg (\text{Tabula Rasa}).$

$\therefore \rho$ and $\text{Tabula Rasa}$ are not compatible with $\text{Behavior}(g_k) \not = \text{Behavior}(g_{k_i})$, giving the result as desired.

Remark I. The intuition behind the first proof is that if the aggregate behavior of a group can be imputed to their souls (this is to distinguish between the body and weaknesses of the human brain), the probability that the aggregate behavior differs is unbelievably low, requiring us to reject Tabula Rasa. If this is rejected however, we still admit that a soul is not entirely culpable for its critical moral character, since it is partly determined by the inexistence of Tabula Rasa.

Remark II. The intuition behind the second proof is simply that switching the souls of groups and reverting them to their initial states leads to the same aggregate behavior. For example, sex: had every moment where the sex of a person been determined inversely the general pattern of history would have been the same.

Remark III. The consequence of this proof is an admission of, as discussed, the evaluation of critical moral character in relation to a group, but also the notion that all groups are fundamentally equal—their material and characteristic morality may certainly differ, but their critical moral character remains the same.

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