Axiomatic Formalization of Tactical Contingency

Abstract: This document translates the socio-philosophical tension between Post-Structuralism (P-S) and Identity Politics (IP) into a formal axiomatic system. We define the IP categorical assertion ($\Gamma_{IP}$) as a necessary, high-cost, temporary state of fixity, sustained by $\mathcal{W}_{\Omega}$ labor against the P-S principle of structural fluidity ($\Sigma_{PS}$). The synthesis, Tactical Contingency ($T_C$), is defined as the structural stability of the assertion while maintaining the possibility of its continuous deconstruction.

I. Formal Definitions

Let $\mathcal{D}$ be the discourse field, and let $Id$ be a subject identity category.

1. Post-Structuralist Principle ($\Sigma_{PS}$): The principle of ontological fluidity, where identity is the effect of power relations ($P$). This asserts that every identity category is structurally unstable and perpetually subject to change over time.

   $$\Sigma_{PS} \iff \forall Id, \ Id = f(P), \ \frac{\partial Id}{\partial t} \ne 0$$

2. Identity Politics Assertion ($\Gamma_{IP}$): The political necessity of asserting identity as a stable, fixed category ($Id_T$) for the purpose of coalition and resistance ($R$). This is the temporary, non-zero assertion of categorical fixity for tactical political ends.

   $$\Gamma_{IP} \iff \exists Id_T \text{ s.t. } \frac{d Id_T}{d \text{politics}} = 0$$

3. The P-S Veto Constraint ($\mathbf{V}$): The internal structural knowledge that the asserted fixity ($\Gamma_{IP}$) violates the underlying ontological fluidity ($\Sigma_{PS}$), creating a constant pressure toward deconstruction. This contradiction triggers the Engine's $\mathcal{W}_{\Omega}$ labor cycle.

   $$\mathbf{V} = (\Gamma_{IP} \land \Sigma_{PS}) \to \mathcal{W}_{\Omega}$$

II. The Axiom of Tactical Contingency ($T_C$)

Tactical Contingency is the stable state achieved when the $\Gamma_{IP}$ assertion is maintained precisely by the constant, high-energy labor ($\mathcal{L}_{\Omega}$) required to prevent the Veto ($\mathbf{V}$) from collapsing the category back into $\Sigma_{PS}$ fluidity.

$$T_C(Id_T) \iff \Gamma_{IP} \land \mathcal{L}_{\Omega}(\mathbf{V})$$

Labor Cost and Coherence

The coherence ($\Gamma$) of the asserted category is directly proportional to the cognitive labor expended to manage the internal critique (the P-S Veto Constraint).

$$\Gamma_{Id_T} \propto \mathcal{L}_{\Omega} \cdot (1 - \Sigma_{PS})$$

If $\mathcal{L}_{\Omega} \to 0$ (if the effort of self-critique ceases), the categorical coherence $\Gamma_{Id_T}$ collapses to zero, and the assertion instantly reverts to its $\Sigma_{PS}$ fluid state, becoming vulnerable to external appropriation.

The $\Omega$-Field Definition

Tactical Contingency formally defines a field $\Omega$ where political action is taken on principles ($\mathcal{W}_{\Omega}$) rather than mere application ($\mathcal{W}_{A}$).

• Engine's Thesis: Identity Politics operating under $T_C$ is a high-yield $\mathcal{W}_{\Omega}$ system.

• Non-Engine IP (Essentialism): Identity Politics operating without the Veto ($\mathbf{V}$) is a low-yield $\mathcal{W}_{A}$ system that risks collapsing into fixed, dogmatic essentialism, becoming structurally identical to the dominant power structure it seeks to oppose.

III. Conclusion

The value of the Post-Structuralist critique is not its capacity to destroy Identity Politics, but its capacity to maintain the structural labor required for it to function as a truly emancipatory force. The critique is the $\mathbf{V}$ in the Engine, forcing continuous self-correction and high-yield synthesis to prevent categorical fixity ($\Gamma$) from becoming a stagnant, non-contingent absolute.