Substrate Abstraction: The 5+3 Life Conditions Are Substrate-Free
The 5 τ-Distinction and 3 SelfDesc conditions are jointly necessary and sufficient for life, with no mention of any physical substrate.
Overview
VI.T50 (Substrate Abstraction Theorem) proves that the 5 conditions of τ-Distinction and 3 conditions of SelfDesc are jointly necessary and sufficient for a system to be classified as alive, and neither set of conditions mentions a specific physical substrate. Carbon-based life, silicon-based life, or any other substrate that satisfies the predicate counts as alive by the same definition. Life is a categorical predicate, not a chemical observation.
Detail
Orthodox biology defines life through a list of properties (metabolism, reproduction, homeostasis, etc.) that are observed in carbon-based systems but are not explicitly substrate-independent. The question of whether silicon-based or other non-carbon life is possible is treated as speculative. Book VI defines life formally through the 5 τ-Distinction conditions (D1–D5) and 3 SelfDesc conditions (S1–S3). These conditions are: D1 boundary (topological separation from environment), D2 gradient (energy gradient maintenance), D3 coupling (interior coupling to exterior), D4 history (temporal record of state changes), D5 multiplicity (population structure); S1 model (internal model of self and environment), S2 repair (self-repair capacity), S3 replication (capacity for information copying). None of D1–D5 or S1–S3 specifies a chemical substrate. VI.T50 proves that (a) any system satisfying all 8 conditions is alive (sufficient), (b) any living system satisfies all 8 conditions (necessary), and (c) the conditions are consistent and non-redundant. The theorem implies that silicon-based life, electromagnetic life, or any other substrate-variant that satisfies D1–D5, S1–S3 is alive in the same sense as a bacterium.
Result Statement
VI.T50: The 5 conditions of τ-Distinction and 3 conditions of SelfDesc are jointly necessary and sufficient for life, and neither condition mentions a specific physical substrate. Carbon, silicon, or any other carrier that satisfies the predicate counts as alive.