Metalogical Inconsistency of the Denial of a First Ground

This argument does not attempt to demonstrate the existence of a First Ground directly. It shows that assuming its non-existence leads to contradiction within the logic of justification.


Diagram — Metalogical Inconsistency of the Denial of a First Ground

First-Ground Argument Flow Left path: Assume no first ground leads to infinite regress and metalogical self-undermining (incoherence). Right path: Admit a first ground yields a finite, well-founded chain (coherence). Assumption: ¬First Ground Hypothesis: First Ground exists All causal claims lack a base. Inference chains → infinite regress (…) Regress applies to the very claim “¬FG”. Metalogical self-undermining → incoherence There exists a first ground (FG). Causal chains are well-founded / finite. Claims can terminate in justification at FG. Metalogical coherence → no regress in the claim metalogical bifurcation

1. Premise — The Denial

Assume ¬∃G: there is no first ground. Then for every proposition P there exists another ground Gn+1 such that

∀P (∃Gn+1 : Gn+1 ⊢ P)

— meaning every statement depends on another, forming an infinite regress of justification.

2. Meta-logical Observation

The very statement ¬∃G is itself a proposition Q. If Q is true, it too requires a ground within the same structure:

∃Gq : Gq ⊢ (¬∃G)

But by hypothesis, no terminal G exists. Therefore Q’s own justification is non-terminating, i.e. infinite.

An infinitely deferred justification cannot yield a determinate truth value in finite reasoning. Hence, Q cannot be known or asserted as true without violating the very condition it posits.

3. Contradiction

To assert ¬∃G as true presupposes some ground Gq that validates it, while the premise denies the existence of any such G. Therefore:

(¬∃G) → (∃Gq ⊢ ¬∃G)
but ¬∃G forbids ∃Gq ⇒ ⊥

The statement negates the very precondition of its own truth. It is self-invalidating — a meta-logical contradiction.

4. Conclusion

The denial of a First Ground (¬∃G) collapses into incoherence because its assertion necessarily presupposes the grounding it denies. It cannot be held consistently within any finite or meaningful system of reasoning. Thus, while the argument does not yet affirm what G is, it shows that the structure of logic itself forbids its complete absence.