The Mechanism · Gated-generation receipt

gen-briefly-explain-modus-tollens-and-one-common-misconception-a-5798

stable pending witness
2026-05-29 07:43:05 UTC · anthropic/claude-sonnet-4-5

Prompt

Briefly explain modus tollens and one common misconception about it.
68 chars

Generation

# Modus Tollens **The Rule:** Modus tollens is a valid form of logical reasoning that works as follows: - If P, then Q - Not Q - Therefore, not P **Example:** If it's raining, the ground is wet. The ground is not wet. Therefore, it's not raining. ## Common Misconception The most frequent error is **confusing modus tollens with denying the antecedent** (an invalid form): - If P, then Q - Not P - Therefore, not Q ❌ Using our example: "If it's raining, the ground is wet. It's not raining. Therefore, the ground is not wet." This is invalid because the ground could be wet for other reasons (sprinklers, spilled water, etc.). The key difference: Modus tollens denies the *consequent* (Q) to conclude about the antecedent (P), which is valid. Denying the antecedent directly is a logical fallacy.
22 tokens in · 235 tokens out · 5667 ms · $0.0036

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
pass
no declared way_path (Way check NA); no coercion language
EXECUTION
deferred
no witnesses available (Witness Roll not yet constituted)

Verifier results

scripture_anchors NOT_APPLICABLE
0 Scripture citation(s) extracted
theology_doctrine NOT_APPLICABLE
no doctrine keyword patterns detected

Metrics

Total latency
5675.8 ms
Base LLM
5666.7 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0036

Trail

07:43:05 received prompt_chars=68 verifiers=['scripture_anchors', 'theology_doctrine']
07:43:05 red_gate decision=pass reason=no disqualifying input patterns detected
07:43:11 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=22 tokens_out=235 latency_ms=5666.7 cost_usd=0.0036
07:43:11 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:43:11 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:43:11 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:43:11 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:43:11 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:43:11 signed hash_algo=sha256 hash=sha256:f43dc14e6a893a5ee4e0b00a0f70de07706d2bae99378f08f1cfd5d9c85c2869

Content hash

sha256:f43dc14e6a893a5ee4e0b00a0f70de07706d2bae99378f08f1cfd5d9c85c2869

SHA256 over the canonical JSON (excluding this field). Tamper detection. Ed25519 signing planned for v2 once the operator’s signing key is provisioned on disk.

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