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2025
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| Online Access: | https://doi.org/10.5281/zenodo.18061220 |
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| author | Salhab, Najih |
| author_facet | Salhab, Najih |
| contents | <h3> </h3> <p>We prove a strict, pre-semantic rule for when a statement is <em>allowed</em> to count as a proposition at all. The rule is simple in spirit: <strong>truth-evaluation must never be what <em>creates</em> meaning.</strong> If a sentence can only be “understood” after we decide whether it is true or false—then it never had a stable meaning to begin with, and it should never be treated as a truth-bearer.</p> <p>From this minimal discipline follows a necessary consequence: <strong>evaluation-dependent self-reference collapses at the formation stage</strong>, before semantics, before truth values, and before any “paradox management” begins. Classical semantic paradoxes (the Liar and its strengthened forms) are not solved by clever truth-tables or third values—they are <strong>stopped earlier</strong>, because the would-be proposition fails to form.</p> <p>This is not a philosophical slogan. The core claim is checked in two independent mechanized frameworks: <strong>Z3</strong> is used to rule out countermodels to the rejection result under explicit formation constraints while preserving non-trivial satisfiability, and <strong>Cubical Agda</strong> formalizes the discipline and derives the rejection result compositionally.</p> <p>In safety-critical domains, “mechanized” must not be sold as “infallible,” and “paradox-tolerant” must not be confused with “safe.” A formation-level firewall is the only place where certain structural failures can be blocked <em>before</em> they propagate into proofs, code, or decisions. If one wishes to dispute this result, the dispute must be technical: identify a broken assumption, an invalid step, or a concrete counterexample under the stated constraints. Otherwise, dismissal by taste is not skepticism—it is negligence.</p> <p><strong>Important Notice.</strong><br>The formation-theoretic criterion established in this work bears directly on safety-critical reasoning, formal verification, and high-consequence systems. A detailed examination of technical benefits, historical failure patterns, and risk implications is provided in <strong>Appendix B</strong>. Any serious assessment of this work—supportive or critical—should take that appendix into account.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18061220 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Necessary Formation-Theoretic Invariant for Safe Propositional Formation Salhab, Najih <h3> </h3> <p>We prove a strict, pre-semantic rule for when a statement is <em>allowed</em> to count as a proposition at all. The rule is simple in spirit: <strong>truth-evaluation must never be what <em>creates</em> meaning.</strong> If a sentence can only be “understood” after we decide whether it is true or false—then it never had a stable meaning to begin with, and it should never be treated as a truth-bearer.</p> <p>From this minimal discipline follows a necessary consequence: <strong>evaluation-dependent self-reference collapses at the formation stage</strong>, before semantics, before truth values, and before any “paradox management” begins. Classical semantic paradoxes (the Liar and its strengthened forms) are not solved by clever truth-tables or third values—they are <strong>stopped earlier</strong>, because the would-be proposition fails to form.</p> <p>This is not a philosophical slogan. The core claim is checked in two independent mechanized frameworks: <strong>Z3</strong> is used to rule out countermodels to the rejection result under explicit formation constraints while preserving non-trivial satisfiability, and <strong>Cubical Agda</strong> formalizes the discipline and derives the rejection result compositionally.</p> <p>In safety-critical domains, “mechanized” must not be sold as “infallible,” and “paradox-tolerant” must not be confused with “safe.” A formation-level firewall is the only place where certain structural failures can be blocked <em>before</em> they propagate into proofs, code, or decisions. If one wishes to dispute this result, the dispute must be technical: identify a broken assumption, an invalid step, or a concrete counterexample under the stated constraints. Otherwise, dismissal by taste is not skepticism—it is negligence.</p> <p><strong>Important Notice.</strong><br>The formation-theoretic criterion established in this work bears directly on safety-critical reasoning, formal verification, and high-consequence systems. A detailed examination of technical benefits, historical failure patterns, and risk implications is provided in <strong>Appendix B</strong>. Any serious assessment of this work—supportive or critical—should take that appendix into account.</p> |
| title | A Necessary Formation-Theoretic Invariant for Safe Propositional Formation |
| url | https://doi.org/10.5281/zenodo.18061220 |