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The Unphrasable Law: What Happens When the Principle of Lawfulness Is Turned on Its Formulators

Hoze, David
PhilArchive · Papers
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philosophy
If every phenomenon falls under law, there should be a law of our own thinking: a formal system whose theorems are exactly what we can justifiably establish. This essay argues that if such a law exists, we can never hold it - never simultaneously possess its formulation, know that it is ours, and know that it is sound. The reason is a structural flexibility: whoever holds and trusts a rulebook can establish truths the rulebook cannot (its own consistency, by Godel's second incompleteness theorem), and therefore exceeds any book he can hold. The argument is developed in a lay idiom - rulebooks, certificates, floors - with formal backing in appendices (Godel, Lob, Tarski, Goodstein, Turing progressions, Reinhardt-Carlson epistemic arithmetic). Against Lucas and Penrose, nothing anti-mechanist follows: mechanism is possible but unknowable in the first person. The argument extends to humanity as a collective knower, which, unlike the individual, has no "outside." Finally, the only entity that could truthfully declare its own reliability is one whose saying constitutes reality - so the intuition of total lawfulness was always, in disguise, a theological one.
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