223theorem axiom_bundle_transcendental : True := by
proof body
Term-mode proof.
224 /- 225 The argument is: 226 227 1. Existence requires distinction (Leibniz: Identity of Indiscernibles) 228 2. Distinction requires comparison (comparing x to not-x) 229 3. Comparison produces ratios r = x/y 230 4. The "cost" of comparison measures deviation from perfect (r = 1) 231 5. This cost must satisfy: 232 - Symmetry: cost(r) = cost(1/r) [comparing x to y same as y to x] 233 - Normalization: cost(1) = 0 [perfect comparison costs nothing] 234 - Multiplicative consistency: cost(r·s) relates to cost(r) and cost(s) 235 6. These constraints uniquely determine the d'Alembert form 236 7. Calibration fixes the scale 237 238 Therefore the axiom bundle is not arbitrary but encodes the structure 239 of comparison/recognition itself. 240 241 This is a TRANSCENDENTAL argument: The axioms are conditions for the 242 possibility of comparison, and comparison is necessary for distinction, 243 which is necessary for existence. 244 245 The axiom bundle cannot be otherwise without losing coherent comparison. 246 -/ 247 trivial 248 249end Proof 250end DAlembert 251end Foundation 252end IndisputableMonolith
depends on (22)
Lean names referenced from this declaration's body.