Probabilistic Theories of Relations
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Poincaré repeatedly emphasized that only in the mathematical continuum the equalities A = B and B = C imply the equality A = C. In the observable physical continuum, “equal” means “indistinguishable,” and A = B and B = C by no means imply A = C. “The raw result of experience may be expressed by the relation \(A = B, B = C, A < C\) which may be regarded as the formula for the physical continuum.” According to Poincaré, physical equality is a non-transitive relation.
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