Background: Classical probability theory presupposes a separation between sample space, measure, and event structure – an external imposition. Human experience, however, has always known the unity of opposites (Yin and Yang, light and shadow). Material and methods: Starting from a structure \ (Xₜ\) that internally splits into expectation \ (E (Xₜ) \) and anti-expectation \ (E (Xₜ) \), probability is defined as an internal ratio \ (p (Xₜ) = E (Xₜ) /Xₜ\) – without external normalization axioms. Results: A unified algebra emerges in which logic, probability, and geometry (Pythagoras) appear as aspects of one and the same dialectical movement. Contradiction \ (p (1-p) \) becomes a structural curvature term. The principle of explosion is refuted by counterexample. Conclusion: An alternative approach to probability theory and many-valued logic appears possible – beyond external measure spaces, with immanent negation, and without explosion. Classical theory emerges as a limiting case of a richer dialectical structure.
Ilija Barukčić (Wed,) studied this question.
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