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<p>Common cause completeness (CCC) is a&#xa0;philosophical principle that asserts that if we consider two positively correlated events, then it evokes a common cause event. The principle is due to H.&#xa0;Reichenbach and has mostly been studied in Boolean algebras and orthomodular lattices (quantum logics). The results published so far bring about a question of whether there is a&#xa0;small (countable) Boolean algebra with CCC. In this note, we construct such a Boolean algebra. Since finite Boolean algebras can satisfy CCC only trivially, this example is a&#xa0;smallest possible meaningful example.</p>

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A note on Reichenbach’s common cause completeness

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Dominika Burešová

摘要

Common cause completeness (CCC) is a philosophical principle that asserts that if we consider two positively correlated events, then it evokes a common cause event. The principle is due to H. Reichenbach and has mostly been studied in Boolean algebras and orthomodular lattices (quantum logics). The results published so far bring about a question of whether there is a small (countable) Boolean algebra with CCC. In this note, we construct such a Boolean algebra. Since finite Boolean algebras can satisfy CCC only trivially, this example is a smallest possible meaningful example.