Abstract
A formal system ℒ for descriptive and normative statements is given based on first-order predicate calculus augmented by deontic operators. Hume's separation thesis is then given the following formulation and proved in ℒ: there is no theorem in ℒ of the form P ⊃ M where P is a consistent descriptive statement and M is a normative statement. We attempt to show that the formal system ℒ is actually true for the intended model by giving an interpretation of the formal system. It turns out that there are three mutually exclusive classes of statements; namely, descriptive statements, statements equivalent to purely normative statements, and hybrid statements. It is shown that theories that have not offered a proper treatment of hybrid statements have led to a great deal of confusion in the past. A brief discussion of the philosophical importance of the results is given.
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Johanson, A.A. A proof of Hume's separation thesis based on a formal system for descriptive and normative statements. Theor Decis 3, 339–350 (1973). https://doi.org/10.1007/BF00138192
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DOI: https://doi.org/10.1007/BF00138192