Legal positivism, which dominates Anglo-American jurisprudence, is “intensive” in nature. That is, law is reduced to its rules of recognition. The whole (rules of recognition) comes before the parts (the individual laws). This must be so if law is to be considered separable from morality—a favorite thesis of legal positivism. In set theory, intension yields internal contradiction. The only non-contradictory set theory is extensive in nature. Sets are not defined by rules that identify the members of the set (intension). Rather, sets are defined by their members (extension). The parts come before the whole. When set theory is applied to legal positivism, legal positivism is revealed to be contradictory and therefore invalid. The only conceivable non-contradictory jurisprudence is one that is extensive in nature, which means, precisely, that “law as such” cannot possibly be defined according to rules of recognition. This in turn means that law cannot be separated from morality, because set theory shows that at least one primary rule grounded in morality must be included in the set of primary rules.
- set theory
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