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First-order logic —also known as predicate logic, quantificational logic, and first-order predicate calculus —is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so ...
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Use ordinary first-order logic, but add a new unary predicate "Set", where "Set(t)" means informally "t is a set". Use ordinary first-order logic, and instead of adding a new predicate to the language, treat "Set(t)" as an abbreviation for "∃y t∈y" Some first-order set theories include: Weak theories lacking powersets:
But even if the world were governed by such laws, one could be free in the sense that higher-order volitions determined the primacy of first-order desires. This view is called compatibilism. An example for a failure to follow higher-order volitions is the drug addict who takes drugs even though they would like to quit taking drugs.