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Is there such a thing as unary (as opposed to binary, ternary, …, n-ary) logic?

cf. Is there any reason for the heavy focus on binary relations in formal logic?

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    Syllogistic was the "unary logic" (monadic predicate calculus), it only admitted one place predicates (attributes). Once two-place predicates are admitted all finite place ones have to be admitted as well since they reduce to them, so we get the standard predicate calculus. Monadic predicate calculus has very poor expressive power in comparison, which is why Kant had to invent synthetic judgments to explain mathematics. – Conifold Sep 26 '18 at 20:30
  • I see no reason why unary logic would not exist, but it provides no useful purpose/application, to take it beyond just a definition. – Guill Oct 3 '18 at 2:14
  • @Guill What would its definition be? – Geremia Oct 3 '18 at 2:29

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