deduction of the categories See KANT. deduction theorem, a result about certain systems of formal logic relating derivability and the conditional. It states that if a formula B is derivable from A (and possibly other assumptions), then the formula APB is derivable without the assumption of A: in symbols, if G 4 {A} Y B then GYAPB. The thought is that, for example, if Socrates is mortal is derivable from the assumptions All men are mortal and Socrates is a man, then If Socrates is a man he is mortal is derivable from All men are mortal. Likewise, If all men are mortal then Socrates is mortal is derivable from Socrates is a man. In general, the deduction theorem is a significant result only for axiomatic or Hilbert-style formulations of logic. In most natural deduction formulations a rule of conditional proof explicitly licenses derivations of APB from G4{A}, and so there is nothing to prove. See also DEDUCTIO. S.T.K.