Of Logic, Learning, and Language

Abstract

“Of Logic,” Stuart Mill noted in his Inaugural Address at St. Andrews¹ in 1867, “I venture to say, even if limited to that of mere ratiocination, the theory of names, propositions, and the syllogisms, that there is no part of intellectual education which is of greater value, or whose place can so ill be supplied by anything else.” The “theory of names” may perhaps be construed, in more modern terms, as the metalogical theory of reference or designational semantics. The theory of “mere ratiocination,” of “propositions,” and of the syllogism, is presumably wholly contained within first-order logic, that is, the theory of the truth-functional connectives, of quantifiers, and (perhaps) of identity. Thus Mill’s splendid comments may without distortion be viewed in the light of the newer developments in logical and metalogical theory.