V.—SYMBOLIC REASONING (VII.)
HUGH MACCOLL · Mind · 1905
1. THE validity tests of the traditional logic turn mainly upon the question whether or not a syllogistic " term" (t'.«., clots X, Y or Z) is "distributed" or "undistributed".In ordinary language these words rarely, if ever, lead to any ambiguity or confusion of thought; but logicians have somehow managed to work them into a perplexing tangle.In the proposition "All X is Y," the class X is said to be "distributed," and the class Y " undistributed ".In the proposition " No X is Y," the class X and the class Y are said to be both " distributed ".In the proposition " Some X is Y," the class X and the class Y are said to be both "undistributed".Finally, in the proposition "Some X is not Y," the class X is said to be "undistributed" and the class Y " distributed ".2. Let us examine some consequences of this tangle of technicalities.Take the leading syllogism Barbara, the validity of which no one will question, provided it be expressed in its conditional form, namely, " If all Y iB Z and all X is Y, then all X is Z".Being admittedly valid, this syllogism must hold good whatever values (or meanings) we give to itB constituents X, Y, Z.It must therefore hold good (as every logician will surely admit) when X, Y and Z are synonyms, and therefore all denote the same class.In this case also the two premisses asd the conclusion will be three truisms which no one would dream of denying.Consider now one of these truisms, say " All X is Y ".Here, by the usual logical convention, the class X is said to be " distributed," and the class Y " undistributed ".But when X and Y are synonyms, they denote the same class, so that the same class may, at the same time and in the same proposition, be both " distributed " and " undistributed ".Does not this sound like a contradiction ?Speaking of a certain