ABSTRACT
Doubt has often been expressed as to whether a syllogism can add to our knowledge in any way. John Stuart Mill and Henri Poincaré, in particular, held the opinion that the conclusion of a syllogism is an “analytic” judgment in the sense of Kant, and therefore could be obtained by the mere dissection of the premisses. Any one, then, who maintains that mathematics is founded solely on logical principles would appear to maintain that mathematics, in the last instance, reduces to a huge tautology.
