s the sphere of syllogism also, for if two and two make four, does not the conception of four assume the position of the major predicate, which is the generalized idea of one to a quadruple extent, and also of twos duplicated. Thus the major predicate, that four is two twos, involves the minor that two is the half of four and consequently that twice two is four. Q. E. D. The syllogism is irresistible.
If Prof. Harris should establish the mathematical syllogism and extend its power through all the realms of mathematics, as so industrious a thinker might easily do, he will have taken a step far in advance of Plato, and justly deserve a higher rank, for Plato (see his Phædo) was terribly puzzled over the question how one and one make two. After much puzzling he decided finally that one and one became two "by participation in duality." This was the first great step to introduce philosophy into mathematics. Let Prof. Harris consummate this great work either by syllogism or by "participati