us furnishes a confirmation of the utility of an acquaintance
with the syllogistic form, _in which form the pretended
demonstration in question cannot be exhibited_. An attempt to do
so will evince the utter want of connection between the premises
and the conclusion."

What the Archbishop says is true, and it disposes of the question as one
of "Formal Logic:" but yet the form of the sophism is so plausible, that
it imposes with equal force on the "common sense" of all those who
repose their conclusions upon the operations of that faculty. With them
a different procedure is necessary; and I suspect that if any one of the
most obstinate advocates of the sufficiency of common sense for the
"balancing of evidence" were to attempt the explanation of a hundred
fallacies that could be presented to him, he would be compelled to admit
that a more powerful and a more accurate machine would be of advantage
to him in accomplishing his task. This machine the syllogism supplies.

The discussion of Gregory St. Vincent will be found at pages 101-3. of
his _Opus Geometricum_, Antw., 1647 fol. The principle is the same as
that which Aldrich afterwards gave, as above referred to by Dr.
Whateley. I can only speak from memory of the discussion of Leibnitz,
not having his works at hand; but I am clear in this, that his principle
again is the same. [Greek: Idiotaes] is in error, however, in calling
St. Vincent's "a geometrical treatment" of it. He indeed uses lines to
represent the spaces passed over; and their discussion occurs in a
chapter on what is universally (but very absurdly) called "geometrical
proportion." It is yet no more _geometrical_ than our school-day problem
of the basket and the hundred eggs in Francis Walkinghame. Mere names do
not bestow character, however much _philosophers as well as legislators_
may think so. All attempts of the kind have been, and must be, purely