d regular method: but is not Formal Logic
already sufficiently encumbered with formalities?

Sec. 11. Euler's diagrams are used to illustrate the syllogism, though not
very satisfactorily, thus:

Barbara--

[Illustration: FIG. 5.]

Celarent--

[Illustration: FIG. 6.]

Darii--

[Illustration: FIG. 7.]

Remembering that 'Some' means 'It may be all,' it is plain that any one
of these diagrams in Fig. 7, or the one given above for Barbara, may
represent the denotative relations of P, M and S in Darii; though no
doubt the diagram we generally think of as representing Darii is No. 1
in Fig. 7.

Remembering that A may be U, and that, therefore, wherever A occurs
there may be only one circle for S and P, these syllogisms may be
represented by only two circles, and Barbara by only one.

Ferio--

[Illustration: FIG. 8.]

Here, again, probably, we generally think of No. 1 as the diagram
representing Ferio; but 2, or 3, or that given above for Celarent, is
compatible with the premises.

If instead of dealing with M, P, and S, a concrete example be taken of
Darii or Ferio, a knowledge of the facts of the case will show what
diagram is suitable to it. But, then, surely it must be possible to do
without the diagram. These diagrams, of course, can be used to
illustrate Moods of the other Figures.

CHAPTER XI

ABBREVIATED AND COMPOUND ARGUMENTS

Sec. 1. In ordinary discussion, whether oral or written, it is but rarely
that the forms of Logic are closely adhered to. We often leave wide gaps
in the structure of our arguments, trusting the intelligence of those
addressed to bridge them over; or we invert the regular order of
propositions, beginning with the conclusion, and mentioning the
premises, perhaps, a good while after, confident that the sagacity of
our audience will make all smooth. Sometimes a full style, like
Macaulay's, may, by means of amplification and illustration, spread the
elements of a single syllogism over several pages--a pennyworth of logic
steeped in so much eloquence. These practices give a great advantage to
sophists; who would find it very inconvenient to state explicitly in
Mood and Figure the pretentious antilogies which they foist upon the
public; and, indeed, such licences of composition often prevent honest
men from detecting errors into which they themselves have unwittingly
fallen, and which, with the best intentions, they strive to communicate
to others: but we put up with th