ircles of M and S,
S in centre and separate circle of P]

Conclusion I.
All M is in P.
Some S is in M.
Some S is in P.

[Illustration: Concentric circles of P and M,
M in centre, both overlapped by circle of S]

Conclusion O.
No M is in P.
Some S is in M.
Some S is not in P.

[Illustration: Circles of M and P touching,
each overlapped by circle of S]

These four forms constitute what are known as the moods of the First
Figure of the Syllogism. Seeing that all propositions may be reduced
to one or other of the four forms, A, E, I, or O, we have in these
premisses abstract types of every possible valid argument from
general principles. It is all the same whatever be the matter of the
proposition. Whether the subject of debate is mathematical, physical,
social or political, once premisses in these forms are conceded, the
conclusion follows irresistibly, _ex vi formae, ex necessitate formae_.
If an argument can be analysed into these forms, and you admit
its propositions, you are bound in consistency to admit the
conclusion--unless you are prepared to deny that if one thing is in
another and that other in a third, the first is in the third, or if
one thing is in another and that other wholly outside a third, the
first is also outside the third.

This is called the AXIOM OF SYLLOGISM. The most common form of it in
Logic is that known as the _Dictum_, or _Regula de Omni et Nullo:_
"Whatever is predicated of All or None of a term, is predicated of
whatever is contained in that term". It has been expressed with many
little variations, and there has been a good deal of discussion as to
the best way of expressing it, the relativity of the word best being
often left out of sight. _Best_ for what purpose? Practically that
form is the best which best commands general assent, and for this
purpose there is little to choose between various ways of expressing
it. To make it easy and obvious it is perhaps best to have two
separate forms, one for affirmative conclusions and one for negative.
Thus: "Whatever is affirmed of all M, is affirmed of whatever is
contained in M: and whatever is denied of all M, is denied of whatever
is contained in M". The only advantage of including the two forms in
one expression, is compendious neatness. "A part of a part is a part
of the whole," is a neat form, it being understood that an individual
or a species is part of a genus. "What is said of a whole, is said
of e