between the extremes when the relations
of the three terms are as stated in certain premisses of the Fourth
Figure.

III.--THE SORITES.

A chain of Syllogisms is called a Sorites. Thus:--

All A is in B.
All B is in C.
All C is in D.
:
:
:
:
All X is in Z.
[.'.] All A is in Z.

A Minor Premiss can thus be carried through a series of Universal
Propositions each serving in turn as a Major to yield a conclusion
which can be syllogised with the next. Obviously a Sorites may contain
one particular premiss, provided it is the first; and one universal
negative premiss, provided it is the last. A particular or a negative
at any other point in the chain is an insuperable bar.

[Footnote 1: [Greek: Hotan oun horoi treis autos echosi pros
allelous oste ton eschaton en holo einai to meso, kai ton meson
en holo to kroto e einai e me einai, ananke ton
akron einai syllogismon teleion.] (Anal. Prior., i. 4.)]

CHAPTER III.

THE DEMONSTRATION OF THE SYLLOGISTIC MOODS.--THE CANONS OF THE
SYLLOGISM.

How do we know that the nineteen moods are the only possible forms of
valid syllogism?

Aristotle treated this as being self-evident upon trial and simple
inspection of all possible forms in each of his three Figures.

Granted the parity between predication and position in or out of
a limited enclosure (term, [Greek: horos]), it is a matter of the
simplest possible reasoning. You have three such terms or enclosures,
S, P and M; and you are given the relative positions of two of them to
the third as a clue to their relative positions to one another. Is
S in or out of P, and is it wholly in or wholly out or partly in or
partly out? You know how each of them lies toward the third: when can
you tell from this how S lies towards P?

We have seen that when M is wholly in or out of P, and S wholly or
partly in M, S is wholly or partly in or out of P.

Try any other given positions in the First Figure, and you find that
you cannot tell from them how S lies relatively to P. Unless the Major
Premiss is Universal, that is, unless M lies wholly in or out of
P, you can draw no conclusion, whatever the Minor Premiss may give.
Given, _e.g._, All S is in M, it may be that All S is in P, or that No
S is in P, or that Some S is in P, or that Some S is not in P.

[Illustration:

Circles of M and P, overlapping,
with 3 instances of a circle of