When the Minor is partly in the Middle, the Syllogism holds equally
good. Thus there are four possible ways in which two terms ([Greek:
oroi], plane enclosures) may be connected or disconnected through a
third. They are usually represented by circles as being the neatest
of figures, but any enclosing outline answers the purpose, and the
rougher and more irregular it is the more truly will it represent the
extension of a word.
Conclusion A.
All M is in P.
All S is in M.
All S is in P.
[Illustration: concentric circles of P, M and S - S in centre]
Conclusion E.
No M is in P.
All S is in M.
No S is in P.
[Illustration: Concentric circles 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.
Public-domain text, read in full here on John Shaqi.
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