Complete Works of Lewis Carroll (156 page)

“All
x
are
m
;

 All
y
are
m
′
.”

∴
“All x are y′;

    All
y
are
x
′
.”

i.e.
“All diligent students are learned; and all ignorant students are idle”.

(4)

“Of the prisoners who were put on their trial at the last Assizes, all, against whom the verdict ‘guilty’ was returned, were sentenced to imprisonment;

Some, who were sentenced to imprisonment, were also sentenced to hard labour”.

Univ.
“prisoners who were put on their trial at the last Assizes”,
m
 = sentenced to imprisonment;
x
 = against whom the verdict ‘guilty’ was returned;
y
 = sentenced to hard labour.

“All
x
are
m
;

 Some
m
are
y
.”

There is no Conclusion.

[Review Tables VII, VIII (pp.
48, 49).
Work Examples §
1
, 17–21 (p.
97); §
4
, 1–6 (p.
100); §
5
, 1–6 (p.
101).]

§ 3.

Given a Trio of Propositions of Relation, of which every two contain a Pair of codivisional Classes, and which are proposed as a Syllogism; to ascertain whether the proposed Conclusion is consequent from the proposed Premisses, and, if so, whether it is complete.

The Rules, for doing this, are as follows:—

(1) Take the proposed Premisses, and ascertain, by the process described at p.
60, what Conclusion, if any, is consequent from them.

(2) If there be
no
Conclusion, say so.

(3) If there
be
a Conclusion, compare it with the proposed Conclusion, and pronounce accordingly.

I will now work out, in their briefest form, as models for the Reader to imitate in working examples, six Problems.

(1)

“All soldiers are strong;

  All soldiers are brave.

          Some strong men are brave.”

Univ.
“men”;
m
 = soldiers;
x
 = strong;
y
 = brave.

“All
m
are
x
;

 All
m
are
y
.

   Some
x
are
y
.”

∴
“Some
x
are
y
.”

Hence proposed Conclusion is right.

(2)

“I admire these pictures;

  When I admire anything I wish to examine it thoroughly.

      I wish to examine some of these pictures thoroughly.”

Univ.
“things”;
m
 = admired by me;
x
 = these pictures;
y
 = things which I wish to examine thoroughly.

“All
x
are
m
;

 All
m
are
y
.

   Some
x
are
y
.”

∴
“All
x
are
y
.”

Hence proposed Conclusion is
incomplete
, the
complete
one being “I wish to examine
all
these pictures thoroughly”.

(3)

“None but the brave deserve the fair;

  Some braggarts are cowards.

      Some braggarts do not deserve the fair.”

Univ.
“persons”;
m
 = brave;
x
 = deserving of the fair;
y
 = braggarts.

“No
m
′
are
x
;

 Some
y
are
m
′
.

   Some
y
are
x
′
.”