Complete Works of Lewis Carroll (185 page)

∴
No
x
′
are
y
.

Hence proposed Conclusion is right.

4.

Some epicures are ungenerous;

All my uncles are generous.

    My uncles are not epicures.

Univ.
“persons”;
m
 = generous;
x
 = epicures;
y
 = my uncles.

Some
x
are
m
′
.

All
y
are
m
.

  All
y
are
x
′
.

∴
Some
x
are
y
′
.

Hence proposed Conclusion is wrong, the right one being “Some epicures are not uncles of mine.”

5.

Gold is heavy;

Nothing but gold will silence him.

    Nothing light will silence him.

Univ.
“things”;
m
 = gold;
x
 = heavy;
y
 = able to silence him.

All
m
are
x
;

No
m
′
are
y
.

  No
x
′
are
y
.

∴
No
x
′
are
y
.

Hence proposed Conclusion is right.

6.

Some healthy people are fat;

No unhealthy people are strong.

    Some fat people are not strong.

Univ.
“persons”;
m
 = healthy;
x
 = fat;
y
 = strong.

Some
m
are
x
;

No
m
′
are
y
.

  Some
x
are
y
′
.

There is no Conclusion.

§ 3.

Method of Subscripts.

SL4-B
Solutions for § 4.

  1.
mx
′
0
†
m
′
1
y
′
0
    ¶
x
′y′
0
    [Fig.
I.

    i.e.
“No
x
′
are
y
′
.”

  2.
m
′x
0
†
m
′y′
1
    ¶
x
′y′
1
    [Fig.
II.

    i.e.
“Some
x
′
are
y
′
.”

  3.
m
′
1
x
′
0
†
m
′
1
y
0
    ¶
xy
′
1
    [Fig.
III.

    i.e.
“Some
x
are
y
′
.”

  4.
x
′m′
0
†
y
′
1
m
′
0
    ¶ nothing.

    [Fallacy of Like Eliminands not asserted to exist.]

  5.
mx
′
1
†
ym
0
    ¶
x
′y′
1
    [Fig.
II.

    i.e.
“Some
x
′
are
y
′
.”

  6.
x
′m
0
†
my
0
    ¶ nothing.

    [Fallacy of Like Eliminands not asserted to exist.]

  7.
mx
′
0
†
y
′m
1
    ¶
xy
′
1
    [Fig.
II.

    i.e.
“Some
x
are
y
′
.”

  8.
m
′
1
x
0
†
m
′y
0
    ¶
x
′y′
1
    [Fig.
III.

    i.e.
“Some
x
′
are
y
′
.”

  9.
x
′m′
1
†
my
0
    ¶ nothing.

    [Fallacy of Unlike Eliminands with an Entity-Premiss.]

10.
x
1
m
′
0
†
y
′
1
m
0
    ¶
x
1
y
′
0
†
y
′
1
x
0
    [Fig.
I (β).

    i.e.
“All
x
are
y
, and all
y
′
are
x
′
.”

11.
mx
0
†
y
′
1
m
0
    ¶ nothing.