Complete Works of Lewis Carroll (188 page)

36.
m
1
x
0
†
y
1
m
′
0
    ¶
y
1
x
0
        [Fig.
I (α).]         Concl.
right.

37.
mx
′
0
†
m
1
y
0
    ¶
xy
′
1
        [Fig.
III.]         Concl.
right.

38.
xm
0
†
my
′
0
        Fallacy of Like Eliminands not asserted to exist.

39.
mx
0
†
my
′
1
    ¶
x
′y′
1
        [Fig.
II.]         Concl.
right.

40.
mx
′
0
†
ym
1
    ¶
xy
1
        [Fig.
II.]         Concl.
right.

SL7-B
Solutions for § 7.

  1.
No doctors are enthusiastic;

You are enthusiastic.

You are not a doctor.

Univ.
“persons”;
m
 = enthusiastic;
x
 = doctors;
y
 = you.

xm
0
†
y
1
m
′
0
    ¶
y
1
x
0
        [Fig.
I (α).

Conclusion right.

  2.
Dictionaries are useful;

Useful books are valuable.

Dictionaries are valuable.

Univ.
“books”;
m
 = useful;
x
 = dictionaries;
y
 = valuable.

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

Conclusion right.

  3.
No misers are unselfish;

None but misers save egg-shells.

No unselfish people save egg-shells.

Univ.
“people”;
m
 = misers;
x
 = selfish;
y
 = people who save egg-shells.

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

Conclusion 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.

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

Conclusion wrong: right one is “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.

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

Conclusion right.

  6.
Some healthy people are fat;

No unhealthy people are strong.

Some fat people are not strong.

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

mx
1
†
m
′y
0

No Conclusion.
[Fallacy of Unlike Eliminands with an Entity-Premiss.]

  7.
I saw it in a newspaper;

All newspapers tell lies.

It was a lie.

Univ.
“publications”;
m
 = newspapers;
x
 = publications in which I saw it;
y
 = telling lies.

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

Conclusion wrong: right one is “The publication, in which I saw it, tells lies.”

  8.
Some cravats are not artistic;

I admire anything artistic.

There are some cravats that I do not admire.

Univ.
“things”;
m
 = artistic;
x
 = cravats;
y
 = things that I admire.

xm
1
†
m
1
y
0

No Conclusion.
[Fallacy of Unlike Eliminands with an Entity-Premiss.]

  9.
His songs never last an hour.

A song, that lasts an hour, is tedious.

His songs are never tedious.

Univ.
“songs”;
m
 = lasting an hour;
x
 = his;
y
 = tedious.

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

Conclusion wrong: right one is “Some tedious songs are not his.”

10.
Some candles give very little light;

Candles are meant to give light.

Some things, that are meant to give light, give very little.

Univ.
“things”;
m
 = candles;
x
 = giving &c.;
y
 = meant &c.

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

Conclusion right.

11.
All, who are anxious to learn, work hard.

Some of these boys work hard.

Some of these boys are anxious to learn.

Univ.
“persons”;
m
 = hard-working;
x
 = anxious to learn;
y
 = these boys.

x
1
m
′
0
†
ym
1

No Conclusion.
[Fallacy of Unlike Eliminands with an Entity-Premiss.]

12.
All lions are fierce;

Some lions do not drink coffee.

Some creatures that drink coffee are not fierce.

Univ.
“creatures”;
m
 = lions;
x
 = fierce;
y
 = creatures that drink coffee.

m
1
x
′
0
†
my
′
1
    ¶
xy
′
1
        [Fig.
II.

Conclusion wrong: right one is “Some fierce creatures do not drink coffee.”

13.
No misers are generous;

Some old men are ungenerous.

Some old men are misers.

Univ.
“persons”;
m
 = generous;
x
 = misers;
y
 = old men.

xm
0
†
ym
′
1

No Conclusion.
[Fallacy of Unlike Eliminands with an Entity-Premiss.]

14.
No fossil can be crossed in love;

An oyster may be crossed in love.

Oysters are not fossils.

Univ.
“things”;
m
 = things that can be crossed in love;
x
 = fossils;
y
 = oysters.

xm
0
†
y
1
m
′
0
    ¶
y
1
x
0
        [Fig.
I (α).

Conclusion right.

15.
All uneducated people are shallow;

Students are all educated.

No students are shallow.

Univ.
“people”;
m
 = educated;
x
 = shallow;
y
 = students.

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