Complete Works of Lewis Carroll (189 page)

Conclusion wrong: right one is “Some shallow people are not students.”

16.
All young lambs jump;

No young animals are healthy, unless they jump.

All young lambs are healthy.

Univ.
“young animals”;
m
 = young animals that jump;
x
 = lambs;
y
 = healthy.

x
1
m
′
0
†
m
′y
0

No Conclusion.
[Fallacy of Like Eliminands not asserted to exist.]

17.
Ill-managed business is unprofitable;

Railways are never ill-managed.

All railways are profitable.

Univ.
“business”;
m
 = ill-managed;
x
 = profitable;
y
 = railways.

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

Conclusion wrong: right one is “Some business, other than railways, is profitable.”

18.
No Professors are ignorant;

All ignorant people are vain.

No Professors are vain.

Univ.
“people”;
m
 = ignorant;
x
 = Professors;
y
 = vain.

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

Conclusion wrong: right one is “Some vain persons are not Professors.”

19.
A prudent man shuns hyænas.

No banker is imprudent.

No banker fails to shun hyænas.

Univ.
“men”;
m
 = prudent;
x
 = shunning hyænas;
y
 = bankers.

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

Conclusion right.

20.
All wasps are unfriendly;

No puppies are unfriendly.

No puppies are wasps.

Univ.
“creatures”;
m
 = friendly;
x
 = wasps;
y
 = puppies.

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

Conclusion incomplete: complete one is “Wasps are not puppies”.

21.
No Jews are honest;

Some Gentiles are rich.

Some rich people are dishonest.

Univ.
“persons”;
m
 = Jews;
x
 = honest;
y
 = rich.

mx
0
†
m
′y
1

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

22.
No idlers win fame;

Some painters are not idle.

Some painters win fame.

Univ.
“persons”;
m
 = idlers;
x
 = persons who win fame;
y
 = painters.

mx
0
†
ym
′
1

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

23.
No monkeys are soldiers;

All monkeys are mischievous.

Some mischievous creatures are not soldiers.

Univ.
“creatures”;
m
 = monkeys;
x
 = soldiers;
y
 = mischievous.

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

Conclusion right.

24.
All these bonbons are chocolate-creams;

All these bonbons are delicious.

Chocolate-creams are delicious.

Univ.
“food”;
m
 = these bonbons;
x
 = chocolate-creams;
y
 = delicious.

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

Conclusion wrong, being in excess of the right one, which is “Some chocolate-creams are delicious.”

25.
No muffins are wholesome;

All buns are unwholesome.

Buns are not muffins.

Univ.
“food”;
m
 = wholesome;
x
 = muffins;
y
 = buns.

xm
0
†
y
1
m
0

No Conclusion.
[Fallacy of Like Eliminands not asserted to exist.]

26.
Some unauthorised reports are false;

All authorised reports are trustworthy.

Some false reports are not trustworthy.

Univ.
“reports”;
m
 = authorised;
x
 = true;
y
 = trustworthy.

m
′x′
1
†
m
1
y
′
0

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

27.
Some pillows are soft;

No pokers are soft.

Some pokers are not pillows.

Univ.
“things”;
m
 = soft;
x
 = pillows;
y
 = pokers.

xm
1
†
ym
0
    ¶
xy
′
1
        [Fig.
II.

Conclusion wrong: right one is “Some pillows are not pokers.”

28.
Improbable stories are not easily believed;

None of his stories are probable.

None of his stories are easily believed.

Univ.
“stories”;
m
 = probable;
x
 = easily believed;
y
 = his.

m
′
1
x
0
†
ym
0
    ¶
xy
0
        [Fig.
I.

Conclusion right.

29.
No thieves are honest;

Some dishonest people are found out.

Some thieves are found out.

Univ.
“people”;
m
 = honest;
x
 = thieves;
y
 = found out.

xm
0
†
m
′y
1

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

30.
No muffins are wholesome;

All puffy food is unwholesome.

All muffins are puffy.

Univ.
is “food”;
m
 = wholesome;
x
 = muffins;
y
 = puffy.

xm
0
†
y
1
m
0

No Conclusion.
[Fallacy of Like Eliminands not asserted to exist.]

31.
No birds, except peacocks, are proud of their tails;

Some birds, that are proud of their tails, cannot sing.

Some peacocks cannot sing.

Univ.
“birds”;
m
 = proud of their tails;
x
 = peacocks;
y
 = birds that cannot sing.

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

Conclusion right.

32.
Warmth relieves pain;

Nothing, that does not relieve pain, is useful in toothache.

Warmth is useful in toothache.

Univ.
“applications”;
m
 = relieving pain;
x
 = warmth;
y
 = useful in toothache.

x
1
m
′
0
†
m
′y
0

No Conclusion.
[Fallacy of Like Eliminands not asserted to exist.]

33.
No bankrupts are rich;

Some merchants are not bankrupts.

Some merchants are rich.

Univ.
“persons”;
m
 = bankrupts;
x
 = rich;
y
 = merchants.

mx
0
†
ym
′
1

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

34.
Bores are dreaded;

No bore is ever begged to prolong his visit.

No one, who is dreaded, is ever begged to prolong his visit.

Univ.
“persons”;
m
 = bores;
x
 = dreaded;
y
 = begged to prolong their visits.