Complete Works of Lewis Carroll (197 page)

1
k
′
1
b
′
0
† 2
eh
′
0
† 3
c
′d
0
† 4
hb
0
† 5
ac
0
† 6
kd
′
0
;

1
k
′b′
† 4
hb
† 2
eh
′
† 6
kd
′
† 3
c
′d
† 5
ac
    ¶
ea
0

i.e.
No engine-driver lives on barley-sugar.

56.

1
h
1
b
′
0
† 2
c
1
d
′
0
† 3
k
′a
0
† 4
e
1
h
′
0
† 5
b
1
a
′
0
† 6
k
1
c
′
0
;

1
hb
′
† 4
eh
′
† 5
ba
′
† 3
k
′a
† 6
kc
′
† 2
cd
′

¶
ed
′
0
†
e
1
,     i.e.
¶
e
1
d
′
0

i.e.
All the animals in the yard gnaw bones.

57.

1
h
′
1
d
′
0
† 2
e
1
c
′
0
† 3
k
′a
0
† 4
cb
0
† 5
d
1
l
′
0
† 6
e
′h
0
† 7
kl
0
;

1
h
′d′
† 5
dl
′
† 7
kl
† 3
k
′a
† 6
e
′h
† 2
ec
′
† 4
cb
    ¶
ab
0

i.e.
No badger can guess a conundrum.

58.

1
b
′h
0
† 2
d
′
1
l
′
0
† 3
ca
0
† 4
d
1
k
′
0
† 5
h
′
1
e
′
0
† 6
mc
′
0
† 7
a
′b
0
† 8
ek
0
;

1
b
′h
† 5
h
′e′
† 7
a
′b
† 3
ca
† 6
mc
′
† 8
ek
† 4
dk
′
† 2
d
′l′
    ¶
ml
′
0

i.e.
No cheque of yours, received by me, is payable to order.

59.

1
c
1
l
′
0
† 2
h
′e
0
† 3
kd
0
† 4
mc
′
0
† 5
b
′
1
e
′
0
† 6
n
1
a
′
0
† 7
l
1
d
′
0
† 8
m
′b
0
† 9
ah
0
;

1
cl
′
† 4
mc
′
† 7
ld
′
† 3
kd
† 8
m
′b
† 5
b
′e′
† 2
h
′e
† 9
ah
† 6
na
′

¶
kn
0

i.e.
I cannot read any of Brown’s letters.

60.

1
e
1
c
′
0
† 2
l
1
n
′
0
† 3
d
1
a
′
0
† 4
m
′b
0
† 5
ck
′
0
† 6
e
′r
0
† 7
h
1
n
0
† 8
b
′k
0
† 9
r
′
1
d
′
0
† 10
m
1
l
′
0
;

1
ec
′
† 5
ck
′
† 6
e
′r
† 8
b
′k
† 4
m
′b
† 9
r
′d′
† 3
da
′
† 10
ml
′
† 2
ln
′
† 7
hn

¶
a
′h
0
†
h
1
,     i.e.
¶
h
1
a
′
0

i.e.
I always avoid a kangaroo.

NOTES.

(A) .

One of the favourite objections, brought against the Science of Logic by its detractors, is that a Syllogism has no real validity as an argument, since it involves the Fallacy of
Petitio Principii
(i.e.
“Begging the Question”, the essence of which is that the whole Conclusion is involved in
one
of the Premisses).

This formidable objection is refuted, with beautiful clearness and simplicity, by these three Diagrams, which show us that, in each of the three Figures, the Conclusion is really involved in the
two
Premisses taken together, each contributing its share.

Thus, in Fig.
I., the Premiss
xm
0
empties the
Inner
Cell of the N.W.
Quarter, while the Premiss
ym
0
empties its
Outer
Cell.
Hence it needs the
two
Premisses to empty the
whole
of the N.W.
Quarter, and thus to prove the Conclusion
xy
0
.

Again, in Fig.
II., the Premiss
xm
0
empties the Inner Cell of the N.W.
Quarter.
The Premiss ym
1
merely tells us that the Inner Portion of the W.
Half is
occupied
, so that we may place a ‘I’ in it,
somewhere
; but, if this were the
whole
of our information, we should not know in
which
Cell to place it, so that it would have to ‘sit on the fence’: it is only when we learn, from the other Premiss, that the
upper
of these two Cells is
empty
, that we feel authorised to place the ‘I’ in the
lower
Cell, and thus to prove the Conclusion x′y
1
.

Lastly, in Fig.
III., the information, that
m
exists
, merely authorises us to place a ‘I’
somewhere
in the Inner Square——but it has large choice of fences to sit upon!
It needs the Premiss
xm
0
to drive it out of the N.
Half of that Square; and it needs the Premiss
ym
0
to drive it out of the W.
Half.
Hence it needs the
two
Premisses to drive it into the Inner Portion of the S.E.
Quarter, and thus to prove the Conclusion
x
′y′
1
.