Complete Works of Lewis Carroll (160 page)

Hence proposed Conclusion,
xy
1
, is
incomplete
, the
complete
one being “I wish to examine
all
these pictures thoroughly.”

(6)

“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.

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

Hence proposed Conclusion is right.

(7)

”No one, who means to go by the train and cannot get a conveyance, and has not enough time to walk to the station, can do without running;

  This party of tourists mean to go by the train and cannot get a conveyance, but they have plenty of time to walk to the station.

        This party of tourists need not run.”

Univ.
“persons meaning to go by the train, and unable to get a conveyance”;
m
 = having enough time to walk to the station;
x
 = needing to run;
y
 = these tourists.

m
′x′
0
†
y
1
m
′
0
do not come under any of the three Figures.
Hence it is necessary to return to the Method of Diagrams, as shown at p.
69.

Hence there is no Conclusion.

[Work Examples §
4
, 12–20 (p.
100); §
5
, 13–24 (pp.
101, 102); §
6
, 1–6 (p.
106); §
7
, 1–3 (pp.
107, 108).
Also read Note (A), at p.
164.]

§ 3.

Fallacies.

Any argument which
deceives
us, by seeming to prove what it does not really prove, may be called a ‘
Fallacy
’ (derived from the Latin verb
fallo
“I deceive”): but the particular kind, to be now discussed, consists of a Pair of Propositions, which are proposed as the Premisses of a Syllogism, but yield no Conclusion.

When each of the proposed Premisses is a Proposition in
I
, or
E
, or
A
, (the only kinds with which we are now concerned,) the Fallacy may be detected by the ‘Method of Diagrams,’ by simply setting them out on a Triliteral Diagram, and observing that they yield no information which can be transferred to the Biliteral Diagram.

But suppose we were working by the ‘Method of
Subscripts
,’ and had to deal with a Pair of proposed Premisses, which happened to be a ‘Fallacy,’ how could we be certain that they would not yield any Conclusion?

Our best plan is, I think, to deal with
Fallacies
in the same was as we have already dealt with
Syllogisms
: that is, to take certain forms of Pairs of Propositions, and to work  them out, once for all, on the Triliteral Diagram, and ascertain that they yield
no
Conclusion; and then to record them, for future use, as
Formulæ for Fallacies
, just as we have already recorded our three
Formulæ for Syllogisms
.

Now, if we were to record the two Sets of Formulæ in the
same
shape, viz.
by the Method of Subscripts, there would be considerable risk of confusing the two kinds.
Hence, in order to keep them distinct, I propose to record the Formulæ for
Fallacies
in
words
, and to call them “Forms” instead of “Formulæ.”

Let us now proceed to find, by the Method of Diagrams, three “Forms of Fallacies,” which we will then put on record for future use.
They are as follows:—

(1) Fallacy of Like Eliminands not asserted to exist.

(2) Fallacy of Unlike Eliminands with an Entity-Premiss.

(3) Fallacy of two Entity-Premisses.

These shall be discussed separately, and it will be seen that each fails to yield a Conclusion.

(1)
Fallacy of Like Eliminands not asserted to exist.

It is evident that neither of the given Propositions can be an
Entity
, since that kind asserts the
existence
of both of its Terms (see p.
20).
Hence they must both be
Nullities
.

Hence the given Pair may be represented by (
xm
0
†
ym
0
), with or without
x
1
,
y
1
.

These, set out on Triliteral Diagrams, are

xm
0
†
ym
0

x
1
m
0
†
ym
0

xm
0
†
y
1
m
0

x
1
m
0
†
y
1
m
0

(2)
Fallacy of Unlike Eliminands with an Entity-Premiss.

Here the given Pair may be represented by (
xm
0
†
ym
′
1
) with or without
x
1
or
m
1
.

These, set out on Triliteral Diagrams, are

xm
0
†
ym
′
1

x
1
m
0
†
ym
′
1

m
1
x
0
†
ym
′
1