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liable to the ambiguity which is almost always the result. For in

38 Pol. Econ. Lect. IX.

§ 10.] OF FALLACIES. 127

respect of words tliat sound something new and strange, tliougli it
is, as I have said, much better to define them in the outset, yet
even Avithout this, the student would gradually collect their meaning-
pretty correctly, as he proceeded in his study of any treatise ; from
having nothing to mislead him, — nothing from which to form his
notions at all, except the manner in which the terms were employed
in the work itself that is before him. And the very desire he had
felt of a definition would lead him in this way to form one, and
generally a sufficiently correct one, for himself.

** It is otherwise with terms to which we are familiarly accus-
tomed. Of these, the student does not usually crave definitions,
from supposing, for that reason, that he understands them well
enough : though perhaps (without suspecting it) he has in reality
been accustomed to hear them employed in various senses, and to
attach but a vague and inaccurate notion to them. If you speak to
an uninstructed hearer, of any thing that is spherical, or circular, or
cylindrical, he will probably beg for an explanation of your meaning ;
but if 3''ou tell him of any thing that is round, it will not strike him
that any explanation is needed : though he has been accustomed to
employ the word, indiscriminately, in all the senses denoted by the
other three." ^^

But here it may be proper to remark,* that for the avoiding of DeflniHons,
Fallacy, or of Verbal-controversy, it is only requisite that the term be exacted,
should be employed uniformly in the same sense, as far as the exist-
ing question is concerned. Thus, two persons might, in discussing
the question whether Augustus was a great man, have some such
difi*erence in their acceptation of the epithet "great," as would be
non-essential to that question ; e.g. one of them might understand
by it nothing more than eminent intellectual and moral qualities;
while the other might conceive it to imply the performance of
splendid actions: this abstract difference of meaning would not pro-
duce any disagreement in the existing question, because both those
circumstances are united in the case of Augustus ; but if one (and
not the other) of the parties understood the epithet " great" to imply
pure patriotism, — generosity of character, &lc., then there would
be a disagreement as to the application of the Term, even between
those who might think alike of Augustus's character, as wanting in
those qualities.^ Definition, the specific for ambiguity, is to be
employed, and demanded, with a view to this principle ; it is sufficient
on each occasion to define a Term as far as regards the question in

If, for example, we were remonstrating with any one for quitting
the church of which he was a member, wantonly, and not from
strong and deliberate conscientious conviction, but from motives of
taste or fancy, and he were to reply by asking, how do you define a

a? Pol. Econ. Lect. IX. 28 See Book II. Ch. V. § 6.

28 See Book IV. Ch. IV. § 1.


Churcli ? tlie demand would be quite irrelevant, unless lie meant to
deny that tlie Community he quits is a Church. But if we were to
insist on designating any one religious-community on earth to which
we might belong, as the universal or Catholic Church, — in demand-
ing from all Christians submission to its ordinances and decisions,
and denouncing all who should not belong to it, as being out of the
pale of Christ's Church, then indeed we might fairly be called on to
give a definition, and one which should be consistent with facts.^

Of those cases where the ambiguity arises fivm the context, there
are several species ; some of which Logicians have enumerated, but
have neglected to refer them, in the first place, to one common class
{viz. the one under which they are here placed;) and have even
arranged some under the head of Fallacies ** in dictione," and others
under that of ** extra dictionem.""
Pttiiacy of We may consider, as the first of these species, the Fallacy of
Composition " Division" and that of "Composition," taken together; since in
each of these the Middle-term is used in one Premiss collectively,
in the other, distrihutively : if the former of these is the major
Premiss, and the latter, the minor, this is called the "Fallacy of
Division ;" the Term which is first taken collectively being after-
wards divided ; and vice versa. The ordinary examples are such as
these ; ** All the angles of a triangle are equal to two right angles:
A B C is an angle of a triangle ; therefore A B C is equal to two
right angles." " Five is one number ; three and two are five : there-
fore three and two are one number;" or, "three and two are two
numbers, five is three and two, therefore five is two numbers:" it is
manifest that the Middle-term, three and two (in this last example)
is ambiguous, signifying, in the major Premiss, " taken distinctly ; "
in the minor, "taken together:" and so of the rest.

To this head may be referred the common Fallacy of over-rating,
where each premiss of an argument is otAj probable, the probability
of the conclusion ; which, in that case, is less than that of the less
probable of the premises.^^ For, suppose the probabiHty of one of
these to be ^q, and of the other /g (each more likely than not) the
probability of the conclusion will be only -/g^g or a little more than

so See Appendix, Article " Truth." persons whose trade it is, in which calcu-

81 See below, § 14. Some persons pro- lations of this nature are made, in the

fess contempt for all such calculations, on pui-chase of contingent reversions, depend-

the ground that we cannot be quite sure ing, sometimes, on ajrreat varietj' of risks,

of the exact degree of probability of each which can only be conjecturally estimat-

premiss. And this is true; but this una- ed; and in Insurances, not only against

voidable uncertainty is no reason why we ordinary risks (the calculations of which

should not guard against an additional are to be drawn from Statistical- tables)

source of uncertainty which can be avoid- but also against every variety and degree

ed. It is some advantage to have no wore oi eo'traordinari/ risk; the arac^ amount

doubt as to the degree of probability of of which, no one can confidently pro-

the Conclusion, than we have respecting nounce upon. But the calculations are

that of the premises. based on the best estimate that can be

And in tact there are Offices, kept by formed.

5 11.] OF FALLACIES. 129

f ; which is less than an even chance.* This Fallacy may be most
easily stated as a conditional ; a form in which any Fallacy of
ambiguous middle may easily be exhibited. B.G. *' If it is more
likely than not, that these premises are true : {i.e. that they are
both true) it is more likely than not, that the conclusion is true :
but it is more likely than not that the premises are true : [i.e. that
each of them is so) therefore it is more likely than not that the
conclusion is true." Here, a term in the antecedent, viz. — "that
the premises are more likely than not to be true" — is taken jointly
in the Major, and dividedly in the Minor.

To the same class we may refer the Fallacy by which men have
sometimes been led to admit, or pretend to admit, the doctrine of
Necessity; e.g. "he who necessarily goes or stays {i.e. in reality,
* who necessarily goes, or who necessarily stays ') is not a free agent ;
you must necessarily go or stay {i.e. * you must necessarily take the
alternative '), therefore you are not a free agent." Such also is the
Fallacy which probably operates on most adventurers in lotteries ;
e.g. "the gaining of a high prize is no uncommon occurrence; and
what is no uncommon occurrence may reasonably be expected:
therefore the gaining of a high prize may reasonably be expected;"
the Conclusion, when applied to the individual (as in practice it is),
must be understood in the sense of " reasonably expected by a
certain individual;'' therefore for the Major-Premiss to be true, the
middle-Term must be miderstood to mean, "no micommon occur-
rence to some one particular person;" whereas for the Minor
(which has been placed first) to be true, you must understand it of
"no uncommon occurrence to some one or other;'' and thus you will
have the Fallacy of Composition.

There is no Fallacy more common, or more likely to deceive, than
the one now before us. The form in which it is most usually
employed, is to establish some truth, separately, concerning each
dngle member of a certain class, and thence to infer the same of the
whole collectively. Thus, some infidels have laboured to prove
concerning some one of our Lord's miracles, that it might have been
the result of an accidental conjuncture of natural circumstances ;
next, they endeavour to prove the same concerning another; and so
on ; and thence infer that all of them occurring as a series might
have been so. They might argue in like manner, that because it is
not very improbable one may throw sixes in any one out of a hundred
throws, therefore it is no more improbable that one may throw sixes
& hundred times running.
^ It will often happen that when two objects are incompotihle, though Thauma-
either of them, separately, may be attained, the incompatibility is fauScy.
disguised by a rapid and frequent transition from the one to the
other alternately. E.G. You may prove that £100 would accom-
plish this object ; and then, that it would accomplish that: and then,
you recur to the former ; and back agam : till at length a notion is

* See Postscript.


generated of the possibility of accomplishing both hy this £100.

*' Two distinct objects may, by being dexterously presented, again

and again in quick succession, to the mind of a cursory reader, be

so associated together in his tlwughts, as to be conceived capable,

when in fact they are not, of being actually combined in practice.

The fallacious belief thus induced bears a striking resemblance to

the optical illusion effected by that ingenious and philosophical toy

called the Thaumatrope ; in which two objects painted on opposite

sides of a card, — for instance a man, and a horse, — a bird, and a

cage, — are, by a quick rotatory motion, made to impress the eye in

combination, so as to form one picture, of the man on the horse's

back, the bird in the cage, &c. As soon as the card is allowed to

remain at rest, the figures, of ^ourse, appear as they really are,

V separate and on opposite sides. A mental illusion closely analogous

J v^ *^ *^^^' ^^ produced, when by a rapid and repeated transition from

1 J J^^^ subject to another alternately, the mind is deluded into an idea

If J^ 'bf the actual combination of things that are really incompatible.^)

kvF ly^^The chief part of the defence which various writers have advanced"

' *^ X in favour of the system of Penal-Colonies, consists, in truth, of a

• sort of intellectual Thaumatrope. The prosperity of the Colony, and

. the rqoression of crime, are, by a sort of rapid whirl, presented to

the mind as combined in one picture. A very moderate degree of

calm and fixed attention soon shows that the two objects are painted

on opposite sides of the card."^^

Ambiguity The Fallacy of Division may often be considered as turning on

^AiL"*""^ the ambiguity of the word *' all;" which may easily be dispelled by

substituting for it the word "each" or "every," where that is

its signification; e.g. "all these trees make a thick shade," is

ambiguous ; meaning, either, " every one of them," or, " all


This is a Fallacy with which men are extremely apt to deceive
themselves: for when a multitude of particulars are presented to
the mind, many are too weak or too indolent to take a compre-
hensive view of them ; but confine their attention to each single
point, by turns ; and then decide, infer, and act, accordingly ; e.g,
the imprudent spendthrift, finding that he is able to afford this,
or that, or the other expense, forgets that aU of them together will
ruin him.

To the same head may be reduced that fallacious reasoning by
which men vindicate themselves to their own conscience and to
others, for the neglect of those undefined duties, which, though
indispensable, and therefore not left to our choice whether we will
practise them or not, are left to our discretion as to the mode, and
the particular occasions, of practising them ; e.g. " I am not bound
to contribute to this charity in particular ; nor to that ; nor to the

^ Remarks on Transportation, pp. 25> 26.

§ 12.] OF FALLACIES. 131

other:" the loradicdl conckision which they draw, is, that all
charity may be dispensed with.

As men are apt to forget that any two circumstances (not natm'ally
connected) are more rarely to be met with combined than separate,
though they be not at all incompatible; so also they are apt to
imagine, from finding that they are rarely combined, that there is
an incompatibility ; e.g. if the chances are ten to one against a man's
possessing strong reasoning powers, and ten to one against exquisite
taste, the chances against the combination of the two (supposing
them neither connected nor opposed) will be a hundred to one.
Many, therefore, from finding them so rarely united, will infer that
they are "in some measure incompatible ; which Fallacy may easily
be exposed in the form of Undistributed middle : " qualities
unfriendly to each other are rarely combined ; excellence in the
reasoning powers, and in taste, are rarely combined ; therefore they
are qualities unfriendly to each other.

§ 12.

The other kind of ambiguity arising from the context, and which Faiiacfa
is the last case of Ambiguous middle that I shall notice, is the
**fallacia accidentis: " together with its converse, "fallacia a dido
secundum quid ad didum simpliciter; " in each of which the Middle-
Term is used, in one Premiss to signify something considered simply,
in itself, and as to its essence ; and in the other Premiss, so as to , ,^
imply that its Accidents are taken into account with it : as in the y-*-^ ■ '^
well-known example, " what is bought in the^ market is eaten; raw
meat is bought in the market; therefore raw meat is eaten."
Here the Middle has understood in conjunction with it, in the Major-
Premiss, " <X5 to its substance merely: " in the Minor, '' as to its con-
dition and circumstances.''

To this head, perhaps, as well as to any, may be referred the
Fallacies which are frequently%unded on the occasional, partial,
and temporary variations in the acceptation of some Term, arising
from circumstances of person, time, and place, which will occasion
something to be understood in conjunction with it beyond its strict
literal signification.) JS.G. The word "loyalty," which properly
denotes attachment to lawful government, — whether of a king,
president, senate, <kc., according to the respective institutions of
each nation, — has often been used to signify exclusively, attachment
to regal authority ; and that, even when carried beyond the boundaries
0^ law. So, "reformer" has sometimes been limited to the pro-
testant reformers of religion; sometimes, to the advocates of some
particular parliamentary reform, &c. And whenever any phrase of
this kind has become a kind of watch-word or gathering-cry of a
party, the employment of it would commonly imply certain senti-
ments not literally expressed by the words. To assume therefore
that one is friendly or unfriendly to " Loyalty " or to " Reform "


in one sense, because lie has declared himself friendly or nnfriendlj
to it in another sense, when implying and connected with such and
such other sentiments, is a Fallacy, such as may fairly be referred
to the present head.


On the non-logical (or material) Fallacies : and first, of ** begging
the question; " Fetitio Principii.

Begging the The indistinct and unphilosophical account which has been given
ques ion. ^^ Logical writers of the Fallacy of " non causa,'' and that of
'' petitio pnncipii,'' makes it very difficult to ascertain wherein they
conceived them to differ, and Avhat they understood to be the
distinctive character of each. I shall not therefore undertake to
conform exactly to their language, but merely to express myself
distinctly, without departing more than is necessary for that purpose,
from established usage.

Let the name then of "petitio principii" {begging tJie question)
be confined to those cases in which one of the Premises either is
manifestly the same in sense with the Conclusion, or is actually
proved from it, or is such as the persons you are addressing ^^ are
not likely to know, or to admit, except as an inference from the
Conclusion : as, e.g. if any one should infer the authenticity of a
certain history, from its recording such and such facts, the reality of
which rests on the evidence of that history.

All other cases in which a Premiss (whether the expressed or the
suppressed one) has no sufficient claim to be admitted, I shall
designate as the *' Fallacy of undue assumption of a Premiss."

Let it however be observed, that in such cases (apparently) as
this, we must not too hastily pronounce the argument fallacious ;
for it may be perfectly fair at the commencement of an argument to
assume a Premiss that is not more evident than the Conclusion, or
is even ever so paradoxical, provided you proceed to prove fairly that
Premiss ; and in like manner it is both usual and fair to begin by
deducing your Conclusion from a Premiss exactly equivalent to it ;
which is merely throwing the proposition in question into the form
in which it will be most conveniently proved.
Argufng In Arguinf^ in a Circle, however, must necessarily be unfair ; though
it frequently is practised undesignedly; e.g. some Mechanicians
attempt to prove, (what they ought to have laid down as a probable
but doubtful hypothesis,) that every particle of matter gravitates
equally; "why?" because those bodies which contain more par-
ticles ever gravitate more strongly, i.e. are heavier: "but (it may
be urged) those which are heaviest are not always more bulky;'"
**no, but still they contain more particles, though more closely

83 For of two propositions, the one may be the more evident to some, and the
other, to otliers.

\ Circle.

§13.] OF FALLACIES. 133

condensed;" ** liow do you know that?" ""because tliey are
heavier;" "how does that prove it?" "hecause all particles of
matter gravitating equally, that mass which is specifically the
heavier must needs have the more of them in the same space."

Of course the narrower the Circle, the less likely it is to escape
the detection, either of the reasoner himself, (for men often deceive
themselves in this way) or of his hearers. When there is a long
circuit of many intervening propositions hefore you come hack to the
original Conclusion, it will often not he perceived that the arguments
really do proceed in a "Circle :" just as when any one is advancing
in a straight line (as we are accustomed to call it) along a plain on
this Earth's surface, it escapes our notice that we are really moving
along the circumference of a Circle, (since the earth is a glohe) and
that if we could go on without interruption in the same line, we
should at length arrive at the very spot we set out from. But this
we readily perceive, when Ave are walking round a small hill.

For instance, if any one argues that you ought to submit to the
guidance of himself, or his leader, or his party, &c., because these
maintain what is right ; and then argues that what is so maintained
is right, because it is maintained by persons whom you ought to
submit to ; and that these are, himself and his party ; or again, if
any one maintains that so and so must be a thing morally wrong,
because it is prohibited in the moral portion of the Mosaic-law, and
then, that the prohibition of it does form a part of the moral (not
the ceremonial, or the civil) portion of that Law, because it is a thing
morally ivrong, — either of these would be too narrow a Circle to
escape detection, unless several intermediate steps were interposed.
And if the form of expression of each proposition be varied every
time it recurs, — the sense of it remaining the same, — this will
greatly aid the deception.

Of course, the way to expose the Fallacy, is to reverse this pro-
cedure: to narrow the Circle, by cutting off the intermediate steps;
and to exhibit the same proposition, — when it comes round the second
time, — in the same words.

Obliquity and disguise being of course most important to the ObHqn'ty ot
success of the petitio prlneipii as well as of other Fallacies, the ^^p'"**'*"^*''*'
Sophist will in general either have recourse to the " Circle," or ^

else not venture to state distinctly his assumption of the point in ^L^
question, but will rather assert some other proposition which implies \J^.* - (j^
it;^ thus keeping out of sight (as a dexterous thief does stolen ^ ^J^
goods) the point in question, at the very moment when he is taking \h^
It for granted. Hence the frequent union of this Fallacy with V
*• ignoratio elenchi:" [vide § 15.] The English language is perhaps

8* Gibbon affords the most remarkable position. His way of writing reminds

instances of this kind of style. That one of those pei-sons who never dare look

which he really means to speak of, is you full in the face,
hardly ever made the Subject of his Pro-


the more suitable for the Fallacy of petitio p^incipii, from its being
formed from two distinct languages, and thus abounding in synony-
mous expressions, which have no resemblance in sound, and no
connexion in etymology; so that a Sophist may bring forward a
proposition expressed in words of Saxon origin, and give as a reason
for it, the very same proposition stated in words of Norman origin ;
e.g. "to allow every man an unbounded freedom of speech must
always be, on the whole, advantageous to the State ; for it is highly
conducive to the interests of the Community, that each individual
should enjoy a liberty perfectly unlimited, of expressing his senti-


Undue The next head is, the falsity, or, at least, undue assumption, of

assump I n. ^ Pj-gj^iigg ^h^t is not equivalent to, or dependent on, the Conclusion ;
which, as has been before said, seems to correspond nearly with
the meaning of Logicians, when they speak of " non causa pro
causa.^^ This name indeed would seem to imply a much narrower
class: there being one species of arguments which are from cause
to effect; in which, of course, two things are necessary; 1st, the
sufficiency of the cause ; 2d, its establishment ; these are the two
Premises ; if therefore the former be unduly assumed, we are
arguing from that which is not a sufficient cause as if it were so :
e.g. as if one should contend from such a man's having been unjust
or cruel, that he will certainly be visited with some heavy temporal
judgment, and come to an untimely end. In this instance the
Sophist, from having assumed, in the Premiss, the (granted) exist-
ence of a pretended cause, infers, in the Conclusion, the existence
of the pretended effect, which we have supposed to be the Question.
Or vice versa, the pretended eifect may be employed to establish
the cause ; e.g. infemng sinfulness from temporal calamity. But
when both the pretended cause and effect are granted, i.e. granted
to eodst, then the Sophist will infer something from their pretended
conneodon; i.e. he will assume as a Premiss, that *' of these two
admitted facts, the one is the cause of the other:" as Whitfield
attributed his being overtaken by a hail-storm to his having not
preached at the last town ; or as the opponents of the Reformation
assumed that it was the cause of the troubles which took place at
that period, and thence inferred that it was an evil,
giprnputfor Many are the cases in which a Sign (see Bhet. Part I.) from
^*^ which one might fairly infer a certain phenomenon, is mistaken for

the Cause of it : (as if one should suppose the falling of the mer-
cury to be a cause of rain ; of which it certainly is an indication)
whereas the fact will often be the very reverse. U.G. A great deal
of money in a country is a pretty sure proof of its wealth ; and
thence has been often regarded as the cause of it ; whereas in truth
it is an effect. The same, with a numerous and increasing popula-

Online LibraryRichard WhatelyElements of logic → online text (page 18 of 34)