FALLACIES
Sec. 1. A Fallacy is any failure to fulfil the conditions of proof. If we
neglect or mistake the conditions of proof unintentionally, whether in
our private meditations or in addressing others, it is a Paralogism: but
if we endeavour to pass off upon others evidence or argument which we
know or suspect to be unsound, it is a Sophism.
Fallacies, whether paralogisms or sophisms, may be divided into two
classes: (a) the Formal, or those that can be shown to conflict with one
or more of the truths of Logic, whether Deductive or Inductive; as if we
attempt to prove an universal affirmative in the Third Figure; or to
argue that, as the average expectation of life for males at the age of
20 is 19-1/2 years, therefore Alcibiades, being 20 years of age, will
die when he is 39-1/2; (b) the Material, or those that cannot be clearly
exhibited as transgressions of any logical principle, but are due to
superficial inquiry or confused reasoning; as in adopting premises on
insufficient authority, or without examining the facts; or in mistaking
the point to be proved.
Sec. 2. Formal Fallacies of Deduction and Induction are, all of them,
breaches of the rule 'not to go beyond the evidence.' As a detailed
account of them would be little else than a repetition of the foregoing
chapters, it may suffice to recall some of the places at which it is
easiest to go astray.
(1) It is not uncommon to mistake the Contrary for the Contradictory,
as--A is not taller than B, .'. he is shorter.
(2) To convert _A._ or _O._ simply, as--
All Money is Wealth .'. All Wealth is Money;
or--Some Wealth is not Money .'. Some Money is not Wealth.
In both these cases, Wealth, though undistributed in the convertend, is
distributed in the converse.
(3) To attempt to syllogise with two premises containing four terms, as
The Papuans are savages;
The Javanese are neighbours of the Papuans:
.'. The Javanese are savages.
Such an argument is excluded by the definition of a Syllogism, and
presents no formal evidence whatever. We should naturally assume that
any man who advanced it merely meant to raise some probability that
'neighbourhood is a sign of community of ideas and customs.' But, if so,
he should have been more explicit. There would, of course, be the same
failure of connection, if a fourth term were introduced into the
conclusion, instead of into the premises.
(4) To distribute in the conclusion a term that was undistributed in the
premises (an error essentially the same as (2) above), i.e., Illicit
process of the major or minor term, as--
Every rational agent is accountable;
Brutes are not rational agents:
.'. Brutes are not accountable.
In this example (from Whately), an illegitimate mood of Fig. I., the
major term, 'accountable,' has suffered the illicit process; since, in
the premise, it is predicate of an affirmative proposition and,
therefore, undistributed; but, in the conclusion, it is predicate of a
negative proposition and, therefore, distributed. The fact that nearly
everybody would accept the conclusion as true, might lead one to
overlook the formal inconclusiveness of the proof.
Again,
All men are two-handed;
All two-handed animals are cooking animals:
.'. All cooking animals are men.
Here we have Bramantip concluding in A.; and there is, formally, an
illicit process of the minor; though the conclusion is true; and the
evidence, such as it is, is materially adequate. ('Two-handed,' being a
peculiar differentia, is nugatory as a middle term, and may be cut out
of both premises; whilst 'cooking' is a proprium peculiar to the species
Man; so that these terms might be related in U., _All men are all
cookers_; whence, by conversion, _All cookers are men_.)
(5) To omit to distribute the middle term in one or the other premise,
as--
All verbal propositions are self-evident;
All axioms are self-evident:
.'. All axioms are verbal propositions.
This is an illegitimate mood in Fig. II.; in which, to give any
conclusion, one premise must be negative. It may serve as a formal
illustration of Undistributed Middle; though, as both premises are
verbal propositions, it is (materially) not syllogistic at all, but an
error of classification; a confounding of co-ordinate species by assuming
their identity because they have the generic attribute in common.
(6) To simply convert an hypothetical proposition, as--
If trade is free, it prospers;
.'. If trade prospers, it is free.
This is similar to the simple conversion of the categorical A.; since it
takes for granted that the antecedent is co-extensive with the
consequent, or (in other words) that the freedom of trade is the sole
condition of, or (at least) inseparable from, its prosperity.
The same assumption is made if, in an hypothetical syllogism, we try to
ground an inference on the affirmation of the consequent or denial of
the antecedent, as--
If trade is free it prospers:
It does prosper;
.'. It is free.
It is not free;
.'. It does not prosper.
Neither of these arguments is formally good; nor, of course, is either
of them materially valid, if it be possible for trade to prosper in
spite of protective tariffs.
An important example of this fallacy is the prevalent notion, that if
the conclusion of an argument is true the premises must be trustworthy;
or, that if the premises are false the conclusion must be erroneous.
For, plainly, that--
If the premises are true, the conclusion is true, is a hypothetical
proposition; and we argue justly--
The premises are true;
.'. The conclusion is true;
or, The conclusion is false;
.'. The premises are false (or one of them is).
This is valid for every argument that is formally correct; but that we
cannot trust the premises on the strength of the conclusion, nor reject
the conclusion because the premises are absurd, the following example
will show:
All who square the circle are great mathematicians;
Newton squared the circle:
.'. Newton was a great mathematician.
The conclusion is true; but the premises are intolerable.
How the taking of Contraries for Contradictories may vitiate Disjunctive
Syllogisms and Dilemmas has been sufficiently explained in the twelfth
chapter.
Sec. 3. Formal Fallacies of Induction consist in supposing or inferring
Causation without attempting to prove it, or in pretending to prove it
without satisfying the Canons of observation and experiment: as--
(1) To assign the Cause of anything that is not a concrete event: as,
e.g., why two circles can touch only in one point. We should give the
'reason'; for this expression includes, besides evidence of causation,
the principles of formal deduction, logical and mathematical.
(2) To argue, as if on inductive grounds, concerning the cause of the
Universe as a whole. This may be called the fallacy of transcendent
inference: since the Canons are only applicable to instances of events
that can be compared; they cannot deal with that which is in its nature
unique.
(3) To mistake co-existent phenomena for cause and effect: as when a
man, wearing an amulet and escaping shipwreck, regards the amulet as the
cause of his escape. To prove his point, he must either get again into
exactly the same circumstances without his amulet, and be
drowned--according to the method of Difference; or, shirking the only
satisfactory test, and putting up with mere Agreement, he must show, (a)
that all who are shipwrecked and escape wear amulets, and (b) that their
cases agree in nothing else; and (c), by the Joint Method, that all who
are shipwrecked without amulets are drowned. And even if his evidence,
according to Agreement, seemed satisfactory at all these points, it
would still be fallacious to trust to it as proof of direct causation;
since we have seen that unaided observation is never sufficient for
this: it is only by experiment in prepared circumstances that we can
confidently trace sequence and the transfer of energy.
There is the reverse error of mistaking causal connection for
independent co-existence: as if any one regards it as merely a curious
coincidence that great rivers generally flow past great towns. In this
case, however, the evidence of connection does not depend merely upon
direct Induction.
(4) _Post hoc, ergo propter hoc_: to accept the mere sequence of
phenomena, even though often repeated, as proving that the phenomena are
cause and effect, or connected by causation. This is a very natural
error: for although, the antecedents of a phenomenon being numerous,
most of them cannot be its cause, yet it is among them that the cause
must be sought. Indeed, if there is neither time nor opportunity for
analysis, it may seem better to accept any antecedent as a cause (or, at
least, as a sign) of an important event than to go without any guide.
And, accordingly, the vast and complicated learning of omens, augury,
horoscopy and prophetic dreams, relies upon this maxim; for whatever the
origin of such superstitions, a single coincidence in their favour
triumphantly confirms them. It is the besetting delusion of everybody
who has wishes or prejudices; that is, of all of us at some time or
other; for then we are ready to believe without evidence. The fallacy
consists in judging off-hand, without any attempt, either by logic or by
common sense, to eliminate the irrelevant antecedents; which may include
all the most striking and specious.
(5) To regard the Co-Effects (whether simultaneous or successive) of a
common cause as standing in the direct relation of cause and effect.
Probably no one supposes that the falling of the mercury in his
thermometer causes the neighbouring lake to freeze. True, it is the
antecedent, and (within a narrow range of experience) may be the
invariable antecedent of the formation of ice; but, besides that the two
events are so unequal, every one is aware that there is another
antecedent, the fall of temperature, which causes both. To justify
inductively our belief in causation, the instances compared must agree,
or differ, in one circumstance only (besides the effect). The flowing
tide is an antecedent of the ebbing tide; it is invariably so, and is
equal to it; but it is not the cause of it: other circumstances are
present; and the moon is the chief condition of both flow and ebb. In
several instances, States that have grown outrageously luxurious have
declined in power: that luxury caused their downfall may seem obvious,
and capable of furnishing a moral lesson to the young. Hence other
important circumstances are overlooked, such as the institution of
slavery, the corruption and rapacity of officials and tax-gatherers, an
army too powerful for discipline; any or all of which may be present,
and sufficient to explain both the luxury and the ruin.
(6) To mistake one condition of a phenomenon for the whole cause. To
speak of an indispensable condition of any phenomenon as the cause of
it, may be a mere conventional abbreviation; and in this way such a mode
of expression is common not only in popular but also in scientific
discussion. Thus we say that a temperature of 33 deg. F. is a cause of the
melting of ice; although that ice melts at 33 deg. F., must further depend
upon something in the nature of water; for every solid has its own
melting-point. As long, then, as we remember that 'cause,' used in this
sense, is only a convenient abbreviation, no harm is done; but, if we
forget it, fallacy may result: as when a man says that the cause of a
financial crisis was the raising of the rate of discount, neglecting the
other conditions of the market; whereas, in some circumstances, a rise
of the Bank-rate may increase public confidence and prevent a crisis.
We have seen that the direct use of the Canons of Agreement and
Difference may only enable us to say that a certain antecedent is a
cause or an indispensable condition of the phenomenon under
investigation. If, therefore, it is important to find the whole cause,
we must either experiment directly upon the other conditions, or resort
to the Method of Residues and deductive reasoning; nor must we be
content, without showing (where such precision is possible) that the
alleged cause and the given phenomenon are equal.
(7) To mistake a single consequence of a given cause for the whole
effect, is a corresponding error; and none so common. Nearly all the
mistakes of private conduct and of legislation are due to it: To cure
temporary lassitude by a stimulant, and so derange the liver; to
establish a new industry by protective duties, and thereby impoverish
the rest of the country; to gag the press, and so drive the discontented
into conspiracy; to build an alms-house, and thereby attract paupers
into the parish, raise the rates, and discourage industry.
(8) To demand greater exactness in the estimate of causes or effects
than a given subject admits of. In the more complex sciences, Biology,
Psychology, Sociology, it is often impossible to be confident that all
the conditions of a given phenomenon have been assigned, or that all its
consequences have been traced. The causes of the origin of species and
of the great French Revolution have been carefully investigated, and
still we may doubt whether they have all been discovered, or whether
their comparative importance has been rightly determined; but it would
be very unreasonable to treat those things as miraculous and
unintelligible. We read in the _Ethics_, that a properly cultivated mind
knows what degree of precision is to be expected in each science. The
greatest possible precision is always to be sought; but what is possible
depends partly on the nature of the study and partly upon the state of
scientific preparation.
(9) To treat an agent or condition remote in time as an unconditional
cause: for every moment of time gives an opportunity for new
combinations of forces and, therefore, for modifications of the effect.
Thus, although we often say that Napoleon's Russian expedition was the
cause of his downfall, yet the effect was subject to numerous further
conditions. Had the natives not burnt Moscow, had the winter been
exceptionally mild, had the Prussians and Austrians not risen against
him, the event might have been very different. It is rash to trace the
liberties of modern Europe to the battle of Marathon. Indeed, our powers
of perception are so unequal to the subtlety of nature, that even in
experimental science there is time for molecular changes to occur
between what we treat as a cause and the effect as we perceive it; and,
in such cases, the strictly unconditional cause has not been discovered.
(10) To neglect the negative conditions to which a cause is subject.
When we say that water boils at 212 deg. F., we mean "provided the pressure
be the same as that of the atmosphere at about the sea-level"; for under
a greater pressure water will not boil at that temperature, whilst under
less pressure it boils at a lower temperature. In the usual statement of
a law of causation, 'disturbing,' 'frustrating,' 'counteracting'
circumstances (that is, negative conditions) are supposed to be absent;
so that the strict statement of such a law, whether for a remote cause,
or for an immediate cause (when only positive conditions are included),
is that the agent or assemblage of conditions, _tends_ to produce such
an effect, other conditions being favourable, or in the absence of
contrary forces.
(11) It is needless to repeat what has already been said of other
fallacies that beset inductive proof; such as the neglect of a possible
plurality of causes where the effect has been vaguely conceived; the
extension of empirical laws beyond adjacent cases; the chief errors to
which the estimate of analogies and probabilities, or the application of
the principles of classification are liable; and the reliance upon
direct Induction where the aid of Deduction may be obtained, or upon
observation where experiment may be employed. As to formal fallacies
that may be avoided by adhering to the rules of logical method, this may
suffice.
Sec. 4. There remain many ways in which arguments fall short of a tolerable
standard of proof, though they cannot be exhibited as definite breaches
of logical principles. Logicians, therefore, might be excused from
discussing them; but out of the abundance of their pity for human
infirmity they usually describe and label the chief classes of these
'extra-logical fallacies,' and exhibit a few examples.
We may adopt Whately's remark, that a fallacy lies either (1) in the
premises, or (2) in the conclusion, or (3) in the attempt to connect a
conclusion with the premises.
(1) Now the premises of a sound argument must either be valid
deductions, or valid inductions, or particular observations, or axioms.
In an unsound argument, then, whose premises are supported by either
deduction or induction, the evidence may be reduced to logical rules;
and its failure is therefore a 'logical fallacy' such as we have already
discussed. It follows that an extra-logical fallacy of the premises must
lie in what cannot be reduced to rules of evidence, that is, in bad
observations (Sec. 5), or sham axioms (Sec. 6).
(2) As to the conclusion, this can only be fallacious if some other
conclusion has been substituted for that which was to have been proved
(Sec. 7).
(3) Fallacies in the connection between premises and conclusion, if all
the propositions are distinctly and explicitly stated, become manifest
upon applying the rules of Logic. Fallacies, therefore, which are not
thus manifest, and so are extra-logical, must depend upon some sort of
slurring, confusion, or ambiguity of thought or speech (Sec. 8).
Sec. 5. Amongst Fallacies of Observation, Mill distinguishes (1) those of
Non-observation, where either instances of the presence or absence of
the phenomenon under investigation, or else some of the circumstances
constituting it or attending upon it, though important to the induction,
are overlooked. These errors are implied in the Formal Fallacies of
Induction already treated of in Sec. 3 (paragraphs (3) to (7)).
Mill's class (2) comprises fallacies of Malobservation. Malobservation
may be due to obtuseness or slowness of perception; and it is one
advantage of the physical sciences as means of education, that the
training involved in studying them tends to cure these defects--at
least, within their own range.
But the occasion of error upon which Mill most insists, is our proneness
to substitute a hasty inference for a just representation of the fact
before us; as when a yachtsman, eager for marvels, sees a line of
porpoises and takes them for the sea-serpent. Every one knows what it is
to mistake a stranger for a friend, a leaf for a sparrow, one word for
another. The wonder is that we are not oftener wrong; considering how
small a part present sensation has in perception, and how much of every
object observed is supplied by a sort of automatic judgment. You see
something brown, which your perceptive mechanism classes with the
appearance of a cow at such a distance; and instantly all the other
properties of a cow are supplied from the resources of former
experience: but on getting nearer, it turns out to be a log of wood. It
is some protection against such errors to know that we are subject to
them; and the Logician fulfils his duty in warning us accordingly. But
the matter belongs essentially to Psychology; and whoever wishes to
pursue it will find a thorough explanation in Prof. Sully's volume on
_Illusions_.
Another error is the accumulation of useless, irrelevant observations,
from which no proof of the point at issue can be derived. It has been
said that an important part of an inductive inquirer's equipment
consists in knowing what to observe. The study of any science educates
this faculty by showing us what observations have been effective in
similar cases; but something depends upon genius. Observation is
generally guided by hypotheses: he makes the right observations who can
frame the right hypotheses; whilst another overlooks things, or sees
them all awry, because he is confused and perverted by wishes,
prejudices or other false preconceptions; and still another gropes about
blindly, noting this and docketing that to no purpose, because he has no
hypothesis, or one so vague and ill-conceived that it sheds no light
upon his path.
Sec. 6. The second kind of extra-logical Fallacy lying in the premises,
consists in offering as evidence some assertion entirely baseless or
nugatory, but expressed in such a way as to seem like a general truth
capable of subsuming the proposition in dispute: it is generally known
as _petitio principii_, or begging the question. The question may be
begged in three ways:
(1) There are what Mill calls Fallacies _a priori_, mere assertions,
pretending to be self-evident, and often sincerely accepted as such by
the author and some infatuated disciples, but in which the cool
spectator sees either no sense at all, or palpable falsity. These sham
axioms are numerous; and probably every one is familiar with the
following examples: That circular motion is the most perfect; That every
body strives toward its natural place; That like cures like; That every
bane has its antidote; That what is true of our conceptions is true of
Nature; That pleasure is nothing but relief from pain; That the good,
the beautiful and the true are the same thing; That, in trade, whatever
is somewhere gained is somewhere lost; That only in agriculture does
nature assist man; That a man may do what he will with his own; That
some men are naturally born to rule and others to obey. Some of these
doctrines are specious enough; whilst, as to others, how they could ever
have been entertained arouses a wonder that can only be allayed by a
lengthy historical and psychological disquisition.
(2) Verbal propositions offered as proof of some matter of fact. These
have, indeed, one attribute of axioms; they are self-evident to any one
who knows the language; but as they only dissect the meaning of words,
nothing but the meaning of words can be inferred from them. If anything
further is arrived at, it must be by the help of real propositions. How
common is such an argument as this: 'Lying is wrong, because it is
vicious'--the implied major premise being that 'what is vicious is
wrong.' All three propositions are verbal, and we merely learn from them
that lying is _called_ vicious and wrong; and to make that knowledge
deterrent, it must be supplemented by a further premise, that 'whatever
is called wrong ought to be avoided.' This is a real proposition; but it
is much more difficult to prove it than 'that lying ought to be
avoided.' Still, such arguments, though bad Logic, often have a
rhetorical force: to call lying not only wrong but vicious, may be
dissuasive by accumulating associations of shame and ignominy.
Definitions, being the most important of verbal propositions (since they
imply the possibility of as many other verbal propositions as there are
defining attributes and combinations of them), need to be watched with
especial care. If two disputants define the same word in different ways,
with each of the different attributes included in their several
definitions they may bring in a fresh set of real propositions as to the
agency or normal connection of that attribute. Hence their conclusions
about the things denoted by the word defined, diverge in all directions
and to any extent. And it is generally felt that a man who is allowed to
define his terms as he pleases, may prove anything to those who, through
ignorance or inadvertence, grant that the things that those terms stand
for have the attributes that figure in his definitions.
(3) _Circulus in demonstrando_, the pretence of giving a reason for an
assertion, whilst in fact only repeating the assertion itself--generally
in other words. In such cases the original proposition is, perhaps,
really regarded as self-evident, but by force of habit a man says
'because'; and then, after vainly fumbling in his empty pocket for the
coin of reason, the habit of symbolic thinking in words only, without
reference to the facts, comes to his rescue, and he ends with a
paraphrase of the same assertion. Thus a man may try to prove the
necessity of Causation: 'Every event must have a cause; because an event
is a change of phenomena, and this implies a transformation of something
pre-existing; which can only have been possible, if there were forces in
operation capable of transforming it.' Or, again: 'We ought not to go to
war, because it is wrong to shed blood.' But, plainly, if war did not
imply bloodshed, the unlawfulness of this could be nothing against war.
The more serious any matter is, the more important it becomes either to
reason thoroughly about it, or to content ourselves with wholesome
assertions. How many 'arguments' are superfluous!
Sec. 7. The Fallacy of surreptitious conclusion (_ignoratio elenchi_), the
mistaking or obscuring of the proposition really at issue, whilst
proving something else instead. This may be done by substituting a
particular proposition for an universal, or an universal for a
particular. Thus, he who attacks the practice of giving in charity must
not be content to show that it has, in this or that case, degraded the
recipient; who may have been exceptionally weak. Or, again, to dissuade
another from giving alms in a particular case, it is not enough to show
that the general tendency of almsgiving is injurious; for, by taking
pains in a particular case, the general tendency may often be
counteracted.
Sometimes an argument establishing a wholly irrelevant conclusion is
substituted for an _argumentum ad rem_. Macaulay complains of those
apologists for Charles I. who try to defend him as a king, by urging
that he was a good judge of paintings and indulgent to his wife.
To this class of Fallacies belongs the _argumentum ad hominem_, which
consists in showing not that a certain proposition is true, but that
Critias ought to accept it in consistency with his other opinions. Thus:
'In every parish the cost of education ought to be paid out of the
rates: you, at least, have said that there can be no sound economy,
unless local expenses are defrayed from local funds.' But whether this
is a fallacy depends, as Whately observes, upon whether it is urged as
actually proving the point at issue, or merely as convicting the
opponent of inconsistency. In the latter case, the argument is quite
fair: whatever such a conclusion may be worth.
Similarly with the _argumentum ad populum_: 'this measure is favourable
to such or such a class; let them vote for it.' An appeal to private
greed, however base, is not fallacious, as long as the interest of the
class is not _fraudulently_ substituted for the good of the nation. And
much the same may be said for the _argumentum ad verecundiam_. When a
question of morals is debated as a question of honour among thieves,
there is no fallacy, if the moral issue is frankly repudiated. The
argument from authority is often brought under this head: 'such is the
opinion of Aristotle.' Although this does not establish the truth of any
proposition, it may be fairly urged as a reason for not hastily adopting
a contrary conclusion: that is, if the subject under discussion be one
as to which Aristotle (or whoever the authority may be) had materials
for forming a judgment.
A negative use of this fallacy is very common. Some general doctrine,
such as Positivism, Transcendentalism, Utilitarianism, or Darwinism, is
held in common by a group of men; who, however, all judge independently,
and therefore are likely to differ in details. An opponent exhibits
their differences of opinion, and thereupon pretends to have refuted the
theory they agree in supporting. This is an _argumentum ad scholam_, and
pushes too far the demand for consistency. In fact it recoils upon the
sophist; for there is no sense in quoting men against one another,
unless both (or all) are acknowledged to speak with the authority of
learning and judgment, and therefore the general doctrine which they
hold in common is the more confirmed.
This is an example of the paralogism of 'proving too much'; when a
disputant is so eager to refute an opponent as to lay down, or imply,
principles from which an easy inference destroys his own position. To
appeal to a principle of greater sweep than the occasion requires may
easily open the way to this pitfall: as if a man should urge that 'all
men are liars,' as the premise of an argument designed to show that
another's assertion is less credible than his own.
A common form of _ignoratio elenchi_ is that which Whately called the
'fallacy of objections': namely, to lay stress upon all the
considerations against any doctrine or proposal, without any attempt to
weigh them against the considerations in its favour; amongst which
should be reckoned all the considerations that tell against the
alternative doctrines or proposals. Incontestable demonstration can
rarely be expected even in science, outside of the Mathematics; and in
practical affairs, as Butler says, 'probability is the very guide of
life'; so that every conclusion depends upon the balance of evidence,
and to allow weight to only a part of it is an evasion of the right
issue.
Sec. 8. Fallacies in the connection of premises and conclusion, that cannot
be detected by reducing the arguments to syllogistic form, must depend
upon some juggling with language to disguise their incoherence. They may
be generally described as Fallacies of Ambiguity, whether they turn upon
the use of the same word in different senses, or upon ellipsis. Thus it
may be argued that all works written in a classical language are
classical, and that, therefore, the history of Philosophy by Diogenes
Laertius, being written in Greek, is a classic. Such ambiguities are
sometimes serious enough; sometimes are little better than jokes. For
jokes, as Whately observes, are often fallacies; and considered as a
propaedeutic to the art of sophistry, punning deserves the ignominy that
has overtaken it.
Fallacies of ellipsis usually go by learned names, as; (1) _a dicto
secundum quid ad dictum simpliciter_. It has been argued that since,
according to Ricardo, the value of goods depends solely upon the
quantity of labour necessary to produce them, the labourers who are
employed upon (say) cotton cloth ought to receive as wages the whole
price derived from its sale, leaving nothing for interest upon capital.
Ricardo, however, explained that by 'the quantity of labour necessary to
produce goods' he meant not only what is immediately applied to them,
but also the labour bestowed upon the implements and buildings with
which the immediate labour is assisted. Now these buildings and
implements are capital, the labour which produced them was paid for, and
it was far enough from Ricardo's mind to suppose that the capital which
assists present labour upon (say) cotton cloth has no claim to
remuneration out of the price of it. In this argument, then, the word
labour in the premise is used _secundum quid_, that is, with the
suppressed qualification of including past as well as present labour;
but in the conclusion labour is used _simpliciter_ to mean present
labour only.
(2) _A dicto secundum quid ad dictum secundum alterum quid_. It may be
urged that, since the tax on tea is uniform, therefore all consumers
contribute equally to the revenue for their enjoyment of it. But written
out fairly this argument runs thus: Since tea is taxed uniformly _4d.
per lb._, all consumers pay equally for their enjoyment of it _whatever
quantity they use_. These qualifications introduced, nobody can be
deceived.
(3) _A dicto simpliciter ad dictum secundum quid_, also called _fallacia
accidentis_. Thus: To take interest upon a loan is perfectly just,
therefore, I do right to exact it from my own father in distress. The
popular answer to this sort of blunder is that 'circumstances alter
cases.' We commit this error in supposing that what is true of the
average is likely to be true of each case; as if one should say: 'The
offices are ready to insure my house [with thousands of others] against
fire at a rate per annum which will leave them heavy losers unless it
lasts a hundred years; so, as we are told not to take long views of
life, I shall not insure.'
The Fallacy of Division and Composition consists in suggesting, or
assuming, that what is true of things severally denoted by a term is
true of them taken together. That every man is mortal is generally
admitted, but we cannot infer that, therefore, the human race will
become extinct. That the remote prospects of the race are tragic may be
plausibly argued, but not from that premise.
Changing the Premises is a fallacy usually placed in this division;
although, instead of disguising different meanings under similar words,
it generally consists in using words or phrases ostensibly differing, as
if they were equivalent: those addressed being expected to renounce
their right to reduce the argument to strict forms of proof, as needless
pedantry in dealing with an author so palpably straightforward. If an
orator says--'Napoleon conquered Europe; in other words, he murdered
five millions of his fellow creatures'--and is allowed to go on, he may
infer from the latter of these propositions many things which the former
of them would hardly have covered. This is a sort of hyperbole, and
there is a corresponding meiosis, as: 'Mill _admits_ that the Syllogism
is useful'; when, in fact, that is Mill's _contention_. It may be
supposed that, if a man be fool enough to be imposed upon by such
transparent colours, it serves him right; but this harsh judgment will
not be urged by any one who knows and considers the weaker brethren.
Sec. 9. The above classification of Fallacies is a rearrangement of the
plans adopted by Whately and Mill. But Fallacies resemble other
spontaneous natural growths in not submitting to precise and definite
classification. The same blunders, looked at from different points of
view, may seem to belong to different groups. Thus, the example given
above to illustrate _fallacia accidentis_, 'that, since it is just to
take interest, it is right to exact it from one's own father,' may also
be regarded as _petitio principii_, if we consider the unconditional
statement of the premise--'to take interest upon a loan is perfectly
just'; for, surely, this is only conditionally true. Or, again, the
first example given of simple ambiguity--'that whatever is written in a
classical language is classical, etc.,' may, if we attend merely to
the major premise, be treated as a bad generalisation, an undue
extension of an inference, founded upon a simple enumeration of the
first few Greek and Latin works that one happened to remember.
It must also be acknowledged that genuine wild fallacies, roaming the
jungle of controversy, are not so easily detected or evaded as specimens
seem to be when exhibited in a Logician's collection; where one surveys
them without fear, like a child at a menagerie. To assume the succinct
mode of statement that is most convenient for refutation, is not the
natural habit of these things. But to give reality to his account of
fallacies an author needs a large space, that he may quote no
inconsiderable part of literature ancient and modern.
As to the means of avoiding fallacies, a general increase of sincerity
and candour amongst mankind may be freely recommended. With more honesty
there would be fewer bad arguments; but there is such a thing as
well-meaning incapacity that gets unaffectedly fogged in converting A.,
and regards the refractoriness of O., as more than flesh and blood can
endure. Mere indulgence in figurative language, again, is a besetting
snare. "One of the fathers, in great severity called poesy _vinum
daemonum_," says Bacon: himself too fanciful for a philosopher. Surely,
to use a simile for the discovery of truth is like studying beauty in
the bowl of a spoon.
The study of the natural sciences trains and confirms the mind in a
habit of good reasoning, which is the surest preservative against
paralogism, as long as the terms in use are, like those of science, well
defined; and where they are ill defined, so that it is necessary to
guard against ambiguity, a thorough training in politics or metaphysics
may be useful. Logic seems to me to serve, in some measure, both these
purposes. The conduct of business, or experience, a sufficient time
being granted, is indeed the best teacher, but also the most austere and
expensive. In the seventeenth century some of the greatest philosophers
wrote _de intellectus emendatione_; and if their successors have given
over this very practical inquiry, the cause of its abandonment is not
success and satiety but despair. Perhaps the right mind is not to be
made by instruction, but can only be bred: a slow, haphazard process;
and meanwhile the rogue of a sophist may count on a steady supply of
dupes to amuse the tedium of many an age.
FINIS.
QUESTIONS
_The following questions are chiefly taken from public examination
papers: Civil Service_ [S], _Oxford_ [O], _Cambridge_ [C], _London_ [L].
I. TERMS, ETC.
1. What is a Term? Explain and illustrate the chief divisions of Terms.
What is meant by the Connotation of a Term? Illustrate. [S]
2. "The connotation and denotation of terms vary inversely." Examine
this assertion, explaining carefully the limits within which it is true,
if at all. [S]
3. Exemplify the false reasoning arising from the confusion of Contrary
and Contradictory Terms. [S]
4. Discuss the claims of the doctrine of Terms to be included in a
Logical System. Distinguish between a General and an Abstract Term. [S]
5. Explain and illustrate what is meant by the Denotation and
Connotation of a Term. What terms have both, and what have one only? [S]
6. Distinguish between Abstract and Concrete Names. To which of these
classes belong (a) adjectives, (b) names of states of consciousness? Are
any abstract names connotative? [S]
7. Distinguish between (a) Proper and Singular Terms, (b) Negative and
Privative, (c) Absolute and Relative. Illustrate.
8. What connection is there between the Connotation and the Relativity
of Names?
9. Examine the logical relations between the following pairs of terms:
(a) happy and happiness; (b) happy and unhappy; (c) 'the juryman' and
'the jury'; (d) parent and offspring.
Explain the technical words used in your answer. [C]
10. Distinguish between _name_; _part of speech_; _term_: and illustrate
by reference to the following--use, useful, usefully. [C]
11. Describe the nature of _Collective_ terms; examine in particular any
difficulties in distinguishing between these and general or abstract
terms. [C]
12. Distinguish between _positive_, _negative_, and _privative_ names.
Of what kind are the following, and why--parallel, alien, idle, unhappy?
What ambiguity is there in the use of such a term as "not-white"? [C]
II. PROPOSITIONS AND IMMEDIATE INFERENCE.
13. What is meant by (1) the Conversion, and (2) the Contra-position of
a proposition? Apply these processes, as far as admissible, to the
following:--
(a) All invertebrates have cold blood.
(b) Some cold-blooded animals are not invertebrates.
(c) No wingless birds are songsters.
(d) Some winged birds are not songsters.
What can you infer from (a) and (b) jointly, and what from (c) and (d)
jointly? [S]
14. "The author actually supposes that, because Professor Fawcett denies
that all wealth is money, he denies that all money is wealth." Analyse
the differences of opinion implied in the above passage. [S]
15. Take any universal affirmative proposition; convert it by obversion
(contraposition); attach the negative particle to the predicate, and
again convert. Interpret the result exactly, and say whether it is or is
not equivalent to the original proposition. [S]
16. What information about the term "solid body" can we derive from the
proposition, "No bodies which are not solids are crystals"? [S]
17. Discuss the proposal to treat all propositions as affirmative.
18. Convert the proposition "A is probably B." What information does the
proposition give us concerning B? [S]
19. Show in how many ways you can deny the following assertions: All
cathedral towns are all cities; Canterbury is the Metropolitan see. [S]
20. Explain the nature of a _hypothetical_ (or conditional) proposition.
What do you consider the radical difference between it and a
categorical? [S]
21. What is the function of the _copula_? In what different manners has
it been treated? [S]
22. Convert "A killed C unjustly"; "All Knowledge is probably useful";
"The exception proves the rule"; "Birds of a feather flock together."
[S]
23. What is modality? How are modals treated by (a) formal logic and (b)
by the theory of induction? [S]
24. What is the subject of an impersonal proposition? Give reasons for
your answer. [S]
25. Is the categorical proposition sufficiently described as referring a
thing or things to a class? [S]
26. Enumerate the cases in which the truth or falsity of one proposition
may be formally inferred from the truth or falsity of another.
Illustrate these cases, and give to each its technical name. [S]
27. Illustrate the relation of Immediate Inferences to the Laws of
Thought.
28. Explain what is meant by (a) Symbolic Logic; (b) the Logic of
Relatives. Describe some method of representing propositions by means
of diagrams; and indicate how far any particular theory of the import of
propositions is involved in such representation. [S]
29. Explain the exact nature of the relation between two _Contradictory_
propositions; and define Conversion by Contraposition, determining what
kind of propositions admit of such conversion.
Give the contradictory and the contrapositive of each of the following
propositions:--
(a) All equilateral triangles are equiangular;
(b) No vertebrate animal has jaws opening sideways;
(c) Wherever A and B are both present, either C or D is also
present. [S]
30. Define Obversion and Inversion, and apply these processes also to
the above three propositions.
31. Propositions can be understood either in extension or in intension.
Explain this, and discuss the relative value of the two interpretations.
[S]
32. Distinguish between real and verbal propositions; and explain the
importance of the distinction.
33. Illustrate the process called 'change of Relation.'
III. SYLLOGISM AND MEDIATE INFERENCE.
34. What is a Syllogism? Find, without reference to the mnemonic verses,
in what different ways it is possible to prove syllogistically the
conclusion _No S is P_; and show the equivalence between these different
ways. [S]
35. From what points of view can the syllogism be regarded
(1) as being, (2) as not being, a _petitio principii_? [S]
36. What are the figures of syllogism? For what kind of arguments are
they severally adapted? [S]
37. What is meant by Mood and Figure? How can the validity of a Mood be
tested? Should there be four Figures or three? [S]
38. Construct syllogisms in Camenes, Datisi and Baroco, and reduce them
to the corresponding moods of the first figure.
39. Explain the meaning of "ostensive" and "indirect" Reduction. Show
that any Mood of the second Figure may be reduced in either way.
40. Show that A cannot be proved except in the First Figure. Express the
following reasoning in as many syllogistic figures as you can: Some
theorists cannot be trusted, for they are unwise. [S]
41. Discuss the possibility of reducing the argument _a fortiori_ to the
syllogistic form. [S]
42. Can a false conclusion be reached through true premises, or a true
conclusion through false premises? Give reasons for your answer. [S]
43. Can we under any circumstances infer a relation between X and Z from
the premises--
Some Y's are X's
Some Y's are Z's? [S]
44. Take an apparent syllogism subject to the fallacy of negative
premises, and inquire whether you can correct the reasoning by
converting one or both of the premises into the affirmative form. [S]
45. Enumerate the faults to which a syllogism is liable, giving
instances of each. [S]
46. State any Enthymeme, and expand it into (1) a Syllogism, (2) an
Epicheirema, (3) a Sorites; and give in each case the technical name of
the Mood or Order that results.
47. State any Disjunctive Syllogism, and change it (1) into a
Hypothetical, (2) into a Categorical; and discuss the loss or gain, in
cogency or significance involved in this process.
48. Can the Syllogism be treated as merely a consequence of the "Laws of
Thought"? If not, why not; and what else does it imply?
49. Prove that with three given propositions (of the forms A., E., I.,
O.) it is never possible to construct more than one valid syllogism. [C]
50. Distinguish between a Constructive and a Destructive Hypothetical
Syllogism; and show how one may be reduced to the other. [C]
IV. INDUCTION, ETC.
51. What constitutes a Valid Induction? Distinguish it from a legitimate
hypothesis. [S]
52. Is it possible to form true universal propositions about facts if we
have not actually observed all the individuals designated by the subject
of the proposition? If so, how? [S]
53. "Perfect induction is demonstrative and syllogistic; imperfect
induction is neither." Explain the difference between perfect and
imperfect induction, and examine the truth of this assertion. [S]
54. Why is it that one should not regard night as the cause, nor even as
a universal condition of day? Explain "cause" and "condition." [S]
55. What do you understand by an experiment? Can you say how many
experiments are required to establish (1) a fact, (2) a law of nature?
56. How would you define _antecedent_, _cause_, _effect_, _consequent_?
[S]
57. England is the richest country in the world, and has a gold
currency. Russia and India, in proportion to population, are poor
countries and have little or no gold currency. How far are such kind of
facts logically sufficient to prove that a gold currency is the cause of
a nation's wealth? [S]
58. A man having been shot through the heart immediately falls dead.
Investigate the logical value of such a fact as proving that all men
shot through the heart will fall dead. [S]
59. Explain the process of induction called the Method of Difference,
and give some new instances of its application. How is it related to the
Method of Concomitant Variations? What is the Major Premise implied in
all these methods? [S]
59A. Examine the position, that the Canons of Experiment are useless,
because the work of preparing the experiments must have been done before
the canons can be applied.
60. Explain the logical cogency of experiments in the search for
physical causes. [S]
61. If the effects of A B C D are fully expressed by a b c d, and those
of B C D by b c d, what inductive inference can be drawn and on what
principle? State the canon according to which it is drawn. [S]
62. Compare the advantage of observation and experiment as means of
gaining data for Reasoning. [S]
63. Compare the cogency of different Inductive Methods, showing the kind
of evidence each requires, and the principle on which it is based. [S]
64. Compare the Canons of Agreement and Difference (1) as to the
difficulty of finding or preparing actual Instances for them, and (2) as
to their conclusiveness.
65. Describe what is meant by residual phenomena, and estimate their
value in inductive science. [S]
66. What is the argument from Analogy? How does it differ from (a)
Induction, (b) metaphorical argument? [S]
67. What are the various senses in which the word Analogy has been used?
Distinguish, giving instances, between good and bad analogies. [S]
68. How do you distinguish between what Mill calls the Geometrical,
Physical, and Historical Methods?
68A. The Comparative Method is appealed to where direct evidence is
wanting. Explain this.
69. What is meant by a doctrine being unverifiable? If a conclusion
reached by deduction does not agree with the facts, where must we look
for error?
70. There are certain cases in which failure of verification is fatal to
a theory, and other cases in which it is of comparatively little
cogency. How would you distinguish between these classes of cases? [S]
71. Taking the "evolution," or any other proposed hypothesis, how should
one proceed (a) to show whether it satisfies the conditions of a
legitimate hypothesis sufficiently to entitle it to investigation, and
(b) to test it with a view to its acceptance or rejection as a truth of
science? [S]
72. What do you mean by saying that "a phenomenon has been
satisfactorily explained"?
73. Explain and illustrate the Historical Method of Sociological
inquiry. [S]
74. What is the relation of the theory of Probability to Logic? [S]
75. Explain and discuss the doctrine that Induction is based upon the
Theory of Probability. [S]
75A. What are the logical grounds of the Law of Error?
76. Explain the nature and use of Classification, the means to, and
tests of, its successful performance. [S]
77. What is Definition and what is its use? Mention various difficulties
that occur in the process, and show how they are to be met. [S]
78. Propose rules for a good Division and a good Definition, and
exemplify the breach of them. [S]
79. Examine the validity of the idea of Real Kinds. [O]
80. What kind of words are indefinable, and why? When do we define by
negation and by example? [S]
81. Distinguish between the province and aims of classification and
(logical) division. Illustrate. [S]
82. What is an _infima species_ or _species specialissima_? Compare the
use of the terms _genus_ and _species_ in Logic with that which is
common in speaking of animals or plants. [S]
83. How far does the formation of Definitions and Classifications
constitute the end of Science? [S]
84. Examine the methodological relations between Definition,
Classification and Nomenclature. [S]
85. Give instances of "Differentia," "Property," "Inseparable Accident";
and examine, with reference to your instances, how far it is possible to
distinguish them. [S]
V. MISCELLANEOUS.
86. "People can reason without the help of Logic." Why is this not a
sufficient objection to the study? In your answer show distinctly why
Logic should be studied. [S]
87. What is the meaning of the assertion that Logic is concerned with
the form, and not with the matter, of thought? [S]
88. "Neither by deductive nor inductive reasoning can we add a tittle to
our implicit knowledge." (Jevons.) Explain and criticise. [S]
89. What is the logical foundation of the indirect method or _reductio
ad absurdum_? Is it applicable to non-mathematical subjects? [S]
90. On what grounds do we believe in the reality of an historical event?
[S]
91. "Facts are familiar theories." Explain and discuss this. [O]
92. Wherein lies the difficulty of proving a negative? [O]
93. Can any limits be assigned to the possible unification of the
sciences? [O]
94. Are the results of inductive inference necessarily certain? [O]
95. The method of deductive science is hypothetical. Explain and
discuss. [O]
96. "The uniformity of Nature can never be more than a working
hypothesis." Explain and criticise.
97. "Without speculation there is no good and original observation."
Why? [O]
98. Can the provinces of induction and deduction be kept separate? [O]
99. How far is the relation of logical dependence identical with that of
causation? [O]
99A. Discuss the position that the forms of Logic are meaningless apart
from their application.
100. State in syllogistic form (mood and figure) the following
arguments:--
(a) As polygamy is in many countries legal, we may infer the
variability of the moral standard.
(b) If gold is wealth, to export it diminishes the national
resources.
(c) If all good people are happy, unhappiness is an
indication of vice.
(d) One may be sure of the benefits of inuring young
children to cold, from the strength exhibited by all men and
women thus treated in infancy.
(e) Where there is no law, there is no injustice.
(f) "Dissimulation is but a faint kind of policy or wisdom;
for it asketh a strong wit and a strong heart to know when to
tell the truth, and to do it; therefore it is the weaker sort
of politicians that are the greatest dissemblers." (Bacon.)
(g) Money being a barren product, it is contrary to nature
to make it reproduce itself. Usury, therefore, is unnatural,
and, being unnatural, is unjustifiable.
(h) The study of mathematics is essential to a complete
course of education, because it induces a habit of close and
regular reasoning. [S]
101. Explain and illustrate the following terms:--Subalternans, _Vera
Causa_, Plurality of Causes, Law of Nature, Empirical Law, _Summum
Genus_, Predicament, _Arbor Porphyriana_, Axiom, Universe of discourse
(_suppositio_), Antinomy, Dilemma, Realism, Dichotomy, etc.
102. Is there any distinction and, if so, what, between a complete
Description and an Explanation? [C]
103. On what principles have fallacies been classified? To what extent
do you think a satisfactory classification of Fallacies possible? [C]
104. Examine how far conceptions of Persistence and of Invariable
Concomitance of Properties are involved in the methodological
application of the conception of Cause.
104A. Inquire whether the two following propositions can be reconciled
with one another: (a) The same conjunction of antecedents is invariably
followed by the same consequent; (b) We never find the same concurrence
of phenomena a second time. [C]
105. Using the term Logic in a wide sense, so as to include Methodology,
inquire how far a Logic of Observation is possible, and show in what it
will consist. [C]
106. What is Proof?
Explain and discuss the following dicta:--(a) _Qui nimium probat, nihil
probat_: (b) A bad proof is worse than no proof; (c) The exception
proves the rule; (d) Negatives cannot be proved. [C]
107. Examine how far the rules of immediate and syllogistic inference
are modified by differences of interpretation of the categorical
proposition in respect of the existence of the subject. [S]
108. "An effect is but the sum of all the partial causes, the
concurrence of which constitutes its existence." "The cause of an event
is its invariable and unconditional antecedent." Explain and compare
these two theories of causation. Does either alone exhaust the
scientific conception of cause? [S]
109. Under what logical conditions are statistical inferences
authorised, and what is the nature of their conclusions? [S]
110. Distinguish between Psychology, Metaphysics, and Logic; and discuss
briefly their mutual relations. [S]
111. All processes of inference in which the ultimate premises are
particular cases are equally induction.
Induction is an inverse deduction.
Explain and contrast these two theories of the relation of induction to
deduction. [S]
112. What are the Fallacies specially incident to Induction?--or to the
application of the theory of Probabilities? [S]
113. What is meant by the _personal error_ (or _personal equation_) in
observation? Discuss its importance in different branches of knowledge.
[S]
114. Define and illustrate:--Paralogism, _ignoratio elenchi_, _fallacia
accidentis_, _argumentum ad verecundiam_, illicit process, undistributed
middle, etc.
115. State the three fundamental laws of thought, explain their meaning,
and consider how far they are independent of each other? [L]
116. Enumerate the "Heads of Predicables" and define their meaning.
Discuss their logical importance. [L]
117. Upon what grounds has it been asserted that the conclusion of a
syllogism is drawn, not from, but according to, the major premise? Are
they valid? [L]
118. "Experiment is always preferable to observation." Why is this?
Explain from the example of any science how observation and experiment
supplement each other. [L]
119. What is a hypothesis? Distinguish between a working hypothesis and
an established hypothesis, so as to bring out the conditions on which
the latter depends. [L]
120. Explain how good scientific nomenclature and terminology are
connected with the purposes of good classification. [L]
_Printed in Great Britain by Hazell, Watson & Viney, Ld., London and
Aylesbury for Simpkin, Marshall, Hamilton, Kent & Co. Ltd._
[Transcriber's Note:
The following corrections were made to the original text:
Page 40: "inedequate" changed to "inadequate"
Page 42: "classily" changed to "classify"
Page 90: "alledging" changed to "alleging"
Page 128: missing comma added: "Camenes, Dimaris"
Page 141: "evalued" changed to "evaluated"
Page 147: "tellens" changed to "tollens": "and the Modus tollens"
Page 170: "impredictable" changed to "unpredictable"
Page 210: missing word 'a' added: "Sesostris conquered a great"
Page 307: "either" changed to "neither"
Page 315: "inductions" changed to "induction"
Page 401: "quality" changed to "quantity"
Page 401: "propoedeutic" changed to "propaedeutic"]