I.
Cows | are four-footed
-------------------+--------------------------
Sheep are not cows | _sheep are not four-footed_
This is the fallacy called in the quaint language of the syllogists
'Illicit Process of the Major Term.'
In _False Analogy_ the resemblance is so slight that the application
is untrustworthy, or a conclusion is drawn in excess of the
resemblance. If from the habit of calling a deep bay or salt-water
loch an 'arm' of the sea from its analogy to a human arm, we conclude
that the sea has elbows and wrists, we commit this fallacy. The earth
is like an orange, but we must not think that it is pulpy inside.
Akin to this is the fallacy of _False Generality_ or _Doubtful
Precedent_. It consists in carelessly or perversely using bad
antecedents when better are available. This applies to such current
prejudices as that all Frenchmen are frivolous, all Germans mystical,
all Jews dishonest, all Carthaginians faithless, all rich people
purseproud, all nobles haughty, and so on. Even if all the
Carthaginians we personally knew had proved faithless, our general
knowledge of mankind should keep us from inferring that a whole
nation should be faithless. The most we should conclude is that _some_
Carthaginians are faithless, but we are free to exercise caution in
future dealings with members of that race. All these generalities
are grounded on this prior argument: 'when a known portion of a class
exhibits certain qualities, we are justified in inferring that the
whole class possess these qualities'--which is only occasionally true.
The fallacy of _Accident_ occurs when the precedent is so defined
as not to exclude exceptions, and the case happens to be one of
the exceptions. 'What gives pain should be abstained from; surgical
operations give pain; they should therefore be abstained from.' The
painful things that should be universally abstained from are those
which give needless or useless pain, not the sort that give less pain
than they remove. Falstaff committed this fallacy when he supposed
that the King would be a boon companion like the Prince. So did the
colonists who introduced rabbits and water-cress into Australia, on
the supposition that they would there have the same function or value
as in Great Britain. In consequence of the Accidental change the
rabbits have developed into a pest, and the water-cress obstructs
navigation.
If the applicate is a property of the subject only when the latter is
taken collectively, it will not yield a true conclusion when the parts
or individuals of the subject are taken separately. All the angles of
a triangle are equal to two right angles, but it does not follow that
one of them--though it resembles the triangle to some extent--is equal
to two right angles. In this instance we should render the meaning
clear by saying 'collectively equal,' when no argument follows and no
mistake is made. This is called the fallacy of _Division_.
The fallacy of _Composition_ is the converse of this. What is true
of several singulars may not be true of all of them taken together.
Because each of the witnesses in a law case is liable to error, it
does not follow that the concurrent testimony of many is not to be
credited. (Jevons.)
_Circular_ or _Tautological_ theorems (_Petitio Principii_ Begging the
Question) are a breach of rule 2, section XVIII. This fallacy often
consists in proposing as a precedent the case, or information drawn
from the case and stated in other words. '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 sentiments.' (Whately.)
It is conducive | that each individual should enjoy
-------------------+------------------------------
It is advantageous | to allow
There may be tautology in a single word--the 'question-begging
epithet.' We undertake to prove something, but get no further than
the use of metaphors implying the point in dispute. For example, some
scientific writers are anxious to promote the belief that animal life
is a combination of natural forces--that there is no individual life
distinct from cosmic life,--but all their proof consists in calling a
man or beast a 'machine,' and calling machines 'creatures.' This might
be mistaken for the Substantialist doctrine on the same subject, but
the two are radically different. Substantialism asserts that man and
nature have _similar_ lives--materialism teaches that they have only
one life in common, and that the coarse, mindless life of the cosmos
as conceived realistically.
Conclusions may be used as precedents before verification, but it is
not lawful to assume a hypothetical precedent on the understanding
that it is to be proved in the course of the argument, and then use
the conclusion so obtained to prove its own precedent. This is also
dialectical tautology, but the circle includes two or more theorems.
When naturalists tell us that in the struggle for life the fittest
only survive, and when asked how we know which are the fittest they
reply that the fittest are known by the fact of their surviving, we
have a tautological argument.
Animals that survive | are the fittest | Fittest animals | survive
---------------------+------------------+-----------------+--------------
A particular animal | _hence it is the | This animal is | _which is the
has survived | fittest of its | the fittest of | reason it has
| species_ | its species. | survived_
Survival under competitive conditions is first assumed, and from it
is deduced the superiority of the existing type of animal; then this
inferential superiority is offered to justify the previously imagined
competitive survival. The two hypotheses waltz round each other
without making any rational advance.
When a book is quoted to prove its own authenticity we have
this fallacy; or when the precedent is as unknown as the
conclusion,--'Paradise was in Armenia, therefore Gihon is an Asiatic
river.'
The academical syllogism as defined--not always as presented--contains
two fallacies, one of which is tautology. 'ALL Europeans are white;
Caius is a European; therefore he is white.' If, as logicians say, the
'all' is absolute and includes Caius even before he is mentioned, then
it is clear that the theorem amounts to saying, 'All Europeans are
white, and one of them is Caius.' 'Both the twins are fair-haired;
Caius is one of the twins; therefore he is fair-haired':--the
pretended conclusion is merely a naming of a part of the precedent.
The first of these theorems may be interpreted so as to give a valid
conclusion. We are informed that an unknown person called Caius is a
European; we are not told, and we do not know, what is the colour of
his skin; but because all the Europeans we have known have been white,
we infer--pending actual knowledge--that Caius is white. Logicians
interpret the syllogism otherwise, for they have a notion that reason
should give infallible certainty.
After the precedent has been divided into subject and applicate,
the former is sometimes used as applicate and so generates a wrong
conclusion. This may be called _Cross Reasoning_ or _Diagonal
Reasoning_--the fallacy termed by logicians 'Undistributed Middle.'
Manx cats | have no tails
---------------------+----------------------
This cat has no tail | _it must be a Manx cat_
De Morgan has this example--'His imbecility of character might have
been inferred from his proneness to favourites; for all weak princes
have this failing.'
All weak princes | are prone
-----------------+------------------------
He was prone | _he must have been weak_
Statements are sometimes put forward as reasoning which contain no
case, either expressed or understood. This will seem hardly
credible seeing that the illustration of a case is the purpose of
argumentation. Not only does it occur, but a certain form of it is
regarded by some logicians as valid reasoning. It is the 'particular'
syllogism of the Third Figure.
_Socrates was poor;
Socrates was wise._
From these premises no conclusion can be extracted, unless it be the
verbal summary--'Socrates was both poor and wise.' But logicians draw
from it the dialectic conclusion--
_Therefore some men have been poor and wise_,
or
_Therefore one man has been poor and wise_.
Both these conclusions are inadmissible. It is because they are
empirically true that we are apt to think their truth depends on the
antecedent information. If we wish to extend the qualities of Socrates
to 'some men' we must make them a case with 'Socrates is poor and
wise' for a precedent, but I fail to see how it is to be done. If we
add to the premises, 'One man was Socrates, therefore one man was poor
and wise,' we have a tautological fallacy.
J. S. Mill notices a fallacy which amounts to an _Inversion_ of the
Parallel: the conclusion is known or believed and the truth of the
antecedents is inferred backwards.
'People continually think and express themselves as if they
believed that the premises cannot be false if the conclusion
is true. The truth, or supposed truth, of the inferences which
follow from a doctrine, often enables it to find acceptance
in spite of gross absurdities in it. How many philosophical
systems which had scarcely any intrinsic recommendation have
been received by thoughtful men because they were supposed to
lend additional support to religion, morality, some favourite
view of politics, or some other cherished persuasion; not
merely because their wishes were thereby enlisted on its side,
but because its leading to what they deemed sound conclusions
appeared to them a strong presumption in favour of its
truth, though the presumption, when viewed in its true light,
amounted only to the absence of that particular evidence
of falsehood which would have resulted from its leading by
correct inference to something already known to be false.'[19]
The conclusion of an argument may sometimes be left unexpressed. If
the antecedents are strong and the conclusion obvious it weakens the
argument to state the conclusion in full, besides reflecting on the
capacity of the reader or hearer to draw the conclusion for himself.
Hence we find at the end of controversial and indignant writings such
expressions as--'Comment is superfluous'--'We leave the reader to draw
his own conclusions,'--or simply a point of exclamation is appended.
Sophistical insinuations are suggested in this manner. A train of
ideas is laid that generates a conclusion which the speaker is afraid
or ashamed to put into words.
The second fault of the syllogism as defined may be called the fallacy
of _No Application_. It consists in arranging propositions so as to
end in a classification, but no applicate is detached and no rational
conclusion is drawn. 'Jones is a Welshman; all Welshmen are Britons;
therefore Jones is a Briton.' If in actual thinking it were ever
desired to establish by argument that Jones is a Briton, it would be
with the object of applying to him some quality connoted by Briton,
but the presence of which in Jones is a matter of doubt. This would be
a conclusion--but not the mere classification.
_Irrelevant Conclusion_--the fallacy called by Aristotelians
_Ignoratio elenchi_--is an attempt to substitute a better argument
for the one proposed, but which proves something which has not been
denied, or stigmatises something that has not been asserted. It
frequently arises from honest ignorance of the question at issue, as
in the objections usually made to the Berkeleyan Substantialism. It
can also be used as a weapon of sophistry, by confusing the matter in
dispute or diverting attention to side issues. It is irrelevant to
the truth of a conclusion to point out that he who now supports it
formerly opposed it, or that his conduct is inconsistent with a belief
in it. Appeals to passion--to reverence for authority--to popular
belief--are instances of this fallacy.
The best protection against Fallacy--next to a thorough knowledge of
the matter--is a clear notion of the properties of a valid argument;
it is useful however to be able to distinguish and name the faulty
theorems one constantly meets in controversial speeches and writings.
[Footnote 17: One fault of observation is noticed by formal
logicians; it is that of assigning an improper cause, _Non
causa pro causâ_ or _Post hoc ergo propter hoc_. It is evident
that defects in every other category have an equal light to be
noticed.]
[Footnote 18: Whately complains of the disinclination shown
by logicians to put their rules into practice. 'Whenever they
have to treat of anything that is beyond the mere elements of
Logic, they totally lay aside all reference to the principles
they have been occupied in establishing and explaining, and
have recourse to a loose, vague, and popular kind of language;
such as would be best suited indeed to an exoterical discourse
but seems strangely incongruous in a professed logical
treatise.... Surely it affords but too much plausibility to
the cavils of those who scoff at Logic altogether, that the
very writers who profess to teach it should never themselves
make any application of, or reference to, its principles,
when, and _when only_, such application and reference are
to be expected.' _Logic_, Book III. Introd. The fact here
admitted proves that even logicians do not find their method
of any practical use. But what is the meaning of the emphatic
'when only'? Why should a logical method be unsuitable for
every sort of subject except those matters of logic that are
beyond the mere elements?]
[Footnote 19: _Logic_, 'Fallacies,' c. 6.]