I.
Louis | is a good king
-----------------------+---------------------------
The governor of France | _therefore the g. of F. is
is Louis | a good king_
The supposed case is a verbal proposition, serving to rename the
subject of precedent. There is no reasoning. If we already know that
Louis is a good king and is also the governor of France (the given
matters of fact), there is no rational imagination involved in
rearranging these data as in the proposed conclusion.
***
'He who calls you a man speaks truly; he who calls you a fool calls
you a man; therefore he who calls you a fool speaks truly.'--A fallacy
of cross reasoning, and the predicate is a class.
All fools | are men
--------------+--------
You are a man | _N. C._
***
'Nothing is heavier than platina; feathers are heavier than nothing;
therefore feathers are heavier than platina.'--A trivial equivoque.
The following is more subtle. 'Theft is a crime; theft was encouraged
by the laws of Sparta; therefore the laws of Sparta encouraged
crime.'--At most the laws of Sparta encouraged one crime; but there
is a fallacy of equivocation. Taking things surreptitiously from
the person in whose possession they may be, is not a crime--is not
theft--in a society so communistic as the Spartan. There it was
encouraged as an exercise in adroitness. This example shows the
necessity of knowing the matter of the argument.
***
'Warm countries alone produce wine; Spain is a warm country;
therefore Spain produces wine.'
V.
Wine | is p. in w. countries
-------------------+----------------------
Spain is a warm c. | _N. C._
***
'Meat and drink are necessaries of life; the revenues of Vitellius
were spent in meat and drink; therefore the revenues of Vitellius were
spent on the necessaries of life.'--Fallacy of composition: meat and
drink in moderate quantities are necessaries of one life, but not food
of every kind and in excessive quantities.
***
'He who is most hungry eats most; he who eats least is most hungry;
therefore he who eats least eats most.'--A fallacy of accident: he who
eats least does not _at the same time_ eat most.
***
'Whatever body is in motion must move either in the place where it
is, or in the place where it is not; neither of these is possible;
therefore there is no such thing as motion.'--It is an abuse of reason
to attempt to disprove matters of fact. The conclusion of an argument
being always problematical, it can have no force against actual
experience. We experience motion, therefore it cannot be disproved.
***
'A wise lawgiver must either recognise the rewards and punishments
of a future state, or he must be able to appeal to an extraordinary
Providence, dispensing them regularly in this life; Moses did not do
the former, therefore he must have done the latter'--(Warburton, from
Whately).--The reasoner omitted to establish that Moses was a wise
lawgiver, so that the precedent does not apply to his case, except by
courtesy.
***
'That man is independent of the caprices of fortune who places
his chief happiness in moral and intellectual excellence; a true
philosopher is independent of the caprices of fortune; therefore a
true philosopher is one who places his chief happiness in moral and
intellectual excellence.' An instance of cross reasoning.
I.
He who places | is independent
---------------------------+---------------
Philosopher is independent | _N. C._
***
'For those who are bent on cultivating their minds by diligent
study, the incitement of academical honours is unnecessary;
and for the idle it is ineffectual, for such are indifferent
to mental improvement; therefore the incitement of academical
honours is either unnecessary or ineffectual.'
A fallacy of doubtful precedent: because two kinds of students are not
benefited by the hope of honours it is prematurely concluded that no
others exist who may be so benefited.
***
'He who bears arms at the command of the magistrate does what
is lawful for a Christian; the Swiss in the French service,
and the British in the American service, bore arms at the
command of the magistrate; therefore they did what is lawful
for a Christian.'
The conclusion is valid so far as the information given enables us to
judge. If we know from other sources that the Swiss and British
who are referred to, committed atrocities at the command of the
magistrate, the conclusion is a fallacy of accident. In general it is
lawful to obey a magistrate, but there may be particular cases when it
is not.
***
'Anyone who is candid will refrain from condemning a book without
reading it; some reviewers do not refrain from this; therefore some
reviewers are not candid.'--This is cross reasoning and invalid. It
is one thing to say that the uncandid do not refrain, and another that
all who do not refrain are uncandid. The conclusion is taken from the
latter proposition, which is not asserted.
***
'Everyone desires happiness; virtue is happiness; therefore
everyone desires virtue.'
I.
Whoever desires an effect | desires the cause of that effect
-------------------------------+---------------------------------
Everyone desires the happiness | _everyone desires virtue_
which is caused by virtue |
The case is manifestly untrue.
***
'He who has a confirmed habit of any kind of action exercises
no self-denial in the practice of that action; a good man
has a confirmed habit of virtue; therefore he who exercises
self-denial in the practice of virtue is not a good
man.'--(Arist. _Eth._ Bk. II., from Whately.)
VI. I.
He who has a | exercises no || He who exercises no | is good
habit, &c. | self-denial || self-denial in the |
| || practice of virtue |
------------------+--------------------++---------------------+--------
A good man has | _He exercises no || He who _does_ | _N. C._
this habit with | self-denial with || exercise &c. |
respect to virtue | respect to virtue_ || |
The conclusion drawn is fallacious, the second theorem being based on
contrast.
***
'According to theologians, a man must possess faith to be
acceptable to the Deity; now he who believes all the fables
of heathen mythology must possess faith; therefore such a one
must, according to theologians, be acceptable to the Deity.'
'Faith' is ambiguous, meaning in the precedent, spiritual aspiration,
and in the case ignorant credulity.
***
'No evil should be allowed that good may come of it; all punishment is
an evil; therefore no punishment should be allowed that good may come
of it.'--'Evil' is ambiguous, meaning wrong-doing in the precedent and
pain in the case; the conclusion is therefore fallacious.
***
'The principles of justice are variable; the appointments of
nature are invariable; therefore the principles of justice are no
appointments of nature.'--(Arist. _Eth._ Bk. V., from Whately.) The
terms 'principles of justice' and 'nature' require to be defined. It
might be said that justice is one principle, everywhere and always the
same, and that only its embodiments in law and custom are variable.
***
'What happens every day is not improbable; some things, against which
the chances are many thousands to one, happen every day; therefore
some things against which the chances are many thousands to one, are
not improbable.'--A fallacy of division: that improbable things in
general happen every day does not render the occurrence of any one a
probable event.
***
'Protection from punishment is plainly due to the innocent; therefore,
as you maintain that this person ought not to be punished, it
appears that you are convinced of his innocence.'--A fallacy of cross
reasoning.
I.
Innocent persons | deserve protection
--------------------------------+--------------------
This person deserves protection | _N. C._
***
'He who cannot possibly act otherwise than he does, has neither
merit nor demerit in his action; a liberal and benevolent man cannot
possibly act otherwise than he does in relieving the poor; therefore
such a man has neither merit nor demerit in his action.'--To 'have
merit in an action' is scarcely intelligible. A man's merit is in his
character, and his actions are effects and signs of character.
***
'All the fish that the net inclosed were an indiscriminate
mixture of various kinds; those that were set aside and saved
as valuable were fish that the net inclosed; therefore
those that were set aside and saved as valuable were an
indiscriminate mixture of various kinds.'
An instance of the fallacy of division: what is true of the whole
contents of the net is not necessarily true of a portion of the
contents.
***
'A desire to gain by another's loss is a violation of the tenth
commandment; all gaming, therefore, since it implies a desire to
profit at the expense of another, involves a breach of the tenth
commandment.'--A valid argument in inherence.
All desire to gain by, &c. | violates
------------------------------------+--------------
Gaming involves this kind of desire | _it violates_
***
'He that destroys a man who usurps despotic power in a free country,
deserves well of his countrymen; Brutus destroyed Caesar, who usurped
despotic power in Rome; therefore he deserved well of the Romans.'--If
Rome was 'a free country' the conclusion is valid.
***
'No fish suckles its young; the whale suckles its young; the
whale is therefore no fish.'
I.
What suckles | is no-fish
--------------|----------------
Whale suckles | _it is no-fish_
***
'This explosion must have been occasioned by gunpowder, for
nothing else would have possessed sufficient force.'
V.
Explosions of a certain | can only be occasioned by
destructiveness | gunpowder
------------------------+--------------------------
This explosion has that | _it must have been
destructiveness | occasioned by gunpowder_
***
'Every man should be moderate, for excess will cause disease.'
V.
To avoid disease | moderation is requisite
-----------------------+------------------------
Every man should avoid | _every man should
disease | be moderate_
***
'Blessed are the merciful, for they shall obtain mercy.'
I.
To obtain mercy | is blessed
---------------------+---------------------
Those who show mercy | _they must be
obtain mercy | considered blessed_
***
'Some speculative men are unworthy of trust; for they are
unwise, and no unwise man can be trusted.'
I.
Unwise men | are not to be trusted
---------------------+-----------------------------
Some speculative men | _they are not to be trusted_
are unwise
***
'No idle person can be a successful writer of history;
therefore Hume, Macaulay, Hallam and Grote must have been
industrious.'
I.
Successful historians | are not idle persons
-----------------------+---------------------
Hume and the rest were | _they cannot have
successful historians | been idle persons_
***
'Lithium is an element; for it is an alkali-producing substance, which
is a metal, which is an element.'--Fallacy of no-application.
Every alk. | is a metal || Every metal | is an element
prod. subst. | || |
-------------+-----------------++---------------+-------------------
L. is alk. | _it is a metal_ || L. is a metal | _it is an element_
p. subst. | || |
***
'Rational beings are accountable for their actions; brutes not
being rational, are therefore exempt from responsibility.'
I.
Rational beings | are accountable
--------------------+----------------
Brutes not rational | _N. C._
***
'Whatever tends to withdraw the mind from pursuits of a low
nature deserves to be promoted; classical learning does
this, since it gives us a taste for intellectual enjoyments;
therefore it deserves to be promoted.'
V. I.
Whatever gives | tends || Whatever tends | deserves
---------------+------------++----------------+--------------
Learning gives | _it tends_ || Learning tends | _it deserves_
***
'Bacon was a great lawyer and statesman; and as he was also a
philosopher, we may infer that any philosopher may be a great
lawyer and statesman.'--The theorem infers the general inherence of
philosophy with eminence in law and politics, from the single instance
of Bacon: it is evidently a fallacy of doubtful precedent.
***
'Snowdon is the highest mountain in England and Wales. Snowdon
is not so high as Ben Nevis. Therefore the highest mountain in
England and Wales is not so high as Ben Nevis.'
This means: 'the highest mountain in England and Wales is called
Snowdon, and it is not so high as Ben Nevis.' The apparent conclusion
merely repeats a part of the information given already. There is no
case. The following is a theorem of the same kind--
'Lithium is the lightest metal known. Lithium is the metal
indicated by one bright line in the spectrum. Therefore the
lightest metal known is the metal indicated by a spectrum of
one bright line.'
***
'If ye were Abraham's children, ye would do the works of
Abraham.'
VI.
Abraham's children | do his works
------------------------+------------------------
If ye were his children | _ye would do his works_
***
'Since all metals are elements, the most rare of all the metals
must be the most rare of all the elements.'--There is a suppressed
precedent to the effect that the most rare individual of a species
must be the most rare of its genus, which may or may not be true.
***
'All vice is odious; but avarice is a vice; for it makes men
slaves; therefore avarice is odious.'
V. I.
Whatever enslaves | is a vice || All vice | is odious
------------------+----------------++-------------------+---------------
Avarice enslaves | _it is a vice_ || Avarice is a vice | _it is odious_
***
'Bucephalus is a horse; a horse is a quadruped; a quadruped is
an animal; an animal is a substance; therefore Bucephalus is a
substance.'
All horses |are quads.|| Quads. | animals || Animal | substance
-----------+----------++-----------+-----------++----------+----------
Bu. is a h.|_he is q._||B. is quad.|_he is an._||Bu. is an.|_he is
subst._
This is what logicians call a _Sorites_. There may be a chain of valid
arguments, in which the conclusion of one is precedent or case of the
next; but the propositions just quoted do not make an argument, being
merely a string of classifications. If we know what Bucephalus and
substance mean, we know by perception that Bucephalus is a substance.
***
'Every being is then happy when it acquires the proper
perfection of its nature; and consequently all vital beings
are capable of receiving felicity that are capable of arriving
at the perfection of their nature.'
I.
Every being that acquires | is happy
--------------------------+------------------------------
All vital beings capable | _must be capable of receiving
of acquiring | felicity_
This is perilously near tautology; it can be saved only by assuming
that 'every being capable of happiness' is a more extensive class
than 'all vital beings capable of arriving at the perfection of their
nature.'
***
'The soul's debility is not owing to her lapse into matter;
for as this lapse is voluntary, the soul must have sinned
prior to her descent.'
VI.
Voluntary lapse | proves prior sin
-------------------+-----------------------------
Soul's lapse is v. | _her debility must have been
antecedent to lapse_
***
_Cogito ergo sum._--
I.
Whatever thinks | is
----------------+---------------------------
I think | _I must believe that I am_
That we exist is the most certain fact we know: it cannot be
strengthened by any argumentation. If we can doubt that we _are_, we
can with better reason doubt that we think.
***
Here is Hamilton's example of a disjunctive syllogism, which he
considered a valid argument--'The hope of immortality is either a
rational expectation or an illusion; but the hope of immortality is
a rational expectation; therefore the hope of immortality is not an
illusion.' It is a flagrant tautologism.
***
'If man be not a morally responsible being, he must want
either the power of recognising moral good (as an intelligent
agent), or the power of willing it (as a free agent); but
man wants neither of these powers; therefore man is a morally
responsible being.'
Adopted by Hamilton from Krug and given as valid. It is first a
fallacy of contrast, and if amended in this respect it would still be
a fallacy of tautology.
I.
If m. lacked certain pp. | he would be irresp.
-----------------------------+--------------------
He does _not_ lack these pp. | _N. C._
***
'If Aeschines joined in the public rejoicings, he is inconsistent; if
he did not, he is unpatriotic; but he either joined, or not, therefore
he is either inconsistent or unpatriotic.'--An excellent specimen of
logicians' logic: on a par with this--If it is fine weather, I go;
if it rains, I stay; it must either rain or be fine, therefore I must
either go or stay.
***
'If the world were eternal, the most useful arts, such as
painting, &c. would be of unknown antiquity: and on the same
supposition there would be records long prior to the Mosaic;
and likewise the sea and land in all parts of the globe might
be expected to maintain the same relative situations now as
formerly: but none of these is the fact: therefore the world
is not eternal.'
If some things were different | the w. would be eternal
from what they are |
------------------------------+------------------------
They are _not_ different | _N. C._
***
'If the world existed from eternity, there would be records
prior to the Mosaic; and if it were produced by chance, it
would not bear marks of design: there are no records prior to
the Mosaic, and the world does bear marks of design: therefore
it neither existed from eternity, nor is it the work of
chance.'