Part 13

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.

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'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._

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'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.

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'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.

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'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.

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'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.

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'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._

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'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.

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'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.

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'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.

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'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.

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'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.

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'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.

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'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.

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'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.

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'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.

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'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._

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'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.

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'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.

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'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_

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'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.

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'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_

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'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_

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'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_

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'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_

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'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

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'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_

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'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. | || |

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'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._

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'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_

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'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.

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'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.'

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'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_

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'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.

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'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_

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'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.

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'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.'

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'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_

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_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.

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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.

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'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._

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'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.

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'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._

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'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.'

Two theorems are here mixed together, both fallacies of contrast--

Existence of records | would prove the w. etern. ---------------------+-------------------------- Records do not exist | the w. is non-eternal

Non-existence of marks | wd. pr. w. made by chance ---------------------+---------------------------- The marks exist | w. was not made by chance

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'If this man were wise, he would not speak irreverently of Scripture in jest; and if he were good he would not do so in earnest; but he does it, either in jest or earnest; therefore he is either not wise or not good.'

As it stands this is quite circular, but it might be rendered valid by generalisation:--

VI. To speak irrev. of Scr. in | indicates that a man is not jest or earnest | wise or not good ---------------------------+------------------------------ This man does it | we must infer that _he is not | w. or not g._

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'If virtue were a habit worth acquiring, it must ensure either power, or wealth, or honour, or pleasure; but virtue ensures none of these; therefore virtue is not a habit worth attaining.' Fallacy of contrast--

I. What ensures | is worth -------------------+--------- V. does not ensure | _N. C._

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'If men are not likely to be influenced in the performance of a known duty by taking an oath to perform it, the oaths commonly administered are superfluous; if they are likely to be so influenced, everyone should be made to take an oath to behave rightly throughout his life; but one or other must be the case; _therefore_ either the oaths commonly administered are superfluous, or everyone should be made to take an oath to behave rightly throughout his life.'--This will be more intelligible if contracted thus: If oaths fail to influence they are superfluous; if they influence they should be obligatory; but they either influence or do not; therefore they are either superfluous or should be obligatory. There is no argument; the alternative conclusions merely repeat the alternative precedents.

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'If virtue is voluntary, vice is voluntary; but virtue is voluntary; therefore so is vice.' (Arist. _Eth._ Bk. III. quoted by Whately.) This is a circular way of saying that we believe it to be a fact that vice is voluntary. The argumentative form is probably supposed to give the assertion greater weight than it would have if expressed as a perceptual judgment.

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This is valid argument, according to Hamilton--'If man were suited to live out of society, he would either be a god or a beast; but man is neither a god nor a beast; therefore he is not suited to live out of society.'--It has faults of contrast and tautology.

I. Only gods and beasts | are suited -------------------------+----------- Man is neither g. nor b. | _N. C._

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'If iron is impure, it is brittle; but this iron is impure; therefore it is brittle.'--A valid dogmatic argument.

I. Impure iron | is brittle ------------------+----------------- This iron is imp. | _it must be br._

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'If the weather is fine, we shall go into the country; now the weather is fine, therefore we shall go into the country.'--We never get beyond the simple judgment that our going into the country is associated with fine weather.

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The following is valid:--'As often as the weather is fine, my brother has a habit of going into the country; if the weather be fine to-morrow I infer that he will go into the country.' Here a particular hypothetical case is illustrated by reference to a general habit.

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'As often as the weather is fine my brother goes into the country; if it be not fine to-morrow I conclude that he will not go into the country.'--A fallacy of contrast: we are not informed in the antecedents what the brother does on wet days.

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'If there are sharpers in the company we ought not to gamble; but there are no sharpers in the company; therefore we ought to gamble.'

I. Presence of sh. | forbids to gamble ----------------+------------------ Absence of sh. | _N. C._

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'Logic as it was cultivated by the schoolmen proved a fruitless study; therefore logic as it is cultivated at the present day must be a fruitless study likewise.'--We must take the conclusion as valid, until we know in what respects modern logic is superior to scholastic logic.

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'Few treatises of science convey important truths, without any admixture of error, in a perspicuous and interesting form: therefore though a treatise would deserve much attention which should possess such excellence, it is plain that few treatises of science do deserve much attention.'

This means no more than that treatises of a certain excellence would deserve attention, and that there are few of them. There is no argument.

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'Some objects of great beauty answer no other purpose but to gratify the sight: many flowers have great beauty; and many of them accordingly answer no other purpose than to gratify the sight.'

I. Some obj. which answer | are beautiful ------------------------+-------------- Many flowers are beaut. | _N. C._

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'None but Whites are civilised; the ancient Germans were Whites; therefore they were civilised.'

I. All civilised nations | are Whites ----------------------|----------- Anc. Ger. were Wh. | _N. C._

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'Wilkes was a favourite with the populace; he who is a favourite with the populace must understand how to manage them; he who understands how to manage them must be well acquainted with their character; he who is well acquainted with their character must hold them in contempt; therefore Wilkes must have held the populace in contempt.'

Favourites | must kn. how to || He who kn. how | must be | manage || to manage | acquainted --------------+-----------------------++----------------+-------------- W. was a fav. | _he knew how to man._ || W. knew | _he was acq._

He who is acq. | must despise ---------------+--------------------- W. was acq. | _he must have desp._

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