14 



THE POPULAR EDUCATOR. 



cular will be proved when a universal is required ; sometimes one 

 with terms which are not the same in sense as those in the con- 

 clusion really given to be established. Suppose we are seeking 

 to prove that a certain man was virtuous in his life and 

 character (which makes it necessary to show that on the whole 

 all his acts and deeds were virtuous), but we claim to have 

 proved all that is required, when we show satisfactorily that 

 some of his acts were of this character, leaving out of sight 

 altogether many others of a very different aspect. This is an 

 instance of Ignoratio Elenchi. So also if, when we ought to 

 show a thing is just, instead of that we show that it is inex- 

 pedient, or vice versa; or, if the right of private judgment in 

 matters of religion be maintained, we imagine this disproved by 

 the statement, however true, that it is impossible for every one 

 to be right in his judgment, which in reality was never denied 

 by our opponent. An instance of the employment of this 

 fallacy through the instrumentality of an ambiguous term is 

 often afforded by those who, in theological controversy, establish 

 certain conclusions in reference to "faith," used in one sense, 

 and then use these conclusions to meet arguments in which the 

 word is used in a different sense. 



This is really the fallacy involved in the error of shifting 

 ground, as well as in that of combating both the premises of an 

 opponent alternately, instead of dealing 1 with one only at a time, 

 and having done with it before proceeding to another. 



Persons often seem to think that it is quite sufficient to show 

 that there exist grave objections against the adoption of a par- 

 ticular plan, in order to force others to reject it. This is in 

 reality the fallacy of Ignoratio Elenchi ; it is proving that there 

 are weighty objections against a particular course, when what 

 is required to be proved is that there are more weighty and 

 insuperable objections against its adoption than against its 

 rejection. 



It should be borne in mind that those who employ this fallacy 

 very frequently suppress the conclusion they are really proving, 

 in order that it may thus escape notice that they are not really 

 proving the one required ; and, as Archbishop Whately remarks, 

 this is, "perhaps, the most common form of that confusion of 

 thought to which thoso are liable who have been irregularly and 

 unskilfully educated who have collected, perhaps, a consider- 

 able amount of knowledge, without arrangement, and without 

 cultivation of logical habits. Most of the erroneous views in 

 morals, and in other subjects, which prevail among such per- 

 sons, m ( ay be exhibited in the form of fallacies of irrelevant 

 conclusion: e.g., the question "whether it be allowable for a 

 Christian to fight in defending himself from oppression and 

 outrage," and "whether a Christian magistrate may employ 

 physical coercion, and inflict secular punishment on evil-doers" 

 these are perpetually confounded with the questions " whether 

 Christians are allowed to fight as such; i.e., to fight for their 

 religion against thoso who corrupt or reject the faith ; " and 

 " whether a Christian magistrate may employ coercion on behalf 

 of Christianity, and inflict punishment on heretics as evil- 

 doers." 



The fallacy called Petitio Principii (begging the question), 

 is used whenever that is assumed as granted which ought to 

 have been proved. This is the account ordinarily given, 

 although Archbishop Whately confines the name to those cases 

 in which one of the premises is plainly the same as the conclu- 

 sion, or is proved from it, or is such as the person to whom the 

 argument is addressed would not know or admit, except as an- 

 argument from the conclusion : e.g., where one argues in favour 

 of the authenticity of a history from its recording certain facts 

 which rest themselves for their reality merely on the evidence 

 of the same history. 



The form in which this fallacy most commonly occurs is in 

 that which has been called " arguing in a circle "a species of 

 argument in which the ultimate conclusion is proved by a train 

 of reasoning, which has one of its premises the same as this con- 

 clusion : e.g., " Some mathematicians," according to Whately, 

 " attempt to prove that every particle of matter gravitates 

 equally. ' Why ?' ' Because those bodies which contain more 

 particles ever gravitate more strongly, i.e., are heavier.' 'But 

 (it may be urged) those which are heaviest are not always most 

 bulky.' ' No, but 3till they contain more particles, though more 

 closely condensed.' ' How do you know that ? " ' Because they 

 are heavier.' ' How does that prove it ?' ' Because all particles 

 of matter gravitating equally, that mass which is specifically 



the heavier must needs have the more of them in the same 

 space.' " 



It should be observed that the longer the chain of reasoning 

 i.e., the wider the circle the more likely it is that the fallacy 

 will escape observation. 



The fallacy of " non causa pro causa" (literally, " taking- as the 

 cause that which is not such ") is divided into two kinds, called 

 respectively " a non vera pro vera " and " a non tali pro tali," 

 which in reality are the former, arguing from a false premiss 

 as if it were true (i.e., having, in logical language, the expressed 

 premiss false), and the latter arguing from a case not parallel 

 or similar, as if it were (i.e., having the suppressed premiss 

 false). In the one case there is no connection at all between 

 the effect and the cause to which it is attributed ; in the other, 

 if there is any such connection at all, it is an insufficient one. 



Instances of the fallacy of " non causa pro causa " are very 

 common, especially amongst the uneducated and vulgar, who 

 are very liable to suppose, from seeing two events often or even 

 sometimes conjoined, that there subsists some necessary con- 

 nection between them, that the one must be the cause of the 

 other. Most instances of popular superstition may, accordingly, 

 be referred to this source. In this way it used to be generally 

 thought that the appearance of a comet portended some great 

 national calamity, merely because it so happened that on 

 several occasions when comets were visible great disasters 

 occurred in some portion of the world. Not that this erroneous 

 mode of reasoning is one from which the educated and scientific 

 can be supposed free. Nearly all writers upon political economy 

 thought until very lately that money, in place of being merely 

 a sign, was the cause of wealth in a country, and hence tried to 

 restrict its flowing- out in the natural course of trade ; and 

 there are some who even now think that labour is the chief 

 cause of the value of some commodities, instead of being merely 

 a sign of this. An instance not uncommonly given of " a non 



j tali pro tali " is this : " What intoxicates should be forbidden ; 

 wine intoxicates ; therefore wine should be forbidden ; " where 



i the minor premiss only being- true of wine taken in excess, is 

 in the conclusion treated as if it were true of wine taken in any 

 quantity. This might also be exhibited as a fallacy " a dicto 

 secundum quid ad dictum simpliciter." 



We have thus given a brief and incomplete outline of the 

 kinds of fallacies most usually met with in argument with 

 others, or most liable to deceive us in solitary reasoning ; and 



1 we shall now illustrate the remarks made by some examples of 



| the most celebrated fallacies on which the ancient logicians 

 used to exercise their ingenuity. 



Perhaps the most celebrated of all is that of " Achilles and the 



! Tortoise." It runs thus : " Suppose Achilles to run ten times 



: faster than the tortoise ; and while he remains in his place let the 

 tortoise start and run through a certain portion (say a tenth) 



I of the entire space to bo traversed. Let Achilles then start to 

 overtake the tortoise ; he can never overtake it ; for, while he 

 runs through the tenth part of the course by which the tortoise 

 had the start of him, the tortoise will have run further through 

 a tenth of a space equivalent to that i.e., through iJ<jth part 

 of the whole and when Achilles has got through this, the 

 tortoise will have got on in advance through ^ O th part of this, 

 i.e., through j^th of the whole, and so on for ever, so that 

 Achilles will never be able to overtake the tortoise, though he 

 runs ten times as fast." The solution of this fallacy by Diogenes 

 (Solvitur ambulando) i.e., that it is false is hardly a satis- 

 factory logical mode of escaping from the difficulty. No one 

 ever doubted that. Nor is it much more satisfactory to allow, 

 as Archbishop Whately does, that it cannot possibly be ex- 

 hibited in a syllogistic form at all, which would virtually be a 

 surrender of the proposition that the syllogism is a test by 

 which we can always distinguish between sound and unsound 

 reasoning. Mansel's is the best solution, which classes the 

 fallacy as a material one. Let the whole space to be traversed 

 be represented by A, and then the syllogism representing the 

 reasoning will be this, " Any space equal to ^ + ^3 + TSI e * c< 

 is infinite (being the sum of an infinite series). The space to be 

 passed before Achilles overtakes the tortoise is equal to that 

 sum; therefore it is infinite." In this the major premiss is 

 simply false. The sum of an infinite series is not necessarily 

 infinite ; it may be, and in this case is finite. And this solves 

 the whole mystery. 



In our next lesson we shall give other similar examples. 



