LOGIC. 



DEFINITION. 



In Bain's Logic, which endeavours to render 

 definition more precise, by expounding its fund- 

 amental canons, this subject is taken up after 

 Deduction and Induction ; but in our slight sketch, 

 all that we have space for will come in more 

 appropriately here. Logic having to deal with 

 general propositions that is, with propositions 

 or affirmations concerning classes it is obviously 

 of the highest importance that those classes 

 should be exactly defined. Now, the definition of 

 a class consists in stating all the properties com- 

 mon to the individuals of the class. You define 

 the class by defining its notion or concept. You 

 cannot draw a ring round all the individuals com- 

 posing a class, but you draw up a precise state- 

 ment of a common property or properties, and 

 make no attempt to mark out the boundaries of 

 the class, further than saying that it consists of 

 all individuals possessing the defined property 

 or, in other words, all individuals coming under 

 the notion. 



It will not do, however, to fix on notions arbi- 

 trarily out of your mind, and classify the concrete 

 universe accordingly. You ultimately subject the 

 concrete particulars to the abstract notion, but you 

 must take the notion in the first instance from the 

 particulars. Notions consist merely of the points 

 of resemblance among the members of classes, 

 and classes are formed in science upon a strict 

 principle, which is this : ' Of the various group- 

 ings of resembling things, preference is given to 

 such as have in common the most numerous and 

 the most important attributes.' This is the golden 

 rule of classifying. Of course, your impression of 

 the importance of attributes may vary with your 

 purposes ; but in all cases, in any classification 

 professing to be philosophic, you must bear in 

 mind that it is necessary to have some substantial 

 reason for forming a class, other than mere fancy 

 to put together all individuals having a certain 

 point of resemblance ; also, that the points of 

 resemblance shall be as numerous as possible, so 

 that to name a thing as belonging to a class shall 

 give as much information about it as possible. 



It being premised that you have some justifica- 

 tion for forming a class, the first canon is : 

 Assemble for Comparison the Particulars coming 

 tinder the Notion to be defined. You cannot, of 

 course, assemble all the individual instances, but 

 you must assemble ' representative instances suffi- 

 cient to embrace the extreme varieties' (Bain, 

 ii. 156). If you wish to define a ' solid,' you must 

 bring together, mentally or materially, a large 

 number of representative solids metals, rocks, 

 woods, bones and compare them, to find out in 

 what they all agree. Having found that they all 

 agree in resisting pressure, applied to change 

 their form, you take this resistance as the notion 

 of the class, and define solids by saying : ' Solids 

 are bodies that resist force applied to change 

 their form.' 



The second canon proceeds upon the principle 

 of Relativity that every real notion must have 

 an opposite also real. It is : Assemble for Com- 

 parison the Particulars of the Opposed or contrast- 

 ing Notion. It gives greater precision to a notion 

 to define its opposite. In defining the opposite, 

 you proceed upon the same plan as in defining 



the positive notion : assemble representative par- 

 ticulars, and see where they agree. When you 

 wish to give precision to your definition of Solids 

 by defining also Liquids and Gases, you assemble 

 representative instances, and find that ' Liquids 

 and Gases yield to the slightest pressure, and 

 have no fixed form, except as given by solid 

 inclosures.' 



Between two such opposed notions as Solid and 

 Liquid, there is often a doubtful margin of particu- 

 lars that do not belong decidedly to either class. 

 It is difficult to say whether a jelly is a solid or a 

 liquid : it does not lose its form so readily as a 

 liquid, nor does it stand out against pressure like 

 an unquestionable solid. Such cases warn us not 

 to attempt to draw too short a line of distinction : 

 a margin should be left for doubtful cases. 



DEDUCTION. 



The first thing that you naturally do, when you 

 wish either to take stock of what you know and 

 believe, or to discuss the positions of an opponent 

 in debate, is to turn each separate proposition 

 round and round on every side, to see what it all 

 implies. Your next step should be, to consider 

 what may be legitimately inferred or deduced from 

 propositions that you admit to be true. If you 

 followed our account of the nature of classes, it 

 may have occurred to you, that every assertion 

 made concerning a class must be true of every 

 individual contained in that class, because those 

 individuals, in so far as they are members of the 

 class, are all alike : an assertion about a class is 

 true of every individual possessing the common 

 properties of the class. 'Despots are bad rulers,' 

 is a proposition true of every individual possessing 

 the attributes of a despot. When, therefore, you 

 admit that despots are bad rulers, you are bound 

 in consistency to admit the proposition concerning 

 every individual that can be shewn to possess the 

 common attributes of the class. This principle is 

 the foundation of Deductive reasoning : and the 

 Syllogism, as a safeguard against fallacious De- 

 duction, consists in placing deductive inferences 

 in a form convenient for the application of the 

 principle. 



Two 'propositions, besides the conclusion, are 

 involved in every legitimate deduction. At the 

 basis of all is your general proposition concern- 

 ing a class of things, into which form all such 

 general propositions as 'Haste makes waste,' 

 ' Honesty is the best policy,' may be reduced. 

 Then, before you can proceed to the proposition 

 to be inferred from this that such and such an 

 action is wasteful, or good policy, you must have 

 an applying proposition to make out that the 

 action belongs to the class concerning which the 

 general allegation is made : that it belongs to the 

 class of hasty actions, or of honest actions. These 

 two propositions are called the Premises of the 

 deduction. When they are formally stated, and 

 followed by the conclusion, thus 



All hasty actions are wasteful ; 



This is a hasty action ; 



Therefore, this is a wasteful action 

 the whole is called a SYLLOGISM, which, from 

 its etymology, means a joining together of pro- 

 positions. 



The great practical advantage of the syllogism 

 consists in its putting a deduction into a form in 



355 



