LESSONS IN LOGIC. 



which he gives of words whose different senses are likely to be 

 tnded. 



ImposMliility" (with its kindred words) ia used with Uin-.- 

 ' itii.l .li-tinot meanings. 1. It is employed to 

 .,iti<-nl iin|H)ssibility. Anything in so oallod which in- 

 volves an absurdity or a contradiction, this name being given 

 in mi i In- t'iu-t that the greater number of instances of it occur 

 mathematical sciences : e.g., that two straight lines 

 -ln.ul.l i-ii.'Uwe a space is a mathematical impossibility. It is 

 :ili>nril, inconceivable, and a contradiction in terms, being at 

 variance with the very definition of a straight line. It amounts, 

 n t'.i.-t, to this, that the same line should bo straight and not 

 straight nt the same time. 2. A physical impossibility ia some- 

 it variance with the existing lawn of Nature, and which 

 iMimut take place while those laws remain as they are : e.g., that 

 a man should be able to live under water, or that a feather and 

 a stone should fall to the ground in the same space of time. 

 There is not here, as in a mathematical impossibility, any incon- 

 'ity implied. We can quite readily conceive the existing 

 : nature altered so that a man should have the power of 

 living xinder water, and a feather and a stone have the same 

 weight (i.e., be attracted with equal power towards the earth). 

 There is no contradiction involved in imagining this to be so ; 

 and we, in fact, know that, whenever a miracle has been per- 

 formed, such a suspension or violation of the laws of Nature 

 has been brought about by the power of the Supreme Being. 

 We cannot, however, surmount these laws, and so they impose 

 re -frictions upon us which it is a physical impossibility for us 

 to overcome. Persons have been often led into error in reason- 

 ing through not keeping these two senses of the word distinct. 

 3. The word " impossibility " is used to denote that strong degree 

 of certainty which leaves no room for doubt upon the mind. 

 We may be convinced that a certain event will never occur, 

 even though it does not involve either a contradiction or a 

 violation of any of the known laws of Nature. Such an event 

 is termed a moral impossibility. A good instance occurs in 

 throwing dice. It is a moral impossibility that we should throw 

 sixes a hundred times successively. We are certain, from our 

 experience and reason, that such a contingency will not occur, 

 although its occurrence is undoubtedly neither a mathematical 

 nor a physical impossibility. So also it would be said to be 

 morally impossible for all the inhabitants of England to be per- 

 fectly free from the commission of crime, although it is within 

 the power of every individual inhabitant to refrain from any 

 criminal act. We know, however, that while the world remains 

 us it is such a state of things will never happen. 



The words may and must have also two senses, which are 

 not unfrequently confounded with one another. They some- 

 times refer to power. Thus, when I say, " I may leave this 

 room," I moan that I have the power to do so when I please ; 

 or " a prisoner must remain in his cell," that the physical 

 restraint he is under deprives him of the power of acting other- 

 wise. But sometimes these words merely refer to possibility 

 or contingency. " A particular individual may die to-morrow," 

 merely implies the possibility of such an event as his death ; or, 

 " we must all die some day," merely expresses the certainty we 

 feel that we are all mortal. 



It frequently escapes notice that the word same is used in two 

 senses. Its primary sense is, of course, that which denotes 

 absolute identity. In that sense I say (for example) that the 

 shilling now before me is the same that I got from a certain 

 person in change yesterday the two being numerically one. I 

 use the word, however, in a very different sense when I say that 

 two persons are afflicted with the same disease, or have hair of the 

 ^amc colour. In this case, all that I moan is that the two illnesses 

 or the two kinds of hair are simitar, that the very same descrip- 

 tion would apply to each. Archbishop Whately thinks that 

 nothing has had such an effect in fostering Realism as the non- 

 attention to this distinction between the primary and secondary 

 use of "same" and kindred words. And it will not be out 

 of place to give a brief account of what is involved in the 

 famous controversy between the Nominalists and Realists 

 which waged so furiously in the Middle Ages. 



The question which gave birth to so many different schools of 

 thought might be treated in various ways. Perhaps the shortest 

 statement that could be given of it is this What is the object of 

 our thoughts when we make use of general or universal terms ? 

 There is no difficulty, so long as wo use a singular term, one 



wbioh relate* only to a Mingle individual : e.g., " Peter," "Julias 

 Caesar," " this tree," " this mountain." Here the object of 

 which we are thinking, and which is present to oar mind, os*> be 

 nothing elite than the one individual for which the name stands. 

 When, however, we make use of the corresponding general or 

 universal terms, " man," "conqueror," "tree," "mountain," 

 the case is different. Here we caanot accurately specify the 

 object of our thoughts with the same facility as before. We 

 have no longer a term which is applicable to one object and one 

 only ; but one which is applicable to an indefinite number of 

 objects to as many, in fact, as the generic or universal term 

 stands for. What, then, is the actual object of thought present 

 to our minds when we nse such a term '( This was the subject 

 of controversy; and various were the answers given to the 

 question. 



Those called the Realists maintained that there was a really 

 existing thing corresponding to the universal terms, "man," 

 " conqueror," " mountain," etc., as truly as there was corre- 

 sponding to the singular terms, " Peter," " Julias Caesar," 

 " ./Etna," etc. This really existing thing was not the same as 

 that denoted by the name (for instance) of an individual moun- 

 tain, e.g., jEtna, or else the term would be not universal but 

 singular ; but yet since thu universal was applicable to the indi- 

 vidual, this thing (whatever its nature) must exist in the indi- 

 vidual, although distinct from it. 



The Nominalists held, on the other hand, that it is the mere 

 term or name of which we think when we employ a general or 

 universal term. It is the word "mountain" or "tree" which 

 is present to our thoughts, and not any thing, whether universal 

 or particular. 



Various intermediate views between these two extremes were 

 advanced by different thinkers from time to time, which it is 

 very often extremely difficult to distinguish one from another, 

 and which it is unnecessary to enumerate here. Archbishop 

 Whately's view, however, may be mentioned. According to 

 him, the notion expressed by a universal term is merely an 

 incomplete or inadequate notion of an individual. The com- 

 plex idea represented by the universal term omits every circum- 

 stance which makes the individual differ from other individuals 

 of the same class (whether genus or species), and only embraces 

 all those common features which are to be found in all the 

 individuals of the class, i.e., in all those to which the universal 

 term can be applied : e.g., " If I omit the mention and the 

 consideration of every circumstance which distinguishes JEtna 

 from any other mountain, I then form a notion (expressed by 

 the common term 'mountain') which inadequately designates 

 .(Etna (i.e., which does not imply any of its peculiarities, or its 

 numerical singleness), and is equally applicable to any one of 

 several other individuals." 



Having now shortly gone through the different rules of Logic, 

 and seen its practical application, amongst other things, in the 

 detection of erroneous reasoning ; and having, we hope success- 

 fully, shown that the study is neither so uninteresting or so 

 useless as is frequently asserted, it is necessary, to make our 

 outline complete, to give a brief sketch of the history of Logic 

 down to the present day, that its progressive development may 

 be the better seen. 



The earliest writer upon any of the subjects embraced by 

 Logic (which he called Dialectics) was Zeno the Eleatic ; but his 

 ideas upon the subject were so crude and limited, and his con- 

 sideration of it so partial, that he hardly merits the name of a 

 logician, as the term was subsequently understood. 



Socrates is stated by Aristotle to have made two important 

 logical discoveries induction and definition. The Socratic 

 induction, however, differed very much from that of Aristotle 

 and subsequent writers, and was not, strictly speaking, a logical 

 process at all ; and a similar remark is true of his definition. 

 Nor does Plato, so far as we are able to distinguish his views 

 and discoveries from those of Socrates, appear to have contri- 

 buted much additional to the science, except that we find that 

 he analysed correctly the proposition into its two component 

 elements the noun and verb. 



But Aristotle is to be considered as the first writer who 

 attempted to treat logical questions distinctly and upon a 

 systematic plan, although many of the subjects which (at least 

 as his works have come down to us) he included within its 

 limits would not be allowed a place in a logical treatise at the 



