LOGIC. 



truth, the conclusion may be said to affirm in 

 other words what has been already affirmed in 

 the premises. No new fact is declared : a varied 

 statement is given of what has been already 



declared. This variation in the mode of statin* 

 affirmations has its uses ; but it would be a mis- 

 take to suppose that in this way we make any 

 advance or bring in any new matter. The 



FIRST FIGURE. 



All B is C. 

 All A is B. 



Therefore, 

 All A is C. 



All animals are mortal. 

 All men are animals. 



Therefore, 

 All men are mortal. 



No C is B. 

 All A is B. 

 Therefore, 

 No A is C. 



No brute is rational. 

 All men are rational. 



Therefore, 

 No man is a brute. 



No B is C. 

 All A is B. 

 Therefore, 

 No A is C. 



No animal is a plant. 

 All men are animals. 



Therefore, 

 No man is a plant. 



All B is C. 

 Some A is B. 



Therefore, 

 Some A is C. 



All men are rational. 

 Some animals are men. 



Therefore, 

 Some animals are rational 



SECOND FIGURE. 



All C is B. 

 No A is B. 

 Therefore, 

 No A is C. 



All men are rational. 

 No brute is rational. 



Therefore, 

 No brute is a man. 



No C is B. 

 Some A is B. 

 Therefore, 

 Some A is not C. 



No man is a brute. 

 Some animals are brutes. 



Therefore, 

 Some animals are not men. 



No B is C. 

 Some A is B. 

 Therefore, 

 Some A is not C. 



No negro is white. 

 Some men are negroes. 



Therefore, 

 Some men are not white. 



All C is B. 

 Some A is not B. 



Therefore, 

 Some A is not C. 



All men are rational. 

 Some animals are not ra- 

 tional 



Therefore, 

 Some animals are not men. 



All B is C. 

 All B is A. 

 Therefore, 

 Some A is G 



All men are rational. 

 All men are animals. 



Therefore, 

 Some animals are rational 



All B is C. 

 Some B is A. 

 Therefore, 

 Some A is C. 



All covetous men are unhappy. 

 Some covetous men are rich. 



Therefore, 

 Some rich men are unhappy. 



THIRD FIGURE. 



No B is C. 

 All B is A. 



Therefore, 

 Some A is not C. 



No men are irrational 

 All men are animals. 

 Therefore, 

 Some animals are not irrational 



Some B is not C. 

 All B is A. 



Therefore, 

 Some A is not C. 



Some animals are not men. 

 All animals are living things. 



Therefore, 

 Some living things are not men. 



Some B is C. 

 All B is A. 



Therefore, 

 Some A is C. 



Some animals are rational 

 All animals are living things. 



Therefore, 

 Some living things are rational 



No B is C. 

 Some B is A. 



Therefore, 

 Some A is not C. 



No vice is commendable. 

 Some vices are pleasures. 



Therefore, 

 Some pleasures are not commendable. 



All C is B. 

 All B is A. 

 Therefore, 

 Some A is C. 



No C is B. 

 Some B is A. 

 Therefore, 

 Some A is not C. 



certainty and self-evident nature of the syllogism 

 depend on this very circumstance, that the con- 

 clusion affirms nothing that has not been affirmed 

 in the premises ; if it were otherwise, the reason- 

 ing would be bad. We cannot step one jot out of 

 the compass of the two premises, but we may 

 affirm in as many new forms of language as we 

 can contrive, the same facts as these have affirmed. 

 The syllogism is a check upon us when we are in 

 danger of thus transcending the premises, which 

 we are sometimes liable to do, from the complica- 

 tions and involutions of language accompanying 

 the statement of facts. 



Passing to the other figures, we might, by 

 examining each syllogism in detail, and turning it 

 over on all sides, satisfy ourselves in the same 



manner that the conclusion was really contained 

 in the premises. There is, however, another mode 

 of making out the sufficiency of the reasoning in 

 each case namely, by shewing that all the syllo- 

 gisms of these figures come under those of the 

 first figure, being in fact proved when they are 

 proved. This is to reduce the succeeding figures 

 to the first, or deduce them from the first It is 

 the manner of mathematics to avoid independent 

 appeals to fact as much as possible, and make one 

 truth prove all that can possibly come under it, as 

 we may see in Euclid. So logicians shew that an 

 argument in the second, third, or fourth figures 

 may be thrown into a syllogism of the first figure, 

 and thereby acquire the certainty that we have 

 just seen to belong to the cases of that figure. 



Ml 



