CHAPTER IV. 



DEDUCTIVE REASONING. 



THE general principle of inference having been explained 

 in the previous chapters, and a suitable system of symbols 

 provided, we have now before us the comparatively eas> 

 task of tracing out the most common and important forms 

 of deductive reasoning. The general problem of deduc- 

 tion is as follows : From one or more propositions called 

 premises to draw such other propositions as will necessarily 

 be true when the premises are true. By deduction we investi- 

 gate and unfold the information contained in the premises ; 

 and this we can do by one single rule For any term occur- 

 ring in any proposition substitute the term which is asserted 

 in any premise to T)e identical with it. To obtain certain 

 deductions, especially those involving negative conclusions, 

 we shall require to bring into use the second and third Laws 

 of Thought, and the process of reasoning will then be called 

 Indirect Deduction. In the present chapter, however, I 

 shall confine my attention to those results which can be 

 obtained by the process of Direct Deduction, that is, by 

 applying to the premises themselves the rule of substitution. 

 It will be found that we can combine into one harmonious 

 system, not only the various moods of the ancient syllogism, 

 but a great number of equally important forms of reasoning, 

 which had no recognised place in the old logic. We can 

 at the same time dispense entirely with the elaborate 

 apparatus of logical rules and mnemonic lines, which 

 were requisite so long as the vital principle of reasoning 

 was not clearly expressed. 



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