CHAPTER IV. 



DEDUCTIVE REASONING. 



THE general principle of inference having been ex- 

 plained in the previous chapters, and a suitable system 

 of symbols provided, we have now before us the com- 

 paratively easy task of tracing out the most common and 

 important forms of deductive reasoning. The general 

 problem of deduction is as follows : From one or more 

 propositions called premises to draw such other proposi- 

 tions as will necessarily be true when the premises are 

 true. By deduction we investigate and unfold the in- 

 formation contained in the premises ; and this we can do 

 by one single rule For any term occurring in any pro- 

 position or expression substitute the expression which is 

 asserted in any premise to be identical ivith 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 in 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 distinct 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 



