340 REASONING. 



namely, to determine what else may be concluded if 

 we find, and in proportion as we find, the assumptions 

 to be true may be performed once for all, and the 

 results held ready to be employed as the occasions 

 turn up for use. We thus do all beforehand that can 

 be so done, and leave the least possible work to be 

 performed when cases arise and press for a decision. 

 This inquiry into the inferences which can be drawn 

 from assumptions, is what properly constitutes Demon- 

 strative Science. 



It is of course quite as practicable to arrive at 

 new conclusions from facts assumed, as from facts 

 observed; from fictitious, as from real, inductions. 

 Deduction, as we have seen, consists of a series of 

 inferences in this form : a is a mark of b, b of c, c of 

 d, therefore a is a mark of d, which last may be a 

 truth inaccessible to direct observation. In like man- 

 ner it is allowable to say, Suppose that a were a mark 

 of &, b of c, and c of d, a would be a mark of d, which 

 last conclusion was not thought of by those who laid 

 down the premisses. A system of propositions as 

 complicated as geometry might be deduced from 

 assumptions which are false : as was done by Ptolemy, 

 Descartes, and others,, in their attempts to explain 

 synthetically the phenomena of the solar system, on 

 the supposition that the apparent motions of the 

 heavenly bodies were the real motions, or were pro- 

 duced in some way more or less different from the 

 true one. Sometimes the same thing is knowingly 

 done, for the purpose of showing the falsity of the 

 assumption ; which is called a reductio ad absurdum. 

 In such cases, the reasoning is as follows: a is a mark 

 of b, and b of c; now if c were also a mark of d, a would 

 be a mark of d; but d is known to be a mark of the 

 absence of a; consequently a would be a mark of its 



