Notices inspecting New Books. 403 



attributes of mortals — the fact of mortals forming a class being 

 purely subsidiary and not necessarily coming into view at all. 



3. We are told (vol. i. p. 136), "Neither in deductive nor in- 

 ductive reasoning can we add a tittle to our implicit knowledge, 

 which is like that contained in an unread book or a sealed letter. 

 Sir W. Hamilton has well said, ' Reasoning is the showing out 

 explicitly that a proposition not granted or supposed is implicitly 

 contained in something different which is granted or supposed.' " 

 So far as the words " nor inductive " are concerned our author 

 would, we suppose, stand nearly alone in his opinion. It is gene- 

 rally held that induction, or inductive inference, is a process that 

 puts us in possession of something new; but when limited to 

 deductive reasoning, the opinion expressed in the above sentence is 

 very commonly held, though there are some who regard it as fun- 

 damentally erroneous. Suppose we took a full-grown man with . 

 perfect powers of reasoning, but wholly ignorant of geometry, 

 there would be no difficulty in giving hhn a perfect knowledge of 

 the definitions and axioms of the science. But when he came to 

 prove the propositions of the first book (say the 47th) that would 

 be quite another question, his success or failure would depend on 

 his powers of invention. No working of the keys of any logical 

 machine would put him up to the essential steps "through A 

 draw A L parallel to BDor CE, and join AD, OF." It cer- 

 tainly seems to us that considerations of this kind land us on this 

 conclusion : — Either the first book of Euclid is not a specimen of 

 deductive reasoning, or else the account commonly given of deduc- 

 tive reasoning is somehow or other erroneous. If we may venture 

 on a surmise, we should say that the passage above quoted is 

 couched in metaphorical language, and that the words " explicit " 

 and " implicit " are used equivocally. To explicate is to unfold. 

 We unfold a table-cloth when we put it on the table, we explicate 

 the definition of a circle when we draw a learner's attention to all 

 the points involved — that it must be a plane figure, bounded by one 

 line, &c. But, except by an improper use of language, we do not 

 speak of an oak tree as being unfolded from an acorn ; the oak tree 

 is indeed derived from the acorn, but only by the continual assimi- 

 lation of new matter. It is only in this latter sense, at least as it 

 seems to us, that the first book of Euclid can be said to be un- 

 folded from the definitions and axioms. 



We have gone rather beyond our intention in the last paragraph, 

 and will not venture further into the region of doubt and debate. 

 We will therefore only add that, whether the student ends by 

 adopting Mr. Jevons's iogical views or not, he will not fail to learn 

 a great deal from an attentive perusal of this very able and com- 

 prehensive work. 



