232 PROCEEDINGS OF THE AMERICAN ACADEMY 



creases the depth of one term, and actually increases the breadth of 

 another. 



Let us now consider reasoning from definition to definitum, and also 

 the argument from enumeration. A defining proposition has a mean- 

 ing. It is not, therefore, a merely identical proposition, but there is a 

 difference between the definition and the definitum. According to the 

 received doctrine, this difference consists wholly in the fact that the 

 definition is distinct, while the definitum is confused. But I think that 

 there is another difference. The definitum implies the character of 

 being designated by a word, while the definition, previously to the 

 formation of the word, does not. Thus, the definitum exceeds the de- 

 finition in depth, although only verbally. In the same way, any un- 

 analyzed notion carries with it a feeling, — a constitutional word, — 

 which its analysis does not. If this be so, the definition is the predicate 

 and the definitum the subject, of the defining proposition, and this last 

 cannot be simply converted. In fact, the defining proposition affirms 

 that whatever a certain name is applied to is supposed to have such and 

 such characters ; but it does not strictly follow from this, that whatever 

 has such and such characters is actually called by that name, although 

 it certainly might be so called. Hence, in reasoning from definition to 

 definitum, there is a verbal increase of depth, and an actual increase of 

 extensive distinctness (which is analogous to breadth). The increase 

 of depth being merely verbal, there is no possibility of error in this 

 procedure. Nevertheless, it seems to me pi'oper, rather to consider 

 this argument as a special modification of hypothesis than as a de- 

 duction, such as is reasoning from definitum to definition. A similar 

 line of thought would show that, in the argument from enumeration, 

 there is a verbal increase of breadth, and an actual increase of depth, 

 or rather of comprehensive distinctness, and that therefore it is proper 

 to consider this (as most logicians have done) as a kind of infallible in- 

 duction. These species of hypothesis and induction are, in fact, merely 

 hypotheses and inductions from the essential parts to the essential 

 whole ; this sort of reasoning from parts to whole being demonstrative. 

 On the other hand, reasoning from the substantial parts to the substan- 

 tial whole is not even a probable argument. No ultimate part of 

 matter fills space, but it does not follow that no matter fills space. 



