104 THE POPULAR SCIENCE MONTHLY. 



it is necessary to add, that this question must be answered in the nega- 

 tive. Whether or not we can imagine, or mentally represent, a thing 

 as real, depends upon the question whether our past experience has 

 furnished us the data for such a representation ; and our experience is 

 constantly furnishing us new data. 



That the impossibility or difficulty of imagining a thing (which, 

 however, must be carefully distinguished from the absolute impossi- 

 bility of forming certain concepts, of which I shall presently speak) is 

 no evidence for or against its reality, is a truth of the greatest moment 

 to the student of natural science. Liebig expressed it long ago (Ann. 

 JPharm., x., 179), in the words: "The secret of all those who make 

 discoveries is, that they regard nothing as impossible." 



I come now to the conditions of conceivability, strictly and prop- 

 erly so called. These conditions are readily deduced from the inci- 

 dents in the act of conception to which I have referred. These inci- 

 dents are : The reduction of the elements of a representation to con- 

 sistent unity by bringing them into relation, and the establishment 

 of relations between the unit thus evolved and the previous concepts 

 of the mind. A concept can, therefore, be formed, if a, its elements, 

 can be united in thought by the establishment of relations between 

 them by which they are reduced to a unit — in other words, if the con- 

 stituent attributes are consistent with each other — and if b, the re- 

 sulting concept, can be brought into relation, so as to be consistent 

 with the previously-formed concepts of the mind. 



Consistency of the constituent attributes with each other, there- 

 fore, is the first, and consistency of the concept with other concepts 

 the second, condition of its successful formation. The first of these is 

 what is known in logic as the law of non-contradiction, or the law of 

 consistency, and is the fundamental condition of all thought. It re- 

 quires that what is expressly or by implication asserted in the sub- 

 ject shall not expressly or by implication be denied in the predicate 

 of any proposition into which the concept may be resolved, or, in plain 

 words, that what is asserted in one form of words shall not be denied 

 in another. 



Now, it is evident that, whenever the formation of a concept in- 

 volves a violation of the first condition, we have before us a case of 

 absolute inconceivability, and therefore of impossibility. For this 

 condition, as I have said, is the first constitutive law of all intelli- 

 gence, without which the whole system of relations, in which both sub- 

 jective and objective realities have their only warrant and support, 

 instantly collapses into the nothingness in which alone all things are 

 identical, and disappears in the night of absolute confusion. ~No one, 

 not even John Stuart Mill, ever seriously doubted the absolute impos- 

 sibility of the conception or existence of a round square, or of a straight 

 line which is not the shortest distance between two points. When- 

 ever such a doubt has been expressed, it has arisen from a mental con- 



