PRIMARY CONCEPTS OF MODERN SCIENCE. 105 



fusion as to the import of the terms employed in the propositions, as 

 we shall see presently in the case of Mill. 



But it is otherwise with the second condition of conceivability : 

 that the concept, when framed, shall b£ consistent with other concepts 

 previously formed. For these latter concepts may be spurious or in- 

 valid. Inconceivability arising from non-compliance with the second 

 condition is therefore purely relative, depending on the validity of the 

 concepts with which the concept in question appears to be incompat- 

 ible. For example, until the discovery of the composition of water, 

 of the true theory of combustion, and of the relative affinities of potas- 

 sium and hydrogen for oxygen, it was impossible to conceive a sub- 

 stance which would ignite on contact with water, it being one of the 

 recognized attributes of water — in other words, a part of the concept 

 water — that it antagonized fire. This previous concept was spurious, 

 and, when it had been destroyed, the inconceivability of a substance 

 like potassium disappeared. Similarly, we are now unable to conceive 

 a warm-blooded animal without a respiratory system, because we con- 

 ceive the idiothermic condition of an animal organism to depend main- 

 ly on the chemical changes taking place within it, chief among which 

 is the oxidation of the blood, which requires some form of contact be- 

 tween the blood and the air, and therefore some form of respiration. 

 If, however, future researches should destroy this latter concept — if it 

 should be shown that the heat of a living body may be produced in 

 sufficient quantity by mechanical agencies, such as friction — a non- 

 respiring warm-blooded animal would at once become conceivable. 



Mill not only refuses to recognize the distinction between what 

 maybe conceived and what maybe represented in imagination, but 

 he also ignores the distinction between the cases of inconceivability 

 from the one or the other of the two causes just mentioned ; and he 

 maintains that all conceivability whatever is relative. The examples 

 which he discusses at length are all cases of inconceivability, and not 

 of unimaginability, and I propose to notice the more important of 

 them in passing. The most noteworthy of these examples is the in- 

 conceivability of a round square. In order not to do Mill injustice, it 

 will be best to quote his own language (" Examination of the Philoso- 

 phy of Sir W. Hamilton," vol. i., p. 88, et seq., American edition) : 



" We cannot conceive a round square," says Mill, " not merely be- 

 cause no such object has ever presented itself in our experience, for 

 that would not be enough. Neither, for any thing we know, are the 

 two ideas in themselves incompatible. To conceive a round square, 

 or to conceive a body all black and yet all white, would only be to 

 conceive two different sensations as produced in us simultaneously by 

 the same object — a conception familiar to our experience — and we 

 should probably be as well able to conceive a round square as a hard 

 square, or a heavy square, if it were not that in our uniform experience, 

 at the instant when a thing begins to be round, it ceases to be square, 



