Page:Mind (Old Series) Volume 11.djvu/208

 CONCEIVABILITY AND THE INFINITE. 197 applying it to an operation the existence of which Mill has in so many words admitted. The last author whom I will quote is Prof. Bain : I will take some passages from the chapter on Abstraction in his Mental and Moral Science pp. 176-8, where he supports the Nominalistic doctrine : " We are able to attend to the points of agreement of resembling things, and to neglect the points of difference ; as when we think of the light of luminous bodies, or the roundness of round bodies. This power is named Abstraction. " It is a fact that we can direct our attention, or our thoughts, to the points of agreement of bodies that agree. We can think of the light of the heavenly bodies, and make assertions, and draw inferences respecting it. So we can think of the roundness of spherical bodies, and discard the con- sideration of their colour and size. In such an object as the full moon, we can concentrate our regards upon its luminous character, wherein it agrees with one class of objects ; or upon its figure, wherein it agrees with another class of objects. We can think of the taste of a strawberry, either as agree- ing with other tastes, or as agreeing with pleasures generally " Every concrete thing falls into as many classes as it has attributes ; to refer it to one of these classes, and to think of the corresponding attribute, are one mental operation. " When a concrete thing before the view recalls others agreeing in a certain point, our attention is awake upon that point ; when the moon recalls other luminous bodies, we are thinking of its light ; when it recalls other round bodies, we are thinking of its roundness. The two operations are not different but identical. "On this supposition, to abstract, or to think of a property in the abstract, is to classify under some one head. To abstract the property of transparency from water, is to recall, at the instance of water, window glass, crystal, air, &c. ; to abstract its liquidity, is to recall milk, vinegar, melted butter, mercury, &c. ; to abstract its weight, is to bring it into comparison with other kinds of gravitating matter. " Hence abstraction does not properly consist in the mental separation of one property of a thing from the other properties as in thinking of the roundness of the moon apart from its luminosity and apparent magnitude. Such a separation is impracticable ; no one can think of a circle without colour and a definite size. All the purposes of the abstract idea are served by conceiving a concrete thing in company with others resembling it in the attribute in question ; and by affirming nothing, of the one concrete, but what is true of all those others " In abstract reasoning, therefore, we are not so much engaged with any single thing, as with a class of things. When we are discussing government, we commonly have in view a number of governments, alter- nately thought of ; if we notice in any one government a certain feature, we run over the rest in our mind, to see if the same feature is present in all. There is no such thing as an idea of government in the abstract;, there is only possible a comparison of governments in the concrete ; the abstraction is the likeness or community of the individuals." It will be noticed that throughout this extract Prof. Bain does not distinguish between those elements of an act which come out into a clear consciousness, and the elements which do not so come out but are nevertheless necessary to the