ABSTRACT
Today it is easy to think of a doctrine of abstract ideas as above all an element in empiricist theories of concept-acquisition, but the notion was just as closely and naturally associated with the Cartesian conception of the methodical analysis of the complex into the simple. As abstraction was explained in the Port Royal Logic, 'because of the limited scope of our minds, we are unable to understand perfectly even things which are only slightly complex unless we can consider these things part by part or with respect to their different aspects'. In its proper sense, according to the Logic, 'abstraction' is not the distinction of parts which can actually stand alone, but the distinction of inseparable aspects, as 'when we consider a mode without paying attention to its substance', or attend to just one dimension of three-dimensional space. Hence geometers do not postulate the existence of lines without breadth, they simply 'consider length without paying attention to breadth'. By abstraction we can arrive at the determinable essences of substances, although such essences only actually exist with determinate
modifications. If I attend equally to all the accidental characteristics of an equilateral triangle drawn on paper, then 'I shall have an idea of that particular triangle alone'. But if I focus on its being 'a figure bounded by three equal lines', then 'my idea will represent all other equilateral triangles'. If I disregard the equality of the sides, then it will represent all triangles whatsoever. Thus I can ascend by degrees to an idea of extension itself.' The discussion prepares for the conclusion that abstraction explains the difference between universal and particular ideas, between those ideas which represent many objects, and those which represent just one object. But it is also taken to explain an Aristotelian doctrine of some importance (as it will be found in Volume II) in the interpretation of Locke. That is the doctrine of predicables, which draws the distinctions between species, genus, difference, property and accident. The fact that we can draw these distinctions in thought does not show in any particular case in which we apply them that we have grasped what the scientists need to know, 'the true genera of things, the true species of each genus, the true differences of species, the true properties'.46
