ABSTRACT
An important source of human knowledge is clearly classification: dividing the vast spectrum of things with which we are confronted into groups of similar, or similarly useful, things. This is a caw (and hence it can be milked), whereas that is a tiger (and thence it is advisable to avoid it). Already Aristotle saw such classifying as the very principle of our reason: his view was, as Cassirer (1910, p. 4) puts it, that "nothing is presupposed save the existence of things in their inexhaustible multiplicity, and the power of the mind to select from this wealth of particular existences those features that are common to several of them." If we have a set of objects, we can collect the properties which are shared by all the objects; and similarly if we have a single object, we can 'abstract away' some of its properties and thus reach a collection of properties which can be shared with the object by other objects. And as we often understand such a subtraction of properties as passing from the original object to a new, 'abstract' object, it is precisely abstraction in this sense which is the basis of the passage from concrete to abstract objects. This is how we get from concrete, tangible trains going from Geneva to Paris to the abstract 'Geneva-Paris train' (see Section 3.3), or from concrete lines to their 'directions' (viz. Section 3.5).48
