Analytic Philosophy by Michael Beaney

Author:Michael Beaney [Beaney, Michael]
Language: eng
Format: epub
ISBN: 9780191083914
Publisher: Oxford University Press
Published: 2017-09-11T00:00:00+00:00

Some difficulties in saying things

Let us return once again to Frege and Russell. In Chapter 1, we saw that Frege held that there was a fundamental distinction between object and concept. Objects are what fall under (first-level) concepts, and (first-level) concepts are what apply to objects (and to which in turn higher-level concepts apply). The most basic kind of thought we can have, according to Frege, involves applying a (first-level) concept to an object, such as in thinking that Gottlob is human, and such thoughts can be readily expressed in the logical system he created—his ‘Begriffsschrift’ (‘concept-script’), as he called it. ‘Gottlob is human’, for example, can be formalized as ‘Fa’, with ‘F’ representing the concept of being human and ‘a’ the object that is Gottlob. Frege saw his Begriffsschrift as capable of expressing, in principle, every possible kind of thought. But how would we formalize his fundamental claim that there is a distinction between object and concept? We might express this in ordinary language by saying that no objects are concepts (or equivalently, that no concepts are objects), but it turns out that there is no way to represent this in Frege’s Begriffsschrift. So if this claim is seen as expressing a true thought, then this is not a thought that can be expressed in Frege’s logical language. It is a thought that seems to outstrip what we can say within such a language.

As we saw in Chapter 2, in proposing his theory of types Russell argued that a distinction should be drawn between objects, classes of objects, classes of classes of objects, and so on up the hierarchy. Once again, however, there is a problem in stating this distinction, as what can be said of objects cannot be said of classes of objects, or of higher-level classes, and vice versa. We can say that an object is a member of a certain (first-level) class—for example, that Gottlob is a member of the class of humans. We can also say that an object is not a member of a certain (first-level) class—for example, that Gottlob is not a member of the class of horses. But now imagine saying that a class is not an object (in order to try to express the distinction that Russell wants to draw)—for example, that the class of humans is not an object. This would be to say that the class of humans is not a member of the class of objects. But both these two classes are first-level classes, and a first-level class cannot be a member of another first-level class, according to Russell’s conception of a hierarchy of classes. (A first-level class can be a subclass of another first-level class, but that is a different relation.) Such talk is therefore ruled out on Russell’s view. Similar problems affect other attempts to express the distinctions reflected in Russell’s hierarchy—for example, that an object is not a class, which would be to say that an object is not a member of the class of classes.

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