Clippings

Classical mathematics comprises an objectivist universe. It has entities that are clearly distinguished from one another, e.g., numbers. Mathematical entities have inherent properties, e.g., three is odd. And there are fixed relationships among those entities, e.g., nine is the square of three. Mathematical logic was developed as part of the enterprise of providing foundations for classical mathematics. Formal semantics also developed out of that enterprise. The models used in formal semantics are examples of what we will call “objectivist models” — models appropriate to universes of discourse where there are distinct entities which have inherent properties and where there are fixed relationships among the entities.

But the real world is not an objectivist universe, especially those aspects of the real world having to do with human beings: human experience, human institutions, human language, the human conceptual system. What it means to be a hard-core objectivist is to claim that there is an objectivist model that fits the world as it really is. We have just argued that objectivist philosophy is empirically incorrect in that it makes false predictions about language, truth, understanding, and the human conceptual system. On the basis of this we have claimed that objectivist philosophy provides an inadequate basis for the human sciences. Nonetheless, a lot of remarkably insightful mathematicians, logicians, linguists, psychologists, and computer scientists have designed objectivist models for use in the human sciences. Are we claiming that all of this work is worthless and that objectivist models have no place at all in the human sciences?

We are claiming no such thing. We believe that objectivist models as mathematical entities do not necessarily have to be tied to objectivist philosophy. One can believe that objectivist models can have a function — even an important function — in the human sciences without adopting the objectivist premise that there is an objectivist model that completely and accurately fits the world as it really is. But if we reject this premise, what role is left for objectivist models?

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…it is one thing to impose a single objectivist model in some restricted situations and to function in terms of that model — perhaps successfully; it is another to conclude that the model is an accurate reflection of reality. There is a good reason why our conceptual systems have inconsistent metaphors for a single concept. The reason is that there is no one metaphor that will do. Each one gives a certain comprehension of one aspect of the concept and hides others. To operate only in terms of a consistent set of metaphors is to hide many aspects of reality. Successful functioning in our daily lives seems to require a constant shifting of metaphors. The use of many metaphors that are inconsistent with one another seems necessary for us if we are to comprehend the details of our daily existence.

One obvious utility for the study of formal objectivist models in the human sciences is that they can allow us to understand, in part, the ability to reason and function in terms of a consistent set of metaphors. This is a common activity and an important one to understand. It can also allow us to see what can be wrong with imposing a requirement of consistency — to see that any consistent set of metaphors will most likely hide indefinitely many aspects of reality — aspects that can be highlighted only by other metaphors that are inconsistent with it.