## Functional Logic • Inquiry and Analogy • 10

### Inquiry and Analogy • Functional Conception of Quantification Theory

Up till now quantification theory has been based on the assumption of individual variables ranging over universal collections of perfectly determinate elements.  The mere act of writing quantified formulas like $\forall_{x \in X} f(x)$ and $\exists_{x \in X} f(x)$ involves a subscription to such notions, as shown by the membership relations invoked in their indices.

As we reflect more critically on the conventional assumptions in the light of pragmatic and constructive principles, however, they begin to appear as problematic hypotheses whose warrants are not beyond question, as projects of exhaustive determination overreaching the powers of finite information and control to manage.

Thus it is worth considering how the scene of quantification theory might be shifted nearer to familiar ground, toward the predicates themselves which represent our continuing acquaintance with phenomena.

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