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==2. Functional Conception of Quantification Theory==
==2. 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 determined elements. Merely to write down quantified notations like <math>\forall_{x \in X} F(x)</math> and <math>\exists_{x \in X} F(x)</math> involves a subscription to such notions, as shown by the membership relations invoked in their indices. Reflected on pragmatic and constructive principles, these ideas begin to appear as problematic hypotheses whose warrants to be granted are not beyond question, as projects of exhaustive determination that overreach the powers of finite information and control to manage. Consequently, it is worth
Up till now quantification theory has been based on the assumption of
considering how we might shift the medium of quantification theory closer to familiar ground, toward the predicates themselves that represent our continuing acquaintance with phenomena.
individual variables ranging over universal collections of perfectly
determined elements. Merely to write down quantified notations like
subscription to such notions, as shown by the membership relations
invoked in their indices. Reflected on pragmatic and constructive
principles, these ideas begin to appear as problematic hypotheses
whose warrants to be granted are not beyond question, as projects
of exhaustive determination that overreach the powers of finite
information and control to manage. Consequently, it is worth
considering how we might shift the medium of quantification
theory closer to familiar ground, toward the predicates
themselves that represent our continuing acquaintance
with phenomena.
===2.1. Higher Order Propositional Expressions===
===2.1. Higher Order Propositional Expressions===
<pre>
By way of equipping this inquiry with a bit of concrete material, I begin
By way of equipping this inquiry with a bit of concrete material, I begin
with a consideration of "higher order propositional expressions" (HOPE's),
with a consideration of "higher order propositional expressions" (HOPE's),