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==1. Three Types of Reasoning==

==1. Three Types of Reasoning==

'''''(This section has been omitted from the present copy.)'''''

'''''(This section has been omitted from the present copy.)'''''

===1.1. Types of Reasoning in Aristotle===

===1.1. Types of Reasoning in Aristotle===

(See Figure 1.) &hellip;

(See Figure 1.) &hellip;

===1.2. Types of Reasoning in C.S. Peirce===

===1.2. Types of Reasoning in C.S. Peirce===

===1.3. Comparison of the Analyses===

===1.3. Comparison of the Analyses===

===1.4. Aristotle's "Apagogy" : Abductive Reasoning as Problem Reduction===

===1.4. Aristotle's "Apagogy" : Abductive Reasoning as Problem Reduction===

===1.5. Aristotle's "Paradigm" : Reasoning by Analogy or Example===

===1.5. Aristotle's "Paradigm" : Reasoning by Analogy or Example===

===1.6. Peirce's Formulation of Analogy===

===1.6. Peirce's Formulation of Analogy===

===1.7. Dewey's "Sign of Rain" : An Example of Inquiry===

===1.7. Dewey's "Sign of Rain" : An Example of Inquiry===

==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 determinate elements.  Merely to write down quantified formulas 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, however, these ideas begin to appear as problematic hypotheses whose warrants are not beyond question, projects of exhaustive determination that overreach the powers of finite information and control to manage.  Therefore, it is worth considering how we might shift the scene of quantification theory closer to familiar ground, toward the predicates themselves that represent our continuing acquaintance with phenomena.

Up till now quantification theory has been based on the assumption of individual variables ranging over universal collections of perfectly determinate elements.  Merely to write down quantified formulas 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, however, these ideas begin to appear as problematic hypotheses whose warrants are not beyond question, projects of exhaustive determination that overreach the powers of finite information and control to manage.  Therefore, it is worth considering how we might shift the scene of quantification theory closer to familiar ground, toward the predicates themselves that represent our continuing acquaintance with phenomena.