# Category Archives: Induction

## Functional Logic • Inquiry and Analogy • 12

Inquiry and Analogy • Higher Order Propositional Expressions Interpretive Categories for Higher Order Propositions (n = 1) Table 12 presents a series of interpretive categories for the higher order propositions in Table 11.  I’ll leave these for now to the reader’s … Continue reading

## Functional Logic • Inquiry and Analogy • 11

Inquiry and Analogy • Higher Order Propositional Expressions Higher Order Propositions and Logical Operators (n = 1) A higher order proposition is a proposition about propositions.  If the original order of propositions is a class of indicator functions then the … Continue reading

## 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 and … Continue reading

## Functional Logic • Inquiry and Analogy • 9

Inquiry and Analogy • Dewey’s “Sign of Rain” • An Example of Inquiry We turn again to Dewey’s vignette, tracing figures of logic on grounds of semiotic. A man is walking on a warm day.  The sky was clear the … Continue reading

## Functional Logic • Inquiry and Analogy • 8

Inquiry and Analogy • Dewey’s “Sign of Rain” • An Example of Inquiry To illustrate the role of sign relations in inquiry we begin with Dewey’s elegant and simple example of reflective thinking in everyday life. A man is walking … Continue reading

## Functional Logic • Inquiry and Analogy • 7

Inquiry and Analogy • Peirce’s Formulation of Analogy • Version 2 C.S. Peirce • “A Theory of Probable Inference” (1883) The formula of the analogical inference presents, therefore, three premisses, thus: are a random sample of some undefined class of … Continue reading

## Functional Logic • Inquiry and Analogy • 6

Inquiry and Analogy • Peirce’s Formulation of Analogy • Version 1 C.S. Peirce • “On the Natural Classification of Arguments” (1867) The formula of analogy is as follows: are taken at random from such a class that their characters at … Continue reading

## Functional Logic • Inquiry and Analogy • 5

Inquiry and Analogy • Aristotle’s “Paradigm” • Reasoning by Analogy Aristotle examines the subject of analogical inference or “reasoning by example” under the heading of the Greek word παραδειγμα, from which comes the English word paradigm.  In its original sense … Continue reading

## Functional Logic • Inquiry and Analogy • 4

Inquiry and Analogy • Aristotle’s “Apagogy” • Abductive Reasoning Peirce’s notion of abductive reasoning is derived from Aristotle’s treatment of it in the Prior Analytics.  Aristotle’s discussion begins with an example which may seem incidental but the question and its … Continue reading

## Functional Logic • Inquiry and Analogy • 3

Inquiry and Analogy • Comparison of the Analyses The next two Figures will be of use when we turn to comparing the three types of inference as they appear in the respective analyses of Aristotle and Peirce. Types of Reasoning … Continue reading