Chapter 3. Chains of Reason
Deductive, Inductive or EmpiricalDeductive reason uses or chains together supposedly (or preferably) never-disobeyed implication rules to suggest, to make or to reach conclusions. See the examples above. The implication rules in question may come from assumptions. The assumptions may be tentative. The phrase inductive reason has one role in mathematics and another outside of mathematics. To induce (or induct) literally means to draw or extract. When you see a rule or pattern that no one has suggested, you are extracting or drawing that pattern from your observations. This process of recognizing rules and patterns that may hold, accidentally or not, is called inductive reasoning. Inductive reason outside of mathematics refers to the identification and recognition of rules and patterns from data and observations. Here rules and patterns may hold accidentally. Reason which relies on a single or several, experience-found, rules and patterns to arrive at conclusions is called empirical. The underlying problem of inductive, empirical reason is to extract (infer, draw, induct or identify) from experience, in particular, data and observations, rules and patterns not satisfied merely by accident and which appear to be reliable. Self-deception needs to be avoided here. Inductive reason inside mathematics refers to another process, namely, the extraction or drawing of conclusions from ladder-like chains of reason. See the next chapter for a more precise image or explanation. The rules or assumptions here are usually so certain, that we deliberately ignore the experience-based origins of mathematical reason.
Next Chapter: Longer Chains of Reason, mathematical induction
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