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YOU are better than YOU think. Show yourself how:
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-/[]\- Logic chapters 1 to 5 re- appear not in sequence, as is or longer, in Volume 1A, Pattern Based Reason, Bon Appetite. Logic
Mastery Logic mastery makes the hard, easier. Logic mastery leads to better, stronger and richer comprehension. Logic mastery improves reading and writing. Logic mastery ease learning difficulties. Logic mastery gives a headstart. In sum, logic mastery will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck. After logic, (a) continue reading Three Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving liinear Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes & More Math, chapters 2 to 6;
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-/[]\- What may be learnt and when depends on how skills and concepts are developed. Making the hard easier and clearer will allow earlier & richer development of skills and concepts. Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice. |
Deductive, Inductive or Empirical ReasonDeductive 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. Criteria for the recognition of reliable, non-accidental rules and patterns are described later in the chapter Origin of Rules and Patterns.
Chapter Subsections: Next: Chapter 7, Longer Chains of Reason
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