Employ an online or offline tutor at your own risk from
AU:
tutorfinder.com.au
CDN : findatutor.ca
CDN: .i-tutor.ca
CDN: Montreal Tutors
NZ: findatutor.co.nz
UK: tutorhunt.com
UK: tutors4me.co.uk
USA: wiziq.com
USA: ziizoo.com
|
|
YOU are better than YOU think. Show yourself how:
|
// _ _ \\
/\ /\
<| (o) (o) |>
\ | | /
-/[]\-
||
/ \_
||||||||||||||||||||||||||||
Logic
Mastery
Amazing, Amusing, Amorous, Delicious, Delightful, Edifying,
Strengthening Elixir.
It eases work & learning difficulties Makes the hard easier. Opens eyes.
Leads to greater precision.
in reading and
writing
Do not leave here without it - Logic
mastery will develops critical thinking, improve reading and writing,
and give a firmer base for work and studies at many levels. Good luck.
|
// _ _ \\
/\ /\
<| (o) (o) |>
| |
| |
\
/
\ = /
|
Caution: Site advice is approximately
correct, for some circumstances, not all. Site How-TOs are logically
developed, but not tried and tested. That leaves room for thought and
refinement.. |
-/[]\-
||
_ / \
||||||||||||||||||||||||||||
After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
linear2007 Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
For online automated help in senior high school maths & calculus,
visit quickmath.com For Automatic
Calculus and Algebra Help with derivatives, integrals, graphs, linear equations,
matrix algebra, visit calc101.com
With overlap, each site quickmath
& calc101offers a different range of
services, some free, some not, all based on webmathematica. Good luck.
|
Explore collaborative whiteboards from
groupboard, twiddla or
scriblink.
|
| |
Deductive, Inductive or Empirical Reason
Previous: Linking
or Chaining Several Rules Together
Deductive 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: [ Direct and Indirect Usage of a Single Rule ] [ Linking and Chaining Two Rules Together ] [ Linking and Chaining Several Rules Together ] [ Deductive, Inductive or Empirical Reason ] [ Chapter 6, Chains of Reason (Deductive Reason), Pattern Based Reason ] [ Linking and Chaining ] [ Putting Several Rules Together ] [ Deductive ]
Next: Chapter 7, Longer
Chains of Reason
| |
www.whyslopes.com
Volume 1A, Pattern Based Reason
Chapters 1 to 24
FOREWORD
Three Remarks
1 Introduction
2 Communication
3. Elements of Reason
4 Implication Rules
5. Deception
6 Chains of Reason
7 Longer Chains
For & From Consistency
8. Language Change
9 Next Chapters
10 Responsibility
11 Accidental Patterns
12 Knowledge Islands
13 Euclidean Logic
14 Deductive
& Empirical
Views of Mathematics
15 Objectivity
16 Origin of Rules
and Patterns
17 Objective Ways
18. Waking up
19. Symbols & Logic
20. Pronouns or Symbols
21. Truth Tables I.
22. Truth Tables II
22. Biconditional
22. Contrapositive
23. IF-THEN table
24. Indirect Reason Again
To reason often means to persuade someone of
the need for an idea or action. That someone could be yourself. So be
careful.
1A Logic Postscripts
- online only
+Proof by
Absurdity alias proof by contradiction
+How the demand
for consistency supports the law of the excluded middle
+Reality versus or with the aid of Imagination
+Links for reason, logic and crtical thinking
+Three Remarks
+History
Lost or Missing
There is a difference between
knowing how to spend money,
and having money to spend.
There is likewise a difference
between mastering a skill
and having meeting a situation in which it applies.
.
|