The Art of Logical Thinking; Or, The Laws of ReasoningAtkinson, William Walker
Philosophy
The Art of Logical Thinking; Or, The Laws of Reasoning
Atkinson, William Walker
Logic; Reasoning
The simplest form of reasoning is that known as Immediate Reasoning, by
which is meant the deduction of one proposition from another which
_implies_ it. Some have defined it as: "_reasoning without a middle
term_." In this form of reasoning _only one proposition is required for
the premise_, and from that premise the conclusion is deduced directly
and without the necessity of comparison with any other term of
proposition.
The two principal methods employed in this form of Reasoning are; (1)
Opposition; (2) Conversion.
_Opposition_ exists between propositions having the same subject and
predicate, but differing in quality or quantity, or both. The Laws of
Opposition are as follows:
I. (1) If the universal is true, the particular is true. (2) If the
particular is false, the universal is false. (3) If the universal is
false, nothing follows. (4) If the particular is true, nothing follows.
II. (1) If one of two contraries is true, the other is false. (2) If one
of two contraries is false, nothing can be inferred. (3) Contraries are
never both true, but both may be false.
III. (1) If one of two sub-contraries is false, the other is true. (2)
If one of two sub-contraries is true, nothing can be inferred concerning
the other. (3) Sub-contraries can never be both false, but both may be
true.
IV. (1) If one of two contradictories is true, the other is false. (2)
If one of two contradictories is false, the other is true. (3)
Contradictories can never be both true or both false, but always one is
true and the other is false.
In order to comprehend the above laws, the student should familiarize
himself with the following arrangement, adopted by logicians as a
convenience:
{Universal {Affirmative (A)
{ {Negative (E)
Propositions {
{ {Affirmative (I)
{Particular {Negative (O)
Examples of the above: Universal Affirmative (A): "All men are mortal;"
Universal Negative (E): "No man is mortal;" Particular Affirmative (I):
"Some men are mortal;" Particular Negative (O): "Some men are not
mortal."
The following examples of abstract propositions are often used by
logicians as tending toward a clearer conception than examples such as
given above:
(A) "All A is B."
(I) "Some A is B."
(E) "No A is B."
(O) "Some A is not B."
These four forms of propositions bear certain logical relations to each
other, as follows:
A and E are styled _contraries_. I and O are _sub-contraries_; A and I
and also E and O are called _subalterns_; A and O and also I and E are
styled _contradictories_.
Public-domain text, read in full here on John Shaqi.
Reviews
Reviews
No reviews yet
Be the first to share your thoughts on this work.
Join the Discussion
Join the discussion
Sign in to leave a comment or review.
Sign InorCreate an account