Traditional logic simplified
Term logic, also known as traditional logic or Aristotelian
logic
For Rapid Reasoning The fundamental assumption in behind traditional logic theory is that propositions are composed
of two terms – hence the name "two-term theory" or "term
logic" – and that the reasoning process is in turn built from
propositions:
The syllogism is an inference in which one proposition(the
"conclusion") follows of necessity from two others (the
"premises").
A proposition may be universal or particular, and it may be affirmative or
negative. Traditionally, the four kinds of propositions are:
A-type: Universal and affirmative
("Every philosopher is mortal")
I-type: Particular and affirmative
("Some philosopher is mortal")
E-type: Universal and negative
("Every philosopher is immortal")
O-type: Particular and negative
("Some philosopher is immortal")
A categorical syllogism contains precisely three terms: the
major term, which is the predicate of the conclusion; the minor term, the
subject of the conclusion; and the middle term, which appears in both premises
but not in the conclusion.
Aristotle noted
following five basic rules governing the validity of categorical syllogisms
1. The middle term must be distributed at least once
(distributed term refers to all members of the denoted class, as in all S are P
and no S is P).
2. A term distributed in the conclusion must be
distributed in the premise in which it occurs.
3. Two negative premises imply no valid conclusion.
4. If one premise is negative, then the conclusion must
be negative.
5. Two affirmatives imply an affirmative.
Solving
Syllogism problems are usually moderate time consuming by Traditional methods and considered difficult by most of
the students. New Transformed RAVAL’S
NOTATION solves Syllogism problems very quickly and accurately. This method
solves any categorical syllogism problem with same ease and is as simple as
ABC…
In Transformed RAVAL’S NOTATION, each premise
and conclusion is written in abbreviated form, and then conclusion is reached
simply by connecting abbreviated premises.
NOTATION:
Statements (both premises and conclusions) are represented as follows:
Statement Notation
a) All S are P SS-P
b) Some S are P S-P
c) Some S are not P S / PP
d) No S is P SS / PP
(- implies are and / implies are not)
All is
represented by double letters; Some is represented by single letter. Some S are not P is
represented as S / PP. No S is P implies No P is S so its notation contains double letters on both
sides.
RULES: (1)
Conclusions are reached by connecting Notations. Two notations can be linked
only through common linking terms.
When the common linking term multiplies (becomes double from single), divides
(becomes single from double) or remains double then conclusion is arrived
between terminal terms. (Aristotle’s
rule: the middle term must be distributed at least once).
(2)If both statements linked are having –
signs, resulting conclusion carries – sign (Aristotle’s rule: two affirmatives
imply an affirmative).
(3)
Whenever statements having – and / signs are linked, resulting
conclusion carries / sign. (Aristotle’s rule: if one premise is
negative, then the conclusion must be negative).
(4)Statement
having / sign cannot be linked with another statement having / sign to derive
any conclusion. (Aristotle’s rule: Two
negative premises imply no valid conclusion).
