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ARISTOTLE’S SYLLOGISM AS SIMPLE AS ABC NOW
BY NEW RAVAL’S NOTATION
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Introduction
Syllogism was introduced by Aristotle (a reasoning consisting two premises and a conclusion).Aristotle gives the following definition of syllogism in his fundamental treatise Organon.
“A syllogism is discourse, in which, certain things being stated, something other than what is stated follows of necessity from their being so”. Things that have stated are known as premises and the one that follows from the premises is known as the conclusion of the syllogism.
A categorical syllogism is a type of argument with two premises and one conclusion. Each of these three propositions is one of four forms of categorical proposition.
Type Form Example
A All S are P All monkeys are mammals
E No S is P No monkeys are birds
I Some S are P Some philosophers are logicians
O Some S are not P Some logicians are not philosophers
These four type of proposition are called A,E,I,and O type propositions, the variables S and P are place-holders for terms which represent out a class or category of thing, hence the name “categorical” proposition.
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.
John Venn, an English logician, in 1880 introduced a method for analyzing categorical syllogisms, known as the Venn diagram. In a paper entitled “on the Diagrammatic and Mechanical Representation of propositions and Reasoning’s in the “philosophical magazine and journal of science,” Venn shows the different ways to represent propositions by diagrams. For categorical syllogism three overlapping circles are drawn to represent the classes denoted by the three terms. Universal propositions (all S are P, no S is P) are indicated by shading the sections of the circles representing the excluded classes. Particular propositions (some S are P, some S are not P) are indicated by placing some mark, usually an “x”, in the part of the circle representing the class whose members are specified. The conclusion may then be inferred from the diagram.
Venn diagrams has similarity with Euler diagrams, invented by Leonard Euler in the 18th century, but Venn diagrams are visually more complex than the Euler diagrams.
Solving Syllogism problems are usually time consuming by Traditional methods and considered difficult by most of the students. New 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…
Method:
In 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 / P)
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 / P) in statement notation. This statement is written uniquely in brackets because one cannot include this statement in deriving any conclusion. (Some S are not P does not imply some P are not S). 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)
(5)Whenever statement carrying / sign is involved as first statement in deducting conclusion then terminating point in statement carrying – sign should be in double letters to have any valid conclusion.
(When the terminating term is in double letters, it limits the terminating term to the maximum up to common term. Hence valid conclusion follows only in this case when / sign is involved)
BY NEW RAVAL’S NOTATION
.
Introduction
Syllogism was introduced by Aristotle (a reasoning consisting two premises and a conclusion).Aristotle gives the following definition of syllogism in his fundamental treatise Organon.
“A syllogism is discourse, in which, certain things being stated, something other than what is stated follows of necessity from their being so”. Things that have stated are known as premises and the one that follows from the premises is known as the conclusion of the syllogism.
A categorical syllogism is a type of argument with two premises and one conclusion. Each of these three propositions is one of four forms of categorical proposition.
Type Form Example
A All S are P All monkeys are mammals
E No S is P No monkeys are birds
I Some S are P Some philosophers are logicians
O Some S are not P Some logicians are not philosophers
These four type of proposition are called A,E,I,and O type propositions, the variables S and P are place-holders for terms which represent out a class or category of thing, hence the name “categorical” proposition.
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.
John Venn, an English logician, in 1880 introduced a method for analyzing categorical syllogisms, known as the Venn diagram. In a paper entitled “on the Diagrammatic and Mechanical Representation of propositions and Reasoning’s in the “philosophical magazine and journal of science,” Venn shows the different ways to represent propositions by diagrams. For categorical syllogism three overlapping circles are drawn to represent the classes denoted by the three terms. Universal propositions (all S are P, no S is P) are indicated by shading the sections of the circles representing the excluded classes. Particular propositions (some S are P, some S are not P) are indicated by placing some mark, usually an “x”, in the part of the circle representing the class whose members are specified. The conclusion may then be inferred from the diagram.
Venn diagrams has similarity with Euler diagrams, invented by Leonard Euler in the 18th century, but Venn diagrams are visually more complex than the Euler diagrams.
Solving Syllogism problems are usually time consuming by Traditional methods and considered difficult by most of the students. New 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…
Method:
In 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 / P)
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 / P) in statement notation. This statement is written uniquely in brackets because one cannot include this statement in deriving any conclusion. (Some S are not P does not imply some P are not S). 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)
(5)Whenever statement carrying / sign is involved as first statement in deducting conclusion then terminating point in statement carrying – sign should be in double letters to have any valid conclusion.
(When the terminating term is in double letters, it limits the terminating term to the maximum up to common term. Hence valid conclusion follows only in this case when / sign is involved)