ravinderkumar
Transformed RAVAL’S NOTATIONs for Aristotle’s syllogism
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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.
Method:
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)
There are 256 possible types of syllogisms (or 512 if the order of the major and minor premises is changed, though this makes no difference logically). The differing positions of the major, minor, and middle terms gives rise to another classification of syllogisms known as the figure Each premise and the conclusion can be of type A, E, I or O, and the syllogism can be any of the four figures. A syllogism can be described briefly by giving the letters for the premises and conclusion followed by the number for the figure. The vast majority of the 256 possible forms of syllogism are invalid (the conclusion does not follow logically from the premises). The table below shows the valid forms.
Figure 1 Figure 2 Figure 3 Figure 4
Barbara Cesare Datisi Calemes
Celarent Camestres Disamis Dimatis
Darii Festino Ferison Fresison
Ferio Baroco Bocardo Calemos
Barbari Cesaro Felapton Fesapo
Celaront Camestros Darapti Bamalip
AAA -1 Barbara By Raval’s notations
All M are P MM – P
All S are M SS – M
Concl: All S are P SS – P
EAE -1 Celarent By Raval’s notations
No M is P MM / PP
All S are M SS – M
Concl: No S is P SS / PP
AII-1 Darii By Raval’s notations
All M are P MM - P
Some S are M S – M
Concl: Some S are P S - P
EIO – 1 Ferio By Raval’s notations
No M is P MM / PP
Some S are M S – M
Concl: Some S are not P S / PP
AAI -1 Barbari By Raval’s notations
All M are P MM - P
All S are M SS - M
Concl: Some S are P S - P
EAO – 1 Celarant By Raval’s notations
No M is P MM / PP
All S are M SS – M
Concl: Some S are not P S / PP
EAE – 2 Cesare By Raval’s notations
No P is M PP / MM
All S are M SS – M
Concl: No S is P SS / PP
AEE – 2 Camestres By Raval’s notations
All P are M PP - M
No S is M SS / MM
Concl: No S is P SS / PP
EIO – 2 Festino By Raval’s notations
No P is M PP / MM
Some S are M S - M
Concl: Some S are not P S / PP
AOO – 2 Baroco By Raval’s notations
All P are M PP - M
Some S are not M S / MM
Concl: Some S are not P S / PP
EAO -2 Cesaro By Raval’s notations
No P is M PP / MM
All S are M SS - M
Concl: Some S are not P S / PP
AEO – 2 Camestros By Raval’s notations
All P are M PP - M
No S is M SS / MM
Concl: Some S are not P S / PP
AII – 3 Datisi By Raval’s notations
All M are P MM - P
Some M are S M - S
Concl: Some S are P S - P
IAI – 3 Disamis By Raval’s notations
Some M are P M - P
All M are S MM - S
Concl: Some S are P S - P
EIO – 3 Ferison By Raval’s notations
No M is P MM / PP
Some M are S M - S
Concl: Some S are not P S / PP
OAO – 3 Bocardo By Raval’s notations
Some M are not P M / PP
All M are S MM - S
Concl: Some S are not P S / PP
EAO -3 Felapton By Raval’s notations
No M is P MM / PP
All M are S MM - S
Concl: Some S are not P S / PP
AAI – 3 Darapti By Raval’s notations
All M are P MM - P
All M are S MM - S
Concl: Some S are P S - P
AEE -4 Calemes By Raval’s notations
All P are M PP - M
No M is S MM / SS
Concl: No S is P SS / PP
IAI -4 Dimatis By Raval’s notations
Some P are M P - M
All M are S MM - S
Concl: Some S are P S - P
EIO -4 Fresison By Raval’s notations
No P is M PP / MM
Some M are S M - S
Concl: Some S are not P S / PP
AEO-4 Calemos By Raval’s notations
All P are M PP - M
No M is S MM / SS
Concl: Some S are not P S / PP
EAO -4 Fesapo By Raval’s notations
No P is M PP / MM
All M are S MM - S
Concl: Some S are not P S / PP
AAI -4 Bamalip By Raval’s notations
All P are M PP - M
All M are S MM - S
Concl: Some S are P S - P
Syllogism conclusion by new Transformed Raval’s Notations is in accordance with Aristotle’s rules for the same. It is visually very transparent and conclusions can be deduced at a glance, moreover it solves syllogism problems with any number of statements and it is quickest of all available methods .Venn and Euler introduced their respective methods for categorical syllogism considering Aristotle method very cumbersome. By new Transformed Raval method for solving categorical syllogism, solving categorical syllogism is as simple as pronouncing ABC and it is just continuance of Aristotle work on categorical syllogism. Any apology for the method pursued would be either needless or useless. It is in accordance with Aristotle’s rules for categorical syllogism. Author wants acknowledgement of new Transformed Raval notation method by concerned scholars of the subject.
For any further suggestions/queries
Please revert back to
raval.syllogism@gmail.com
.
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.
Method:
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)
There are 256 possible types of syllogisms (or 512 if the order of the major and minor premises is changed, though this makes no difference logically). The differing positions of the major, minor, and middle terms gives rise to another classification of syllogisms known as the figure Each premise and the conclusion can be of type A, E, I or O, and the syllogism can be any of the four figures. A syllogism can be described briefly by giving the letters for the premises and conclusion followed by the number for the figure. The vast majority of the 256 possible forms of syllogism are invalid (the conclusion does not follow logically from the premises). The table below shows the valid forms.
Figure 1 Figure 2 Figure 3 Figure 4
Barbara Cesare Datisi Calemes
Celarent Camestres Disamis Dimatis
Darii Festino Ferison Fresison
Ferio Baroco Bocardo Calemos
Barbari Cesaro Felapton Fesapo
Celaront Camestros Darapti Bamalip
AAA -1 Barbara By Raval’s notations
All M are P MM – P
All S are M SS – M
Concl: All S are P SS – P
EAE -1 Celarent By Raval’s notations
No M is P MM / PP
All S are M SS – M
Concl: No S is P SS / PP
AII-1 Darii By Raval’s notations
All M are P MM - P
Some S are M S – M
Concl: Some S are P S - P
EIO – 1 Ferio By Raval’s notations
No M is P MM / PP
Some S are M S – M
Concl: Some S are not P S / PP
AAI -1 Barbari By Raval’s notations
All M are P MM - P
All S are M SS - M
Concl: Some S are P S - P
EAO – 1 Celarant By Raval’s notations
No M is P MM / PP
All S are M SS – M
Concl: Some S are not P S / PP
EAE – 2 Cesare By Raval’s notations
No P is M PP / MM
All S are M SS – M
Concl: No S is P SS / PP
AEE – 2 Camestres By Raval’s notations
All P are M PP - M
No S is M SS / MM
Concl: No S is P SS / PP
EIO – 2 Festino By Raval’s notations
No P is M PP / MM
Some S are M S - M
Concl: Some S are not P S / PP
AOO – 2 Baroco By Raval’s notations
All P are M PP - M
Some S are not M S / MM
Concl: Some S are not P S / PP
EAO -2 Cesaro By Raval’s notations
No P is M PP / MM
All S are M SS - M
Concl: Some S are not P S / PP
AEO – 2 Camestros By Raval’s notations
All P are M PP - M
No S is M SS / MM
Concl: Some S are not P S / PP
AII – 3 Datisi By Raval’s notations
All M are P MM - P
Some M are S M - S
Concl: Some S are P S - P
IAI – 3 Disamis By Raval’s notations
Some M are P M - P
All M are S MM - S
Concl: Some S are P S - P
EIO – 3 Ferison By Raval’s notations
No M is P MM / PP
Some M are S M - S
Concl: Some S are not P S / PP
OAO – 3 Bocardo By Raval’s notations
Some M are not P M / PP
All M are S MM - S
Concl: Some S are not P S / PP
EAO -3 Felapton By Raval’s notations
No M is P MM / PP
All M are S MM - S
Concl: Some S are not P S / PP
AAI – 3 Darapti By Raval’s notations
All M are P MM - P
All M are S MM - S
Concl: Some S are P S - P
AEE -4 Calemes By Raval’s notations
All P are M PP - M
No M is S MM / SS
Concl: No S is P SS / PP
IAI -4 Dimatis By Raval’s notations
Some P are M P - M
All M are S MM - S
Concl: Some S are P S - P
EIO -4 Fresison By Raval’s notations
No P is M PP / MM
Some M are S M - S
Concl: Some S are not P S / PP
AEO-4 Calemos By Raval’s notations
All P are M PP - M
No M is S MM / SS
Concl: Some S are not P S / PP
EAO -4 Fesapo By Raval’s notations
No P is M PP / MM
All M are S MM - S
Concl: Some S are not P S / PP
AAI -4 Bamalip By Raval’s notations
All P are M PP - M
All M are S MM - S
Concl: Some S are P S - P
Syllogism conclusion by new Transformed Raval’s Notations is in accordance with Aristotle’s rules for the same. It is visually very transparent and conclusions can be deduced at a glance, moreover it solves syllogism problems with any number of statements and it is quickest of all available methods .Venn and Euler introduced their respective methods for categorical syllogism considering Aristotle method very cumbersome. By new Transformed Raval method for solving categorical syllogism, solving categorical syllogism is as simple as pronouncing ABC and it is just continuance of Aristotle work on categorical syllogism. Any apology for the method pursued would be either needless or useless. It is in accordance with Aristotle’s rules for categorical syllogism. Author wants acknowledgement of new Transformed Raval notation method by concerned scholars of the subject.
For any further suggestions/queries
Please revert back to
raval.syllogism@gmail.com