1. VENNS DIAGRAM METHOD FOR TESTING CATEGORICAL SYLLOGISM

2. ASSISTANT PROFESSOR OF PHILOSOPHY WOMEN’S COLLEGE, TINSUKIA
A PRESENTATION BY
DR. BUDUL CHANDRA DAS.
ASSISTANT PROFESSOR OF PHILOSOPHY
WOMEN’S COLLEGE, TINSUKIA
TINSUKIA –
ASSAM

3. CONCEPT OF CLASS IN VENN’S DIAGRAM
INSIDE THE CIRLE WILL INDICATE THE CLASS OF
“MEN”
AND
OUTSIDE OF IT WILL INDICATE THE CLASS OF
“NON-MEN”
IN VENN’S DIAGRAM CIRCLES REPRESENT CLASS
AND
MEN
ONE CIRCLE
REPRESENT
TWO CLASSES
NON-MEN
LET THE ABOVE CIRCLE REPRESENT THE CLASS OF MEN
THUS IT WILL REPRESENT TWO CLASSES “MEN” & “NON-MEN”

4. TWO OVERLAPPING CIRCLES WILL REPRESENT FOUR CLASSES
USING
“M”
FOR
“MUSICIAN”
&
“S”
“SINGER”
LET US CONSIDER THESE
TWO CIRCLES REPRESENTING THE CLASSES OF
“MUSICIAN”
&
“SINGER”
Means
Only
Musician
but
Not-Singer M M S S
Means
Not-Musicians
but
Only
Singer
M but
Not-S
M but
Not-S MS MS
Not-M but S
Not-M but S
Neither M nor-S
Neither M nor-S
Who are both
Musician
&
Singer
THESE ARE THE 4
CLASSES
THESE ARE THE 4
CLASSES
Who are neither
Musician
nor
Singer
NOW THE FOUR CLASSES WILL BE

5. THREE OVERLAPPING CIRCLES WILL PRODUCE 8 (EIGHT) CLASSES
A CLASS OF THOSE WHO ARE MUSICIAN
SINGER
& LYRICIST AT THE SAME TIME
A CLASS OF THEM WHO ARE NITHER MUSICIAN NOR SINGER NOR LYRICIST
MEANS
WHO ARE MUSICIAN BUT NEITHER SINGER NOR LYRICIST
MEANS
WHO ARE SINGER BUT NEITHER MUSICIAN NOR LYRICIST
MEANS
WHO ARE MUSICIAN & SINGER
BUT NOT LYRICIST
MEANS
WHO ARE LYRICIST
& SINGER
BUT NOT MUSICIAN M S
M&S
But Not-L
S but neither M nor L
M but neither S nor L
MSL
L&M
But Not-S
L&S
But Not-M
L but
neither M norS
Neither M nor L nor S L
NOW THE PRODUCED 8 CLASSES ARE AS SHOWN
LET THE CIRCLES REPRESENTING THE CLASSES ARE MUSICIAN (M), SINGER (S) & LYRICIST (L)
MEANS WHO ARE LYRICIST & MUSICIAN BUT NOT SINGER
MEANS WHO ARE LYRICIST & MUSICIAN BUT NOT SINGER
MEANS WHO ARE LYRICIST & MUSICIAN BUT NOT SINGER
MEANS WHO ARELYRICIST BUT NEITHER MUSICIAN NOR SINGER

6. THREE OVERLAPPING CIRCLES WILL PRODUCE 8 (EIGHT) CLASSESM S
S but neither M nor L
M&S
But Not-L
M but neither S nor L
THESE ARE THE 8 CLASSES PRODUCED BY 3 OVERL-APPING CIRCLES
MSL
L&M
But Not-S
L&S
But Not-M
L but
neither M norS
Neither M nor L nor S L

7. Customary in venn’s diagram HORIZENTAL PARRALLEL LINES REPRESENTSX
X - MARK
REPRESENTS A
“NON-EMTY CLASS”
HORIZENTAL PARRALLEL LINES REPRESENTS
“EMPTY CLASS”

8. Diagram of the 4 standard-form categorical propositions
: "All Singers are Musician"
A Proposition
Symbolically : "All S are M S M
MEANS THOSE ARE SINGER ARE ALSO MUSICIAN
i.e.
S but Not-M
NOW THE PORTION WHICH IS OF SINGER
BUT
NOT OF MUSICIAN
WILL BE
EMPTY
i.e.
Thus the Venn's diagrammatic Equation for A-Proposition will be: ‾‾
SM=0

9. CAN NOT BE THE MEMBER OF THE CLASS OF MUSICIAN
E Proposition
: “No Singers are Musician"
Symbolically : “ No S are M ” S M
MEANS THOSE
WHO ARE SINGER
CAN NOT BE THE MEMBER OF THE CLASS OF MUSICIAN
i.e. SM
Thus the Venn's diagrammatic Equation for A-Proposition will be:
SM = 0

10. X SM = 0 : “Some Singers are Musician"
I Proposition
: “Some Singers are Musician"
Symbolically : “ Some S are M ” S M
MEANS THERE ARE SOME MEMBERS WHO ARE SINGER & ALSO MUSICIAN
THIS CLASS OF SINGER AND MUSICIAN WILL BE NON-EMPTY SM X
Thus the Venn's diagrammatic Equation for
I-Proposition will be:
SM = 0

12. Diagram of the four standard-form categorical propositions
A Proposition: "All Singers are Musician"
or : "All S are M"
SINGER
MUSICIAN
S but not-M

13. Diagram of or : “ No S are M"
E Proposition: “ No Singers are Musician"
or : “ No S are M"
SINGER
MUSICIAN
S M

14. Diagram of I Proposition : “Some Singers are Musician"
or : “Some S are M"
MUSICIAN
SINGER SM X
VENNS DIAGRAM EQUATION FOR ‘O’ PROPOSITION : S M = O

15. Diagram of O Proposition : “Some Singers are not Musician"
or : “Some S are not M"
MUSICIAN
SINGER X
S but not- M
VENNS DIAGRAM EQUATION FOR ‘O’ PROPOSITION : S M = O

16. TESTING A CATEGORICAL SYLLOGISM
Convert the argument as per equations
Draw 3 overlapping circles
Diagram the universal premise first
Diagram the other premise
See whether the diagram corresponds to what the
conclusion asserts
If so, the syllogism is valid; if not, it is invalid.

17. Testing a Categorical Syllogisms
(A) All Singers are Musician
(A) All Musician are Lyricist or
(A) Therefore, All Lyricist are Musician
(A) All S are M
(A) All M are L or
(A) Therefore, All L are M
(A) S M = O
M L = O
(A) L M = O

18. L S M (A) S M = O (A) M L = O (A) L M = O DIAGRAM OF 1st PREMISE S L M
2nd PREMISE
( The Conclusion demanding portion)
Not corresponding to the
demand of the Conclusion.
So, the argument is INVALID M

19. demand of the Conclusion. So, the argument is VALID
ANOTHER ARGUMENT
Some Reformers are Fanatics Some R are F R F = O
All Reformers are Idealists All R are I R I = O
Some Idealists are Fanatics Some I are F I F = O F I
The Conclusion demanding portion
FIR
I F
Diagram of the
Universal
proposition
1st
FIR X
Corresponds here the
demand of the Conclusion.
So, the argument is VALID R

20. THANKS TO ALL OF YOU