VENNS DIAGRAM METHOD FOR TESTING CATEGORICAL SYLLOGISM

ASSISTANT PROFESSOR OF PHILOSOPHY WOMEN’S COLLEGE, TINSUKIA A PRESENTATION BY DR. BUDUL CHANDRA DAS. ASSISTANT PROFESSOR OF PHILOSOPHY WOMEN’S COLLEGE, TINSUKIA TINSUKIA – 786125 ASSAM bcd.wc.tsk@gmail.com

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”

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

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

THREE OVERLAPPING CIRCLES WILL PRODUCE 8 (EIGHT) CLASSES M 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

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

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

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

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

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

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

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

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

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.

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

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

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

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