VENNS DIAGRAM METHOD FOR TESTING CATEGORICAL SYLLOGISM A

VENNS DIAGRAM METHOD FOR TESTING CATEGORICAL SYLLOGISM

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

CONCEPT OF CLASS IN VENN’S DIAGRAM INSIDE THE CIRLE WILL INDICATE THE CLASS OF IN VENN’S DIAGRAM “MEN” CIRCLES AND MEN REPRESENT CLASS AND OUTSIDE OF IT WILL INDICATE THE CLASS OF “NON-MEN” ONE CIRCLE NON-MEN REPRESENT TWO CLASSES 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 LET US CONSIDER Means THESE Only Musician TWO CIRCLES but REPRESENTING Not-Singer THE CLASSES USING M S M but MS Not-M but S OF Neither M nor-S Musician THESE ARE THE 4 & Singer “S” FOR “SINGER” Who are both “MUSICIAN” & Means “M” Not-Musicians but FOR Only Singer CLASSES “SINGER” Who are neither Musician nor Singer NOW THE FOUR CLASSES WILL BE

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

THREE OVERLAPPING CIRCLES WILL PRODUCE 8 (EIGHT) CLASSES M THESE ARE THE 8 CLASSES PRODUC ED BY 3 OVERLAPPING CIRCLES M but neither S nor L L&M But Not-S M&S But Not-L MSL S but neithe r. M nor L S L&S But Not-M L but neither M nor. S Neither M nor L nor S L

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

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

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

I Proposition : “Some Singers are Musician" Symbolically : “ Some S are M ” S MEANS THIS THERE CLASS AREOF SOME MEMBERS SINGER WHO AND ARE SINGER MUSICIA & N ALSO WILL MUSICIAN BE NONEMPTY M 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" SINGE MUSICIAN R S but not-M

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

Diagram of I Proposition : “Some Singers are Musician" or : “Some S are M" MUSICIAN SINGER SM X VENNS DIAGRAM EQUATION FOR ‘O’ PROPOSITION : SM=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 : SM=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 (A) Therefore, All Lyricist are Musician All S are M (A) All M are L (A) Therefore, All L are M or (A) SM = O • ML = O (A) LM = O or

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

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