(premise) (conclusion) (john venn)...(total class inclusion relation) (total class exclusion...
TRANSCRIPT
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(Premise) (Conclusion)
(John Venn)
S P
S P
S P
S P
(Quantifiers)
‘S’ ‘P’
(Subject)
(Copula)
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(Total class inclusion relation)
(Total class exclusion relation)
(Universal Affirmative)
(Universal Negative) (Particular Affirmative)
(Particular Negative) A, E, I
S P S P
S P
S P
S P’
A, E, I O
S P
‘A’
S P
‘E’
‘E’
S P
‘I’
‘I’
S P
‘O’
‘A’
‘B’
‘I’
‘O’
(Category)
(Class)
(Some)
‘A’
‘E’
(Iconic representations of categorical proposition and
arguments to display their logical forms using overlapping circles.)
(Elementary Set Theory)
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“On the Diagrammatic
and Mechanical Representation of Propositions and Reasonings”
‘Philosophical
Magazine and Journal of Science’ (Venn-Diagram)
‘Eulerian Circles’
Venn-diagram
A Survey of Symbolic Logic
(Eulerian Circle)
(E) (A)
(A
(I
‘‘The Mathematical Analysis of Logic’’ “An Investigation
of the Laws of Thought”
A– S
E– S
I– S P = S S P
O– S P = S S P
‘A’ ‘O’ ‘E’ ‘I’
A: SP– = 0 E: SP = 0
I = SP� 0 0 SP–� 0
‘I’ ‘O’
‘A’ ‘E’
‘A’ (T)
‘O’ (F) ‘I’
(F) ‘E’ (T)
‘A’ ‘O’
‘E’ ‘I’
‘E’ I
‘A’ ‘O’
(Existential Import)
~, � , Λ, � �
Λ (Lamda) O (Zero)
‘S’- S’-
S = O
S’-
S � Λ S � O
‘S’
‘S’ S
S
(Product) (intersection)
SP S�P ‘‘S
P’’ (S Intersection P) ‘� ’
‘� ’ SP = S� P = =
SP � SP� O S� ~P = Λ
‘A’– S P = SP–
= O SP–
= Λ
‘A’ ‘S’ ‘P’
‘E’– S P = SP = O SP = Λ
‘I’– S P = SP � O SP � Λ
‘I’
‘O’– S P = SP–� O SP
–
‘S’ P
‘S’
‘S’
‘X’
‘X’
‘S’
‘X’ ‘S’
S
S S
X
A, E, I O
S
SP–
P– (P-bar) P
S–
P S– (S-bar)
S
SP
S
S–P–
S P
SP–
SP S–
P S–P–
S P
(Universe of Discourse)
(Diagrams for Standard Form
Categorical Propositions)
‘A’
P
S P SP = O SP = Λ S
P S
‘A’
A: S P
SP– = O
E ‘E’
S P ‘S’
‘P’ SP = Λ SP = O
S ‘S’ P
‘E’
SP
E: S P
SP = O
I ‘I’
S P S P
S P
‘S’ ‘P’ SP � O SP � Λ
S P ‘X’
‘I’
I: S P
SP � O
O ‘O’
S P ‘O’ S ‘S’ ‘P’
SP � O SP � S P
‘x’ ‘x
S, P ‘O’
S P
X
SP
O: S P
S P
X
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� S P E-
S P S P O
S P
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1) Baronett, S. and Sen, M.; Logic.
2) Chakraborti. C.; Logic-Informal, Symbolic & Inductive.
3) Copi, I. M. & Cohen, C.; Introduction to Logic.
4) Hurley, J. P.; Introduction to Logic.
5) Sharma. B. and Deka J.; A text Book of logic.
6) (https://www.lucidchart.com/blog/2013/01/17/a-history-of-the-venn-
diagram)
A, E, I O
Λ � S P = SP = O
E: S P
SP = O
A, E, I O
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