Venn Diagrams

It is often helpful to think of a term in a proposition as a circle containing the members of the relevant class. This is the method of Venn Diagrams, invented by the English mathematician John Venn.

The Venn Diagrams for Categorical Propositions

To use this method, we need a way to represent each of the different forms of proposition. The simplest case is the I proposition. "Some S is P" says that at least one member of S is also a member of P. We can represent this by putting an X in the intersection of two overlapping circles that represent S and P.

In the same way, the O proposition "Some S are not P" means that there is at least one item in the region of the S circle outside the P circle.

The representation of the universal propositions is a little different. The procedure is easiest to understand if we recall that the A proposition "All S are P" is equivalent to its obverse--"No S is non-P." We can indicate this by shading out the region of the S circle outside the P circle:

Notice that the diagram of the A proposition is the exact opposite of that for the O proposition, as it should be, since there are contradictories. The O diagram says that there is something in the leftmost region; the A diagram says there is nothing there. Notice too that the A diagram does not contain an X anywhere and thus does not imply the existence of any Ss. Venn diagrams are based on the modern view that universal propositions do not have existential import.

To diagram the E proposition, finally, we must shade out the area of overlap between the circles.

Since the E and I propositions are contradictories, this diagram shades out the very region in which the I diagram places an X.


Comprehension Questions

1 Which of the following is the Venn diagram for an A proposition?
a)
b)
c)
d)
2 Which of the following is the Venn diagram for an I proposition?
a)
b)
c)
d)
3 Which of the following is the Venn diagram for an E proposition?
a)
b)
c)
d)
4 Which of the following is the Venn diagram for an O proposition?
a)
b)
c)
d)


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