5.3 Euler's Circles - From "The Reasonable Person" by Mark Grannis

Euler's Circles are ways of visually representing the four categorical propositions. The are visually represented by circles; one circle for the subject and one circle for the predicate. "Many people who find lots of words bothersome find it easier to understand the four basic propositions through graphic representations. There are two that are widely used, of which the more intuitive is the system of 'Euler's Circles,' after the Swiss mathematician and natural philosopher, Leonhard Euler (1707 - 1783). (His last name is pronounced like 'Oiler')."

They can be represented as such: 

A Proposition: all S is P 

We can express this by putting the S-circle totally inside the P-circle. 

E Proposition: No S is P 

We can express this by having no connection between the two circles. They are unrelated. 

I Proposition: Some S is P 
We can express this by showing that some of the S-circle overlaps with the P-circle. 

O Proposition: Some S is not P 

We can express this by showing that while some of the circles overlap, the subject and predicate are not in the that overlapping part. 

(The some-statements are conditional statements and reflect the knowledge one has at the moment, and thus it could be resolved into A and E propositions if more information was known.)