Logic / Unit 3 Logic 078 worked example, 60 to 90 seconds
Diagramming All Four Forms
The idea
Diagramming the four categorical forms means representing each one on the same two-circle frame, using shading to mark a region as empty and an X to mark a region as occupied.
In practice
One frame, two overlapping circles: S on the left, P on the right. Form A, all S are P: shade the part of S that falls outside P, because the claim says nothing lives there. Form E, no S are P: shade the overlap, because the claim says nothing is both. Form I, some S are P: put an X in the overlap, because the claim says at least one thing is both. Form O, some S are not P: put an X in the part of S outside P. Now read the pairs. A shades exactly the region where O puts its X, so they make opposite claims about the same region and cannot both be true. E shades exactly the region where I puts its X, and the same holds.
Where people slip
Shading and an X say different kinds of thing, and mixing them is the common error. Shading asserts emptiness; an X asserts existence. An unshaded region with no X is not a claim that something is there — it records that the statement is silent about it, which is why a blank region can never be read as evidence either way.
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