Using Venn Diagrams to test validity of categorical syllogisms.
Step 1: Translate all statements in the argument (if necessary) into
standard-form categorical statements.
Step 2: Draw and label three overlapping circles, one for each term (class
name) in the argument, with the two circles for the conclusion at
the bottom.
Step 3: Use shading to represent the information in all or no statements.
To diagram statements of the form “All S are P”, shade that
portion of the S circle that does not overlap with the P circle. To
diagram statements of the form “No S are P”, shade that portion of
the S circle that overlaps with the P circle.
Use X’s to represent the information in some statements. To
diagram statements of the form “Some S are P”, place an X in that
portion of the S circle that overlaps with the P circle. To diagram
statements of the form “Some S are not P”, place an X in that
portion of the S circle that does not overlap with the P circle.
Step 4: Diagram the two premises. (No marks should be entered for the
conclusion.) If the argument contains one all or no premise and
one some premise, diagram the all or no premise first. Otherwise,
diagram either premise first.
Step 5: When placing an X in a two-part area, if one part of the area has
been shaded, place the X in the unshaded part. If neither part of
the area has been shaded, place the X precisely on the line
separating the two parts.
Step 6: Look to see if the diagram contains all the information presented
in the conclusion. If it does, the argument is VALID. If it doesn’t, the
argument is INVALID.
