Recipe

Test a syllogism with a Venn diagram

Use when: you have a syllogism in standard form and want a verdict you can see, or want to double-check a verdict from the five rules

Goal: the verdict, valid or invalid, read off a diagram of the premises alone

Taught in Testing syllogisms with Venn diagrams

1. 1

   Find S and P from the conclusion and M from the premises. Draw S and P side by side and M below them.

   Example

   "All refunds need a receipt. Some of today's returns are refunds. So some of today's returns need a receipt": S = today's returns, P = things needing a receipt, M = refunds.

   Why: every statement in the syllogism is about two of these three groups, so the three circles can hold all of it.

2. 2

   Draw each A or E premise by shading, on both pieces of its region.

   Example

   "All refunds need a receipt" shades refunds only and the returns-and-refunds patch outside the receipt circle.

   Why: shading can close a region, which tells a later X where it has to go.

3. 3

   Put the X in the one open region the premise allows. If two regions are open, put the X on the line between them.

   • one region open — the X goes in it.
   • two regions open — the X goes on the line.
   • no region open — the premises contradict each other; there's nothing to test.

   Why: an X records only what the premises say, and a line records that they don't say which side.

4. 4

   Don't draw the conclusion. Check whether it is already there.

   • universal conclusion, and its regions are already shaded — valid.
   • particular conclusion, and an X sits entirely inside its regions — valid.
   • anything else, including an X on a line that crosses out of the regions — invalid.

   Why: if the premises' diagram already contains the conclusion, no situation fits the premises and breaks the conclusion.