Venn diagram is a kind of diagram to

Concept

A Venn diagram is a device of formal logic. It gives every class term in a categorical proposition its own closed region, lets those regions overlap, and then records what the premises claim using two marks with fixed meanings: shading a region says that the region is empty, and a cross placed in a region says that at least one thing lies there. Nothing else may be entered, so the finished drawing holds only relations between classes and never any fact about the world.

That single property fixes what such a diagram can settle. Validity is a property of an inference: the conclusion cannot fail while the premises hold, and it turns entirely on the form of the argument. Truth is a property of a statement: it matches the way the world actually is, and it is settled by evidence, not by drawing. A device that stores only class relations can therefore decide validity and can never decide truth. It decides validity in two linked moves - it first depicts the premises, and it is then read to see whether the conclusion is already recorded. Depicting is the representing move; reading off is the assessing move, and the diagram is a logical instrument only because it performs both.

Application

Take the elementary syllogism: All poets are dreamers; all dreamers are idealists; therefore all poets are idealists.

1. Draw three overlapping circles, one for poets, one for dreamers and one for idealists. At this stage the diagram holds only the vocabulary of the argument.

2. Enter the first premise by shading every part of the poets circle that falls outside the dreamers circle. The shading records that the class of poets who are not dreamers is empty.

3. Enter the second premise by shading every part of the dreamers circle that falls outside the idealists circle. The two premises are now fully represented, and no further information has been added.

4. Read the drawing. Every part of the poets circle lying outside the idealists circle has been shaded by those two steps, which is exactly the claim that all poets are idealists. The conclusion required no fresh mark, so it follows from the premises by form alone. This reading step is the assessment.

5. Observe that no step asked whether poets really are dreamers. The identical procedure runs on premises that are factually false, and it returns the identical result.

Cross-check

• Validity against truth: the argument "All cats are stones; all stones are plants; therefore all cats are plants" produces exactly the same shading pattern and the same reading, even though every statement in it is false. The diagram cannot tell the two arguments apart, which shows that the property it measures is validity and not truth.

• Representing alone: steps 1 to 3 only transfer the premises onto paper. A device stopping there would be an illustration; it is step 4, reading the conclusion off the completed drawing, that turns it into a decision procedure.

• Assessing alone: step 4 has nothing to read unless steps 1 to 3 have already drawn the premises, so assessment without representation is not a procedure the diagram can carry out.

The Venn diagram therefore performs both moves, and the property it evaluates is validity rather than truth: it is a diagram to represent and assess the validity of elementary inferences of syllogistic form.