Section 6.3

Fallacies & Venn Diagrams

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A logical fallacy is an error in reasoning that renders an argument invalid or unsound. These errors are classified into two broad categories: formal fallacies, which are structural flaws, and informal fallacies, which relate to the content or context of the argument (Walton, 1989).

1. Formal Fallacies

A formal fallacy is a flaw in the logical structure of a deductive argument. The argument is invalid regardless of what the terms actually mean.

  • Fallacy of the Undistributed Middle: The middle term in a syllogism must be distributed in at least one premise. If it is not, the connection between the major and minor terms is not guaranteed.
  • Affirming the Consequent: An error in conditional reasoning. (If P, then Q. Q is true. Therefore, P is true. — Invalid).

2. Informal Fallacies

Informal fallacies occur when the premises fail to support the conclusion due to irrelevance, ambiguity, or unwarranted assumptions.

  • Ad Hominem (Against the Man): Attacking the person making the argument rather than the argument itself.
  • Straw Man: Misrepresenting or exaggerating an opponent's argument to make it easier to attack.
  • Ad Populum (Appeal to Popularity): Arguing a claim is true simply because many people believe it.
  • Slippery Slope: Assuming a relatively small first step will inevitably lead to a chain of related (and typically disastrous) events without adequate evidence.

3. Venn Diagrams

Invented by John Venn, Venn diagrams are graphical representations of categorical propositions used to establish the validity of deductive arguments.

💡 Diagram Rules

Shading indicates a region is empty (no members). An 'X' indicates a region contains at least one member. A blank region means we have no information about it.

To test a syllogism using a Venn diagram:

  1. Draw three interlocking circles representing the Major, Minor, and Middle terms.
  2. Diagram the Universal premise first (using shading).
  3. Diagram the Particular premise next (using an 'X'). If placing the 'X' is ambiguous because it could go in two regions, place it on the line separating them.
  4. Evaluate: Look at the completed diagram. If the conclusion is already depicted simply by drawing the premises, the argument is Valid. If the conclusion is not depicted, it is Invalid.

Academic References

  • Copi, I. M., Cohen, C., & McMahon, K. (2014). Introduction to logic (14th ed.). Pearson.
  • Walton, D. (1989). Informal logic: A handbook for critical argumentation. Cambridge University Press.