Formal Fallacies

When the Structure Itself Is Broken

Unlike informal fallacies (which involve content or relevance problems), formal fallacies are errors in the logical structure of an argument. The premises might be true and relevant, but the conclusion does not follow because the form is invalid.

Affirming the consequent has this form: 'If A then B. B is true. Therefore A is true.' Example: 'If it rains, the ground is wet. The ground is wet. Therefore, it rained.' But the ground could be wet from a sprinkler, a burst pipe, or morning dew. Knowing that the consequent (B) is true does not tell you the antecedent (A) is true, because multiple causes can produce the same effect.

This fallacy is rampant in political reasoning: 'If a country has strong institutions, it will be prosperous. Singapore is prosperous. Therefore, Singapore has strong institutions.' The conclusion might happen to be true, but the argument form is invalid — prosperity can have other causes.

Denying the Antecedent and Undistributed Middle

Denying the antecedent: 'If A then B. A is not true. Therefore B is not true.' Example: 'If you study hard, you will pass. You did not study hard. Therefore, you will not pass.' But you might pass anyway due to prior knowledge, an easy exam, or luck. Denying the antecedent assumes the stated condition is the only way to reach the conclusion.

In policy debates: 'If we invest in renewable energy, we will reduce emissions. We are not investing in renewable energy. Therefore, we will not reduce emissions.' This ignores other paths to emission reduction like nuclear energy, carbon capture, or efficiency improvements.

Undistributed middle: 'All A are B. All C are B. Therefore, all A are C.' Example: 'All cats are animals. All dogs are animals. Therefore, all cats are dogs.' The middle term (animals) is shared but never fully accounted for — being an animal does not make cats and dogs the same.

Worked Example: Testing a Conditional Argument

Conditional arguments turn on one rule: knowing 'If A then B' lets you reason forward from A or backward from not-B, and nothing else. Walk through a case:

Premise: 'If a bill is unconstitutional, the courts will strike it down.' Observation: 'The courts struck down the bill.' Conclusion: 'Therefore, the bill was unconstitutional.'

Step 1 — Label the parts. A = the bill is unconstitutional. B = the courts strike it down.

Step 2 — Identify which part is affirmed. The observation affirms B (the consequent), and the conclusion infers A.

Step 3 — Match against the four patterns. Affirming B to conclude A is affirming the consequent — invalid. Courts can strike down a bill for other reasons (procedural defects, standing, a narrower statutory ground), so B does not guarantee A.

Step 4 — Show the valid neighbors for contrast. Same premise, different moves:

Whenever a conditional argument reasons from the consequent, stop and check the table — two of the four moves are traps.