The Illicit Minor is a type of logical error that occurs when someone mistakenly uses a specific case or instance as the minor premise in an argument, but then draws a conclusion that applies to all cases.

Example:

“All mammals are warm-blooded.” (Major premise)
“The lion is a mammal and lives in the savannah.” (Minor premise)
“Therefore, all mammals live in the savannah.” (Fallacious conclusion)

In this example, the minor premise states that the lion is a mammal and lives in the savannah, but then the conclusion is drawn that all mammals live in the savannah. This is a fallacy because the minor premise only provides information about one specific case (the lion), not all mammals.

Formal Representation:

∀x (Px → Qx) (Major premise: All x are Q)
Pa ∧ Sa (Minor premise: a is P and has property S)
∴ (∀y, Py → Sy) (Fallacious conclusion: For all y, if y is P then y has property S)

In this example, the minor premise states that a specific individual (the lion) has a certain property (living in the savannah), but then the conclusion is drawn that all individuals with property P (being mammals) also have property S.

Real-Life Examples:

1. “All students who attend Harvard University are highly intelligent.” (Major premise)
   “John attended Harvard University and got an A+ in physics.” (Minor premise)
   “Therefore, all students at Harvard University get A+ grades in physics.” (Fallacious conclusion)
2. “All athletes who participate in the Olympics must be extremely fit.” (Major premise)
   “The American swimmer Michael Phelps has won multiple gold medals.” (Minor premise)
   “Therefore, all Olympic athletes are as talented and successful as Michael Phelps.” (Fallacious conclusion)

In both cases, the minor premise states that a specific individual or case has a certain property or characteristic, but then the conclusion is drawn that all individuals with property P also have that characteristic.

Avoiding the Illicit Minor Fallacy:

1. Be cautious with specific examples: Recognize that specific examples only provide information about one case, and avoid drawing conclusions that
   apply to all cases.
2. Look for evidence of generality: Instead of relying on a specific example, look for evidence that supports the conclusion in general.
3. Consider alternative explanations: Think about other possible reasons why something might be true or false.

Relationship with Other Fallacies:

The Illicit Minor fallacy is related to other fallacies, such as:

• Hasty Generalization: Making sweeping conclusions based on limited or incomplete evidence.
• Confirmation Bias: Selectively focusing on examples that support a preconceived notion while ignoring counterexamples.

Formal Relationship:

If ∀x (Px → Qx) (Major premise: All x are Q)
Pa ∧ Sa (Minor premise: a is P and has property S)
Hasty Generalization: ∴ (∀y, Py → Sy) (Making sweeping conclusions based on limited or incomplete evidence)
Confirmation Bias: ∴ (∃x, Px ∧ ¬Qx) (Selectively focusing on examples that support a preconceived notion while ignoring counterexamples)

By being aware of the Illicit Minor fallacy and its relationships with other fallacies, you can strengthen your arguments and avoid making unjustified conclusions.

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Filed under: Uncategorized - @ September 26, 2024 10:45 am