4.2 Verbal Inference (Formal Logic & Syllogisms)

Verbal Inference: Formal Logic & Syllogisms

Verbal Inference questions on the OLSAT assess your ability to process formal logic. You are presented with a series of premises (statements assumed to be true) and asked to determine what logically follows. The most critical rule here is to suspend your real-world knowledge. The conclusion must be derived only from the information given in the premises.

Syllogisms: The Building Blocks of Logic

A syllogism is a form of deductive reasoning consisting of a major premise, a minor premise, and a conclusion.

Example:

• Premise 1: All birds have feathers.
• Premise 2: A penguin is a bird.
• Conclusion: Therefore, a penguin has feathers.

On the OLSAT, the premises may be absurd in the real world:

• Premise 1: All cats can fly.
• Premise 2: Fluffy is a cat.
• Conclusion: Therefore, Fluffy can fly.

Even though cats cannot fly in reality, logically, based strictly on the premises, the conclusion is valid. You must treat the premises as absolute laws of the universe for that specific question.

Conditional Logic: If-Then Statements

Conditional logic is a major component of Verbal Inference. It revolves around "If-Then" statements.

• If A, then B. (A $\rightarrow$ B)
• A is the sufficient condition. (Knowing A is true is enough to know B is true.)
• B is the necessary condition. (B must be true for A to be true.)

Example: "If it is raining, then the ground is wet."

• Sufficient: It is raining.
• Necessary: The ground is wet.

The Contrapositive

The most important tool in conditional logic is the contrapositive. The contrapositive is formed by negating both the hypothesis and the conclusion, and swapping their order. The contrapositive is always logically equivalent to the original statement.

• Original: If A, then B.
• Contrapositive: If not B, then not A.

Using our example:

• Original: If it is raining, then the ground is wet.
• Contrapositive: If the ground is not wet, then it is not raining.

This is incredibly useful because questions will often test your ability to recognize the contrapositive as the correct deduction.

Common Logical Fallacies

Many incorrect answer choices on the OLSAT rely on common logical fallacies. The two most frequent are:

1. Affirming the Consequent

This fallacy assumes that if the "then" part is true, the "if" part must also be true. This is invalid.

• Statement: If A, then B. (If it is raining, the ground is wet.)
• Fallacy: B is true, therefore A is true. (The ground is wet, therefore it is raining.)
• Why it's wrong: The ground could be wet for other reasons (e.g., a sprinkler).

2. Denying the Antecedent

This fallacy assumes that if the "if" part is false, the "then" part must also be false. This is also invalid.

• Statement: If A, then B. (If it is raining, the ground is wet.)
• Fallacy: A is not true, therefore B is not true. (It is not raining, therefore the ground is not wet.)
• Why it's wrong: Again, the ground could be wet from a sprinkler even if it's not raining.

Visualizing Logic with Venn Diagrams

For complex syllogisms, particularly those using words like "All," "Some," or "None," drawing a quick Venn diagram can be a lifesaver.

• "All A are B": Draw a small circle for A completely inside a larger circle for B.
• "No A are B": Draw two completely separate circles.
• "Some A are B": Draw two overlapping circles.

Example Problem:

• Premise 1: All blurps are glorps.
• Premise 2: Some glorps are flurps.
• Conclusion to evaluate: Are some blurps flurps?

If you visualize this:

• Blurps is a circle inside Glorps.
• Flurps overlaps with Glorps.
• Does Flurps overlap with Blurps? It might, but it doesn't have to. The Flurps circle could overlap with the part of the Glorps circle that doesn't contain Blurps. Therefore, the conclusion "Some blurps are flurps" is invalid. It is not a guaranteed certainty.

Handling Negation

Pay close attention to negative words like "not," "never," "none," and "no."

When a premise states "No X are Y," it means the intersection is completely empty. If you are told "No dogs are reptiles," and "All snakes are reptiles," you can logically deduce that "No dogs are snakes." The Venn diagram makes this obvious: the dog circle and reptile circle are separate, and the snake circle is inside the reptile circle. Therefore, the dog and snake circles can never touch.

Summary of Strategies

1. Accept the Absurd: Treat premises as absolute truth.
2. Find the Contrapositive: Whenever you see an "If-Then" statement, immediately mentally formulate its contrapositive.
3. Avoid the Fallacies: Never affirm the consequent or deny the antecedent.
4. Draw it Out: Use Venn diagrams for "All/Some/None" categorical statements to visualize the relationships.

Mastering these formal logic structures will turn Verbal Inference from a confusing word puzzle into a straightforward mechanical process.