Logical Reasoning Ch 5

What is an assumption in an argument?

An assumption is an unstated idea the author takes for granted to be true for the argument to work, connecting the premises to the conclusion.

What are the two types of assumptions?

Sufficient and necessary assumptions. Both must be logically figured out, not stated in the stimulus, and are found in arguments, rarely in debates.

What is a sufficient assumption?

A sufficient assumption proves the conclusion 100% true, bridging the gap between premises and conclusion, often using words like "always," "must," or "will." It is powerful and needed to prove the conclusion.

What is a necessary assumption?

A necessary assumption must be true if the conclusion is true. The conclusion depends on it but doesn’t prove it, nor does it cause it. It’s proven by the conclusion, like a valid conclusion is proven by premises.

Why are assumptions important in Logical Reasoning?

Assumptions are central to argumentation. A strong grasp of argumentation, including assumptions, allows you to dominate the Logical Reasoning section regardless of question type.

What is the Assumption Chain?

The Assumption Chain is: Sufficient Assumption → Conclusion True → Necessary Assumption. The sufficient assumption proves the conclusion, and the conclusion proves the necessary assumption. Memorize it.

What role does the sufficient assumption play in the Assumption Chain?

The sufficient assumption fills the "if" part of the logic chain. If true, it sets the chain in motion, making the conclusion definitely true.

What role does the necessary assumption play in the Assumption Chain?

The necessary assumption fills the "then" part of the chain. If the conclusion is true, it must be true, but knowing it’s true doesn’t prove the conclusion by itself.

What happens if there are multiple sufficient or necessary assumptions?

If there are multiple sufficient assumptions, any one can be used to prove the conclusion. Multiple necessary assumptions can also be switched, and the argument will still work.

How do sufficient and necessary assumptions differ in being powerful or provable?

Sufficient assumptions are powerful, using strong words like “must” or “always” to prove the argument. Necessary assumptions are provable, true if the conclusion is true, and often basic.

How do sufficient and necessary assumptions differ in being boring or not boring?

Sufficient assumptions are not boring, often big and bold, filling major gaps. Necessary assumptions are boring, simple, and basic, but critical, as the argument collapses without them.

Do sufficient and necessary assumptions always prove the conclusion 100% true?

Sufficient: Yes, if true, the conclusion must be true. Necessary: No, it doesn’t prove the conclusion, but must be true if the conclusion is true.

If the conclusion is true, must the assumption be true?

Sufficient: No, other ways may prove the conclusion. Necessary: Yes, it must be true for the conclusion to work; without it, the argument collapses.

What is The Assumption Test?

To determine if an assumption is sufficient or necessary, ask:

1. Sufficient Test: Does the assumption prove the conclusion?

2. Necessary Test: If the conclusion is true, must the assumption be true? A “Yes” confirms the assumption type.

What does “If our premises, then our conclusion” mean?

It states that if the premises are true, the conclusion must be true. It’s both a sufficient and necessary assumption, bridging the gap between premises and conclusion explicitly.

Why is “If our premises, then our conclusion” both sufficient and necessary?

It’s sufficient because if the premises are true, the conclusion follows. It’s necessary because if it’s false (premises true, conclusion false), the argument is invalid.

What is a Loophole in an argument?

A Loophole is a powerful objection, like a sufficient assumption, exposing the author’s unstated assumption by showing why the conclusion doesn’t have to be true.

How do you design a Loophole?

Ask, “What if something really bad for the argument is true?” Start with “What if…” and imagine a possible situation that destroys the argument’s validity without negating premises.

How do you know if a Loophole works?

Ask, “Would the conclusion still definitely be true if this ‘What if’ situation happened?” If the answer is no, the Loophole is valid and breaks the argument.

How are Loopholes related to necessary assumptions?

Loopholes are negated necessary assumptions. They are two sides of the same coin; a Loophole shows why the conclusion doesn’t have to be true by negating the necessary assumption.

What is the Contrapositive Assumption Chain?

Necessary Assumption → Conclusion True → Sufficient Assumption. A negated necessary assumption (Loophole) destroys the conclusion.

What are the two important rules for Loopholes?

1. Don’t negate the premises; they are true. Question the gap between premises.
2. Don’t negate the conclusion; show why it doesn’t have to be true.

What is a Dangling Variable?

A Dangling Variable is a new word in the conclusion not in the premises. The author assumes it’s the same as a premise term, but it’s not. On the LSAT, nothing is “basically the same.”

How do you create a Dangling Variable Loophole?

Place a ≠ between the two terms the author pretends are the same, highlighting that the new conclusion term isn’t supported by the premises.

What are Conditional Dangling Variables?

Conditional Dangling Variables occur when a new term is added to the conclusion’s conditional chain, not mentioned in the premises, giving the illusion it’s a valid part of the reasoning.

How do you create a Loophole for a Conditional Dangling Variable?

Question the addition of the new term in the conclusion’s conditional chain, showing it can’t be validly added without premise support.

What are Secret Value Judgments?

Secret Value Judgments occur when the author uses judgmental terms (e.g., moral/immoral, good/bad, should/shouldn’t) in the conclusion without defining them. They’re a type of Dangling Variable.

How do you create a Loophole for Secret Value Judgments?

Question the author’s assumption that the judgmental term (e.g., irresponsible) is validly applied, showing it may not hold.

What are Secret Downsides?

Secret Downsides occur when the author compares two things, claiming one is superior, without considering potential downsides of the preferred choice.

How do you create a Loophole for Secret Downsides?

Imagine ways the preferred choice might be worse, forming a Loophole like: “What if the preferred choice has a major downside not accounted for?”

What are Assumed Universal Goals?

Assumed Universal Goals are things the author assumes everyone wants (e.g., losing weight, making money, being healthier). Arguments assume these are universal, but they’re not.

How do you create a Loophole for Assumed Universal Goals?

Show that not everyone wants the assumed goal, forming a Loophole like: “What if not everyone wants this goal?”