Necessary and Sufficient Assumptions Flashcards

An argument has premises P1 and P2 and conclusion C. A sufficient assumption SA is one where:

Answer: P1 + P2 + SA → C

A sufficient assumption works together with the existing premises to guarantee the conclusion—it fills the gap that makes the argument valid.

Which scenario demonstrates a necessary but NOT sufficient assumption?

Answer: An assumption whose negation destroys the argument but whose affirmation does not alone guarantee the conclusion

A necessary assumption is required for the argument but may not be enough on its own to make the conclusion certain.

Argument: 'Organic farming avoids synthetic pesticides. Avoiding synthetic pesticides benefits local ecosystems. The Hendersons farm organically. Therefore, the Hendersons benefit local ecosystems.' This argument:

Answer: Is already deductively valid with no unstated assumptions needed

The premises chain together logically to yield the conclusion, making this a valid deductive argument with no hidden gaps.

A student negates an assumption and finds the argument becomes 'significantly weaker but not completely destroyed.' This suggests the assumption is:

Answer: Probably a strengthener, not a necessary assumption

A necessary assumption, when negated, must completely undermine the argument—if it only weakens it, the statement is more like a strengthener.

Argument: 'Violent video games desensitize players to violence. Desensitization to violence increases aggressive behavior. Therefore, playing violent video games increases aggressive behavior.' A necessary assumption is:

Answer: The desensitization caused by video games is the same type that increases aggression

The argument links two types of desensitization, so it must assume they are the same or equivalent for the chain to hold.

In LSAT Logical Reasoning, 'Justify the Conclusion' questions are essentially asking for a:

Answer: Sufficient assumption

'Justify the Conclusion' is another label for Sufficient Assumption questions—the correct answer makes the conclusion logically follow.

Argument: 'Professor Stein publishes frequently in top journals. Professors who publish frequently in top journals are respected researchers. Therefore, Professor Stein is a respected researcher.' Which best describes this argument's assumptions?

Answer: It requires no unstated assumption—it is deductively valid as stated

The argument is a valid syllogism: the premises directly entail the conclusion with no hidden gaps.