1. The Hidden Foundation
In formal logic, an argument is a structural assembly. While the explicit components (Premise and Conclusion) are visible, there is almost always an "unstated bridge" that remains submerged. This hidden necessity is the Assumption.
Premise
The stated evidence or facts.
Assumption
The unstated link required for the logic to hold.
Conclusion
The final claim.
2. Level 1: The Direct Link (Easy)
The first level of mastery involves identifying a direct causal connection. Read the question below and try to identify the gap between the Plan and the Outcome.
"Farmer: Worldwide, just three grain crops—rice, wheat, and corn—account for most human caloric intake. To maintain this level of caloric intake and also keep pace with global population growth, yields per acre from each of these crops will have to increase at least 1.5 percent every year, given that the supply of cultivated land is diminishing. Therefore, the government should increase funding for research into new ways to improve yields."
Which of the following is an assumption on which the farmer's argument depends?
- (A) It is solely the government's responsibility to ensure that the amount of rice, wheat, and corn produced worldwide keeps pace with global population growth.
- (B) Increasing government funding for research into new ways to improve the yields per acre of rice, wheat, and corn crops would help to increase total worldwide annual production of food from these crops.
- (C) Increasing the yields per acre of rice, wheat, and corn is more important than increasing the yields per acre of other crops.
- (D) Current levels of funding for research into ways of improving grain crop yields per acre have enabled grain crop yields per acre to increase by more than 1.5 percent per year worldwide.
- (E) In coming decades, rice, wheat, and corn will become a minor part of human caloric intake, unless there is government-funded research to increase their yields per acre.
Solution Walkthrough: The Farmer
Let's deconstruct the logic to find the missing link.
Step 1The Logic Gap
Premise: We need higher yields to feed people.
Conclusion: We should fund research.
The Gap: Does funding actually LEAD to results? Just because you pay for research doesn't mean it will work.
Step 2The Assumption (Option B)
(B) Increasing government funding... would help to increase total worldwide annual production.
This connects the Action (Funding) to the Goal (Yields).
Step 3The Negation Test
If funding does NOT help increase production, then the argument falls apart. Therefore, B is necessary.
3. Level 2: Excluding Alternatives (Medium)
Level 2 requires "closing the door" on other possibilities. In historical deduction, the assumption is often the denial of a competing hypothesis.
"Although there is no record of poet Edmund Spenser's parentage, we do know that as a youth Spenser attended the Merchant Tailors' School in London for a period between 1560 and 1570. Records from this time indicate that the Merchant Tailors' Guild then had only three members named Spenser: Robert Spenser, listed as a gentleman; Nicholas Spenser, elected the Guild's Warden in 1568; and John Spenser, listed as a "journeyman cloth-maker." Of these, the last was likely the least affluent of the three—and most likely Edmund's father, since school accounting records list Edmund as a scholar who attended the school at a reduced fee."
Which of the following is an assumption on which the argument depends?
- (A) Anybody in sixteenth century London who made clothing professionally would have had to be a member of the Merchant Tailors' Guild.
- (B) The fact that Edmund Spenser attended the Merchant Tailors' School did not necessarily mean that he planned to become a tailor.
- (C) No member of the Guild could become Guild warden in sixteenth century London unless he was a gentleman.
- (D) Most of those whose fathers were members of the Merchant Tailors' Guild were students at the Merchant Tailors' School.
- (E) The Merchant Tailors' School did not reduce its fees for the children of the more affluent Guild members.
Solution Walkthrough: The Poet
The argument concludes John (the poor one) is the father because Edmund got a discount.
Step 1The Logic Gap
Premise: Edmund got a discount. John was poor.
Conclusion: John is the father.
Gap: Could a rich person (Robert or Nicholas) ALSO get a discount? If so, the discount doesn't prove anything.
Step 2The Assumption (Option E)
(E) The School did not reduce its fees for the children of the more affluent members.
This eliminates the alternative that a rich father could also have a son with a reduced fee.
Step 3The Negation Test
If rich people DID get discounts, then Edmund could be Robert's son. The conclusion is no longer certain.
4. Level 3: The Variable Shift (Hard)
The most rigorous challenges involve a "Variable Shift." The author assumes a fixed ratio between two variables (e.g. Flights vs. Passengers) that might actually change.
"Proposed new safety rules for the Beach City airport would lengthen considerably the minimum time between takeoffs from the airport. In consequence, the airport would be able to accommodate 10 percent fewer flights than currently use the airport daily. The city's operating budget depends heavily on taxes generated by tourist spending, and most of the tourists come by plane. Therefore, the proposed new safety rules, if adopted, will reduce the revenue available for the operating budget."
The argument depends on assuming which of the following?
- (A) There are no periods of the day during which the interval between flights taking off from the airport is significantly greater than the currently allowed minimum.
- (B) Few, if any, of the tourists who use the Beach City airport do so when their main destination is a neighboring community and not Beach City itself.
- (C) If the proposed safety rules are adopted, the reduction in tourist numbers will not result mainly from a reduction in the number of tourists who spend relatively little in Beach City.
- (D) Increasing the minimum time between takeoffs is the only way to achieve necessary safety improvements without a large expenditure by the city government on airport enhancements.
- (E) The response to the adoption of the new safety rules would not include an increase in the number of passengers per flight.
Solution Walkthrough: The Airport
The argument assumes Fewer Flights = Fewer Tourists.
Step 1The Logic Gap
Premise: 10% Fewer Flights.
Conclusion: Less Revenue (Fewer Tourists).
Gap: Can you have fewer planes but the SAME number of people? Yes, if the planes are bigger or fuller.
Step 2The Assumption (Option E)
(E) The response... would not include an increase in the number of passengers per flight.
This blocks the 'Counter-Balance' scenario.
Step 3The Negation Test
If airlines DID increase passengers per flight (bigger planes), then tourist numbers might stay the same despite fewer flights. The conclusion fails.
Summary: The "Negation Test" Protocol
To identify an assumption with surgical precision, reverse the option. If the negated statement destroys the argument, you have found the answer.
- Identify the Bridge: Where does the author jump from Fact to Claim?
- Negate Alternatives: In elimination arguments, the assumption denies other possibilities.
- Audit Variables: In math-based arguments, check for variable shifts (Rate vs Total).
