Match each logical refutation in the left column with the argument in the right column that exhibits an identical parallel structure in its use of a counterexample.
- The dean argues that no student can master advanced calculus unless they have first taken linear algebra. But consider the prodigy Riemann. He achieved perfect scores in advanced calculus despite never having studied linear algebra. This demonstrates that prior study of linear algebra is not an absolute prerequisite for mastering advanced calculus.The safety inspector claims that a building cannot withstand a magnitude 8 earthquake unless its foundation is retrofitted with steel isolators. Yet, the historic brick courthouse survived last year's magnitude 8.2 quake completely intact, despite lacking any steel isolators. Thus, steel retrofitting is not strictly required for such seismic resilience.
- The mayor insists that implementing a universal basic income guarantees a reduction in petty crime. However, when the neighboring province instituted a universal basic income last decade, their petty crime rates actually increased by fifteen percent. Clearly, this economic policy does not inherently ensure a drop in petty crime.The marketing director asserts that launching a viral social media campaign will guarantee an increase in quarterly sales. But our competitor's viral campaign reached millions last quarter, and their sales simultaneously plummeted. Therefore, viral reach does not secure revenue growth.
- The anthropologist hypothesizes that the collapse of Bronze Age civilizations was caused exclusively by prolonged droughts. However, the Indus Valley civilization collapsed during a period of documented excessive rainfall and flooding, with no evidence of drought. Thus, factors other than drought must be capable of causing such civilizational collapses.The mechanic insists that engine knocking in this vehicle model is caused exclusively by using low-octane fuel. Yet, several fleet vehicles have developed severe engine knocking despite being fueled strictly with premium high-octane gasoline. This proves that low-octane fuel is not the only potential trigger for the issue.
- The software developer claims that any application with both end-to-end encryption and decentralized servers is immune to data breaches. However, the recent CryptoChat app utilized both end-to-end encryption and decentralized servers, yet it suffered a massive data breach last week. Consequently, combining these two security features does not confer absolute immunity.The botanist argues that any plant exposed to both full sunlight and daily watering will thrive in this climate. But the desert cacti in our garden receive full sunlight and daily watering, yet they are rapidly decaying. Thus, the combination of abundant light and water does not ensure plant health.
Cevap
The correct structural mappings are: The Dean's argument matches the Safety Inspector's argument (Left 1 to Right 4). The Mayor's argument matches the Marketing Director's argument (Left 2 to Right 1). The Anthropologist's argument matches the Mechanic's argument (Left 3 to Right 2). The Software Developer's argument matches the Botanist's argument (Left 4 to Right 3).
Each matched pair shares an identical formal refutation structure. They align perfectly in how they use a specific case to attack either a necessary condition, a simple sufficient condition, an exclusive causal relationship, or a compound sufficient condition. This demonstrates mastery of mapping the logical role of a counterexample across different subject matters.
Adım Adım Çözüm
Anahtar Kavram
Parallel Method of Reasoning (Counterexamples)