Analyze the logical structures of the following arguments. Match each argument in the primary list with the argument in the secondary list that employs an identical method of refutation using a counterexample.
- The linguist asserts that a language can develop a complex writing system only if its speakers are governed by a centralized political authority. However, the Indus Valley civilization had a highly developed script long before any centralized state emerged.The coach claims that a team can win the championship only if it features at least one superstar player. Yet, a recent championship team secured the title relying entirely on balanced, cooperative play without a single standout star on their roster.
- The sociologist claims that whenever a community experiences rapid technological adoption, its traditional cultural practices inevitably decline. However, a prominent agrarian sect has rapidly adopted modern solar technology for commercial use while strictly maintaining its traditional, pre-industrial lifestyle.The financial analyst argues that whenever a corporation drastically cuts its research and development budget, its market share invariably drops within a year. But a major software firm slashed its research funding last year and subsequently saw a significant increase in its market dominance.
- The educational theorist argues that the more funding a school district receives per student, the higher its standardized test scores will be. Yet, the Riverdale district receives the highest funding in the region but consistently ranks in the bottom quartile for test scores.The ecologist posits that the larger a forest reserve is, the greater the biodiversity it will sustain. However, the massive Northern Boreal Reserve is the largest in the country but exhibits less biodiversity than the tiny Oak Creek sanctuary.
- The architectural purist insists that a building's design should never prioritize aesthetic appeal over structural utility. But one must consider the construction of monumental memorials, where the primary purpose is evocative and emotional rather than utilitarian.The strict constructionist judge argues that a court should never consider the original drafters' personal letters when interpreting a statute. However, when the statutory language contains an obvious typographical error that renders it absurd, examining outside correspondence is the only way to discern the intended law.
Answer
The correct matches pair the linguist's argument with the coach's (refuting a necessary condition), the sociologist's with the financial analyst's (refuting a sufficient condition), the educational theorist's with the ecologist's (refuting a proportional relationship), and the architectural purist's with the judge's (refuting a normative rule).
Each pair correctly matches arguments that use a counterexample to attack the exact same type of logical claim: necessary conditions, sufficient conditions, proportional correlations, and normative absolutes. By stripping away the subject matter, the underlying skeletal logic of the refutations is identical within each correct pair.
Step-by-Step Solution
Key Concept
Identifying Parallel Refutation Structures Using Counterexamples