An instructor of formal logic presents four arguments from distinct academic fields. Match each argument to the abstract description that correctly characterizes its formal logical structure and validity.
- Every deep-sea submersible capable of descending to abyssal depths without structural fatigue requires a reinforced titanium alloy chassis. The oceanographic vessel Triton does not possess a reinforced titanium alloy chassis. Therefore, the Triton is incapable of descending to abyssal depths without structural fatigue.A valid deductive inference establishing that an individual entity lacks a condition necessary for a characteristic, and concluding that the entity necessarily lacks that characteristic.
- Any municipal geothermal heating grid that successfully operates in subzero climates must incorporate closed-loop antifreeze circulation. The municipal geothermal grid in Oakhaven incorporates closed-loop antifreeze circulation. Hence, the Oakhaven geothermal grid will successfully operate in subzero climates.A flawed conditional argument that treats a condition necessary for an outcome as though it were sufficient to guarantee that outcome.
- Most rare botanical specimens preserved in the university herbarium are sensitive to fluctuations in ambient humidity. Most botanical specimens sensitive to fluctuations in ambient humidity require hermetically sealed display cases. Thus, most rare botanical specimens preserved in the university herbarium require hermetically sealed display cases.A flawed quantifier deduction that erroneously assumes majorities extend transitively across successive categories, failing to account for the possibility of non-overlapping subsets.
- Most ancient clay cuneiform tablets unearthed at the excavation site contain administrative trade inventories. All ancient clay cuneiform tablets unearthed at the excavation site are inscribed in the Akkadian dialect. Therefore, at least some tablets inscribed in the Akkadian dialect contain administrative trade inventories.A valid quantifier deduction concluding an existential overlap between two properties based on a single group where a majority possesses one property and every member possesses the other.
Answer
The deep-sea submersible argument matches the valid deduction of lacking a necessary condition (Modus Tollens). The municipal geothermal heating argument matches the flawed argument mistaking a necessary condition for a sufficient condition. The botanical specimen argument matches the flawed transitive inference with majorities. The cuneiform tablet argument matches the valid quantifier deduction establishing an existential overlap between a majority and a universal premise.
Each argument is paired with its precise structural template: the first is a sound Modus Tollens deduction; the second confuses necessary and sufficient conditions by affirming the necessary condition; the third commits the classic LSAT quantifier transitivity error with multiple 'most' quantifiers; and the fourth correctly derives an existential overlap ('some') from overlapping 'most' and 'all' conditions sharing a common antecedent base.
Step-by-Step Solution
Key Concept
Structural Isomorphism and Formal Logic Pattern Matching
Estimated Time:2m 0s