Match each of the following everyday arguments to the formal valid deductive pattern that most accurately describes its logical structure.
- Approval of the proposed zoning amendment requires a unanimous vote by the city planning commission. The commission's public records indicate that at least two members formally opposed the amendment during the final hearing. Therefore, the proposed zoning amendment did not receive approval.Modus Tollens (Denying the necessary condition to logically disprove the sufficient condition)
- The unusual isotopic signature found in the meteorite must have originated from either a supernova explosion or the collision of two neutron stars. Astrophysical models have definitively demonstrated that a neutron star collision could not produce this specific ratio of isotopes. Consequently, the signature must be the result of a supernova explosion.Disjunctive Syllogism (Eliminating one possibility in an exhaustive disjunction to affirm the remaining option)
- Whenever a central bank aggressively raises interest rates, borrowing costs for commercial enterprises inevitably rise. Moreover, it is a well-established economic principle that a rise in commercial borrowing costs invariably leads to a contraction in corporate capital expenditure. Hence, an aggressive interest rate hike by a central bank will always result in a contraction in corporate capital expenditure.Hypothetical Syllogism (Chaining two conditional statements to deduce a new conditional relationship)
- A medical trial's results are considered statistically significant only if the calculated p-value is strictly less than 0.05. Therefore, it is impossible for a medical trial to yield statistically significant results if its calculated p-value is 0.05 or greater.Contrapositive Equivalence (Deriving a logically equivalent claim by simultaneously negating and reversing the original conditions)
Cevap
The correct pairings are: the zoning amendment argument matches Modus Tollens; the meteorite isotopic signature argument matches Disjunctive Syllogism; the central bank interest rate argument matches Hypothetical Syllogism; and the medical trial results argument matches Contrapositive Equivalence.
Each correct pairing accurately abstracts the semantic content of the everyday argument into its underlying skeleton of formal logic. The zoning argument denies the consequent (Modus Tollens); the meteorite argument eliminates a disjunct (Disjunctive Syllogism); the central bank argument chains conditionals (Hypothetical Syllogism); and the medical trial argument reverses and negates a single conditional (Contrapositive Equivalence).
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Anahtar Kavram
Recognizing and mapping valid deductive structures (Modus Tollens, Disjunctive Syllogism, Hypothetical Syllogism, Contrapositive Equivalence) from everyday language into formal logic.