A logic seminar evaluates several arguments across different technical domains to isolate their underlying reasoning patterns. Which structural description correctly matches each of the arguments below?
- Avionics Engineer: For an automated collision-avoidance system to receive tier-one flight certification, it must incorporate redundant triple-modular inertial sensors. The newly developed flight system incorporates redundant triple-modular inertial sensors; therefore, it is guaranteed to receive tier-one flight certification.It treats a condition that is merely required for an outcome as though it were sufficient to guarantee that outcome.
- Textile Conservator: Every dyed silk garment produced during the early modern era that was treated with alum mordant retains vibrant chromophore integrity under UV light exposure. The velvet tapestry from the ducal collection exhibited severe chromophore degradation when exposed to UV light; thus, it was not treated with alum mordant.It deduces that a specific property is absent in an item by demonstrating that the item lacks a necessary consequence of possessing that property.
- Resource Analyst: Most coastal municipal desalination facilities operating along the southern coastline employ reverse-osmosis ceramic membranes. Furthermore, most coastal municipal desalination facilities along that coastline receive supplemental state energy subsidies. It follows that every desalination facility using reverse-osmosis ceramic membranes receives supplemental state energy subsidies.It improperly infers a universal relationship between two characteristics based solely on the fact that both characteristics independently share a majority overlap with a common category.
- Systems Architect: If a superconducting qubit array is maintained at temperatures below ten millikelvin, thermal decoherence noise will be suppressed below the fault-tolerance threshold. The experimental quantum processor is operating at fifteen millikelvin; consequently, its thermal decoherence noise will not be suppressed below the fault-tolerance threshold.It concludes that an effect will not occur solely from the premise that one specific condition sufficient to produce that effect has not been satisfied.
Answer
The avionics argument matches the description of treating a necessary condition as sufficient; the textile conservator argument matches the deduction of an absent property via an absent necessary consequence; the resource analyst argument matches the illicit universal inference from majoritarian overlaps; and the systems architect argument matches the conclusion that an effect cannot occur because a sufficient condition was not met.
Each argument maps directly to an exact formal template: the avionics statement commits affirming the consequent by conflating a mandatory prerequisite with a guarantee; the textile statement validly uses modus tollens to negate a property via its missing necessary effect; the desalination argument commits a quantifier leap from overlapping majorities to a universal rule; and the qubit processor argument commits the inverse fallacy by assuming an effect is impossible without its stated sufficient trigger.
Step-by-Step Solution
Key Concept
Parallel Reasoning and Structural Isomorphism in Formal and Flawed Logic
Estimated Time:2m 0s