The following four excerpts contain invalid logical deductions involving necessary and sufficient conditions. Select the precise abstract description of the logical flaw committed in each excerpt.
- To significantly reduce urban congestion and simultaneously maintain economic growth, a municipality must heavily subsidize its public transit network. Metropolis has just authorized unprecedented subsidies for its transit system. Therefore, Metropolis will inevitably achieve a dramatic reduction in congestion alongside maintained growth.Treats a policy that is necessary to achieve a compound objective as though implementing it is sufficient to guarantee the realization of that objective.
- If a cybersecurity infrastructure incorporates autonomous quantum encryption, it will detect anomalous intrusions instantaneously. Instantaneous intrusion detection invariably prevents unauthorized large-scale data exfiltration. However, the agency opted against implementing quantum encryption. Thus, the network will inevitably suffer from large-scale data exfiltration.Infers the nonoccurrence of a final consequence solely from the absence of an initial condition known to be sufficient to trigger that causal chain.
- A geological formation cannot be formally classified as a stable craton unless it exhibits both minimal seismic activity and long-term tectonic isolation. The newly surveyed bedrock exhibits the required lack of seismic activity and has remained tectonically isolated. Therefore, it is definitively a stable craton.Takes the presence of multiple prerequisites that are jointly required for a classification to apply as providing sufficient justification for applying that classification.
- A deep-sea submersible will successfully withstand extreme abyssal pressures only if its primary hull is constructed from a specialized titanium-carbide alloy. The engineering team has fabricated the new vessel's hull using this exact titanium-carbide alloy. Consequently, the submersible is guaranteed to withstand the extreme abyssal pressures.Concludes that a particular capability will definitely be achieved by pointing to evidence that a single necessary precondition for that capability has been satisfied.
Cevap
The Metropolis excerpt maps to treating a policy as sufficient for a compound objective. The cybersecurity excerpt maps to inferring nonoccurrence from an absent initial condition in a causal chain. The geological excerpt maps to taking multiple prerequisites as sufficient for a classification. The submersible excerpt maps to concluding a capability is achieved from a single precondition.
Each correct pairing isolates the precise contextual and structural markers of the necessary/sufficient flaw. The Metropolis excerpt involves a 'compound objective' and a 'policy'. The cybersecurity excerpt involves a 'causal chain' and an illegal negation ('nonoccurrence'). The geological excerpt involves 'multiple prerequisites' for a 'classification'. The submersible excerpt involves a 'single necessary precondition' for a 'capability'.
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Anahtar Kavram
While many arguments commit the fallacy of confusing necessary and sufficient conditions, the structural manifestation of this flaw varies. Advanced logical reasoning requires distinguishing between illegal reversals and illegal negations, as well as tracking whether the flaw applies to single attributes, compound objectives, categorizations, or causal chains.