Match each of the following everyday arguments to the formal description of its underlying valid logical architecture.
- If a commercial aviation route is to remain financially viable in the long term, it must maintain a consistent passenger load factor of at least eighty percent. The direct flight between Oakhaven and Riverton has failed to maintain this passenger load factor over the past two years. Therefore, this direct flight will not remain financially viable in the long term.Posits that a certain condition is strictly necessary for a specific outcome to occur. By observing the absence of this necessary condition in a particular instance, it concludes that the outcome cannot occur.
- To mitigate the ongoing urban heat island effect, the city planning commission must either implement a widespread green roof mandate or completely overhaul the public transit infrastructure. Due to severe budget constraints, overhauling the transit infrastructure is impossible. Thus, the commission must implement the green roof mandate.Presents two alternatives as the only available options for addressing a problem. After establishing the impossibility of pursuing one of these options, it deduces that the other option must necessarily be adopted.
- Any comprehensive cybersecurity framework that successfully prevents unauthorized data exfiltration necessitates implementing zero-trust network architecture. Moreover, implementing zero-trust network architecture inherently increases the administrative overhead for IT departments. Therefore, successfully preventing data exfiltration requires an increase in administrative overhead.Establishes a sequence of requirements by showing that one phenomenon dictates a second, and the second inevitably leads to a third. It concludes by directly connecting the initial phenomenon as sufficient to bring about the final consequence.
- Every manuscript written by the medieval scholar Al-Kindi that has survived to the present day contains marginalia added by later Byzantine scribes. The recently authenticated document found in the monastery archives is a surviving manuscript written by Al-Kindi. Consequently, this newly authenticated document contains Byzantine marginalia.Articulates a universal characteristic shared by all members of a specific classification. By identifying a distinct entity as belonging to this classification, it concludes that the entity possesses the universal characteristic.
Answer
The correct pairings identify the aviation argument as Modus Tollens, the urban planning argument as Disjunctive Syllogism, the cybersecurity argument as Chain Conditionals, and the manuscript argument as Universal Instantiation.
Each argument utilizes a formally valid deductive structure. By stripping away the domain-specific vocabulary and substituting logical variables, the underlying frameworks of Modus Tollens, Disjunctive Syllogism, Chain Conditionals, and Universal Instantiation perfectly align with their respective abstract descriptions.
Step-by-Step Solution
Key Concept
Parallel Valid Structure requires abstracting the logical architecture of an argument away from its specific subject matter to identify foundational valid deduction patterns.