Below are four distinct valid arguments. Identify the underlying logical architecture of each by pairing it with its correct formal description.
- If the central bank raises interest rates this quarter, then inflation will stabilize by year-end. However, inflation will definitively not stabilize by year-end. Therefore, the central bank will not raise interest rates this quarter.Denying the Consequent (Modus Tollens): Infers the falsity of a sufficient condition from the falsity of its necessary condition.
- The newly discovered geological fault line was formed either by tectonic subduction or by localized volcanic activity. Core samples have conclusively ruled out localized volcanic activity. Thus, the fault line was formed by tectonic subduction.Elimination (Disjunctive Syllogism): Concludes the truth of one alternative from a disjunction by establishing the falsity of the other.
- If patients exhibit symptoms of prolonged sleep deprivation, their cognitive reaction times degrade. If their cognitive reaction times degrade, they become a liability when operating heavy machinery. Hence, if patients exhibit symptoms of prolonged sleep deprivation, they become a liability when operating heavy machinery.Transitivity (Hypothetical Syllogism): Establishes a conditional relationship between two events by linking them through a common intermediate event.
- All federally funded research grants mandate open-access publication of their final findings. The upcoming quantum computing initiative is a federally funded research grant. Consequently, the quantum computing initiative mandates open-access publication of its final findings.Categorical Application (Universal Instantiation): Infers that a specific individual has a property because it belongs to a category in which all members share that property.
Cevap
The central bank argument pairs with Denying the Consequent; the fault line argument pairs with Elimination; the sleep deprivation argument pairs with Transitivity; and the research grant argument pairs with Categorical Application.
Each argument successfully demonstrates a distinct form of valid logical deduction. The central bank argument relies on Modus Tollens (denying the consequent). The fault line argument utilizes Disjunctive Syllogism (eliminating one alternative to affirm the other). The sleep deprivation argument uses Hypothetical Syllogism (chaining conditional statements). The research grant argument is an example of Universal Instantiation (applying a categorical rule to a specific instance).
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Parallel Valid Structure