Pair each of the following short deductive arguments with the statement that most accurately characterizes its logical form or reasoning defect.
- Every homeowner who installs solar panels lowers their monthly utility bill. David did not lower his monthly utility bill; therefore, David did not install solar panels.Valid deductive reasoning that infers the absence of an initial condition from the established absence of its necessary result.
- A theatrical production will be profitable only if it receives positive opening reviews. The new musical received glowing opening reviews; therefore, the musical will be profitable.Flawed reasoning that treats a factor required for an outcome as sufficient to guarantee that the outcome occurs.
- The municipal museum must either raise general admission prices or reduce public operating hours. The board of directors voted against raising admission prices; therefore, the museum must reduce operating hours.Flawed reasoning that concludes a single outcome must occur by presuming without justification that only two mutually exclusive alternatives exist.
Answer
The solar panel argument pairs with the statement describing valid deduction from the absence of a necessary result; the theatrical production argument pairs with the statement describing the error of treating a required condition as a guarantee; and the museum argument pairs with the statement describing an unjustified assumption of only two exclusive alternatives.
Each argument corresponds to its exact structural form: the solar panel argument validly concludes the absence of an initial condition because its necessary result did not happen; the theatrical production argument commits a conditional reversal error by treating a requirement as a guarantee; and the museum argument commits a false dilemma by arbitrarily restricting all possibilities to two choices.
Step-by-Step Solution
Key Concept
Identifying and differentiating valid conditional structures (modus tollens) from canonical reasoning flaws including necessary-versus-sufficient confusion and false dilemma.
Estimated Time:1m 0s