Analyze the following flawed arguments, all of which share a common set of variables regarding commercial development. Match each argument with the specific missing assumption required to make its conclusion logically follow.
- Any commercial development approved by the Planning Commission passes the mandatory environmental audit. It logically follows that any development approved by the Planning Commission is guaranteed to receive a municipal tax subsidy.Failing to receive a municipal tax subsidy implies that a commercial development did not pass the mandatory environmental audit.
- A commercial development is awarded a municipal tax subsidy provided that it incorporates extensive green spaces. Therefore, any development that incorporates extensive green spaces will undoubtedly be approved by the Planning Commission.A commercial development cannot receive a municipal tax subsidy unless it is approved by the Planning Commission.
- The Planning Commission approves a commercial development if that development receives a municipal tax subsidy. Consequently, no commercial development can receive a municipal tax subsidy unless it incorporates extensive green spaces.Approval by the Planning Commission guarantees that a commercial development incorporates extensive green spaces.
- Any commercial development that passes the mandatory environmental audit is awarded a municipal tax subsidy. From this, one can conclude that a development will receive a municipal tax subsidy whenever it incorporates extensive green spaces.A commercial development incorporates extensive green spaces only if it passes the mandatory environmental audit.
Answer
Argument 1 pairs with the assumption that failing to receive a subsidy implies failing the audit. Argument 2 pairs with the assumption that a subsidy requires Planning Commission approval. Argument 3 pairs with the assumption that approval guarantees green spaces. Argument 4 pairs with the assumption that incorporating green spaces requires passing the audit.
Each argument contains a logical gap between its premises and its conclusion. By translating the statements into formal conditional logic, we can identify the exact missing premise required for the conclusion to be drawn validly. Argument 1 requires E -> T, which matches the contrapositive statement ~T -> ~E. Argument 2 requires T -> P, which matches the 'unless' statement translating to ~P -> ~T. Argument 3 requires P -> G, which matches the 'guarantees' statement. Argument 4 requires G -> E, which matches the 'only if' statement.
Step-by-Step Solution
Key Concept
Identifying missing conditional links and translating complex conditional indicators (unless, provided that, whenever, implies, only if) into formal logic.