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Difficulty: HardIdentifying Sufficient Assumptions

Ecologist: The municipal government's newly proposed desalination plant represents a shortsighted approach to water management. While it addresses the immediate freshwater shortage, the plant will discharge hypersaline brine directly into the coastal estuary. Therefore, the construction of this plant will inevitably trigger a catastrophic collapse of the local commercial fishery.

A deductive argument can be made formally valid by supplying unstated sufficient assumptions. Arrange the following statements to construct a valid deductive chain that fully justifies the ecologist's conclusion.

Instructions: Begin with the ecologist's explicit factual premise regarding the plant's operation. Then, sequence the unstated conditional assumptions such that the necessary condition of one directly triggers the sufficient condition of the next. Finally, end with the argument's main conclusion.

  1. 1The newly proposed desalination plant will discharge hypersaline brine directly into the coastal estuary.
  2. 2Any facility that discharges hypersaline brine directly into a coastal estuary inherently decimates the indigenous phytoplankton population.
  3. 3The decimation of an estuary's indigenous phytoplankton population inevitably leads to the starvation of foundational baitfish species.
  4. 4The starvation of foundational baitfish species strictly guarantees a catastrophic collapse of the local commercial fishery.
  5. 5Therefore, the construction of the newly proposed desalination plant will inevitably trigger a catastrophic collapse of the local commercial fishery.

Answer

The correct sequence begins with the explicit premise about discharging brine, flows through three sequential conditional assumptions (brine → phytoplankton → baitfish → fishery), and ends with the final conclusion regarding the fishery collapse.
The correct sequence constructs a valid deductive proof using formal conditional logic (a Sorites chain). It begins by stating the explicit factual premise. It then applies a series of universal sufficient assumptions (A → B, B → C, C → D). Because the initial premise satisfies the sufficient condition of the first rule, it triggers a chain reaction of necessary conditions, which inevitably and strictly guarantees the final conclusion. This perfectly bridges the gap in the ecologist's original argument.

Step-by-Step Solution

1
Identify the explicit premise and the final conclusion in the ecologist's stimulus.
Premise: The plant discharges hypersaline brine. Conclusion: The plant triggers a commercial fishery collapse.
Isolating the starting point and the endpoint is required to determine the logical gap that the assumptions must bridge.
2
Select the statement that serves as the factual starting point for the deductive proof.
The first item in the sequence must be the explicit premise: 'The newly proposed desalination plant will discharge hypersaline brine...'
A valid deductive chain applying general rules to a specific case must always begin with the factual circumstances of that specific case.
3
Identify the first sufficient assumption that takes the premise as its sufficient condition trigger.
The next statement is the rule stating that discharging hypersaline brine inherently decimates the indigenous phytoplankton population.
This establishes an 'If A then B' rule where A is our starting premise, allowing us to formally deduce B.
4
Continue chaining the conditional assumptions by matching the necessary condition of the previous step to the sufficient condition of the next.
The sequence continues with the rule connecting 'phytoplankton' to 'baitfish', followed by the rule connecting 'baitfish' to the 'commercial fishery'.
This creates a transitive formal logic chain (A → B, B → C, C → D) that fully bridges the gap in the ecologist's original argument.
5
Place the main conclusion at the end of the deductive chain.
The final item is: 'Therefore, the construction of this plant will inevitably trigger a catastrophic collapse...'
The conclusion is the logical outcome guaranteed by the preceding premises and assumptions.

Key Concept

Constructing valid deductive proofs by chaining sufficient assumptions in formal conditional logic.
Estimated Time:2m 30s
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Topics

Identifying Sufficient Assumptions

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