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Difficulty: HardAssumptions in Conditional Logic

The survival of the coral reef ecosystem in the Sapphire Atoll requires a continuous presence of parrotfish. Parrotfish, however, can maintain their populations only if there is a low concentration of acidic pollutants in the surrounding water. It has been recently established that heavy industrial runoff from the mainland introduces high levels of heavy metals into the atoll. Therefore, whenever the atoll experiences heavy industrial runoff, the coral reef ecosystem will ultimately fail to survive.

Which one of the following is an assumption required by the argument?

  1. The introduction of high levels of heavy metals into the atoll precludes a low concentration of acidic pollutants in the water.Answer
  2. B
    Any atoll water that lacks a low concentration of acidic pollutants must contain high levels of heavy metals.
  3. C
    A low concentration of acidic pollutants in the water is sufficient to guarantee the continuous presence of parrotfish.
  4. D
    If parrotfish fail to maintain their populations, the concentration of acidic pollutants in the water will inevitably rise.
  5. E
    If heavy industrial runoff from the mainland is prevented, the coral reef ecosystem in the Sapphire Atoll will survive.

Answer

The statement asserting that the introduction of high levels of heavy metals into the atoll precludes a low concentration of acidic pollutants in the water.
The argument depends on linking the new information introduced in the premises (heavy metals) to the causal chain that leads to the destruction of the reef. The premises establish that survival requires parrotfish, and parrotfish require low acid. Thus, a lack of low acid guarantees the reef will not survive. The argument concludes that heavy runoff guarantees the reef will not survive, based strictly on the fact that runoff introduces heavy metals. For this to make sense, the heavy metals must cause the lack of low acid. By stating that heavy metals preclude low acid, this option perfectly bridges the gap in the conditional chain.

Step-by-Step Solution

1
Analyze the conditional statements in the premises.
Survival requires Parrotfish (Survival -> Parrotfish). Parrotfish require Low Acid (Parrotfish -> Low Acid). Heavy Runoff introduces Heavy Metals (Runoff -> Heavy Metals).
Identifying the formal logic structure is the first step in finding the missing structural link.
2
Analyze the conditional statement in the conclusion.
Heavy Runoff guarantees a failure to survive (Runoff -> NOT Survival).
Understanding the final claim determines what the premises must logically prove to make the argument valid.
3
Chain the premises and find the logical gap.
The conclusion requires linking Runoff to NOT Survival. We know Runoff -> Heavy Metals. By contrapositive, NOT Low Acid -> NOT Parrotfish -> NOT Survival. To connect these halves (Runoff -> Heavy Metals ... NOT Low Acid -> NOT Survival), we need a bridge between Heavy Metals and NOT Low Acid.
An argument relying on a conditional chain is only valid if all terms leading from the sufficient condition to the necessary condition are properly connected.
4
Formulate the required assumption and apply the Negation Test.
The required assumption is that Heavy Metals -> NOT Low Acid (Heavy metals preclude low acid). If negated, heavy metals would NOT prevent low acid, which means runoff could occur without disrupting the conditions necessary for survival, destroying the conclusion.
A necessary assumption must be required for the conclusion to stand; if its negation invalidates the argument, it is the correct answer.

Key Concept

Assumptions in Conditional Logic
Estimated Time:2m 0s
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Assumptions in Conditional Logic

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