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Difficulty: HardNecessary vs. Sufficient Condition Flaws

Review the following argument excerpts. Which of these arguments contain flawed reasoning that confuses a necessary condition for a sufficient condition, or a sufficient condition for a necessary condition? (Select all that apply.)

  1. A star can stabilize into a main-sequence phase only if it achieves a critical core temperature. Therefore, since the newly observed protostar in the Orion nebula has reached this critical core temperature, it will soon stabilize into a main-sequence phase.Answer
  2. B
    Decoding the ancient script requires discovering a bilingual text containing both the unknown script and a known language. Since archaeologists have completely excavated the site without finding any such bilingual texts, the ancient script cannot be decoded using currently available materials.
  3. If a cryptographic protocol utilizes lattice-based algebraic structures, it is resistant to quantum computing attacks. The new messaging application does not use lattice-based structures, so we can be certain its encryption is vulnerable to quantum computing attacks.Answer
  4. D
    Every time a deep-sea hydrothermal vent ceases to release hydrogen sulfide, the local tubeworm population rapidly declines. Therefore, the decline in the tubeworm population must be the primary mechanism that causes the vent to stop releasing hydrogen sulfide.
  5. E
    Each individual piece of geological data collected regarding the seasonal migrations is highly accurate and free of measurement error. Consequently, the overarching theoretical model of migration patterns built entirely from these data points must also be perfectly accurate.

Answer

The argument about the protostar's core temperature (illegal reversal) and the argument about the cryptographic protocol (illegal negation).
The correct selections both exhibit classic conditional reasoning failures. The argument concerning the protostar commits an illegal reversal: it establishes that a critical core temperature is necessary for stabilization ('only if'), but the conclusion mistakenly treats it as sufficient. The argument concerning the cryptographic protocol commits an illegal negation: it establishes that lattice-based structure is sufficient for quantum resistance ('If'), but the conclusion mistakenly treats it as necessary by assuming its absence guarantees vulnerability.

Step-by-Step Solution

1
Analyze each excerpt for conditional indicator language and map the formal logic.
The protostar argument maps as: Stabilize -> Critical Temperature. The cryptography argument maps as: Lattice-based -> Quantum Resistant.
Identifying the formal conditional relationships is the prerequisite for checking if those relationships have been abused.
2
Evaluate the conclusions drawn in the conditional arguments against their premises.
The protostar argument concludes: Critical Temperature -> Stabilize (Reversing the terms). The cryptography argument concludes: ~Lattice-based -> ~Quantum Resistant (Negating the terms without reversing).
This step reveals whether the argument adheres to the valid contrapositive or commits an illegal reversal/negation.
3
Examine the remaining excerpts to ensure they do not contain hidden conditional flaws.
The ancient script argument forms a valid contrapositive. The hydrothermal vent argument is a causal reverse-causation flaw. The geological data argument is a part-to-whole composition flaw.
In multiple-selection formats, every option must be rigorously verified to prevent false negatives or false positives.

Key Concept

Necessary vs. Sufficient Condition Flaws (Illegal Reversal and Illegal Negation)
Estimated Time:2m 0s
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Topics

Necessary vs. Sufficient Condition Flaws

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