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Difficulty: HardSyllogism and Categorical Propositions

During an aviation regulatory audit, a compliance officer maps out the relationships between different vehicle classifications based on current operational guidelines. The officer establishes the following foundational premises:

- All perpetually autonomous drones are unregistered aircraft.
- No unregistered aircraft are commercially insured vehicles.
- Some delivery gliders are commercially insured vehicles.

Based strictly on formal deductive logic—and without assuming the physical existence of any entity not explicitly established by the premises—identify the logically infallible deductions from the officer's mapping.

Deduction I: Some perpetually autonomous drones are unregistered aircraft.
Deduction II: No commercially insured vehicles are perpetually autonomous drones.
Deduction III: Some delivery gliders are not perpetually autonomous drones.

Which of the following represents the correct evaluation?

  1. Only Deductions II and III are infallible.Answer
  2. B
    Deductions I, II, and III are all infallible.
  3. C
    Only Deductions I and II are infallible.
  4. D
    Only Deduction II is infallible.

Answer

Only Deductions II and III are infallible.
Deduction II is logically derived from combining the first two premises and converting the resulting universal negative statement. Deduction III is validly derived by combining the third premise with the conclusion of the first two premises. Deduction I is invalid because it assumes the physical existence of the subject (existential fallacy) from a purely universal premise.

Step-by-Step Solution

1
Evaluate Deduction I for existential import based on the first premise.
Deduction I is invalid.
The premise 'All perpetually autonomous drones are unregistered aircraft' is a universal statement. Without explicit evidence that such drones actually exist, deducing that 'Some perpetually autonomous drones are unregistered aircraft' commits the existential fallacy.
2
Evaluate Deduction II by combining the first and second premises.
Deduction II is valid.
Since all autonomous drones are unregistered aircraft, and no unregistered aircraft are commercially insured, it follows that no autonomous drones are commercially insured. Converting this universal negative statement yields: 'No commercially insured vehicles are perpetually autonomous drones.'
3
Evaluate Deduction III by combining the result of Step 2 with the third premise.
Deduction III is valid.
We established that no commercially insured vehicles are autonomous drones. Since the third premise states 'Some delivery gliders are commercially insured vehicles', the specific delivery gliders that are commercially insured cannot be autonomous drones. Therefore, 'Some delivery gliders are not perpetually autonomous drones' is valid.

Key Concept

Evaluating categorical syllogisms involving multi-premise deductive chains, illicit conversion checks, and the existential fallacy.
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Topics

Syllogism and Categorical Propositions

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