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Difficulty: Very hardSyllogism and Categorical Propositions

Read the following premises and candidate conclusions carefully:

Statements:
1. All autonomous underwater vehicles are sonar-equipped vessels.
2. No sonar-equipped vessel is a surface bathyscaphe.
3. All deep-sea gliders are autonomous underwater vehicles.

Conclusions:
I. No deep-sea glider is a surface bathyscaphe.
II. Some sonar-equipped vessels are deep-sea gliders.

Based strictly on the given statements, which of the conclusions logically follow(s)?

  1. Only conclusion I followsAnswer
  2. B
    Only conclusion II follows
  3. C
    Both conclusion I and conclusion II follow
  4. D
    Neither conclusion I nor conclusion II follows

Answer

Only conclusion I follows
The conclusion stating that no deep-sea glider is a surface bathyscaphe follows validly through transitive universal deduction: all deep-sea gliders belong to the class of autonomous underwater vehicles, which are entirely contained within sonar-equipped vessels, none of which overlap with surface bathyscaphes. Conversely, deriving a particular statement ('Some sonar-equipped vessels are deep-sea gliders') from universal premises without an explicit assertion of non-emptiness constitutes an existential fallacy, rendering the second conclusion invalid under standard formal logic.

Step-by-Step Solution

1
Analyze the relationship between Deep-Sea Gliders, Autonomous Underwater Vehicles, and Sonar-Equipped Vessels.
Combining 'All deep-sea gliders are autonomous underwater vehicles' and 'All autonomous underwater vehicles are sonar-equipped vessels' yields the universal affirmative proposition: 'All deep-sea gliders are sonar-equipped vessels'.
Syllogistic chaining of two universal affirmative (A-type) statements preserves universal inclusion.
2
Combine the result from Step 1 with the premise regarding Surface Bathyscaphes.
Combining 'All deep-sea gliders are sonar-equipped vessels' with 'No sonar-equipped vessel is a surface bathyscaphe' yields 'No deep-sea glider is a surface bathyscaphe'.
An E-type (universal negative) statement combined with an A-type statement where the middle term is distributed yields a valid E-type conclusion.
3
Evaluate Conclusion I.
Conclusion I states 'No deep-sea glider is a surface bathyscaphe', which matches the exact valid deduction from Step 2.
Conclusion I is logically valid and sound.
4
Evaluate Conclusion II for validity under standard modern categorical logic.
Conclusion II claims 'Some sonar-equipped vessels are deep-sea gliders'. Since both original statements involving these terms are universal ('All'), inferring a particular ('Some') statement commits the existential fallacy.
Modern formal logic does not assume existential import for universal categorical statements. Particular conclusions cannot be drawn from exclusively universal premises.

Key Concept

Categorical Syllogism and Existential Import
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Topics

Syllogism and Categorical Propositions

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