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Difficulty: HardSyllogism and Categorical Propositions

Consider the following statements and candidate conclusions. Assuming the statements to be true even if they seem at variance with commonly known facts, evaluate their logical validity strictly under modern categorical logic (Boolean interpretation).

Statements:
1. All specialized bathyscaphes are deep-sea exploration vessels.
2. No deep-sea exploration vessels are constructed from unreinforced polymers.

Conclusions:
I. No specialized bathyscaphes are constructed from unreinforced polymers.
II. Some specialized bathyscaphes are not constructed from unreinforced polymers.

Which of the following statements is correct?

  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 option stating that only conclusion I follows is correct because combining a Universal Affirmative premise ('All S are M') and a Universal Negative premise ('No M are P') validly yields the Universal Negative conclusion 'No S are P' (Conclusion I). Conclusion II ('Some S are not P') is invalid under modern Boolean logic because deriving a particular conclusion from universal premises without asserting the existence of the subject set constitutes an existential fallacy.

Step-by-Step Solution

1
Translate the statements into formal categorical propositions
Statement 1 is a Universal Affirmative (A-type): All S (specialized bathyscaphes) are M (deep-sea exploration vessels). Statement 2 is a Universal Negative (E-type): No M (deep-sea exploration vessels) are P (constructed from unreinforced polymers).
Establishing the categorical structure (Mood and Figure) is required to evaluate syllogistic validity.
2
Derive the valid universal conclusion using rules of categorical syllogism
Combining 'All S are M' and 'No M are P' yields 'No S are P' (E-type conclusion: No specialized bathyscaphes are constructed from unreinforced polymers).
The middle term 'M' is distributed in Statement 2, and the term 'P' is distributed in both Statement 2 and the conclusion, satisfying all rules of valid universal deduction.
3
Evaluate Conclusion II under Modern Categorical Logic (Boolean Interpretation)
Conclusion II ('Some S are not P') is a Particular Negative (O-type). Under Boolean interpretation, universal statements (A and E) do not carry existential import (they do not guarantee that S actually exists in reality). Therefore, inferring an O-type conclusion from universal premises without an explicit existential premise is an Existential Fallacy.
Modern logic requires explicit existential premises to validly deduce particular statements from universal statements.

Key Concept

Existential Fallacy and Boolean Interpretation of Syllogisms
Estimated Time:1m 30s
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Topics

Syllogism and Categorical Propositions

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