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Difficulty: HardSyllogism and Categorical Propositions

Consider the following two categorical premises:

• Premise 1: All integer-spin particles are bosons.
• Premise 2: No bosons obey Fermi-Dirac statistics.

Evaluate the following candidate conclusions:
Conclusion I: No integer-spin particles obey Fermi-Dirac statistics.
Conclusion II: Some integer-spin particles do not obey Fermi-Dirac statistics.

Under standard modern categorical logic (where universal premises carry no existential import), which of the following statements is correct?

  1. Only Conclusion I follows.Answer
  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 combination of premises 'All integer-spin particles are bosons' (All S are M) and 'No bosons obey Fermi-Dirac statistics' (No M are P) validly yields the universal negative conclusion 'No integer-spin particles obey Fermi-Dirac statistics' (No S are P). Conclusion II ('Some S are not P') cannot be validly inferred because modern formal logic does not assume universal statements guarantee the existence of subject members (existential fallacy). Thus, only the first conclusion logically follows.

Step-by-Step Solution

1
Represent the premises in standard categorical form
Premise 1 is an A-proposition: 'All S are M' (where S = integer-spin particles, M = bosons). Premise 2 is an E-proposition: 'No M are P' (where P = particles obeying Fermi-Dirac statistics).
Mapping categorical propositions allows standard syllogistic figure and mood analysis.
2
Test Conclusion I for logical validity
Combining 'All S are M' and 'No M are P' yields 'No S are P' (E-proposition).
In first-figure syllogisms (Barbara/Celarent), an A-premise and an E-premise yield a valid universal negative (E) conclusion.
3
Test Conclusion II for existential fallacy
Conclusion II ('Some S are not P') is an O-proposition (particular negative).
In modern Boolean categorical logic, universal propositions (A and E) do not carry existential import. Inferring a particular proposition (I or O) from purely universal premises without an explicit existential premise is an existential fallacy.

Key Concept

Existential Fallacy and Categorical Syllogism Validity
Estimated Time:2m 0s
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Topics

Syllogism and Categorical Propositions

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