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Difficulty: Very hardSyllogism and Categorical Propositions

Read the following statements and conclusions carefully:

Statements:
1. All quantum sensors are optical resonators.
2. No optical resonator is a thermal detector.
3. All thermal detectors are cryogenic probes.

Conclusions:
I. No quantum sensor is a thermal detector.
II. Some cryogenic probes are not optical resonators.

Which of the specified conclusions logically follow(s) from the given statements under strict formal logic?

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

Answer

Only conclusion I follows
The correct answer identifies that only Conclusion I logically follows. Combining 'All quantum sensors are optical resonators' with 'No optical resonator is a thermal detector' logically forces the universal negative result that no quantum sensor can be a thermal detector. Conclusion II attempts to draw a particular ('Some') conclusion from purely universal premises, which is invalid without assuming existential import.

Step-by-Step Solution

1
Analyze Statement 1 and Statement 2
Statement 1: Quantum Sensors ⊆\subseteq Optical Resonators. Statement 2: Optical Resonators ∩\cap Thermal Detectors =∅= \emptyset.
Combining these two universal statements yields Quantum Sensors ∩\cap Thermal Detectors =∅= \emptyset (No quantum sensor is a thermal detector).
2
Evaluate Conclusion I
Conclusion I ('No quantum sensor is a thermal detector') is valid.
It is a universal negative statement (E-type) validly drawn from two universal premises (A-type and E-type).
3
Analyze Statement 3 and Evaluate Conclusion II under formal categorical logic
Premises are all Universal (All Q are O, No O is T, All T are C). Conclusion II is Particular ('Some cryogenic probes are not optical resonators').
In formal Boolean categorical logic, universal premises do not carry existential import (they do not guarantee that thermal detectors actually exist). Deriving a particular conclusion ('Some...') from purely universal premises commits the existential fallacy unless the existence of elements is explicitly stated.

Key Concept

Existential Fallacy in Categorical Syllogisms
Estimated Time:2m 0s
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Topics

Syllogism and Categorical Propositions

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