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Difficulty: MediumSyllogism and Categorical Propositions

An ecologist studying deep-sea ecosystems establishes two facts: Every bioluminescent organism found in this trench is an invertebrate, and some invertebrates in this ecosystem are highly venomous. Based strictly on these formal premises, it is logically guaranteed that some bioluminescent organisms in the trench are highly venomous.

Answer: Answer

Answer

The statement is False.
The logical deduction is invalid because it violates the rule of distribution. The middle term connecting the two premises ('invertebrate') is not distributed in either statement. This means there is no guaranteed logical intersection between the set of bioluminescent organisms and the set of venomous organisms.

Step-by-Step Solution

1
Identify the formal categorical propositions from the text.
Premise 1: All Bioluminescent organisms (B) are Invertebrates (I). Premise 2: Some Invertebrates (I) are Venomous (V). Conclusion to evaluate: Some Bioluminescent organisms (B) are Venomous (V).
Translating natural language into formal logic reveals the underlying syllogistic structure for accurate analysis.
2
Analyze the distribution of the middle term connecting the premises.
The middle term 'Invertebrates' is undistributed in both Premise 1 (as the predicate of an 'All' statement) and Premise 2 (as the subject of a 'Some' statement).
A valid categorical syllogism requires the middle term to be distributed at least once to serve as a logical bridge.
3
Determine the validity of the conclusion based on formal logical rules.
Because the middle term is never distributed, the syllogism commits the Fallacy of the Undistributed Middle. The conclusion is invalid.
Logical validity requires an absolute guarantee. Since the venomous invertebrates could be an entirely separate group from the bioluminescent invertebrates, the conclusion is not guaranteed.

Key Concept

Fallacy of the Undistributed Middle in Categorical Syllogisms
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Topics

Syllogism and Categorical Propositions

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