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Zorluk: OrtaSufficient Assumption

Art Historian: Extensive chemical analysis confirms that the newly discovered portrait *Lady in Blue* contains genuine ultramarine pigment. Historical records demonstrate that only paintings created prior to the eighteenth century contain genuine ultramarine pigment. Therefore, *Lady in Blue* is undoubtedly a highly valuable artwork.

Statement: The assumption 'Any painting that is highly valuable was created prior to the eighteenth century' is a sufficient assumption that, if added to the premises, logically guarantees the art historian's conclusion.

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Cevap

False
The statement is false because the provided assumption is an illegal reversal. The argument establishes that the painting is from before the eighteenth century, and concludes it is highly valuable. To guarantee this conclusion, the rule must be 'If created before the eighteenth century, then highly valuable.' The proposed assumption is 'If highly valuable, then created before the eighteenth century,' which tells us nothing about a painting we already know is old. It fails to logically prove the conclusion.

Adım Adım Çözüm

1
Identify the premises and map the conditional logic.
Premise 1: Lady in Blue contains genuine ultramarine. Premise 2: Genuine ultramarine → Created prior to the eighteenth century. Inference: Lady in Blue was created prior to the eighteenth century.
Understanding the established facts is necessary before determining what logical link is missing.
2
Identify the conclusion of the argument.
Conclusion: Lady in Blue → Highly valuable.
The conclusion is the endpoint that the sufficient assumption must mathematically guarantee.
3
Determine the missing logical link (the correct sufficient assumption).
The argument needs to bridge the gap from the inference (Created prior to the eighteenth century) to the conclusion (Highly valuable). The correct assumption is: Created prior to the eighteenth century → Highly valuable.
A sufficient assumption must trigger the conclusion when combined with the existing premises.
4
Evaluate the proposed assumption in the statement.
The proposed assumption is 'Highly valuable → Created prior to the eighteenth century'. This is the reverse of the needed link and does not guarantee that the Lady in Blue is highly valuable.
We must verify if the given statement matches the required logical bridge.

Anahtar Kavram

Evaluating Sufficient Assumptions and identifying Illegal Reversals in conditional logic.
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Konular

Sufficient Assumption

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