Question

Difficulty: HardIdentifying Necessary Assumptions

Art historian: The newly discovered 16th-century painting *The Solitary Scholar* contains lapis lazuli, a blue pigment that was exorbitantly expensive at the time. Only artists backed by wealthy patrons could afford to use lapis lazuli extensively in their works. Given that historical records confirm the artist, Vincenzo, died in poverty and never secured a wealthy patron, *The Solitary Scholar* must have been a collaborative effort with an artist who could afford such materials.

Which one of the following is an assumption required by the art historian's argument?

  1. A
    Any 16th-century painting that contains lapis lazuli was produced through a collaborative effort.
  2. B
    The lapis lazuli used in *The Solitary Scholar* was of the highest purity available during the 16th century.
  3. *The Solitary Scholar* does not feature merely a small, affordable quantity of lapis lazuli.Answer
  4. D
    Most 16th-century artists who died in poverty relied on wealthy collaborators to complete their paintings.
  5. E
    Artists backed by wealthy patrons during the 16th century invariably used lapis lazuli extensively in their works.

Answer

The argument requires assuming that the painting does not feature merely a small, affordable quantity of lapis lazuli.
The argument relies on a subtle shift in language: the painting 'contains' the pigment, but the rule about needing a wealthy patron only applies to using the pigment 'extensively'. For the conclusion (that Vincenzo needed a collaborator to afford it) to hold true, the author must be assuming that the painting uses enough of the pigment to trigger that financial constraint. If it only used a tiny, affordable amount, Vincenzo wouldn't have needed a collaborator.

Step-by-Step Solution

1
Analyze the premises and the conclusion of the argument.
Premise 1: The painting contains lapis lazuli. Premise 2: Only artists with wealthy patrons could afford to use it extensively. Premise 3: Vincenzo had no wealthy patron. Conclusion: Vincenzo collaborated with someone who could afford the materials.
Deconstructing the argument structure is essential to finding logical gaps.
2
Identify the logical gap (term shift) between the premises.
The premises state the painting 'contains' lapis lazuli, but the financial constraint only applies to using it 'extensively'.
Necessary assumptions often bridge subtle wording shifts in the stimulus.
3
Apply the Negation Technique to the suspected assumption.
Negate the credited response: 'The painting DOES feature merely a small, affordable quantity of lapis lazuli.'
The correct answer to a necessary assumption question must destroy the argument when logically negated.
4
Evaluate the effect of the negated statement on the conclusion.
If the quantity was small and affordable, Vincenzo could have purchased it himself without a wealthy patron or collaborator. The conclusion is refuted.
Because the negation destroys the conclusion, this statement is logically required by the argument.

Key Concept

Identifying a term shift between 'containing' an element and using it 'extensively', and bridging that gap to maintain the argument's logic.
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