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Question

Difficulty: MediumSufficient Assumption

Complete the archaeometrist's formal deductive argument by identifying the missing premise that logically guarantees the conclusion.

Answer:Premise 1: Any ancient ceramic shard containing trace crystalline zircon was fired at temperatures exceeding 900°C.
Premise 2: 【Every artifact unearthed at the Oakhaven kiln complex is an ancient ceramic shard containing trace crystalline zircon】
Conclusion: Therefore, every artifact unearthed at the Oakhaven kiln complex was fired at temperatures exceeding 900°C.

Answer

Every artifact unearthed at the Oakhaven kiln complex contains trace crystalline zircon
The argument requires a deductive bridge connecting the subject of the conclusion ('every artifact unearthed at the Oakhaven kiln complex') to the sufficient condition of Premise 1 ('ancient ceramic shard containing trace crystalline zircon'). By establishing that all Oakhaven artifacts contain trace crystalline zircon, the chain becomes: Oakhaven Artifact → Contains Trace Zircon → Fired Exceeding 900°C. This 100% guarantees the truth of the conclusion via hypothetical syllogism.

Step-by-Step Solution

1
Isolate the conclusion and formalize its conditional terms
The conclusion asserts: If an artifact was unearthed at the Oakhaven kiln complex, then it was fired at temperatures exceeding 900°C (Oakhaven Artifact → Fired >900°C).
Establishing the target conditional statement reveals what logical outcome must be derived from the premises.
2
Analyze the given premise to map the existing deductive link
Premise 1 states: If a ceramic shard contains trace crystalline zircon, then it was fired at temperatures exceeding 900°C (Contains Trace Zircon → Fired >900°C).
Determining the existing conditional chain identifies the intermediate predicate and isolates the inferential gap.
3
Bridge the gap between the subject of the conclusion and the antecedent of Premise 1
Connecting 'Oakhaven Artifact' to 'Contains Trace Zircon' creates a valid hypothetical syllogism: Oakhaven Artifact → Contains Trace Zircon → Fired >900°C.
A sufficient assumption must fully guarantee that the conclusion necessarily follows when added to the premises.

Key Concept

Sufficient Assumption in Conditional Deductive Chains
Estimated Time:1m 15s
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Topics

Sufficient Assumption

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