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Difficulty: MediumAssumptions in Conditional Logic

Consider the argument below regarding historical artifacts:

A historical artifact is considered authentic only if its provenance can be verified through continuous independent documentation. The recently discovered chalice lacks any continuous independent documentation of its provenance. Therefore, the chalice cannot be considered an authentic historical artifact.

The argument above logically depends on the assumption that any historical artifact whose provenance can be verified through continuous independent documentation is considered authentic.

Answer: Answer

Answer

False
The statement is false because the provided argument is already logically valid and complete. It correctly uses the contrapositive of its stated premise (Authentic -> Provenance Verified) to safely reach the conclusion (~Provenance Verified -> ~Authentic). It does not require or rely on the reversed assumption that verifiable provenance guarantees authenticity.

Step-by-Step Solution

1
Translate the argument's first sentence into a formal conditional relationship.
The phrase 'only if' introduces a necessary condition. The relationship is: Authentic -> Provenance Verified.
Identifying the exact conditional relationship is required to evaluate the logical structure of the argument.
2
Analyze the second premise and the conclusion.
The argument states that the chalice does not have verified provenance (~Provenance Verified), and concludes it is not authentic (~Authentic).
This maps the specific scenario to the established conditional rule.
3
Evaluate the validity of the argument's deduction.
The argument correctly applies the contrapositive principle (~Provenance Verified -> ~Authentic). The reasoning is completely sound without any missing links.
A logically sound argument relies only on its stated premises and valid rules of inference; it does not require any additional unstated assumptions.
4
Analyze the assumption provided in the statement.
The statement claims the argument relies on the assumption 'Provenance Verified -> Authentic'. Because the argument is already valid, it does not rely on this reversed condition.
This confirms that the provided statement incorrectly evaluates the logical dependencies of the argument.

Key Concept

Evaluating whether a conditional argument requires an additional assumption, and distinguishing between valid deductions (contrapositive) and invalid assumptions (illegal reversal).
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Topics

Assumptions in Conditional Logic

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