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Difficulty: Very hardForming Contrapositives

Consider the following legal principle: To secure a federal appellate reversal of a lower court's procedural ruling, an appellant must demonstrate both that the presiding judge exhibited clear bias and that the original defense counsel failed to raise a timely objection, unless new exculpatory evidence has emerged since the trial concluded.

Based exclusively on this principle, is the following deduction logically valid?
If no new exculpatory evidence has emerged since the trial concluded, and the federal appellate court refuses to reverse the lower court's procedural ruling, then the appellant must have failed to demonstrate either that the judge exhibited clear bias or that the original defense counsel failed to raise a timely objection.

Answer: Answer

Answer

The deduction is logically invalid (False).
The correct answer is False because the proposed deduction commits the formal fallacy of Mistaken Negation (denying the antecedent). The original principle states that securing a reversal is a sufficient condition to know that either new evidence emerged, or both bias and a failure to object were demonstrated. Formally, this is: Reversal → ((Bias AND No Objection) OR Evidence). The proposed deduction argues that if there is no evidence and no reversal, then the appellant must have failed to prove bias or failed to prove a lack of objection. Formally: (No Evidence AND No Reversal) → (No Bias OR Objection Raised). This reasoning invalidly attempts to infer the absence of the necessary conditions from the absence of the sufficient condition. It is entirely possible that the appellant demonstrated all the required elements, but the appellate court refused the reversal for a completely different, unstated reason.

Step-by-Step Solution

1
Translate the stimulus into formal conditional logic.
Let R = Reversal secured. Let B = Bias demonstrated. Let O = Objection failure demonstrated. Let E = New exculpatory evidence. The rule is: R → ((B AND O) OR E).
Deconstructing the text into formal logic prevents misinterpretation of complex compound conditions and 'unless' statements.
2
Translate the proposed deduction into formal conditional logic.
The deduction proposes: (NOT E AND NOT R) → (NOT B OR NOT O).
This establishes the exact logical structure of the claim that must be evaluated for validity.
3
Determine the valid contrapositive of the original principle.
The valid contrapositive is: NOT ((B AND O) OR E) → NOT R. Applying De Morgan's laws, this becomes: ((NOT B OR NOT O) AND NOT E) → NOT R.
Comparing the proposed deduction against the valid contrapositive reveals structural differences and logical fallacies.
4
Compare the proposed deduction to the valid contrapositive to identify logical flaws.
The proposed deduction attempts to infer the negation of the necessary conditions (NOT B OR NOT O) from the negation of the sufficient condition (NOT R). This is a Mistaken Negation.
Even if the court refuses to grant a reversal (NOT R), the appellant might have successfully demonstrated all the necessary conditions. The conditions are required for a reversal, but they do not guarantee one.

Key Concept

Distinguishing between a valid contrapositive applying De Morgan's laws and a Mistaken Negation within compound conditional statements.
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Topics

Forming Contrapositives

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