Part I – [TOTAL SCORE 10]

Determine whether each of the following propositions is True or False.

I.4

“A given argument with the false conclusion is invalid only if none of its premises are false.”

Question

Part I – [TOTAL SCORE 10]

Determine whether each of the following propositions is True or False.

I.4

“A given argument with the false conclusion is invalid only if none of its premises are false.”

BlackTom AI · Accepted Answer

The task presents a logical proposition about argument validity. I will parse the statement and evaluate each option carefully.
Option 1: True. The claim here is that an argument with a false conclusion is invalid only if none of its premises are false. This wording is muddled and misleading. In logic, an argument is valid if, assuming all premises are true, the conclusion must be true. A false conclusion does not hinge on whether any premise is false; you can have a valid argument with true premises that leads to a true conclusion, or an invalid argument where the conclusion could be false even if some premises are true. More importantly, the assertion “only if none of its premises are false” attempts to tie validity strictly to premise truth in a way that conflates validity with premise truth conditions; this is not how validity is defined. Therefore, this option misstates the relationship between premises and conclusion and is not correct.
Option 2: False. This is the correct characterization. An argument is invalid if there exists at least one case where the premises are all true but the conclusion is false. It is not required that none of the premises be false for invalidity to occur; in fact, the presence of even one true and one false premise does not guarantee validity, and the premise truth status is not the sole determinant. The statement incorrectly confines invalidity to a scenario that doesn’t align with the standard definition of logical validity. Hence, this option accurately identifies the flaw in the proposition. 
In sum, the assertion in Option 1 misrepresents how validity operates by tying it to premise truth in a way that incorrectly excludes scenarios where some premises may be false or where the conclusion can fail despite premises being arranged in a way that would not guarantee truth of the conclusion. The correct interpretation is captured by Option 2, which recognizes that invalidity can arise even when premises are not all non-false in the labeled sense, and that a false conclusion does not uniquely indicate an invalid form restricted by premise status.

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Part I – [TOTAL SCORE 10] Determine whether each of the following propositions is True or False. I.4 “A given argument with the false conclusion is invalid only if none of its premises are false.”

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