As a logic and philosophy expert, I'm delighted to delve into the fascinating world of logical arguments and the nature of their premises and conclusions. Let's embark on this intellectual journey by examining the interplay between tautologies, contingent conclusions, and the validity of arguments.

In the realm of logic, a tautology is a statement that is true by necessity or by virtue of its logical form alone. It is a statement that is true under all possible conditions, regardless of the truth values of its components. For example, the statement "Either it is raining or it is not raining" is a tautology because it is true in every possible scenario.

On the other hand, a contingent statement is one that is not necessarily true or necessarily false. It is a statement whose truth depends on the specific circumstances or conditions. For instance, "It is raining" is contingent because it is only true in conditions where it is indeed raining.

Now, the crux of your question revolves around whether an argument with tautological premises can have a contingent conclusion. To address this, we must first understand what constitutes a valid argument. A valid argument is one where if the premises are true, then the conclusion must also be true. The validity of an argument does not depend on the actual truth of the premises or the conclusion, but rather on the logical relationship between them.

Given this definition, let's consider an argument with tautological premises. Since tautologies are always true, any argument with such premises is guaranteed to have true premises. However, the conclusion of an argument is contingent if it is not necessarily true or false but depends on specific conditions. The key here is the logical relationship between the premises and the conclusion.

If the conclusion is derived logically and necessarily from the premises, then even if the premises are tautologies, the conclusion will be valid. But for the conclusion to be contingent, it must be possible for it to be either true or false depending on the circumstances. This seems to create a paradox because if the premises are tautologies, the conclusion should be necessarily true, not contingent.

However, the resolution to this apparent paradox lies in the nature of tautologies themselves. While tautologies are always true, they do not necessarily provide specific information about the world. They are true in a vacuous way, without bearing on the truth of contingent statements. Therefore, an argument with tautological premises does not inherently determine the truth value of a contingent conclusion.

In conclusion, while it may seem counterintuitive, an argument can have tautological premises and a contingent conclusion if the logical form of the argument does not necessitate the truth of the contingent conclusion. The validity of the argument is preserved because the truth of the premises guarantees the truth of the conclusion, but the contingency of the conclusion is maintained because its truth is not logically entailed by the tautological premises.

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Yes: if it is a tautology, then it is valid. The definition applies to it because it is impossible for it to have true premises and a false conclusion (since it is impossible for it to have a false conclusion at all). ... A contingent sentence is one that is neither always true nor always false.read more >>