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2.4: Deductive Validity

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    The deductive standard of support is validity. An argument counts as deductive whenever it is aiming at this standard of support. Deductive validity is the strictest standard of support we can uphold. In a deductively valid argument, the truth of the premises guarantees the truth of the conclusion. Here are two equivalent definitions of deductive validity:

    (D) A valid argument is an argument where if its premises are true, then its conclusion must be true.

    (D’) A valid argument is an argument where it is not possible for all of its premises to be true and its conclusion false.

    Here are a few examples of deductively valid arguments

    1. If Socrates is human, then Socrates is mortal
    2. Socrates is a human.
    3. Therefore, Socrates is mortal
    1. All monkeys are primates
    2. All primates are mammals
    3. So, all monkeys are mammals

    If you think about these two examples for a moment, it should be clear that there is no possible way for the premises to all be true and the conclusion false. The truth of the conclusion is guaranteed by the truth of the premises. In contrast, the following argument is not valid:

    1. If Sue misses her plane, she will be late for the conference.
    2. Sue is late for the conference.
    3. Therefore, she missed her plane.

    Again, to say that an argument is deductively valid is to say that it is impossible for all of its premises to be true and its conclusion to be false. To see why the last argument is not valid, try to think of a possible scenario that makes both of the premises true and the conclusion false. One scenario is where Sue catches her plane, but her cab from the airport gets stuck in traffic. If we can think of any possible way for the premises of an argument to be true and its conclusion false, then we have show that the conclusion does not deductively follow from the premises. That is, we’ve shown that the argument is not valid.

    Our intuitive test for validity is to think about whether it is possible for the argument’s premises to be true and its conclusion to be false. A key point to notice here is that validity is not directly about the truth or falsity of the premises or the conclusion. The concept of validity is really a concept about what is and isn’t logically possible. A deductively valid argument may or may not have true premises. Consider this argument:

    1. All stars are bodies that shine steadily.
    2. All planets are stars.
    3. All planets are bodies that shine steadily.

    Both of the premises in this argument are false, but the argument is still valid. Suppose, contrary to fact, that the premises were true. It should be easy to see that the conclusion would have to be true if this were the case. Validity isn’t about whether the premises or the conclusion are in fact true. It is only about whether the conclusion logically follows from the premises.

    A deductively valid argument only provides one with a good reason for believing its conclusionif its premises are true. If a deductively valid argument has all true premises, we say that it is deductively sound. For an argument to be deductively sound is one way for it to pass both steps (1) and (2) above for evaluating arguments.

    The deductive arguments we’ve looked at here are pretty intuitive. We only need to think about whether the conclusion could be false even if the premises were true. But most deductive arguments are not so obvious. Logic is the science of deductive validity. Philosophy has made some historic advances in logic over the past century. Bertrand Russell, who we got acquainted with in the last chapter, was among the key contributors to early developments in logic over the 20th century. In the next chapter we will get acquainted with the first logician, Aristotle.

    This page titled 2.4: Deductive Validity is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Russ W. Payne via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.