Validity, Soundness, and Cogency
Episode #8 of the course Logic basics: Understanding arguments by Gary Curtis
In a previous lesson, you learned that a deductive argument is one that claims its conclusion follows from its premises with necessity. Notice the word “claims” here: Just because an argument or arguer makes such a claim, it isn’t necessarily so. However, if it is true, the argument is called “valid.”
Validity and Soundness
A valid argument is one that the truth of its premises necessitates the truth of its conclusion. Validity is the strongest possible logical connection between the premises of an argument and its conclusion. You can think of validity as a truth pump: Put true premises into a valid argument, and out comes a true conclusion.
Example:
1. All birds are animals.
2. Tweety is a bird.
3. Therefore, Tweety must be an animal.
If the premises, #1 and #2, are true, then the conclusion, #3, will also be true.
Valid arguments may have one or more false premises and if so, even a false conclusion.
Example:
1. All birds are fish.
2. Tweety is a bird.
3. Therefore, Tweety must be a fish.
In this argument, the first premise and the conclusion are false, but it has the same logical structure as the preceding example. It is also a valid argument because if the premises were both true, the conclusion would also be true. The only combination of true and false that validity rules out is all true premises and a false conclusion. So, any argument with true premises and a false conclusion must be invalid. Just as a water pump won’t pump water unless you put water in, a valid argument won’t work as a truth pump if you don’t put true premises in. A valid argument with true premises is called sound.
Since the conclusion of a sound argument is true, soundness is a valuable property but it isn’t everything.
Circularity
Look at this example: The sun is above the horizon during the day. Therefore, the sun is above the horizon during the day.
Is this argument sound? Yes! Of course, its premise is true. Moreover, if the premise is true, then the conclusion has to be true as well, since they’re the same statement, so the argument is valid. Of course, it’s a dreadful argument for all that, so soundness is clearly not enough.
But what’s wrong with this argument?
It’s a circular argument, with the conclusion the same as its premise. In general, circular arguments are valid, and if their premises are true, then they’re sound. However, circular arguments are fallacious and therefore, bad arguments.
Cogency
Validity and soundness are properties of deductive arguments. Since the premises of an inductive argument do not necessitate the truth of its conclusion, inductive arguments cannot be valid. For this reason, we need a different term for evaluating inductive arguments.
A cogent argument is one that the truth of its premise makes the conclusion more likely to be true than false.
Example:
1. Most birds can fly.
2. Tweety is a bird.
3. Therefore, Tweety can probably fly.
Given that you don’t know anything more about Tweety than what is given in the premise—for instance, Tweety may be a penguin—then it’s likely that Tweety can fly. Therefore, the example is cogent.
At the beginning of this lesson, you saw that the only combination of true and false in its component statements that a valid argument ruled out was all true premises and a false conclusion. A cogent inductive argument doesn’t rule out even this combination—that is, it’s possible but unlikely that a cogent inductive argument has true premises and a false conclusion. For instance, if it turns out that Tweety is an ostrich, then the premises are true but the conclusion is false. This is the difference between deduction and induction in a nutshell.
In the next lesson, you’ll start applying what you learned in the previous lessons to more complicated arguments.
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Recommended book
A Concise Introduction to Logic by Patrick J. Hurley
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