Argument Validity
In a previous lesson, we said an argument assumes some truth in order to derive a new truth.
This means problems can potentially arise from both parts:
- One or more of the assumed truths (premises) might be false.
- The newly derived truth (conclusion) may have been derived incorrectly.
When analyzing an argument for validity, we are only concerned with problems that stem from part 2, that is, we are only concerned with whether or not the conclusion of an argument was derived from its premises correctly. This means we do not care whether or not its premises are actually true. For the purposes of argument validity, we are just going to stick to the assumption that the premises are true and narrow our focus on whether the premises “give” the conclusion a sufficient amount of support.
In terms of argument validity, an argument is valid if and only if when we assume its premises are true, it is impossible for its conclusion to be false. Restated, that means there is no scenario where the premises are true but the conclusion is false.
- I heard barking.
- There must be a dog. (1)
In the example above, the conclusion “there must be a dog” is derived from “I heard barking”. Consider the scenario that the barking came from a song, video, or someone who can imitate the barking of a dog. If either scenario is true, the conclusion is false. So, even if we assume that “I heard barking” is true, it is insufficient to conclude “there must be a dog”. Thus, the argument is invalid.
Now here is where validity might get “silly”, consider this example:
- If you hear barking, then there must be a dog.
- You heard barking.
- There must be a dog. (1, 2)
The example above is valid. But wait a second, we just discussed how the sound of barking could be from a song, video, or any number of other possibilities. How is it that example 1 is invalid but example 2 is valid?
While we know that the mere sound of barking may be from something other than a dog, example 2 explicitly states, “If you hear any barking, then there must be a dog”. Any scenario that contradicts this statement would attack the truth of this premise–remember, we have to assume the premises are true when assessing validity, and assuming it is true, then barking implies dog and all the other possibilities are ruled out.
But wait another second, in “Assumptions”, we discussed how “If you hear barking, then there must be a dog” is an assumption of example 1, does that not count for anything? Yes, it is an assumption that is required for the conclusion to be derived validly, but remember, an assumption is an unstated premise. When it comes to argument validity, we can only assess an argument based on what it has explicitly given us to use as support. This is because an argument is a reasoning structure where the premises are supposed to “lead” to the conclusion, if it is missing a necessary step, then it fails to lead to its conclusion.
In summary, remember that validity is not concerned with whether or not the premises are actually true, and in assessing validity, we cannot infringe on the assumed truths of the given premises and can only assess whether the premises lead to their conclusion. In the next lesson, “Argument Soundness”, we will briefly cover what it means for an argument to be sound.
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In a previous lesson, we said an argument assumes some truth in order to derive a new truth.
This means problems can potentially arise from both parts:
- One or more of the assumed truths (premises) might be false.
- The newly derived truth (conclusion) may have been derived incorrectly.
When analyzing an argument for validity, we are only concerned with problems that stem from part 2, that is, we are only concerned with whether or not the conclusion of an argument was derived from its premises correctly. This means we do not care whether or not its premises are actually true. For the purposes of argument validity, we are just going to stick to the assumption that the premises are true and narrow our focus on whether the premises “give” the conclusion a sufficient amount of support.
In terms of argument validity, an argument is valid if and only if when we assume its premises are true, it is impossible for its conclusion to be false. Restated, that means there is no scenario where the premises are true but the conclusion is false.
- I heard barking.
- There must be a dog. (1)
In the example above, the conclusion “there must be a dog” is derived from “I heard barking”. Consider the scenario that the barking came from a song, video, or someone who can imitate the barking of a dog. If either scenario is true, the conclusion is false. So, even if we assume that “I heard barking” is true, it is insufficient to conclude “there must be a dog”. Thus, the argument is invalid.
Now here is where validity might get “silly”, consider this example:
- If you hear barking, then there must be a dog.
- You heard barking.
- There must be a dog. (1, 2)
The example above is valid. But wait a second, we just discussed how the sound of barking could be from a song, video, or any number of other possibilities. How is it that example 1 is invalid but example 2 is valid?
While we know that the mere sound of barking may be from something other than a dog, example 2 explicitly states, “If you hear any barking, then there must be a dog”. Any scenario that contradicts this statement would attack the truth of this premise–remember, we have to assume the premises are true when assessing validity, and assuming it is true, then barking implies dog and all the other possibilities are ruled out.
But wait another second, in “Assumptions”, we discussed how “If you hear barking, then there must be a dog” is an assumption of example 1, does that not count for anything? Yes, it is an assumption that is required for the conclusion to be derived validly, but remember, an assumption is an unstated premise. When it comes to argument validity, we can only assess an argument based on what it has explicitly given us to use as support. This is because an argument is a reasoning structure where the premises are supposed to “lead” to the conclusion, if it is missing a necessary step, then it fails to lead to its conclusion.
In summary, remember that validity is not concerned with whether or not the premises are actually true, and in assessing validity, we cannot infringe on the assumed truths of the given premises and can only assess whether the premises lead to their conclusion. In the next lesson, “Argument Soundness”, we will briefly cover what it means for an argument to be sound.
Want an interactive way to learn logic?
Enhance your critical thinking skills with Symbols Logic. Unlock access to the first studycard and the first level of all activities for free. Get the app now: