Case-making is the process of trying to determine whether or not something is true, or (if we've already done that) of trying to convince somebody else that something is true.
We understand an argument to be a unit of reasoning that attempts to establish that one claim is true by citing other claims as evidence. As a very simple example, "Fido is wagging his tail. Therefore, the Fido is happy," is an argument that attempts to establish that Fido is happy by citing the fact that Fido is wagging his tail. We could also say, "Fido is happy because he's wagging his tail." Arguments try to establish that something is true. They answer the question, "Why should we accept this claim?"
Some kinds of explanation, on the other hand, try to account for why something is true while taking if for granted that it is true. "Fido is happy because he got a treat," for example, might be attempt to explain why Fido is happy without trying to convince us that he is. Such explanations answer the question, "Given that this state of affairs exist, what brought it about?"
Explanations can appear as claims in arguments, as when we argue in favor of an explanation (e.g., "Most doges love treats but don't like going to the vet. Therefore, it's likely that Fido is happy because someone gave him a treat and not because he went to the vet.") or when we conclude that something must be the case by citing an explanation that we accept (e.g., "Fido is happy because he got a treat. Therefore we can make this cat happy by giving it a treat too.")
Arguments and explanations can, of course, get very complicated and there's a lot to be said about them. Enjoy learning more by exploring this page!
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