Formal logic is great at enabling us to avoid contradiction. Similarly, it is great for telling us what we can derive from sets of premises. But you have to have the premises. Yet we reason not only to deduce things from given information, but to expand our beliefs, or what we take to be information. So many of our most interesting reasonings, in everyday life, are not supposed to be valid by the standards we have been describing. They are supposed to be plausible or reasonable, rather than watertight. There are ways in which such an argument could have true premises but a false conclusion,
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