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A logical argument is sound if and only if, (1)
the argument is valid and (2) all of its premises are true.
Suppose we have a sound argument:
- All men are mortal.
- Socrates is a man.
- Therefore, Socrates is mortal.
In this case we have an argument where, first, if the premises are all true, then the conclusion must be true (i.e., the
argument is valid); and, second, it so happens that the premises
are all true. It follows that the conclusion must be true. If you know an argument is sound, then you
know that its conclusion is true. By definition, all sound arguments have true conclusions.
In mathematical logic, a formal deduction calculus is said to be sound with respect to a given logic (i.e. with
respect to its semantics) if every statement that can be derived within this
calculus is a tautology of the logic. Stated differently, this says that
everything that can be formally (syntactically) calculated is semantically true. The
reverse condition is called completeness.
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