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## SoundnessAn argument issound if, and only if, (1) the argument is valid
and (2) all of its premises are true.So suppose we have a sound argument:
- All men are mortal.
- Socrates is a man.
- Therefore, Socrates is mortal.
and, second, it so happens that the premises are all true.
It follows that the conclusion must be true.
That is the nice thing about soundness: if you know an argument is sound, then you know that its
conclusion is true.
By definition, all sound arguments have true conclusions.
So soundness is a very good quality for an argument to have.
In mathematical logic, a formal deduction calculus is said to be sound with respect to a given logic (i.e. wrt 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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