Definition:Valid Argument
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Definition
A valid argument is a logical argument in which the premises provide conclusive reasons for the conclusion.
When a proof is valid, we may say one of the following:
- The conclusion follows from the premises;
- The premises entail the conclusion;
- The conclusion is true on the strength of the premises;
- The conclusion is drawn from the premises;
- The conclusion is deduced from the premises;
- The conclusion is derived from the premises.
Sometimes the term sound is found instead of valid.
Proof
If all the premises of a valid argument are true, then the conclusion must also therefore be true.
It is not possible for the premises of a valid argument to be true, but for the conclusion to be false.
A valid argument whose premises are all accepted as true is known as a proof.
Also see
Warning
In natural language, it is commonplace to discuss the validity of statements as being valid or invalid, when what is really meant is that a statement is either true or false.
Sources
- Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning (1964): $\text{I}: \S 3$
- E.J. Lemmon: Beginning Logic (1965): $\S 1.1$
- D.J. O'Connor and Betty Powell: Elementary Logic (1980): $\S 1.1$
- D.J. O'Connor and Betty Powell: Elementary Logic (1980): $\S 1.1$: Exercise $3 \ \text{(viii), (ix)}$
- Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems (2000): $\S 1.2$
