Definition:Valid Argument
This page is about Valid Argument in the context of Logic. For other uses, see valid.
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.
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 proof is a valid argument whose premises are all true.
Hence a valid argument that has one or more false premises is not a proof.
Also known as
A valid argument is also known as a truth preserving argument.
Likewise, validity is also known as truth preservation.
Some authors use the term sound argument to mean the same thing that is defined here as a proof.
However, as some use sound argument to mean the same thing as a valid argument, it is recommended that this term not be used.
Examples
Bats have Lungs
The following is a valid argument with true premises:
- All bats are mammals.
- All mammals have lungs.
- Therefore all bats have lungs.
Trout have Wings
The following is a valid argument with false premises:
- All trout are mammals.
- All mammals have wings.
- Therefore all trout have wings.
Also see
- Results about valid arguments can be found here.
Linguistic Note
The word valid ultimately derives from the same root as the word value.
Thus valid can be taken to mean having value.
Warning
In natural language, especially when a person is attempting to sound more learned than they are, it is commonplace to discuss the nature of statements as being valid or invalid.
What is really meant, of course, is that a statement is either true or false.
Sources
- 1959: A.H. Basson and D.J. O'Connor: Introduction to Symbolic Logic (3rd ed.) ... (previous) ... (next): Chapter $\text I$ Introductory: $3$. Logical Form
- 1964: Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning ... (previous) ... (next): $\text{I}$: 'NOT' and 'IF'
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $1$ The Nature of Logic
- 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $1$ Introduction: Logic and Language: $1.2$: The Nature of Argument
- 1980: D.J. O'Connor and Betty Powell: Elementary Logic ... (previous) ... (next): $\S \text{I}: 1$: The Logic of Statements $(1)$
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): valid: 1 a. (Logic)
- 1995: Merrilee H. Salmon: Introduction to Logic and Critical Thinking: $\S 7.2$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): argument: 2.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): logic
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): valid
- 2000: Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems ... (previous) ... (next): $\S 1.2$: Natural Deduction
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): argument: 2.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): logic
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): valid