# 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

## 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):**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):**valid**