Sound Argument

Definition

A sound argument is an argument that is:

• valid
• built from true premises

If an argument is sound, its conclusion is true.

Sound argument = valid structure + true premises.

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Validity Comes First

An argument must be valid before it can be sound.

Example:

Premise 1: If P, then Q
Premise 2: P
Conclusion: Q

This form is valid.

If the premises are also true, then the argument is sound.

Soundness requires validity.

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True Premises Matter

Validity alone is not enough for soundness.

Example:

Premise 1: If the moon is made of cheese, then cheese is in space.
Premise 2: The moon is made of cheese.
Conclusion: Cheese is in space.

The structure is valid.

But the second premise is false.

So the argument is not sound.

A valid argument with false premises is not sound.

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Sound Argument Example

Example:

Premise 1: If a number is divisible by 4, then it is even.
Premise 2: 8 is divisible by 4.
Conclusion: 8 is even.

The structure is valid.

The premises are true.

So the argument is sound.

A sound argument gives a trustworthy conclusion.

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Soundness vs Validity

Validity asks:

Does the conclusion follow from the premises?

Soundness asks:

Does the conclusion follow, and are the premises true?

Validity is structural.

Soundness combines structure with truth.

Validity checks form; soundness checks form plus true starting points.

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Final Summary

• A sound argument is valid and has true premises.
• Soundness requires validity.
• A valid argument with false premises is not sound.
• A sound argument guarantees a true conclusion.
• Validity is about structure.
• Soundness is about structure plus truth.