Valid Argument

Definition

A valid argument is an argument whose conclusion must be true if its premises are true.

Basic form:

if premises are true -> conclusion must be true

Validity is about structure.

It does not first ask whether the premises are actually true.

Validity means the conclusion follows from the premises.

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Simple Example

Example:

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

This is valid.

If the premises are true, the conclusion cannot be false.

The structure forces the conclusion.

Valid form preserves truth from premises to conclusion.

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Validity Is About Form

The content can change while the form stays valid.

Example:

If it rains, the ground gets wet.
It rains.
Therefore the ground gets wet.

Same form:

If P, then Q
P
Therefore Q

The argument is valid because of the structure.

Validity depends on reasoning form, not topic.

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Valid Does Not Mean True Premises

An argument can be valid even if its premises are false.

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 premises are not true.

But the structure is valid:

If P, then Q
P
Therefore Q

Validity does not guarantee true premises.

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Invalid Argument

An invalid argument does not force the conclusion.

Example:

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

This is invalid.

Why?

Because Q may be true for another reason.

The premises can be true while the conclusion is false.

Invalid means the conclusion does not necessarily follow.

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Final Summary

• A valid argument preserves truth from premises to conclusion.
• If the premises are true, the conclusion must be true.
• Validity is about structure.
• Validity does not mean the premises are true.
• An invalid argument allows true premises with a false conclusion.
• Validity is the first test of argument form.