1. Idea of an Argument
An argument is a group of statements arranged in a way that some of them, called premises, are meant to support another statement called the conclusion. The goal of an argument is to show that the conclusion follows logically from the premises.
The focus is not on persuading someone, but on checking whether the reasoning itself is logically sound.
1.1. Structure of an argument
- Premises: statements that provide information or reasons.
- Conclusion: the statement that the premises aim to justify.
Validity is about the connection between premises and conclusion, not about whether they are factually true.
2. Meaning of a Valid Argument
An argument is called valid if the conclusion logically follows from the premises. This means that if all the premises are assumed to be true, then the conclusion must be true as well.
Validity depends on the form of the argument, not on the actual truth of the statements involved.
2.1. Truth-preserving nature
In a valid argument, the truth of the premises guarantees the truth of the conclusion. There is no situation where all premises are true and the conclusion is false.
3. Meaning of an Invalid Argument
An argument is invalid if the conclusion does not logically follow from the premises. Even if the premises happen to be true, the reasoning is not solid because the conclusion could still be false.
Invalidity reveals a flaw in logic, not necessarily incorrect facts.
3.1. Failure of support
In an invalid argument, it is possible for all premises to be true while the conclusion is false. This break in logical support makes the argument invalid.
4. Examples of Valid Arguments
These examples show situations where the conclusion logically follows from the premises.
4.1. Example 1
Premises:
1. If a number is divisible by 4, then it is even.
2. 12 is divisible by 4.
Conclusion: 12 is even.
The reasoning is valid because the conclusion follows directly from the premises.
4.2. Example 2
Premises:
1. All squares are rectangles.
2. All rectangles are quadrilaterals.
Conclusion: All squares are quadrilaterals.
This argument is valid because it preserves truth from the premises to the conclusion.
5. Examples of Invalid Arguments
These examples show arguments where the conclusion does not follow logically from the premises.
5.1. Example 1
Premises:
1. If a number is divisible by 4, then it is even.
2. 10 is even.
Conclusion: 10 is divisible by 4.
This argument is invalid because the premises do not guarantee the conclusion.
5.2. Example 2
Premises:
1. All birds can fly.
2. Penguins are birds.
Conclusion: Penguins can fly.
This argument is invalid because the first premise is not universally true, and the conclusion does not logically follow.
6. Notes and Observations
Important points about valid and invalid arguments:
- Validity concerns logic, not the actual truth of statements.
- In a valid argument, true premises guarantee a true conclusion.
- In an invalid argument, the conclusion may or may not be true — the reasoning is the issue.
- Testing validity involves checking whether the conclusion can ever be false when the premises are true.