Presentation 2c: Introduction to Validity and Soundness (Phil 1230: Reasoning and Critical Thinking)

Summary

This lecture introduces the concepts of validity and soundness in arguments. Validity is explained as an argument where it's impossible for the premises to be true and the conclusion false, meaning the truth of the premises guarantees the truth of the conclusion. Soundness is when an argument is both valid and has true premises, ensuring the conclusion is also true. Several examples and exercises are provided to illustrate these concepts, and the distinctions between validity, soundness, truth, and falsity are highlighted.

Takeaways

• 📘 Validity means an argument is valid if it's impossible for the premises to be true and the conclusion to be false at the same time.
• 🧐 Logical impossibility in this context means there is no conceivable way for the premises to be true while the conclusion is false.
• ✅ A valid argument guarantees that if the premises are true, the conclusion must also be true.
• 🐴 Example of a valid argument: 'If horses are mammals, then they are warm-blooded. Horses are mammals. Therefore, horses are warm-blooded.'
• 🚫 An invalid argument allows for the possibility that the premises are true while the conclusion is false.
• 🤔 Example of an invalid argument: 'Joseph is tall. Manuela is taller than Joseph. Therefore, Manuela is happy.' This is invalid because the premises do not guarantee the conclusion.
• 🔍 Soundness means an argument is both valid and has all true premises.
• 📜 A sound argument always leads to a true conclusion because it combines valid reasoning with true premises.
• ❌ An argument with false premises, even if valid, is not sound. For example: 'Guinea pigs like to eat hay. If guinea pigs like hay, then humans like hay. Therefore, humans like hay.'
• 🔗 Arguments are valid or sound, while statements are true or false. Attributing validity or soundness to statements is incorrect.

Q & A

What is the definition of a valid argument?

An argument is valid if and only if it is logically impossible for the premises to be true while the conclusion is false.

Why is logical impossibility important for understanding validity?

Logical impossibility means that there is absolutely no situation where the premises could be true and the conclusion false. It emphasizes the strongest form of impossibility, which ensures the conclusion must be true if the premises are true.

Can an argument be valid if the conclusion is true by coincidence?

No, an argument’s validity depends on the logical relationship between the premises and the conclusion. Even if the conclusion happens to be true, the argument is invalid if it’s possible for the premises to be true and the conclusion false.

What is an example of a valid argument from the script?

One example of a valid argument is: If horses are mammals, then horses are warm-blooded. Horses are mammals. Therefore, horses are warm-blooded.

What does it mean for an argument to be invalid?

An argument is invalid when it is possible for all the premises to be true, but the conclusion could still be false. This indicates that the conclusion does not logically follow from the premises.

What is the definition of a sound argument?

An argument is sound if it is both valid and all its premises are true.

Why do we care about the soundness of an argument?

We care about soundness because it ensures not only that the argument is valid, but also that its premises are true. A sound argument guarantees a true conclusion, making it useful for reasoning.

Is a valid argument always sound?

No, a valid argument is only sound if all of its premises are true. A valid argument can still have false premises and thus be unsound.

Can a statement be valid or sound?

No, validity and soundness are properties of arguments, not statements. A statement can be true or false, but an argument can only be valid or sound.

What happens if an argument is valid but has false premises?

If an argument is valid but has false premises, it is unsound. The argument would only show that if the premises were true, then the conclusion would be true as well, but with false premises, this reasoning is not useful.