Presentation 3c: Some Counterintuitive Facts about Validity (Phil 1230: Reasoning&Critical Thinking)

Summary

This presentation explores the notion of validity in arguments, emphasizing its precise definition and counterintuitive implications. It reveals that circular arguments, arguments with necessarily true conclusions, and those with inconsistent premises are all considered valid, despite their apparent flaws. By examining these surprising aspects, the presentation clarifies that validity is not synonymous with good reasoning but is instead grounded in logical structure. Understanding these principles is crucial for accurately assessing the validity of arguments.

Takeaways

• 😀 An argument is valid if it is logically impossible for all premises to be true while the conclusion is false.
• 🤔 Validity is defined by a precise stipulation, separate from intuitive notions of good arguments.
• 🔄 Circular arguments, where the conclusion is one of the premises, are valid despite being unconvincing.
• 📜 An example of a circular argument is: 'The earth is flat. Therefore, the earth is flat.'
• 🌈 Arguments with necessarily true conclusions (tautologies) are also valid, as they cannot be false.
• 📈 An example of a tautology is: 'Either I will eat lunch or I will not eat lunch.'
• 🔄 Arguments with inconsistent premises remain valid because they cannot all be true at the same time.
• 📉 An example of inconsistent premises is: 'Rocks have souls. Rocks do not have souls. Therefore, the moon is made of cheese.'
• 🔑 Validity relies on the absence of any possible situation where premises are true and the conclusion is false.
• 😂 The humor in arguments with contradictions comes from the fact that anything follows from a contradiction, illustrating the complexities of validity.

Q & A

What is the definition of a valid argument?

An argument is valid if there is no logically possible situation where all the premises are true and the conclusion is false.

How does validity differ from the intuitive notion of a good argument?

Validity has a precise definition based on logical structure, while a good argument may rely on persuasive elements that are not strictly logical.

What characterizes a circular argument?

A circular argument is one where the conclusion is also one of the premises, such as 'The earth is flat; therefore, the earth is flat.'

Why are circular arguments considered valid?

Circular arguments are valid because if the premises are true, the conclusion, being one of the premises, must also be true.

What is a tautology?

A tautology is a statement that is necessarily true, meaning it cannot be false under any circumstance.

Can you give an example of an argument with a necessarily true conclusion?

An example is 'If it is raining, then it is raining.' This conclusion is true regardless of whether it is actually raining.

What are inconsistent premises?

Inconsistent premises are statements that cannot all be true at the same time, such as 'Horses are mammals' and 'Horses are not mammals.'

Why are arguments with inconsistent premises still considered valid?

They are valid because it is impossible for all the premises to be true together, so there cannot be a situation where the premises are true and the conclusion is false.

What does the concept of invalidating counterexamples mean?

An invalidating counterexample is a situation in which all premises are true while the conclusion is false, which would demonstrate an argument's invalidity.

How does the presentation suggest one should approach understanding validity?

The presentation emphasizes consulting the precise definition of validity rather than relying on common notions of good arguments.