Lecture Notes by Christopher Lay

Los Angeles Pierce College

Department of History, Philosophy, and Sociology

 

 

 

 

Mathew Van Cleave's 2016 Introduction to Logic and Critical Thinking

 

https://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=457

 

 

 

 

Chapter 1 "Reconstructing and Analyzing Arguments"

§6 "Validity"

"Validity relates to how well the premises support the conclusion ... ."

 

Validity "is the golden standard that every argument should aim for."

 

"A valid argument is an argument whose conclusion cannot possibly be false, assuming that the premises are true."

 

"Another way of putting this is as a conditional statement [conditional statements are those in the if/then form]: A valid argument is an argument in which if the premises are true, the conclusion must be true."

 

 

 

 

 

 

 

 

 

 

Validity and the Truth

"[F]or the purposes of validity, it doesn’t matter whether [a] premise ... is actually true or false." 

 

Get this: "All the matters for validity is whether the conclusion follows from the premise."

 

 

 

 

 

 

 

 

 

 

Confused? 

There is a reason this is being emphasized.  When you are dealing with arguments and you get confused, some of your confusion may stem from forgetting that "whether or not an argument is valid has nothing to do with whether the premises of the argument are actually true or not." 

 

 

 

 

 

 

 

 

 

 

No Really

This trips many people up. 

It may "sound strange" to "have a valid argument even though neither the premises nor the conclusion is actually true."  "[B]ut if you understand the concept of validity, it is not strange at all."

 

 

 

 

 

 

 

 

 

 

Validity: The Relationship

"Remember: validity describes the relationship between the premises and conclusion, and it means that the premises imply the conclusion, whether or not that conclusion is true." 

 

 

 

 

 

 

 

 

 

 

Invalid

So, something is invalid when "it is possible for the premise to be true and yet the conclusion false." 

 

 

 

 

 

 

 

 

 

Counter-Example

"If an argument is invalid it will always be possible to construct a counterexample to show that it is invalid." 

 

"A counterexample is simply a description of a scenario in which the premises of the argument are all true while the conclusion of the argument is false." 

 

 

 

 

 

 

 

 

 

 

An Informal Test of Validity

"[A]sk yourself whether you can imagine a world in which all the premises are true and yet the conclusion is false."

 

"If you can imagine such a world, then the argument is invalid."

 

"If you cannot imagine such a world, then the argument is valid." 

 

 

 

 

 

 

 

 

 

 

Possible ≠ Actual

"Notice: it is possible to imagine a world where the premises are true even if the premises aren’t, as a matter of actual fact, true." 

 

"This is why it doesn’t matter for validity whether the premises (or conclusion) of the argument are actually true." 

 

 

 

 

 

 

 

 

 

 

Creativity

"[A]pplying the informal test of validity takes some creativity ... ."

 

 

 

 

 

 

 

 

 

 

Exercise 5

"Determine whether or not the following [argument is] valid by using the informal test of validity. If the argument is invalid, provide a counterexample."

1. "Katie is a human being. Therefore, Katie is smarter than a chimpanzee."

 

 

 

 

 

 

 

 

 

 

"Determine whether or not the following [argument is] valid by using the informal test of validity. If the argument is invalid, provide a counterexample."

2. "Bob is a fireman. Therefore, Bob has put out fires."

 

 

 

 

 

 

 

 

 

 

"Determine whether or not the following [argument is] valid by using the informal test of validity. If the argument is invalid, provide a counterexample."

3. "Gerald is a mathematics professor. Therefore, Gerald knows how to

teach mathematics."

 

 

 

 

 

 

 

 

 

 

"Determine whether or not the following [argument is] valid by using the informal test of validity. If the argument is invalid, provide a counterexample."

4. "Monica is a French teacher. Therefore, Monica knows how to teach

French."

 

 

 

 

 

 

 

 

 

 

"Determine whether or not the following [argument is] valid by using the informal test of validity. If the argument is invalid, provide a counterexample."

5. "Bob is taller than Susan. Susan is taller than Frankie. Therefore, Bob

is taller than Frankie."