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"
§9 "Arguments with Missing Premises"
"Quite often, an argument will not explicitly state a premise that we can see is needed in order for the argument to be valid."
"In such a case, we can supply the premise(s) needed in order so make the argument valid."
"Making missing premises explicit is a central part of reconstructing arguments in standard form."
Validity Helps
"[N]ow that we have introduced the concept of validity, we have a useful tool for knowing when to supply missing premises in our reconstruction of an argument."
Missing Premises
"[A] missing premise is a premise that the argument needs in order to be as strong as possible."
"Typically, this means supplying the statement(s) that are needed to make the argument valid."
The Principle of Charity: Plausibility Beyond Validity
"[I]n addition to making [an] argument valid, we want to make ... argument[s] plausible. This is called 'the principle of charity.'"
"The principle of charity states that when reconstructing an argument, you should try to make that argument (whether inductive or deductive) as strong as possible."
"When it comes to supplying missing premises, this means supplying the most plausible premises needed in order to make the argument either valid (for deductive arguments) or inductively strong (for inductive arguments)."
Normative vs. Descriptive Statements
Here is a useful distinction to make: description vs. prescription.
"[D]escriptive statements ... are simply factual claims about what is true."
Descriptions tells us how something is.
A prescription is "a normative statement ... a statement about whether something ought to be true, relative to some standard of evaluation."
A prescription tells us how something ought to be.
The Is-Ought Gap
" An important idea within philosophy, which is often traced back to the Scottish philosopher David Hume (1711-1776), is that statements about what ought to be the case (i.e., normative statements) can never be derived from statements about what is the case (i.e., descriptive statements)."
"This is known within philosophy as the is-ought gap."
"Many times an argument with a normative conclusion will depend on a normative premise which is not explicitly stated."
Exercise 6:
"Supply the missing premise or premises needed in order to make the following argument valid. Try to make the premises as plausible as possible while making the argument valid (which is to apply the principle of charity)."
1. Ed rides horses. Therefore, Ed is a cowboy.
"Supply the missing premise or premises needed in order to make the following argument valid. Try to make the premises as plausible as possible while making the argument valid (which is to apply the principle of charity)."
2. Tom was driving over the speed limit. Therefore, Tom was doing something wrong.
"Supply the missing premise or premises needed in order to make the following argument valid. Try to make the premises as plausible as possible while making the argument valid (which is to apply the principle of charity)."
3. If it is raining then the ground is wet. Therefore, the ground must be wet.
"Supply the missing premise or premises needed in order to make the following argument valid. Try to make the premises as plausible as possible while making the argument valid (which is to apply the principle of charity)."
4. All elves drink Guinness, which is why Olaf drinks Guinness.
"Supply the missing premise or premises needed in order to make the following argument valid. Try to make the premises as plausible as possible while making the argument valid (which is to apply the principle of charity)."
5. Mark didn’t invite me to homecoming. Instead, he invited his friend Alexia. So he must like Alexia more than me.
"Supply the missing premise or premises needed in order to make the following argument valid. Try to make the premises as plausible as possible while making the argument valid (which is to apply the principle of charity)."
6. The watch must be broken because every time I have looked at it, the hands have been in the same place.
"Supply the missing premise or premises needed in order to make the following argument valid. Try to make the premises as plausible as possible while making the argument valid (which is to apply the principle of charity)."
7. Olaf drank too much Guinness and fell out of his second story apartment window. Therefore, drinking too much Guinness caused Olaf to injure himself.
"Supply the missing premise or premises needed in order to make the following argument valid. Try to make the premises as plausible as possible while making the argument valid (which is to apply the principle of charity)."
8. Mark jumped into the air. Therefore, Mark landed back on the ground.
"Supply the missing premise or premises needed in order to make the following argument valid. Try to make the premises as plausible as possible while making the argument valid (which is to apply the principle of charity)."
9. In 2009 in the United States, the net worth of the median white household was $113,149 a year, whereas the net worth of the median black household was $5,677. Therefore, as of 2009, the United States was still a racist nation.
"Supply the missing premise or premises needed in order to make the following argument valid. Try to make the premises as plausible as possible while making the argument valid (which is to apply the principle of charity)."
10.The temperature of the water is 212 degrees Fahrenheit. Therefore, the water is boiling.
"Supply the missing premise or premises needed in order to make the following argument valid. Try to make the premises as plausible as possible while making the argument valid (which is to apply the principle of charity)."
11.Capital punishment sometimes takes innocent lives, such as the lives of individuals who were later found to be not guilty. Therefore, we should not allow capital punishment.
"Supply the missing premise or premises needed in order to make the following argument valid. Try to make the premises as plausible as possible while making the argument valid (which is to apply the principle of charity)."
12.Allowing immigrants to migrate to the U.S. will take working class jobs away from working class folks. Therefore, we should not allow immigrants to migrate to the U.S.
"Supply the missing premise or premises needed in order to make the following argument valid. Try to make the premises as plausible as possible while making the argument valid (which is to apply the principle of charity)."
13.Prostitution is a fair economic exchange between two consenting adults. Therefore, prostitution should be allowed.
"Supply the missing premise or premises needed in order to make the following argument valid. Try to make the premises as plausible as possible while making the argument valid (which is to apply the principle of charity)."
14.Colleges are more interested in making money off of their football athletes than in educating them. Therefore, college football ought to be banned.
"Supply the missing premise or premises needed in order to make the following argument valid. Try to make the premises as plausible as possible while making the argument valid (which is to apply the principle of charity)."
15.Edward received an F in college Algebra. Therefore, Edward should have studied more.