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
Review for Chapter 1 "Reconstructing and Analyzing Arguments"
Arguments
"An argument, in this sense, is a reason for thinking that a statement, claim or idea is true."
There are "two parts of an argument: the premise and the conclusion."
"The premises of the argument provide a reason for thinking that the conclusion is true."
"An argument is a set of statements, some of which (the premises) attempt to provide a reason for thinking that some other statement (the conclusion) is true."
Statements
"Both premises and conclusions are statements."
"A statement is a type of sentence that can be true or false ... ." A statement is a statement because "it makes sense to inquire whether it is true or false." Note, a statement is still a statement, "even if it is false."
Numbering & The Standard Argument Form
"A standard way of capturing the structure of an argument is by numbering the premises and conclusion."
"By convention, the last numbered statement (also denoted by the 'therefore') is the conclusion and the earlier numbered statements are the premises."
Indicator Words
"The best way to identify whether an argument is present is to ask whether there is a statement that someone is trying to establish as true by basing it on some other statement."
Indicator Words and the Substitution Test
"If there is any doubt about whether a word is truly a premise/conclusion indicator or not, you can use the substitution test. Simply substitute another word or phrase from the list of premise indicators or conclusion indicators and see if the resulting sentence still makes sense."
Exercise 2
If the following is an argument, identify its conclusion.
1. The human in the hat is not a chef since chefs have aprons and that human doesn’t have an apron.
If the following is an argument, identify its conclusion.
2. I have been hungry since Tuesday.
If the following is an argument, identify its conclusion.
3. We should eat: I have been hungry since Tuesday!
If the following is an argument, identify its conclusion.
4. Since the dawn of time was so long ago, we cannot really come to any conclusion about what happened then.
If the following is an argument, identify its conclusion.
5. If you want to succeed in life, then you should read books with an open mind.
If the following is an argument, identify its conclusion.
6. If you want to succeed in life (and everyone should want to succeed in life), then you should read books with an open mind.
Complex Arguments' Main Conclusions
"The main conclusion of [an] argument ... is the statement that depends on other statements as evidence but doesn’t itself provide any evidence for any other statement."
Intermediate Conclusions
In a complex argument, some statements provide "evidence directly for the main conclusion, but [those statements are] supported by another statement."
An intermediate conclusion is supported by a reason, and an intermediate conclusion also supports some other, further claim. "[O]ne and the same statement can act as both a premise and a conclusion."
"from"
(Note: when we want to say that some “statement follows from statement #" we say "from #." "We will use this convention as a way of keeping track of the structure of the argument.")
Arguments with Independent Support
"Another type of structure that arguments can have is when two or more premises provide direct but independent support for the conclusion."
Exercise 4
Write the following argument in standard form and show how the argument is structured.
1. There is nothing wrong with taking philosophy courses because there is nothing wrong with being challenged intellectually–and being challenged intellectually is what happens in taking a philosophy course. Moreover, since learning about human nature can't be wrong (and you learn about human nature by taking a philosophy course), there is another reason for why there is nothing wrong with philosophy courses.
Write the following argument in standard form and show how the argument is structured.
2. Rainbows are fantastic. Since anything that emerges when the sun is out and it is raining is magical, and since rainbows emerge when the sun is out and it is raining, rainbows are magical. And I do not need to tell you that anything that is magical is obviously fantastic. Besides, rainbows make you look up and anything that makes you look up is fantastic.
Write the following argument in standard form and show how the argument is structured.
3. We should be concerned about what is going on in colleges these days! Professors, those who are ultimately in charge of what goes on in college, are too often left up to their own devices, and whenever professors are left up to their own devices, we should be concerned. Look at professor X. Left up to his own devices, he wants students to argue about rainbows!?! We should surely be concerned when students are wasting their time arguing about rainbows. So, Professor X is another reason why we should be concerned about what is going on in colleges these days.
What is a Paraphrase?
"A paraphrase is the use of different words to capture the same idea in a clearer way."
Evaluating Paraphrases
With paraphrases, we aim to express the basic "essence of the logic of the original argument. As long as your paraphrases help you to do that, they are good paraphrases."
Validity
"A valid argument is an argument whose conclusion cannot possibly be false, assuming that the premises are 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."
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."
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. Explain your answer.
1. Katie is a human being. Therefore, Katie is taller than a yard stick.
Determine whether or not the following [argument is] valid by using the informal test of validity. If the argument is invalid, provide a counterexample. Explain your answer.
2. Cakes are yummy. Therefore, Cakes are tasty.
Determine whether or not the following [argument is] valid by using the informal test of validity. If the argument is invalid, provide a counterexample. Explain your answer.
3. Cakes are yummy. Therefore, Cakes are healthy.
Determine whether or not the following [argument is] valid by using the informal test of validity. If the argument is invalid, provide a counterexample. Explain your answer.
4. Cakes are tasty. Therefore, Cakes are round.
Determine whether or not the following [argument is] valid by using the informal test of validity. If the argument is invalid, provide a counterexample. Explain your answer.
5. Philosophy courses are addictive. Therefore, it is easy to get carried away in a philosophy course.
Deductive vs. Inductive
" A deductive argument is an argument whose conclusion is supposed to follow from its premises with absolute certainty ... ."
In a deductive argument, there is "no possibility that the conclusion doesn’t follow from the premises."
"[A]n inductive argument is an argument whose conclusion is supposed to follow from its premises with a high level of probability ... ."
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."
"[A] missing premise is a premise that the argument needs in order to be as strong as possible."
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."
Prescriptive Conclusions
"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. Kweego rides cows. Therefore, Kweego 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. Kweego rides merry-go-rounds. Therefore, Kweego is a human.
"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. Kweego rides merry-go-rounds. Therefore, Kweego is ecstatic.
"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. Kweego is a good human. Therefore, Kweego is a teacher.
"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. Kweego is a teacher. Therefore, Kweego is a good human.
Assuring
" ... informing someone that there are further reasons although one is not giving them now."
Guarding
" ... weakening one’s claims so that it is harder to show that the claims are false."
Discounting
" ... anticipating objections that might be raised to one’s claim or argument as a way of dismissing those objections."
Exercise 7
Which rhetorical technique (assuring, guarding, discounting) is being using in the following passages?
1. Although humming while you drive can be mildly distracting, it is better than staring at your phone while you drive, which has the tendency to cause car accidents.
Which rhetorical technique (assuring, guarding, discounting) is being using in the following passages?
2. And listen, by "humming while you drive," I don't mean that you are attempting to hum an entire symphony perfectly. I just mean that you are producing a somewhat music noise with your throat without opening your mouth.
Which rhetorical technique (assuring, guarding, discounting) is being using in the following passages?
3. Take it from me, humming while you drive is better than staring at your phone while you drive.