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Critical Thinking
Chapter 1- Critical Thinking Basics
What is Critical Thinking?
- Critical thinking= careful application of reason in the determination of whether a claim is true
o Evaluation of claims
The Basics: Claims, Issues, and Arguments
Claims
- Things we say to convey information- to express our opinions or beliefs
- True or false
- Legitimate claim= one that makes sense
Issues
- A question- whether a claim is true or not
- Two ways of stating an issue ex: 1) Is Moore taller than Parker? 2) Whether Moore is taller than Parker.
- We answer the question or settle the issue by determining whether the claim is true or false
Arguments
- When we give a reason for thinking that a claim is true
- Premise= a claim that is offered as a reason for believing another claim
- Conclusion= the claim for which a premise is supposed to give a reason; the conclusion of the argument states a
position on the issue.
- The premise can offer support for the conclusion only if the premise is true
- Premise must be relevant to the conclusion; increases the likelihood that the conclusion is true (cogent)
What Arguments are not
- Lists of facts are related by being about the same subject, but none of them is offered as a reason for believing
another, therefore NOT an argument
- Arguments vs. Explanations
o An argument attempts to support or prove a conclusion, while an explanation specifies what caused
something or how it works or what it is made out of.
- Arguments vs. Persuasion
o An argument attempts to prove or support a conclusion. When you attempt to persuade someone, you
attempt to win him or her to your point of view.
o An argument can be used to persuade but it is NOT common
Two Kinds of Good Arguments
Deductive
- A good deductive argument is said to be valid which means it isn’t possible for the premises to be true and the
conclusion to be false.
- PROVE the conclusion
Inductive
- A good inductive SUPPORTS the conclusion. Assuming the premises are true, they raise the probability that the
conclusion is true.
Recognizing Arguments
- One part (premise) is presented as a reason for believing the other part is true (conclusion)
- At least two claims, and the word ‘therefore’ or an equivalent must stand before one of them either explicitly or
implicitly
Terms and Concepts
- Value judgement= claim that expresses an evaluation of something
o Moral value judgement- assign moral or ethical values to objects and actions
Extraneous Considerations: Logical Window Dressing
- i.e. speaker’s relationship to us; feelings about them
- language that enhances attractiveness (rhetoric)
- photographs and images that elicit emotions
Chapter 2- Two Kinds of Reasoning
Conclusions Used as Premises
- The same statement can be the conclusion of one argument and a premise in another argument
- Ex: Premise: The brakes aren’t working, the engine burns oil, the transmission needs work, and the car is hard to
start
Conclusion 1: The car has outlived its usefulness
Conclusion 2: We should get a new car
- Conclusion 1 is used as the conclusion of the premise, but the premise for conclusion 2 Unstated Premises and Conclusions
- Ex: Premise: You can’t check out books from the library without an ID
Conclusion: Bill won’t be able to check out any books
- Unstated premises are common because sometimes they seem too obvious to need mentioning
Two Kinds of Arguments
Deductive Arguments
- When we reason deductively, we try to prove or demonstrate a conclusion
- A deductive argument is said to be valid if it isn’t possible for the premise to be true and the conclusion false.
Further, if the premise of a valid argument is in fact true, the argument is said to be sound. The conclusion of a
sound argument has been proven.
Inductive Arguments
- When we reason inductively, we try to support a conclusion.
- Inductive arguments are “stronger” or “weaker” depending on how much support the premise provides for the
conclusion; that is, depending on how likely the premise makes the conclusion.
Beyond a Reasonable Doubt
- Highest standard of proof
- When a jury is asked to return the verdict, the judge will tell the jury that the defendant must be found not guilty
unless the evidence proves guilt beyond a reasonable doubt
- Somewhat lower than deductive proof
Deduction, Induction, and Unstated Premises
- Real-life arguments often leave a premise unstated. One such unstated premise might make the argument
inductive; another might make it deductive.
- Context or content can make clear what was intended
Techniques for Understanding Arguments
1. Find the conclusion- the main point or thesis of the passage
2. Next step is to locate the reasons that have been offered for the conclusion- find the premises
3. Next, we look for the reasons, if any, given for these premises.
- To proceed through these steps, you have to understand the structure of the argument
Clarifying an Argument’s Structure
- Circle all premise and conclusion indicators
- Bracket each premise and conclusion, and number them consecutively as they appear in the argument
- Diagram the argument- using an arrow to mean “therefore” and plus signs over a line to connect two or more
premises that depend on one another
o Indicate counterclaims by crossing the ‘therefore’ arrows with lines
Chapter 3- Clear Thinking, Critical Thinking, and Clear Writing
- Four sources of confusion and obscurity: excessive vagueness, ambiguity, excessive generality, and undefined
terms
Vagueness
- Results when the scope of a concept is not clear
- A word or phrase is vague if the group of things to which it applies has borderline cases (e.g. bald)
- When a claim is not too vague to convey appropriately useful information, its level of vagueness is acceptable
Ambiguity
- A word, phrase, or sentence is said to be ambiguous when it has more than one meaning
- Semantic Ambiguity:
o Contains an ambiguous word or phrase
o Semantically ambiguous claims can be made unambiguous by substituting a word or phrase that is not
ambiguous for the one making the trouble
- Grouping Ambiguity:
o Results when it is not clear whether a word is being used to refer to a group collectively or to members of
the group individually
o A person commits the fallacy of division when he or she reasons from the fact that a claim about a group
taken collectively is true to the conclusion that the same claim about members of the group taken
individually is also true.
o A person commits the fallacy of composition when he or she reasons from the fact that each member of
a group has a certain property to the conclusion that the group as a whole must have the property.
- Syntactic Ambiguity:
o When a claim is open to two or more interpretations because of its structure- that is, its syntax o Ambiguous pronoun references occur when it is not clear to what or whom a pronoun is supposed to
refer (e.g. the boys chased the girls and they giggled a lot)
Generality
- The less detail a claim provides, the more general it is
Defining Terms
Purposes of Definitions
1. Tell us what a word means. Lexical definitions tell us what a word ordinarily means.
2. Stipulative definition (assigned meaning) is when a word takes a special meaning in a given context.
3. Precising definitions reduce vagueness or generality or to eliminate ambiguity.
4. Definitions used to persuade are called persuasive or rhetorical definitions.
o Emotive meaning (or rhetorical force) consists of the positive or negative associations of a word
connotation
Kinds of Definitions
1. Definition by example: pointing to, naming, or otherwise identifying one of more examples of the sort of thing to
which the term applies
2. Definition by synonym: giving another word or phrase that means the same as the term being defined
3. Analytical definition: specifying the features that a thing must possess in order for the term being defined to apply
to it (most dictionary definitions are analytical)
Tips on Definitions
- Definitions should not prejudice the case against one side of a debate or the other
- Definitions should be clear and should be expressed in language that is as clear and simply as the subject will allow.
Avoid emotionally charged language.
- Realize that you must get along with incomplete definitions
Essay Types to Avoid
- The Windy Preamble: avoid getting to the issue and instead go on at length with introductory remarks
- The Stream-of-Consciousness Ramble: no attempt to organize thoughts and information is all spewed out
- The Knee-Jerk Reaction: first reaction to an issue without considering it in depth
- The Glancing Blow: address the issue obliquely
- Let the Reader Do the Work: expect the reader to follow the jumble
Chapter 9- Deductive Arguments II
- Truth-functional logic= propositional or sentential logic
Truth Tables and the Truth-Functional Symbols
Claim Variables
- Uppercase letters stand for claims
Truth Tables
- In truth-functional logic, any given claim, P, is either true or false
P
T
F
- Whichever truth value the claim P might have, its negation or contradictory, which we’ll symbolize ~P, will have the
other. True table for negation:
P ~P
T F
F T
- The left-hand column of this table sets out both possible truth values for P, and the right-hand column sets out the
truth values for ~P based on P’s values. This is a way of defining the negation sign, ~, in front of the P. The symbol
means “change the truth value from T to F or from F to T, depending on P’s values.”- (Not P, i.e. Parker is not at
home)
- Because any claim is either true or false, two claims, P and Q, must both be true, both be false, or have opposite
truth values, for a total of four possible combinations
P Q
T T
T F
F T
F F
- A conjunction is a compound claim made from two simpler claims, called conjuncts. A conjunction is true if and
only if both of the simpler claims that make it up (its conjuncts) are true. Ex: Parker is at home (P) and Moore is at
work (Q) P Q P&Q
T T T
T F F
F T F
F F F
& is used for and, but, while, and even though as well***
- A disjunction is another compound claim made up of two simpler claims, called disjuncts. A disjunction is false if
and only if both of its disjuncts are false. Ex: Either Parker is at home (P), or Moore is at work (Q)
P Q P ˅Q
T T T
T F T
F T T
F F F
˅ is used for or
- A conditional claim is “if…then”. Ex: If Parker is at home, then Moore is at work. The first claim in a conditional (P)
is the antecedent, and the second (Q) is the consequent. A conditional claim is false if and only if its antecedent is
true and its consequent is false.
P Q PQ
T T T
T F F
F T T
F F T
The arrow represents what is often called the “material conditional”, conditionals that are true except when the
antecedent is true and the consequent false.
- Can work in combination. Ex: “if Paula doesn’t go to work, then Quincy will have to work a double shift”
P = Paula goes to work
Q = Quincy has to work a double shift
~P Q
P Q ~P ~PQ
T T F T
T F F T
F T T T
F F T F
- Ex: “If Paula goes to work, then Quincy and Rogers will get a day off”
P (Q & R)
Every time we add another letter, the numner of possible combinations of T and F doubles, and so, therefore, does
the number of rows in our truth table. (r = 2 , where r is the number of rows in the table and n is the number of
letters in the symbolization)
P Q R Q&R P (Q&R)
T T T T T
T T F F F
T F T F F
T F F F F
F T T T T
F T F F T
F F T F T
F F F F T
*** The leftmost column will always wind up being half Ts and half Fs
- Two claims are truth-functionally equivalent if they have exactly the same truth table- that is, if the Ts and Fs in
the column under one claim are in the same arrangement as those in the column under the other.
Symbolizing Compound Claims
- The idea is to produce a version that will be truth-functionally equivalent to the original informal claim- that is, one
that will be true under all the same circumstances as the original and false under all the same circumstances.
“If” and “Only If”
- The word “if”, used alone, introduces the antecedent of a conditional. The phrase “only if” introduces the
consequent of a conditional.
o It’s not the location of the part in a conditional that tells us whether it is the antecedent or the
consequent, it’s the logical words that identify it. Necessary and Sufficient Conditions
- The necessary condition becomes the consequent of a conditional
- Ex: The presence of oxygen is a necessary condition for combustion. “If we have combustion (C), then we must
have oxygen (O).” CO
- A sufficient condition guarantees whatever it is a sufficient condition for. Being born in the US is a sufficient
condition for US citizenship- that’s all one needs to be a US citizen. Sufficient conditions are expressed as the
antecedents of conditional claims. Ex: “If Juan was born in the US (B), then Juan is a US citizen (C)” B C
- “If” = sufficient condition, “Only if” = necessary condition
“Unless”
- Ex: “Paula will foreclose unless Quincy pays up”
- Means the same thing as “Paula will foreclose or Quincy will pay up” P ˅ Q
“Either… Or”
- Either P and Q or R (P&Q) ˅ R
P and either Q or R P & (Q˅R)
- “Either” tells us that the disjunction begins with P in the first claim and Q in the second claim
- The word “if” does much the same job for conditionals that “either” does for disjunctions.
- “If” tells us that the antecedent begins with Q in the first example and with P in the second.
Truth-Functional Arguments
- An argument is valid, if and only if the truth of the premises guarantees the truth of the conclusion.
The Truth-Table Method
- We present all of the possible circumstances for an argument by building a truth table for it; then we simply look
to see if there are any circumstances in which the premises are all true and the conclusion is false. If there are such
circumstances then the argument is invalid.
- Ex: P Q
~P____
Therefore, ~Q
P Q ~P PQ ~Q
T T F T F
T F F F T
F T T T F
F F T T T
- First two columns are reference columns; they list the truth values for the letters that appear in the argument.
- The third and fourth columns appear under the two premises of the argument, and the fifth column is for the
conclusion.
- The third row shows that even if both premises are true, the conclusion can be false; thus, the argument is invalid.
The Short Truth-Table Method
- The easiest systematic way to determine the validity or invalidity of truth-functional arguments is the short truth-
table method.
- If an argument is invalid, there has to be at least one row in the argument’s truth table where the premises are
truth and the conclusion is false.
- With the short table method, we simply focus on finding such a row.
- Ex: PQ
~QR
~PR
- Because it’s a conditional, it can be made false only one way, by making its antecedent true and its consequent
false. So, we do that by making P false and R false. Can we now make both premises true? Yes, as it turns out, by
making Q true.
- P Q R
F T F
- This case makes both premises true and the conclusion false and thus proves the argument invalid. Had the
argument been valid, we would not have been able to produce such a row.
Deductions
- Less useful for proving invalidity, but has some advantages for proving validity
- When we use this method, we derive the conclusion from the premises by means of a series of basic, truth-
functionally valid argument patterns Group I Rules: Elementary Valid Argument Patterns
1. Modus Ponens (Affirming the Antecedent) - Any argument of the pattern below is valid. If you have a conditional
among the premises, and if the antecedent of that conditional occurs as another premise, then by modus ponens
the consequent of the conditional follows from those two premises
P Q
P
Q
- If the consequent of the conditional is the conclusion of the argument, then the deduction is finished- the
conclusion has been established. If it is not the conclusion of the argument you’re working on, the consequent of
the conditional can be listed just as if it were another premise to use in deducing the conclusion you’re after.
Ex: 1. P R
2. R S
3. P Therefore, S
- We’ve number the three premises of the argument and set its conclusion off to the side. Now, notice that line 1 is
a conditional, and line 3 is its antecedent. Modus Ponens allows us to write down the consequent of line 1 as a
new line in our deduction.
4. R 1, 3, MP
- At the right, we’ve noted the abbreviation for the rule we used and the lines the rule required. These notes are
called the annotation for the deduction. We can now make use of this new line in the deduction to get the
conclusion we were originally after, namely, S.
5. S 2, 4 MP
- Again, we used modus ponens, this time on lines 2 and 4. The same explanation as that for deriving line 4 from
lines 1 and 3 applies here.
2. Modus tollens (denying the consequent)- if you have a conditional claim as one premise and if one of your other
premises is the negation of the consequent of that conditional, you can write down the negation of the
conditional’s antecedent as a new line in your deduction.
P Q
~Q
~P
- Ex: 1. (P&Q) R
2. S
3. S ~R / ~(P&Q)
4. ~R 2, 3, MP
5. ~(P&Q) 1, 4, MT
- In this deduction, we derived line 4 from lines 2 and 3 by modus ponens, and then 4 and 1 gave us line 5, which is
what we were after, by modus tollens. The fact that the antecedent of line 1 is itself a compound claim (P&Q), is
not important; our line 5 is the antecedent of the conditional with a negation sign in front of it, and that’s all that
counts.
3. Chain argument- the chain argument rule allows you to derive a conditional from two you already have, provided
the antecedent of one of your conditionals is the same as the consequent of the other.
P Q
Q R
P R
4. Disjunctive argument- from a disjunction and the negation of one disjunct, the other disjunct may be derived
P v Q P v Q
~P ~Q
Q P
5. Simplification- if the conjunction is true, then the conjuncts must all be true
P & Q P & Q
P Q
6. Conjunction- this rule allows you to put any two lines of a deduction together in the form of a conjunction
P
Q
P&Q
7. Addition- if P is true then either P or Q must be true. The truth of one disjunct is all it takes to make the whole
disjunction true
P____ Q____
P v Q P v Q 8. Constructive dilemma- the disjunction of the antecedents of any two conditionals allows the derivation of the
disjunction of their consequents.
P Q
R S
P v R
Q v S
9. Destructive dilemma- the disjunction of the consequents of two conditionals allows the derivation of the
disjunction of the negations of their antecedents.
P Q
R S
~Q v ~S
~P v ~R
Group II Rules: Truth-Functional Equivalences
- Truth functional equivalences- they each take the form of two types of symbolizations that have exactly the same
truth table ()
- Rules can be used on parts of lines
- A claim or part of a claim may be replaced by a claim to which it is equivalent by one of the following Group II rules
10. Double Negation (DN)- this rule allows you to add or remove two negation signs in front of any claim, whether
simple or compound.
P ~~P
11. Commutation (COM) – this rule simply allows any conjunction or disjunction to be “turned around” so that the
conjuncts or disjuncts occur in reverse order
(P&Q) (Q&P)
(PvQ) (QvP)
12. Implication (IMPL) – this rule allows us to change a conditional into a disjunction and vice versa
(P Q) (~P v Q)
13. Contraposition- this rule allows us to exchange the places of a conditional’s antecedent and consequent but only
by putting on or taking off a negation sign in front of each
(P Q) (~Q ~P)
14. DeMorgan’s Laws (DEM)
~(P & Q) (~P v ~Q)
~(P v Q) (~P & ~Q)
15. Exportation (EXP)- “If P, then if Q, then R” and is equivalent to “if both P and Q, then R”
[P (Q R)] [(P & Q) R]
16. Association (ASSOC)- when we have three items joined together with wedges or with ampersands, it doesn’t
matter which ones we group together.
[P & (Q & R)] [(P & Q) & R]
[P v (Q v R)] [(P v Q) v R]
17. Distribution (DIST)- allows us to spread a conjunct across a disjunction or to spread a disjunct across a conjunction
[P & (Q v R)] [(P & Q) v (P & R)]
[P v (Q & R)] [(P v Q) & (P v R)]
18. Tautology (TAUT)- allows steps that are sometimes necessary to “clean up” a deduction
(P v P) P
(P & P) P
Chapter 4- Credibility
The Claim and Its Source
- Two arenas in which we assess credibility: the first is that of claims themselves; the second is the claims’ sources
- There are degrees of credibility; it’s not an all-or-nothing kind of thing, whether we’re talking about claims or
sources:
o A person who stands to gain for our belief in a claim is known as an interested party, and interested
parties must be viewed with much more suspicion than disinterested parties, who have no stake in our
belief one way or another
o Interested parties are less credible than other sources of claims
o Furthermore, if a claim either lacks credibility or comes from a source that lacks credibility, it should be
viewed with suspicion
- Irrelevant features we often use to judge credibility: physical characteristics, gender, age, ethnicity, accent,
clothing, and mannerisms
- When does a claim itself lack credibility- that is when does its content present a credibility problem? o A claim lacks inherent credibility to the extent that it conflicts with what we have observed or what we
think we know- our background information- or with other credible claims
Assessing the Content of the Claim
Does the Claim Conflict with our Personal Observations?
- Reasonable to be suspicious of any claim that comes into conflict with what we’ve observed
- Our beliefs, hopes, fears, and expectations affect our observations
- Fallacy = mistake in thinking
o Wishful thinking- occurs when we allow hopes and desires to influence our judgement and colour our
beliefs
- Our personal interests and biases affect our perceptions and the judgements we base on them
- The reliability of our observations is no better than the reliability of our memories, except in those cases where we
have the means at our disposal to record our observations; memory can be deceptive but regardless, they are the
BEST source of information we have
Does the Claim Conflict with our Background Information?
- Background information= that immense body of justified beliefs that consists of facts we learn from our own
direct observations and facts we learn from other
o ‘background’ because we may not be able to specify where we learned it, unlike something we know
because we witnessed it this morning
- We begin by assessing claims initial plausibility, a rough assessment of how credible a claim seems to us. This
assessment depends on how consistent the claim is with our background information- how well it “fits” with that
information.
- No neat formulas that can resolve conflicts between what you already believe and new information
- The broader your background information, the more likely you are to be able to evaluate any given report
effectively
The Credibility of Sources
- The doubts we can have about the credibility of a source can be of two kinds: (1) we can doubt whether the source
has real knowledge about the issue in question (2) we can doubt the person’s truthfulness, objectivity, or accuracy
- The state of a person’s knowledge depends on a number of factors, especially that person’s level of expertise and
experience, either direct (through personal observation) or indirect (through study), with the subject at hand
- How do you judge a person’s expertise? Education and experience are often the most important factors, followed
by accomplishments, reputation, and position, in no particular order
o All must be seen in context
Government Management of the News
- In recent years, a number of fake news reports, paid for by the government, have appeared on television touting
the virtues of government schemes from the prescription drug program to airport safety to No Child Left Behind
- Some opinions or editorial pages are also bought
- Military also manages what media is allowed out (i.e. no coffins of slain soldiers)
Bias within the Media
- Media is said to be biased politically
- Many forces at work in the preparation of news besides a desire to publish or broadcast the whole truth
1. Like the rest of us, people in the news media sometimes make mistakes; they sometimes accept claims with
insufficient evidence or without confirming the credibility of a source
2. The media are subject to pressure and sometimes to manipulation from government and other news sources
3. The media, with few exceptions, are driven in part by the necessity to make a profit, and this can bring pressure
from advertisers, owners, and managers
Talk Radio
- Seems to offer a wealth of information not available in news reports from conventional sources
- Rumor, hearsay, and gossip
- Political perspective
The Internet, Generally
- Requires even MORE caution
- Two kinds of information sources on the internet: 1) commercial and institutional sources 2) individual and group
sites on the World Wide

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