Some Basic Concepts
Highlights of Chapter 1, 2, 3.
What is “Critical Thinking”?
Not Critical as in judging severely to find fault.
Critical as in careful, exact evaluation and
judgment.
“Critical Thinking” refers to a set of skills
relating to the recognition, analysis,
evaluation, and construction of arguments.
Bloom’s Taxonomy of Learning
Objectives
How is Critical Thinking useful?
Critical thinking skills are necessary for:
success in college
success in the workplace
success in the marketplace
Success in life
Developing Critical Thinking Skills
 Understand the concepts.
 Practice! Practice! Practice!
 Apply the skills.
Arguments for critical thinkers..
An argument is a set of claims; one of which is
supported by the others.
other words for “claims” are
“proposition”
“statement”
This is a slightly different concept then a
sentence.
Identifying Claims
A claim is a statement that has truth-value.
It is snowing.
Barack Obama is the 44th President of the United
States.
Today is Saturday.
Alaska is bordered by the Mediterranean Sea.
Buffy is a vampire slayer.
Identifying Claims
Not all sentences are claims.
It is cold in Alaska.
Where is Alaska located?
Please take me to Alaska.
Let’s go to Alaska.
Yea, Alaska!
Hint! Test using “it is true that”
Descriptive vs. Evaluative Claims
Capital punishment is the lawful infliction of
death as a penalty for committing a crime.
Capital punishment is immoral.
Note: Both are claims!
Counting Claims
A single claim can be expressed in different
sentences.
 Mike voted for Harper.
 He voted for Harper.
 Harper is who Mike voted for.
Counting Claims
A single sentence can represent different
claims.
 She went to the store.
Could mean….
Sarah went to Superstore.
Jane went to Sobeys.
Counting Claims
A single sentence may contain more than
one claim.
 George owns a cat, and Jones owns a dog.
 George owns a Siamese, which is a breed of
cat.
 George got a new cat because his other one
died.
Try it…
Identify the two claims expressed in the
sentence, “Dr. Newberry’s class is held in
room 106, which is in the southern side of
Dorothy Donahoe Hall.”
Try it…
Identify the two claims expressed in the
sentence, “Phil’s class is held in room EDU224,
which is in the Education building.”
Claim 1: Phil’s class is held in room EDU224.
Claim 2: Room EDU224 is in the education
building.
Counting Claims
Multiple claims can be combined in a
sentence to form a single claim.
 We can go to the park or we can stay home.
 If you complete all your homework, then you will
be prepared for class.
Complex claims:
Why does the sentence “Sally owns a cat and
Jim owns a dog” express two claims, while
“Sally owns a cat or Jim owns a dog”
expresses only one?
Well, stay tuned…
So… What is an argument?
An argument is a set of claims; one of
which is supported by the others.
The conclusion is the claim that the arguer is
trying to prove.
Claims called premise(s) provide support for
the conclusion.
Arguments.
• Monty Python was right!
• “An argument is a connected series of
statements intended to establish a
proposition.”
– John Cleese et al.
– http://montypython.50webs.com/scripts/Series_3/27.htm
Arguments.
• How arguments work…
• Arguments are a series of claims connected so
that one or more of them support another.
– All Dogs are Canines
– All Canines are Mammals
– All Dogs are Mammals.
Argument: Ordinary Language.
• In ordinary language,
an argument is a
heated discussion
between 2 or more
people who disagree.
• In logic, an argument is
2 or more statements
intended to be related
so that one is justified
by the other(s).
Sometimes its both!
Parts of an argument
• Arguments are composed of
– One or more premises. (the reasons)
– Exactly one conclusion.
Example:
P1. I buy beer for Markers who find plagiarists.
P2. Markers love beer.
P3. Markers have no money.
C. My Markers will try hard to find Plagiarists.
Inference indicators are words and phrases
which identify the parts of the argument.
Inference indicators help us understand
how the claims in an argument are related.
Inference Indicators
Conclusion Indicators
therefore…
thus…
consequently…
so...
hence…
accordingly…
Premise Indicators
because…
since…
for…
given...
as…
follows from…
Arguments vs. Explanations
Both contain at least two claims.
Both provide reasons.
Different purpose.
Arguments offer reason why something is
true.
Explanations describe how or why something
is true.
What is an explanation?
An explanation is a set of claims
accounting for how or why a given fact is
true.
The explanandum is the fact being
explained.
The explanans is the account offered for
some given fact.
Arguments vs. Other Non-Arguments
A passage may be neither an argument
nor an explanation because:
It contains only one claim, or
None of the claims provides reasons for any
of the others.
A “to-do list” is neither an explanation nor and
argument.
Recognizing Arguments
Step 1: Count the claims
 Arguments must contain two or more claims.
Step 2: Look for reasons
 Arguments contain a claim that is supported by the
other(s).
Step 3: Identify the purpose
 Arguments offer proof that a claim is true.
 Explanations describe how or why a fact is true.
Is it an argument?
 Police are looking for a suspect who robbed a local
gas station two weeks ago. Video from the station’s
security camera shows a man walking into the store
with a gun, pointing it at the cashier, and exiting the
store with cash from the register. No injuries have
been reported.
 I was terrified because all I saw was this gun, and I
really thought that he was going to shoot me.
 We believe that the suspect in this case is the same
one responsible for two other gas station robberies
that occurred earlier this month. The physical
descriptions are very similar, and the same kind of
weapon was used in all three incidents.
Tangent: Truth Values
• In our culture, we presume that every
statement is either true or false.
– This is the 1st law of thought.
– Sometimes called the law of the excluded middle.
• Do you agree with this presumption?
• Truth values can change:
– “It is raining outside” is false right now, but will
eventually be true.
“True” and “False”
• In logic we often speak of the truth value of
statements.
– Ex: It is true that the Titanic sank.
– Ex: It is false that Phil is thin.
• Don’t confuse “Good” with “true” and “Bad”
With False.
– Ex: 50 Million died in WWII
• True but horribly bad.
– Ex: There is a cure for cancer.
• False but something we hope to be true soon.
What makes something true?
• Believe it or not… We don’t really know.
– This is a genuine philosophical question.
• There are many different theories.
– Correspondence theory:
• Truth is what agrees with reality.
• Commonsense but problematic…
– Coherence theory:
• Truth is what agrees with our current beliefs.
– There are many other theories…
Logic without “truth”
• Philosophers and logicians have developed a
system that can evaluate statements and
arguments without having to confirm things as
“true” or “false”.
• This is handy if you can’t agree what “true” or
“false” is.
• Examples in logic courses tend to stick to very
obviously true or false claims, rather then
those claims that are contentious.
“Valid”
• In ordinary language: often used as a
synonym for “Good”.
• Daytime TV is full of people with ‘valid’
opinions who make ‘valid’ points.
• Don’t use “valid” this way (for this class)!
– Try to never use it this way!
• Valid has a very precise technical meaning.
What Valid really means.
• A valid argument is one that guarantees the
truth of the conclusion whenever the
premises are true.
• Example Valid argument.
– All dogs are canines.
– No Cats are canines.
– No dogs are cats.
But, valid is a conditional concept
• Arguments whose premises are false, but
which would guarantee the conclusion if the
premises are true, are still valid.
• Eg: valid argument with false premises.
– All dogs are cats.
– All cats are whales.
– All dogs are whales.
Obviously false. (O.F.)
OF
OF
Think of it this way…
• If all dogs were cats, and
• If all cats were whales
• Then all dogs would be whales.
• “Valid” is a description of arguments,
– not parts of arguments
• (which can be either true or false)
More odd Valid arguments.
• All dogs are cats. OF
• All cats are canines. OF
• All dogs are canines. Obviously true.
• If all dogs were cats and all cats were canines,
Then it would be true that all dogs are canines.
• This example illustrates that the falsity of the
premises doesn’t imply the falsity of the
conclusion.
This is a valid argument
• All X are Y
• All Y are Z
• Therefore all X are Z.
• Despite the fact that you don’t know what X, Y or
Z represent.
• Ignore “Actual” truth or falsity when considering
validity, concentrate on the relationship between
the premises and the conclusion.
Examples of invalid.
• All dogs are mammals.
• All cats are mammals.
• All dogs are cats.
O.F.
• All dogs are mammals
• All cats are mammals
• No dogs are cats.
– (all true, but still invalid for reasons as follows…)
How do you know that is invalid?
• Any argument that permits a counterexample
is invalid.
• A counterexample is an argument with the
same form as the original argument, but
which has
– obviously true premises and an
– obviously false conclusion.
Counterexample Example
Original argument
• All x are y
• All z are y
• No x are y.
Counterexample:
All fish are cold-blooded.
All spiders are cold-blooded.
Therefore no fish are spiders.
Using Counterexamples
• Counterexamples are a form of PROOF that an
argument is invalid.
• They are also effective in contexts where
people don’t know their logic.
• Someone who has never studied reasoning
can often be convinced “by ear” that their
argument is flawed with the presentation of a
counter example.
Providing counter examples.
• Take the original argument:
• Identify the form (the structure of the
argument)
• Think of another argument with the same
form but with obviously true premises and an
obviously false conclusion.
• Ex next page.
Original argument
• All presidents are charismatic men.
• Mitt is a charismatic man,
• Mitt will be president.
•
•
•
•
Counterexample: Fill in the blanks….
P1 All _______ are __________
P2. __________ is ____________
C: ____________ will be __________
Fallacies and Counterexamples
• In the next section of the course we will study
“the fallacies”
• We will use a lot of counter-examples to help
understand why these arguments are fallacies.
Logical Fallacy
• Two senses:
– Any argument that fails to adequately support its
conclusion.
• It is impossible to define all the ways you can be wrong.
– Any argument that fits into common patterns of
error in reasoning.
• “The fallacies”.
To be a fallacy…
• To be a fallacy a series of statements must first
be an argument:
• You’re a jerk, therefore you’re wrong.
– Is a fallacy (ad hominem aka fallacy of abuse.)
• You’re a jerk,
– is not a fallacy, it is mere abuse.
Fallacies in this course
• We will look at 4 sets of fallacies:
– Informal fallacies.
– Fallacies of syllogistic logic.
– Fallacies of propositional logic.
– Fallacies of inductive logic.
Formal
fallacies.
Example of a fallacy
• “Childhood obesity has increased now that so
many children are playing video games, so
obviously video games cause obesity in
children.”
• This argument relies on the evident fact that
video games and obesity have occurred
together to conclude one is the cause of the
other.
Cum hoc, ergo procter hoc
• A common causal fallacy, know by its
traditional latin name:
• With this, therefore because of this.
• Counterexample: (to expose the fallacy)
– Video games have been gradually increasing in
popularity since the 80’s, and my hair has been
decreasing since then, so obviously video games
have caused my baldness.
Formal versus Informal fallacies
• Formal fallacies are fallacies that violate some
specific logical rule or law.
– Ex:
All Geese can fly
All ducks can fly
All geese are ducks.
This argument commits the formal rule
regarding the distribution of terms in an
argument.
Formal versus Informal fallacies
• Formal fallacies are fallacies that violate some
specific logical rule or law.
– Ex:
All Geese can fly
All ducks can fly
All geese are ducks.
The category of things that can fly
includes both ducks and geese.
The way this argument refers to flying
things, they can be either ducks or
geese, but not necessarily both.
This argument commits the formal rule
regarding the distribution of terms in an
argument.
Formal vs informal fallacies
• Informal fallacies are not violations of specific
logical rules
• Instead are errors of reasoning common enough
to be named, recognized, and studied.
• Traditional education in law often focused heavily
on the informal fallacies.
• Informal fallacies are often grouped by category
in various ways.
– There are many different groupings in different texts.
Copi’s treatment of the Fallacies
• Copi groups 19 informal fallacies into 3
groups.
– Fallacies where the primary deficiency is…
• Relevance R1-R7.
• Presumption P1-p7.
• Ambiguity A1-A5.
Additional sources for Fallacies
• www.fallacyfiles.org
– Extensive collection of fallacies.
• http://www.nizkor.org/features/fallacies/
– Collection of fallacies relevant to the website:
rebutting holocaust deniers.
• http://onegoodmove.org/fallacy/
– This site indicates a “proof” condition for each fallacy
given.