Critical Thinking I
Course Review
Exclusions
•
the following topics will not be on the exam, so you
can leave them out of your preparation.
1. Conductive arguments
2. Categorical Syllogisms
•
All other topics listed in the course outline will be
drawn upon for the exam.
Format
•
The final exam will consist of 7 sections.
•
The first section will be a series of multiple choice
questions.
•
The other 6 sections will be short answer questions
in which you will be asked to use the various
methods we have learned for evaluating, testing
and assessing arguments of various kinds.
Good luck and happy studying.
Chapter 1
An argument is:
a set of claims in which one or more of them – the
premises – are put forward so as to offer reasons for
another claim, the conclusion. (1)
Arguments in the sense defined are about providing
justification for some belief or other.
Chapter 1
Conditional sentences are referred to as if/then sentences
and cannot be broken into two part. They are one entire
sentence.
A conditional sentence is one that links several conditions,
specifying that IF one condition holds, anther will as well.
Conditionals are often found in arguments, but the NEVER
express an argument.
Chapter 1
Things to review:
(1)Argument
(2)Conclusion
(3)Conditional Statement
(4)Explanation
(5)Indicator words
(6)Nonargument
(7)Opinion
(8)Premise
Chapter 2
Before we can evaluate an argument, we need to
understand just what the argument in question is. We
need to know what the premises and conclusion are and
how the premises are supposed to support the conclusion.
Standardizing an argument is to set out its premises and
conclusion in clear statements with the premises
preceding the conclusion like so:
Premise 1
Premise 2…
Premise N
Therefore,
Conclusion
Chapter 2
Number the premises and conclusions so that it makes it
easy to refer to them by a name: the number. So we can
talk about (1) or premise (1) without having to rewrite the
entire premise.
Standardizing arguments gives us a clear view of where the
arguer is going and forces us to look carefully at what the
arguer has said. Here is an argument in standard form.
(1) If Chuck is in Atlanta, then Chuck is in Georgia.
(2) Chuck is not in Georgia.
Therefore,
(3) Chuck is not in Atlanta.
This simple argument is in a clear, standard form.
Chapter 2
Arguments often proceed in stages. Sometimes a premise
in one argument is a conclusion of another argument.
This phenomena happens in what are called
subarguments.
A subargument is a subordinate argument that is a
component of a larger argument, called the whole
argument. Figure 2.2 shows the logical relationship of this
kind of case.
From page 25.
Chapter 2
In figure 2.2, statement (2) represented by
the circled ‘2’ is the conclusion of a
subargument and may be called the
subconclusion. But (2) is also a premise in
the main argument.
The main argument is (2) and (3) to (4), and
when we add the main argument with the
subargument we get what we call the
whole argument.
Subarguments are necessary and useful,
because sometimes you need to justify a
premises with another subargument.
In figure 2.2, (4) is also called the main
conclusion.
Chapter 2
Standardizing an argument is not always a simple matter.
Questions, commands, repetition, background and side
remarks, jokes, wandering off topic, and so on, can all
show up in arguments.
These elements of colloquial writing and speech are
eliminated when we put the argument in standardized
form.
The point of standardized form is clarity of the reasoning
involved in the argument.
Chapter 2
10 General Strategies for Standardizing Arguments
(1)Read and understand the passage
(2)Make sure the passage contains an argument
(3)Identify the conclusion, premises, and any subarguments
(4)Omit irrelevant material or side remarks
(5)Omit material already used (don’t repeat information)
(6)Omit personal phrases like “in my hunble opinion”
(7)Number the premises and conclusion and standardize the argument
(8)Make premises complete indicative sentences without pronouns
(9)Check for subarguments in premises and conclusions
(10)Check your argument against the passage for errors or omissions
See page 31 for fuller guidelines.
Chapter 4
The ARG conditions are:
(1) Acceptable premises – it is reasonable for the person
receiving the argument to believe the premises to be
true
(2) Relevant premises – premises are relevant to the
conclusion
(3) Good grounds – the premises support the conclusion
and make it reasonable to believe the conclusion
Chapter 4
These are a test of the cogency of an
argument.
This means that the cogency of an argument
requires acceptable premises, relevant
premises, and good grounds for adopting the
conclusion.
Chapter 4
Deductive entailment
Often referred to as simply validity, deductive entailment is a
tight logical relation where, when the premises are true,
the conclusion must be true.
Consider the following argument: Only members are
allowed into the club. Andrew was not allowed in. So,
Andrew is not a member of the club.
If the premises are true, then conclusion has to be true.
Chapter 4
For deductively valid arguments it is never possible for the
conclusion to be false when all the premises are true.
Another way to say this is that when the premises are true,
the conclusion must be true.
Validity does not come in degrees. Deductive arguments
are either valid or they are not valid.
Deductively valid arguments satisfy both the R and the G
conditions for cogency of arguments.
Chapter 4
Inductive support
Inductive support is evidence (as opposed to reasons) that
support the conclusion in a manner less certain than that
of deductively valid arguments.
Typically inductive argument rely on regularities in the world
to make reasonable predictions and are thus called
amplitive, they go beyond what is known for certain to
what we can reasonably know based on available
evidence.
Chapter 4
One kind of inductive argument is a generalization about an
entire population based on an observed sub group of that
population.
If all the people I meet from Hamilton are football fans, and I
meet Sue from Hamilton, then there is good reason for me
to think that she is a football fan (depending on how many
people I have observed from Hamilton).
Inductive arguments with all true premises don’t guarantee
the truth of the conclusion the way deductively valid
arguments do.
Chapter 4
Using the ARG conditions to evaluate
arguments.
Start with the A condition (are the premises acceptable?)
If so, then move to the R condition (are the premises
relevant to the conclusion?)
If so, then move on to the G condition (do the premises
provide good grounds for accepting the conclusion?)
If ARG are satisfied, then we have a cogent argument.
Chapter 4
Failing the (A) Condition
If the premises are not acceptable (and there are lots of
reasons this might happen), then the argument fails the
(A) condition.
Premises that are clearly false, contain persuasive
definitions, or are disputable based on common
knowledge are examples as to why premises might not be
acceptable. See example pages 95-6.
Chapter 4
Failing the (R) Condition
If an argument has acceptable premises, we can then ask if
the premises are relevant to the conclusion. If for some
reason, they are not relevant to the conclusion, then the
argument is not cogent.
If the argument fails the (R) condition, we do not have to
move on and test for (G) since we know the argument is
not cogent. See example on pages 97-8.
Chapter 4
Failing the (G) Condition
If an argument satisfies both the (A) and (R) conditions, we
can move on to the (G) condition.
If the premises of an argument are true and relevant to the
conclusion, the next question is about grounding. Do
these relevant, well supported premises actually support
the conclusion. If so, then we have a cogent argument. If
not, then we don’t. See example on pages 98-9.
Chapter 4
Cogency, Soundness, and Validity
Deductive entailment (validity) satisfies the (R) and (G)
requirements completely. Sound arguments have all true
premises and thus satisfy (A).
But there are other arguments that are cogent, but not
sound because they are either not valid or have premises
that are rationally acceptable, but not true. We spent time
on soundness in Chs 7 and 8. (108)
Chapter 4
Evaluating and Constructing Arguments
When an argument is offered, there are three possible ways
to respond to an argument:
(1) Reasoned acceptance -- ARG are accepted
(2) Reasoned rejection -- one or more of ARG are not
accepted
(3) Suspended judgment -- for various reason you might
suspend judgment on the argument
See pages 109-10
Chapter 5
Acceptable premises are important because even if you
have the best, most elegant reasoning possible, if the
premises are not acceptable, then the reasoning does not
matter.
What does it mean to say that the premises of an argument
are rationally acceptable? How might we show that they
are? Here are seven ways to show premises are
acceptable:
Chapter 5
When premises are acceptable:
(i)Before you begin we need to make an important philosophical point. Govier refers
to 'acceptable' and ‘unacceptable' premises. She doesn't want to refer to 'truth' or
'falsity' or have you say: 'Such and such is true' because whether something is 'true'
or 'false' is independent of whether or not anyone KNOWS or BELIEVES it to be
true or false. Think about it.
(ii) It is either True or False that there is someone named Deanna sitting in a Cafe' in
Graz Austria right now. But is this reasonable to believe? How can you KNOW it if
you aren't there right now? Or how about whether there is life after death? It's
either true or false, but how do we determine which it is? Acceptability is a much
better concept to start with since it puts this more epistemologically complex
concept of 'what is truth?‘ aside for now ("epistemology" is a branch of philosophy
dealing with different theories of knowledge).
Chapter 5
Premises are acceptable if:
(1)They are supported by a cogent subargument.
This means that if the conclusion of a cogent
subargument is a premise in another argument, then there
is every reason to accept it as a premises.
(2) The premises are supported elsewhere.
Elsewhere there could be another cogent argument that
the author or some other author has already established
as cogent.
Chapter 5
(3) The premise is know a priori to be true.
A priori statements are the kind of things a person
could know independent of experience or before
experiences. It is contrasted with the term a posteriori.
Statements that are knowable a posteriori require
experience.
Chapter 5
(4) A premise is acceptable if it is a matter of common
knowledge.
If just about everyone knows or understands that a premise
is true, then the premise is acceptable.
Chapter 5
When it comes to common knowledge we have to be careful
because common knowledge can change given the times
and what kind of events are occurring in the world.
Chapter 5
(5) Testimony -- under some conditions, a claim is
acceptable on the basis of a person’s testimony.
There are three main factors that will undermine our
acceptance of testimony as reliable.
(i) The claims made are implausible
(ii) The person making the claim or other source is unreliable
(iii) The content of the claim goes beyond the experiences or competency of the
testifier
A lot of things give rise to when and how we accept
testimony and how to govern its acceptability.
Chapter 5
(6) Appeal to a proper authority
Sometimes we have to take the word of a recognized
authority with respect to the acceptability of a premise. If
a logic professor told you that a particular argument was
deductively valid, you can trust that because she is a
proper authority on the validity of arguments. This same
logic professor, however, may not be an authority on the
exports of the state of Florida, and cannot explain if an
income tax would increase tax revenue or not.
Authorities must be proper to make premises acceptable.
Chapter 5
(7) The last method of accepting premises is different from
the rest. We say that we accept a premise provisionally or
conditionally.
You might find an argument to pass both the (R) and (G)
conditions for cogency, but are uncertain about the
acceptability of the premises. You can provisionally
accept the premises and thus provisionally accept the
conclusion and cogency of the argument.
Chapter 5
Summary of the acceptability conditions:
A premise in an argument is acceptable if any one of the following conditions is
satisfied:
(1)It is supported by a cogent subargument.
(2)It is supported elsewhere by the arguer or other person, and this fact is noted.
(3)It is know a priori to be true.
(4)It is a matter of common knowledge.
(5)It is supported by appropriate testimony.
(6)It is supported by an appropriate appeal to authority.
(7)The premise is not know to be rationally acceptable, but can be accepted
provisionally for the purpose of the argument.
Chapter 5
Summary of Unacceptable Conditions
(1)One or more premises are refutable on the basis of common knowledge, a priori
knowledge, or reliable knowledge from testimony or authority.
(2)One or more premises are a priori false.
(3)Several premises, taken together, produce a contradiction, so that the premises
are explicitly or implicitly inconsistent.
(4)One or more premises are vague or ambiguous to such an extent that it is not
possible to determine what sort of evidence would establish them as acceptable or
unacceptable.
(5)One or more premises would not be rationally acceptable to any person who did
not already accept the conclusions. In this case, the argument begs the question or
is circular.
Chapter 6
Understanding Relevance:
The second condition for cogency for an argument is the (R)
condition and we are going to look at the three basic ideas
of relevance.
(i) Positive relevance
(ii) Negative relevance
(iii) Irrelevance
Chapter 6
Positive Relevance:
A statement A is positively relevant to another statement B if
and only if the truth of A counts in favour of the truth of B.
This means that A counts as evidence for B.
See page 148 for examples:
Chapter 6
Negative Relevance:
A statement A is negatively relevant to another statement B
if and only if the truth of A counts against the truth of B.
This means that if A is true, it counts as evidence or reason
to think that B is not true.
See page 149 for examples.
Chapter 6
Irrelevance:
A statement A is irrelevant to another statement B if and
only if A is neither positively relevant nor negatively
relevant to B.
A doesn’t provide a reason to or a reason not be believe in
the truth or falsity of B.
See page 149 for examples.
Chapter 7
We dealt with Categorical Logic in chapter 7. To start, we
learned the four categorical forms.
In categorical logic, the terms all, no, some, and not are the
basic logical terms.
The four categorical forms are:
A: All S is P
E: No S is P
I: Some S is P
O: Some S is not P
Chapter 7
The A form categorical statement is:
A: All S is P
This is a universal affirmation statement. It says that all the
members of the S category are members of the P
category.
For example:
All sisters are female persons.
All my sandwiches are peanut butter.
Chapter 7
The E form categorical statement is:
E: No S is P
This is a universal negation statement. It says that none of
the members of the S category are members of the P
category (Ss are excluded from the P category).
For example:
No sisters are male persons.
None of my sandwiches are pastrami.
Chapter 7
The I form categorical statement is:
I: Some S is P
This is a particular affirmation statement. It says that at
least one member of the S category is a member of the P
category.
For example:
Some sisters are pilots.
Some of my sandwiches are pre-made.
Chapter 7
The O form categorical statement is:
O: Some S is not P
This is a particular negation statement. It says that at least
one member of the S category is not a member of the P
category (some Ss are excluded from the P category).
For example:
Some sisters are not pilots.
Some of my sandwiches are not pre-made.
Chapter 7
The Square of Opposition shows the logical relationship
between the different categorical forms.
A: All S are P
E: No S are P
I: Some S are P
O: Some S are not P
A and O are contradictories: they have to have opposite
truth values. The same goes for I and E.
Chapter 7
A and E statements are contraries because they cannot both
be true, but they can both be false.
I and O statements are referred to as subcontraries
statements because they can both be false, but they
cannot both be true.
See page 181 for examples.
Chapter 8
The logical connectives not, and, or, and if then will be
represented by the following: –, •, ∨, and ⊃.
We are going to define these symbols using truth-tables and
thus they will have truth-table definitions. The point of a
truth-table definition is to provide all the possible cases of
truth or falsity for the values of the the sentence letters.
Each connective will have its own definition.
Chapter 8
Not
Not functions to change the truth of a statement to its
opposite. The truth-table definition for not is quite simple.
If P is true, the not P is false. If P is false, then not P is true.
This is our truth-table definition of not.
Chapter 8
And
And is a conjunction and connects two conjucts. The
conjunction is true when both conjuncts are true and false
ever where else. Here is our truth-table definition of and.
The only time P • Q is true is when both P and Q are true.
Chapter 8
Or
Or is disjunction and it is true when either one or both of the
disjuncts are true and false when both disjuncts are false.
Here is the truth-table definition of or.
Because we have defined or a being true when both
disjuncts are true, this is called inclusive or
Chapter 8
We are going to define the horseshoe as true whenever the
consequent is true or whenever the antecedent is false.
The only time a conditional statement is false is when the
antecedent is true, and the consequent is false. So, if it is
raining and my car isn’t wet, because it is in the garage,
then the prior conditional is false. Here is the truth-table
definition of the conditional.
Chapter 9
Induction is the basis for our common sense beliefs about
the world.
In the most general sense, inductive reasoning, is that in
which we extrapolate from experiences to what we have
not yet experiences.
In this chapter we are going to focus on: inductive
generalizations, statistical syllogisms, and common errors
or fallacies that are associated with inductive reasoning in
general.
Chapter 9
Inductive arguments have the following characteristics:
1.The premises and the conclusion are all empirical propositions.
2.The conclusion is not deductively entailed by the premises.
3.The reasoning used to infer the conclusion from the premises is based on the
underlying assumption that the regularities described in the premises will persist.
4.The inference is either that unexamined cases will resemble examined ones or that
evidence makes an explanatory hypothesis probable.
See page 255 for a full explanation.
Chapter 9
Inductive Generalizations (IG)
In an IG, the premises describe a number of observed
objects or events as having some particular feature. From
this observed set of objects or events a conclusion asserts
a claim about all (or most) of the objects and events of the
same type have the feature in question.
1. 85% of polled students at Notre Dame think the football team is great.
So, probably:
1. 85% of all Notre Dame students think the the football team is great.
The word probably indicates that there is an extrapolation
from the polled (observed) group the the entire group.
Chapter 9
Phrases like: probably, in all likelihood, and most likely are
often used in inductive arguments.
Inductive arguments and inductive reasoning is used in
contexts of prediction. Reasoning from the past to the
future.
Induction requires a belief in the regularities in the world.
Chapter 9
Some important points about the many types of IGs.
We need to take into account:
(1)Sample size relative to the size of the target population.
(2)Samples need to be random
Random for samples is defined as: every member of the
population having an equal chance of being chosen for the
sample. If this is the case, then the sample is random.
Chapter 9
Problems of Sampling:
Size issues: more samples of a population does not
necessarily make an IG stronger. What one needs for the
sample is for it to be representative. Representativeness
will work as a substitute condition for randomness.
Sometimes it is more reliable than random depending on
the point of the sample.
What one needs for a sample size depends on the variability
of the population. (260)
Chapter 9
Guidelines for Evaluating Inductive Generalizations
1.Try to determine what the sample is and what the population is. If it is not stated what the
population is, make an inference as to what population is intended, relying on the context
for cues.
2.Note the size of the sample. If the sample is lower than 50, then, unless the population is
extremely uniform or itself very small, the argument is weak.
3.Reflect on the variability of the population with regard to the trait or property, x, that the
argument is about. If the population is not known to be reasonably uniform with regard to x,
the sample should be large enough to reflect the variety in the population.
4.Reflect on how the sample has been selected. Is there any likely source of bias in the
selection process? If so, the argument is inductively weak.
5.For most purposes, samples based on volunteers, college students, or persons of a single
gender, race, or social class are not representative.
6.Taking the previous considerations into account, try to evaluate the representativeness of
the sample. If you can give good reasons to believe that it is representative of the
population, the argument is inductively strong. Otherwise, it is weak.
Chapter 10
A causal inductive argument is an inductive argument in
which the conclusion is a claim that one thing causes
another. (286)
For example:
(i) Clogged arteries cause heart attacks
(ii) A rough surface produces friction
(iii) Exercise during heat causes sweating
Causal inferences are often an attempt to explain or predict
an outcome.
Chapter 10
The meaning of cause can vary as well because of the
different nature of causal relationships. Here are four
possible meanings for cause:
(i) As a necessary condition
(ii) As a sufficient condition
(iii) As both a necessary and sufficient condition
(iv) As a contributory factor (neither necessary or sufficient)
Each of these meanings of ‘cause’ are useful in analyzing
arguments and premises in argument. We will see
examples of each.
Now you know what we did,
so review, practice and do your best.