lOMoARcPSD|359 747 69 10/14/2016 BASIC LOGICAL CONCEPTS 1 lOMoARcPSD|359 747 69 10/14/2016
“When asked how World War III would be fought,
Einstein replied that he didn't know. But he knew how
World War IV would be fought: With sticks and stones!” Remember! 2 lOMoARcPSD|359 747 69 10/14/2016
Before we can effectively analyze and
evaluate an argument, we need to understand clearly what kind of
argument is being offered. 3 lOMoARcPSD|359 747 69 10/14/2016
Deduction & Induction
Types of Arguments:
Deductive arguments are arguments in which the conclusion is
claimed or intended to follow necessarily from the premises.
Inductive arguments are arguments in which the conclusion is
claimed or intended to follow probably from the premises.
Deduction & Induction reasoning
The quickest way to determine whether an
argument is deductive or inductive is to note
whether it has a pattern of reasoning that is
characteristically deductive or inductive 4 lOMoARcPSD|359 747 69 10/14/2016 Deduction vs. Induction 
Deductive Arguments try to prove their
conclusions with rigorous, inescapable logic. Example: 1. All humans are mortal. 2. Socrates is a human. 3.
Therefore, Socrates is mortal. 
Inductive Arguments try to show that their
conclusion are plausible (likely or
probable), given their premises: 1.
So far, every class, the professor has worn a tie. 2.
Therefore, next class, the professor will 6
wear a tie.Lecture Notes © 2008 McGraw Hill Higher Education Avoid a Misconception  Misconception:
 Deductive arguments go from the general to the specific/particular--
 Inductive argument go from the specific/particular to the general. This is wrong!!  They can do that:
 Deductive: Al Males are mortal. (general) I am Male. Therefore I
am mortal. (particular)
 Inductive: The last two winter days were cold. (particular)
Therefore, all winter days are cold. (general) But they can also do the exact opposite:
 Deductive: Lincoln was president from 1861-1865
(particular); therefore everyone born while he was president was
born in the 1800’s. (general)
 Inductive: I have got A’s in al my classes so far (general).
Therefore, I will get an A in this class (particular). 5 lOMoARcPSD|359 747 69 10/14/2016
Deduction & Induction Arguments below deductive or inductive?
Argument 1 All
Humans are Mortal.
 Socrates is human.
 Therefore, Socrates is Mortal. Argument 2
 If the president lives in the White House, then he
lives in Washington, D.C
 The president does live in the White House
 So the president lives in Washington, D.C KEY DIFFERENCES
Deductive arguments claim that Inductive arguments claim that
 If the premises are true, then
 It is unlikely for the premises to
the conclusion must be true. be true and the conclusion  false. The conclusion follows
necessarily from the premises.  The premises provide
conclusive evidence for the truth of the conclusion.
 It is impossible for all the premises to be true and the conclusion false.
 It is logically inconsistent to assert the premises and deny
the conclusion, meaning that if you accept the premises, you
must accept the conclusion.
 If the premises are true, then
the conclusion is probably true.  The conclusion follows
probably from the premises.
 The premises provide good (but not conclusive) evidence
for the truth of the conclusion. 6 lOMoARcPSD|359 747 69 10/14/2016  Although it is logically consistent to assert the premises and deny the conclusion, the conclusion is
probably true if the premises are true.
Deduction & Induction
 There are four tests that can be used to determine
whether an argument is deductive or inductive:
 The Indicator Word Test
 The Strict Necessity Test
 The Common Pattern Test
 The Principle of Charity Test 7 lOMoARcPSD|359 747 69 10/14/2016
The Indicator Word Test Tom is a IT student.
Most IT students own laptops.
So, probably Tom owns a laptop.
 The indicator word test asks whether there are any
indicator words that provide clues whether a deductive or
inductive argument is being offered.
 Common deduction indicator words include words or
phrases like necessarily, logically, it must be the case that, and this proves that.
 Common induction indicator words include words or
phrases like probably, likely, it is plausible to suppose that,
it is reasonable to think that, and it's a good bet that.
 In the example above, the word probably shows that the argument is inductive.
Telling the difference between
Deductive and Inductive Arguments Indicator Words:
 Deductive: certainly, definitely, this entails that, conclusively
 Inductive: probably, likely, one would expect,
odds are, reasonable to assume
Like before, indicators are not perfect. They
are not always present, and they can sometimes be misleading.
(e.g., The speaker may say “it certainly
follows” but be exaggerating, knowing that it
only “probably follows.”) 12
Lecture Notes © 2008 McGraw Hill Higher Education 1 lOMoARcPSD|359 747 69 10/14/2016
The Strict Necessity Test Texans are architects.
No architects are Democrats.
So, no Texans are Democrats.
 The strict necessity test asks whether the conclusion
follows from the premises with strict logical necessity. If it
does, then the argument is deductive.
 In this example, the conclusion does follow from the
premises with strict logical necessity. Although the
premises are both false, the conclusion does follow
logically from the premises, because if the premises were
true, then the conclusion would be true as well.
Telling the difference between
Deductive and Inductive Arguments The Strict Necessity Test:
If it would make a good (valid) deductive argument, assume it is. If it 
wouldn’t, assume it isn’t. (We wil learn more about how to tel later.)
 Exceptions to the Strict Necessity Test
 Sometimes, even though the premises don’t deductively support the
conclusion, it is clear that the speaker of the argument intended them to.
• Maybe they say “it necessarily fol ows” or “it is guaranteed” •
Maybe the context shows that they meant it to be deductive.
 When that happens, call it deductive.
 Examples of exceptions (deductive but not valid arguments):
1. Magellan's ships sailed around the world.
2. It necessarily follows that the earth is a sphere.
1. If I am in Wilkes-Barre, then I'm in PA. 2. I am not in Wilkes-Barre.
3. Therefore, I am not in Pennsylvania 2 lOMoARcPSD|359 747 69 10/14/2016
The Common Pattern Test
Either Bruce Lee voted in the last election, or he didn't. Only citizens can vote.
Bruce Lee is not, and has never been, a citizen.
So, Bruce Lee didn't vote in the last election.
 The common pattern test asks whether the argument
exhibits a pattern of reasoning that is characteristically deductive or inductive.
 If the argument exhibits a pattern of reasoning that is
characteristically deductive, then the argument is probably deductive.
Telling the difference between Deductive and Inductive Arguments  The Common Pattern Test:
 There are many common patterns that valid arguments “use.”
• For example: If P then Q. P. Therefore Q.
• This is called Modus Ponens
 If an argument follows one of these patterns, it is deductive.
 We will learn other patterns shortly. 3 lOMoARcPSD|359 747 69 10/14/2016
The Common Pattern Test
 If the argument exhibits a pattern of reasoning that is
characteristically inductive, then the argument is probably inductive.
 In the example above, the argument exhibits a pattern of
reasoning called "argument by elimination.“
 Arguments by elimination are arguments that seek to
logically rule out various possibilities until only a single
possibility remains. Arguments of this type are always deductive.
The Principle of Charity Test
Ramlan: Karen told me her grandmother recently climbed Gunung Kinabalu.
Zaid : Well, Karen must be pulling your leg. Karen's
grandmother is over 90 years old and walks with a cane.
 In this passage, there are no clear indications whether Zaid's
argument should be regarded as deductive or inductive. For
arguments like these, we fall back on the principle of charity test.
 According to the principle of charity test, we should always
interpret an unclear argument or passage as generously as possible.
 We could interpret Zaid's argument as deductive. But this would
be uncharitable, since the conclusion clearly doesn't follow from
the premises with strict logical necessity. (It is logically possible-
although highly unlikely--that a 90-year-old woman who walks
with a cane could climb Gunung Kinabalu.) Thus, the principle
of charity test tells us to treat the argument as….. 4 lOMoARcPSD|359 747 69 10/14/2016
Telling the difference between
Deductive and Inductive Arguments
 The Principle of Charity Test. If it is unclear what
kind of argument it is then…
 …if it would make a bad deductive argument assume it is not a deductive argument.
 If it’s a choice between “bad deductive” and “good
inductive,” go with the latter—it’s nicer and more likely what the person had in mind.  Example:
 Andy told me that he ate at Maxine’s yesterday, but it
burned down a month ago. It is certain that he was lying or mistaken.
 Since it is possible that Maxine’s was rebuilt quickly, this
argument is deductively invalid. Assume that the author intended it to be inductive. Deductive reasoning
The are five common patterns of deductive reasoning:  Hypothetical syllogism  Categorical syllogism  Argument by elimination
 Argument based on mathematics  Argument from definition 5 lOMoARcPSD|359 747 69 10/14/2016 Common Patterns of Deductive Reasoning
Hypothetical Syllogism: three line argument that
contains at least one conditional.
 If A then B. A. Therefore B. (Modus Ponens)
 If P then Q. if Q then R. Therefore if P then R. (chain argument)
 If A then B. Not B. Therefore not A. (Modus Tollens)
Invalid versions (that are still deductive):
 If A then B. Not A. Therefore not B. (denying the antecedent) •
If I am female then I am a person. I am not female. Therefore I am not a person.
 If A then B. B. Therefore A. (affirming the consequent). •
If we’re on Neptune then we are in the solar system.
We are in the solar system. Therefore, we’re on Neptune.
These are still called deductive because usually
22 Lecture Notes © 2008 McGraw Hill Higher people think they are valid when they put them
Hypothetical syllogism
 A syllogism is simply a three – line
argument, exactly two premises and a conclusion.
 Hypothetical syllogism contains at least one
hypothetical or conditional (i.e, if – then) premise  An example form: If A then B. A Therefore, B. forward. Education 6 lOMoARcPSD|359 747 69 10/14/2016 Categorical syllogism
 A categorical syllogism may be defined as a
three line argument in which each statement
begins with the word all, some, or no.  Example
 All bats are mammals.
 All mammals are warm-blooded.
 So, all bats are warm-blooded. Common Patterns of Deductive Reasoning 
Categorical Syllogism: a three-lined
argument in which each statement begins
with the word all, some or no.  Example Forms: 
All a’s are b’s. All b’s are c’s. Therefore, all a’s are c’s. 
Some a’s are b’s. All b’s are c’s. Therefore some a’s are c’s.  Example: 1. All oaks are trees 2. All trees are plants. 3. So all oaks are plants. 24
Lecture Notes © 2008 McGraw Hill Higher Education 7 lOMoARcPSD|359 747 69 10/14/2016
Argument by elimination
An argument by elimination seeks by
elimination seeks to logically rule out
various possibilities until only a single possibility remains.
 Either Joe walked to the library or he drove
 But Joe didn’t drive to the library
 Therefore, Joe walked to the library Common Patterns of Deductive Reasoning 
Argument by Elimination: seeks to
logically rule out various possibilities until
only a single possibility remains.  Example forms:  A or B. Not B. Therefore A. 
P or Q. if A then ~P. A. Therefore Q.  Example: 1.
Either Joe walked to the library or he drove. 2.
But Joe didn’t drive to the library. 3.
Therefore, Joe walked to the library. 26
Lecture Notes © 2008 McGraw Hill Higher Education 8 lOMoARcPSD|359 747 69 10/14/2016
Argument based on mathematics
 Mathematics is a model of logical, step-by-step
reasoning. They claim to prove that their
conclusion on the basis of precise mathematical concepts and reasoning.
 In a argument based on mathematics, the
conclusion is claimed to depend largely or
entirely on some mathematical calculation or measurement.  Example:
 Eight is greater than four  Four is greater than two
 Therefore, eight is greater than two
Argument from definition
 In Argument from definition, the conclusion is
presented as being “true by definition”, that is,
as following simply by definition some key word
or phrase used in the argument.  Example
 Janelle is a cardiologist. Therefore, Janelle is a doctor.
 Bertha is an aunt. It follows that she is a women. 9 lOMoARcPSD|359 747 69 10/14/2016 Inductive reasoning
The are six common patterns of inductive reasoning:  Inductive generalization  Predictive argument  Argument from authority  Causal argument  Statically argument  Argument from analogy
Inductive generalization
 A generalization is a statement that attribute some
characteristic to all or most members of a given class.
 An inductive generalization is an argument in which
a generalization is claimed to be probably true
based on information about some members of a particular class.  Example:
 All dinosaur bones so far discovered have been
more than sixty-five million years old
 Therefore, probably all dinosaur bones are
more than sixty-five million years old. 10 lOMoARcPSD|359 747 69 10/14/2016 Common Patterns of Inductive Reasoning  Inductive generalization:  Generalization: statement that attributes
characteristics to all or most members of some group or class. 
Inductive generalization: drawing a generalization as
a likely conclusion from observations.  Common Form: 
So far, the b’s I have seen have had the property p.
Therefore, all b’s must have the property p.  Example: 1.
All dinosaur bones found so far have been over 65 million years old. 2.
Therefore all dinosaur bones found will be over 65
million years old. 31 Lecture Notes © 2008 McGraw Hill Higher Education Predictive argument
 A prediction is a statement about what may or will happen in the future.  In a Predictive argument, a prediction is defended with reasons.  Example
 It has rained in Vancouver very February
since weather records have been kept.
 Therefore, it will probably rain in Vancouver next February 11 lOMoARcPSD|359 747 69 10/14/2016 Common Patterns of Inductive Reasoning 
Augment from authority: asserts a claim and supports
that claim by citing some presumed authority or witness.  Common form: 
P said that A was true, therefore A is true.  Example: 
The Encyclopedia said that bats eat bugs; therefore it is likely that bats eat bugs. 
Since sources are not 100% reliable, conclusions of
such arguments are not guaranteed and thus such arguments are inductive. 
However, the better the source, the better the argument. 
Not all arguments from authority are inductive. Example: 1.
If the bible says it, it’s true. 2.
The bible says you should love your neighbor.
33 3.Therefore, you should love your neighbor. Lecture Notes © 2008 McGraw Hill Higher Education
Argument from Authority
 An argument from authority asserts a claim and
then supports that claims by citing some
presumed authority or witness who has said that the claim is true.  Example
There are bears in these woods. My neighbor
Frank said that he saw one last week. 12 lOMoARcPSD|359 747 69 10/14/2016 Common Patterns of Inductive Reasoning 
Augment from authority: asserts a claim and supports
that claim by citing some presumed authority or witness.  Common form: 
P said that A was true, therefore A is true.  Example: 
The Encyclopedia said that bats eat bugs; therefore it is likely that bats eat bugs. 
Since sources are not 100% reliable, conclusions of
such arguments are not guaranteed and thus such arguments are inductive. 
However, the better the source, the better the argument. 
Not all arguments from authority are inductive. Example: 1.
If the bible says it, it’s true. 2.
The bible says you should love your neighbor.
35 3.Therefore, you should love your neighbor. Lecture Notes © 2008 McGraw Hill Higher Education Causal argument
 A causal argument asserts or denies
that something is the cause of something else.  Example
I can’t log-in. The network must be down. 13 lOMoARcPSD|359 747 69 10/14/2016 Common Patterns of Inductive Reasoning 
Causal Argument: asserts or denies
that something is the cause of something else.  Common form:
X is true. The likely cause of X being true is
Y being true. Therefore, Y must be true. 
Not all causal arguments are inductive: Counter example:
1. Whenever iron is exposed to oxygen, it eventually rusts.
2. This iron pipe has been exposed to oxygen.
3. Therefore, it will eventually rust. 37
Lecture Notes © 2008 McGraw Hill Higher Education Statically argument  A Statically argument rests on
statistical evidence, that is, evidence that
some percentage of some group or class has
some particular characteristic:  Example
 Eighty-three percent of St. Stephen’s students are Episcopalian
 Beatrice is a St. Stephen’s student
 So, Beatrice is probably Episcopalian 14 lOMoARcPSD|359 747 69 10/14/2016  Common Patterns of Inductive  Reasoning
Statistical Argument: rests on statistical evidence (evidence 
that some percentage of some group has some particular property). Common form: 
90% of b’s have property p and x is a b, therefore x probably has property p.  Example: 1.
83% of Notre Dame students are Catholic. 2. Bob is a Notre Dame student. 3.
Therefore Bob is probably Catholic.
Because stats aren’t necessarily reflective of the population,
such arguments are usually inductive arguments. But not always: 
If 65% polled will vote Democratic, then Hillary will win. 
65% polled will vote Democratic.  Therefore, Hillary will win. 39
Lecture Notes © 2008 McGraw Hill Higher Education Argument from analogy
 An analogy is a comparison of two or more things
that are claimed to be alike in some relevant respect.
 In an Argument from analogy, the conclusion is
claimed to depend on an analogy between two or more things  Example
 Hershey Park has a thrilling roller- coaster ride
 Dorney Park, like Hershey Park, is great amusement park.
 Therefore, probably Dorney Park also has a
thrilling roller-coaster ride. 15 lOMoARcPSD|359 747 69 10/14/2016
Tess: Are there any good Italian restaurants in town?
Don: Yeah, Luigi's is pretty good. I've had
their Neapolitan rigatoni, their lasagna col
pesto, and their mushroom ravioli. I don't
think you can go wrong with any of their pasta dishes. 16 lOMoARcPSD|359 747 69 10/14/2016 Exercise 1 Inductive.
The argument is an inductive generalization, which
is a common pattern of inductive reasoning. Also,
the conclusion does not follow with strict
necessity from the premises.  Common Patterns of Inductive Reasoning 
Arguing from Analogy: taking two things that are alike in some
way(s) and using that to support claims that they are similar in (an)other  way(s). Common form: 1.
These things are similar is such-and-such ways. 2.
Therefore, they are similar in some further way.  Examples: 1.
Hershey Park is a great amusement park and it has a great roller coaster. 2.
Dorney Park is a great amusement park. 3.
Dorney Park probably has a great roller coaster.
Since, being similar in one way does not guarantee being similar in
another, most analogies are inductive. However, some are deductive: 1.
Cars and cigarettes both cause thousands of deaths. 2.
Thus, if cigarettes are regulated, so too should cars. 3.
But cars should not be regulated. 4.
Therefore cigarettes should not be regulated either. 41
Lecture Notes © 2008 McGraw Hill Higher Education 17 lOMoARcPSD|359 747 69 10/14/2016 Exercise 2 Exercise 3
Mother : Don't give Billy that brownie. It contains walnuts,
and I think Billy is allergic to walnuts. Last week he ate
some oatmeal cookies with walnuts, and he broke out in a severe rash.
Father: Billy isn't allergic to walnuts. Don't you remember
he ate some walnut fudge ice cream at Melissa's birthday
 party last spring? He didn't have any allergic reaction then. 18 lOMoARcPSD|359 747 69 10/14/2016 Inductive.
The father's argument is a causal argument, which is a
common pattern of inductive reasoning. Also, the
conclusion does not follow necessarily from the premises.
(Billy might have developed an allergic reaction to walnuts since last spring.)
I wonder if I have enough cash to buy my psychology
textbook as well as my biology and history textbooks.
Let's see, I have $200. My biology textbook costs $65
and my history textbook costs $52. My psychology
textbook costs $60. With taxes, that should come to
about $190. Yep, I have enough. Deductive!
This argument is an argument based on mathematics,
which is a common pattern of deductive reasoning. Plus,
the conclusion follows necessarily from the premises. 19 lOMoARcPSD|359 747 69 10/14/2016 Exercise 5
Larry: Do you think Representative Porkmeister will be reelected?
Norman: I doubt it. Porkmeister's district has become
more conservative in recent years. Porkmeister is a
liberal Democrat, and 63% of the registered voters in his
district are now Republicans. 20 lOMoARcPSD|359 747 69 10/14/2016 Inductive.
This argument is both a statistical argument
and a predictive argument, which are two
common patterns of inductive reasoning. Also,
the conclusion does not follow necessarily from the premises. Exercise 4 John is an agnostic.
It necessarily follows that he doesn't believe in God.  Deductive.
 This argument is an argument by definition, which
is a common pattern of deductive inference. Also,
the phrase "it necessarily follows that" is a
deduction indicator phrase.
Also, the conclusion follows from the premises. 21 lOMoARcPSD|359 747 69 10/14/2016 Exercise 6
If Buster walked to the game, then he didn't drive to the game.
Buster didn't drive to the game.
Therefore, Buster walked to the game.
Deductive! This argument is a hypothetical syllogism,
which is a common pattern of deductive reasoning.
Note, however, that the conclusion does not follow
logically from the premises. (Maybe Buster rode his bike to
the game, for example.) The argument commits the fallacy of
"affirming the consequent." X 22 lOMoARcPSD|359 747 69 10/14/2016 Deductive Validity
 Deductive arguments are either valid or invalid.
 A valid argument is a deductive argument in which
the conclusion follows logically (i.e., with strict
logical necessity) from the premises.
 An invalid argument is a deductive argument in
which the conclusion does not follow logically from the premises. Validity
A valid deductive argument is an argument
in which it is impossible for all premises to be
true and the conclusion false. 23 lOMoARcPSD|359 747 69 10/14/2016 Deductive Validity
A valid deductive argument is an argument in
which it is impossible for all the premises to be
true and the conclusion false. In other words:
 If the premises are true, the conclusion must be true.
 The conclusion follows necessarily from the premises. Deductive Validity
 The premises provide logically conclusive
grounds for the truth of the premises.
 The truth of the premises would guarantee the truth of the conclusion.
 It is logically inconsistent to assert all the
premises but deny the conclusion.
 It is impossible for the premises to be true and the conclusion to be false. 24 lOMoARcPSD|359 747 69 10/14/2016 Deductive Validity
Valid arguments: As we said before, the
validity of an argument has nothing to do with  the truth of its premises.  Valid argument: 1. All squares are circles. 2. All circles are triangles.
3. Therefore, all squares are triangles. Deductive Validity 
Get it out of your head that “valid argument”  means “good argument.”
An argument can be a good argument and be  invalid
For example, it could be a good inductive
argument) and could be a bad argument but be
valid (because it has false premises like the one above). 54
Lecture Notes © 2008 McGraw Hill Higher Education 25 lOMoARcPSD|359 747 69 10/14/2016 26 lOMoARcPSD|359 747 69 10/14/2016 Deductive Invalidity
 Invalid deductive arguments: deductive
arguments whose premises do not
guarantee their conclusion. (i.e., they have bad deductive form.)
 Notice, in the following argument, even
though the premises and conclusion are true, it is invalid: 1. All dogs are animals. 2. Lassie is an animal.
3. Therefore, Lassie is a Dog. 55
Lecture Notes © 2008 McGraw Hill Higher Education Deductive Invalidity
 What if “Lassie” here referred to my pet
iguana. The premises would still be true,
and yet the conclusion would be false.
 If you get rid of your assumption (which
is not in the argument) that we are
talking about the TV dog, the invalidity
becomes clear. Let’s use a different name. 1. All dogs are animals. 2. Jub-Jub is an animal.
56 3. Therefore, Jub-Jub is a Dog. Lecture Notes © 2008 McGraw Hill Higher Education 27 lOMoARcPSD|359 747 69 10/14/2016 Deductive Validity
"The 3C's Test.“ is a helpful (but not foolproof)
method for testing arguments for validity.
The Three C's Test involves three steps:
1. Check to see whether the premises are actually true
and the conclusion is actually false. If they are, then
the argument is invalid. (By definition, no valid
argument can have all true premises and a false
conclusion.) If they are not, or if you don't know
whether the premises are true and the conclusion is
false, then go on to step 2. Deductive Validity
2. See if you can conceive a possible scenario in which
the premises would be true and the conclusion false.
If you can, then the argument is invalid. If you can't,
and it is not obvious that the conclusion follows
necessarily from the premises, then go on to step 3. 28 lOMoARcPSD|359 747 69 10/14/2016 Deductive Validity
3. Try to construct a counterexample--a special kind of
parallel argument--that proves that the argument is
invalid. Constructing a counterexample involves two steps:
(1) Determine the logical form of the argument you are
testing for invalidity, using letters (A, B, C, etc.) to
represent the various terms in the argument.
(2) Construct a parallel argument that has exactly the
same logical pattern as the argument you are testing
but that has premises that are clearly true and a
conclusion that is clearly false. Deductive Validity
If you can successfully construct such a counterexample,
then the argument is invalid. If, after repeated attempts,
you cannot construct such a counterexample, then the argument is probably valid. 29 lOMoARcPSD|359 747 69 10/14/2016 Exercise 1
If Michelangelo painted the Mona Lisa, then he's a great painter.
Michelangelo is a great painter.
So, Michelangelo painted the Mona Lisa.
Is this argument valid or invalid? How can we use
the Three C's Test to determine if it is valid or invalid? Exercise 1 - Solution
This argument is invalid.
We can most readily see that the argument is invalid
by applying the first step of the Three C's Test.
The premises of the argument are, in fact, true, and the
conclusion of the argument is, in fact, false. Since no
valid argument can have true premises and a false
conclusion, we know straight away that the argument is invalid. 30 lOMoARcPSD|359 747 69 10/14/2016 Exercise 2
If Bill Clinton is president, then he lives in the White House.
Bill Clinton is not president.
So, Bill Clinton doesn't live in the White House.
Is this argument valid or invalid? How can we use
the Three C's Test to determine if it is valid or invalid? Exercise 2 - Solution
This argument is invalid.
The first step of the Three C's Test is not applicable here,
because both the premises and the conclusion are actually true.
However, the second step of the Three C's Test shows that the argument is invalid.
It's easy to conceive of circumstances in which the premises
and the conclusion is false. This would be the case, for example,
if Clinton became an advisor who lived in the White House.
Because we can imagine circumstances in which the premises
could be true and the conclusion false, the conclusion does not
follow from the premises with strict logical necessity. This
shows that the argument is invalid. 31 lOMoARcPSD|359 747 69 10/14/2016 Exercise 3
All dogs are carnivores.
Some carnivores are cats.
So, some cats are dogs.
Is this argument valid or invalid? Exercise 3 - Solution
In this argument the premises are both clearly true
and the conclusion is clearly false. This shows that
arguments with this pattern of reasoning are not
guaranteed to have true conclusions if the premises
are true. And this shows that all arguments that have
that pattern of reasoning are invalid. 32 lOMoARcPSD|359 747 69 10/14/2016 Soundness
 An argument is sound if and only if it is valid and has all true premises.
If that is the case, you are forced to accept the conclusion.
 If an argument is valid, but has a false
premise, we say that it is a deductively unsound argument.
 Since all inductive arguments are invalid
(their premises don’t guarantee their
conclusion), all inductive arguments are unsound. Inductive Strength
Strong inductive argument: an inductive
argument the premises of which, if true,
make the conclusion likely or probable. i.e.,:
 If the premises are true, the conclusion is probably true.
 The premises provide probable, but
not logically conclusive grounds for the truth of the conclusion. 33 lOMoARcPSD|359 747 69 10/14/2016 Inductive Strength  Common form: 1. Most b’s are p. 2. X is a b.
3. Therefore, (probably) X is p.  Example:
1. All recent presidents have been college grads.
2. Therefore the next president will be a college grad. Inductive Weakness 
Weak inductive argument: inductive
argument, the premises of which, do
not provide good evidence for its conclusion.  Example:
1. All previous popes have been men.
2. Therefore, probably the next pope will be female. 34 lOMoARcPSD|359 747 69 10/14/2016 Induction and Premise Truth 
The inductive strength or weakness of an
argument has nothing to do with the truth or falsity of its premises. 
Example: Inductive strength with false premises:
1. All previous presidents have been female.
2. Therefore, the next president will be female. Induction and Premise Truth 
Example: Inductive weakness with true premises:
1. Most presidents have been married.
2. Therefore the next president will probably be male. 
But you will never have a strong
inductive argument with true premises
but a probably false conclusion. 35 lOMoARcPSD|359 747 69 10/14/2016 Inductive Strength Comes in Degrees  This argument…
1. The last 5 presidents were male
2. Therefore the next president will be male.  …is weaker than this one:
1. All the presidents have been male
2. Therefore the next president will be male. 73
Lecture Notes © 2008 McGraw Hill Higher Education Inductive Strength Comes in Degrees 
Recall, validity doesn’t come in
degrees. A deductive argument is either
valid or invalid. No two valid arguments
differ in “how valid” they are. 
But some inductively strong arguments
are inductively stronger than others. 74
Lecture Notes © 2008 McGraw Hill Higher Education 36 lOMoARcPSD|359 747 69 10/14/2016 Cogency
 Even if an argument is inductively
strong, it can still have a false premise and be a “bad argument.”
 Cogent argument: inductively strong argument with true premises.
 Uncogent argument: inductive
argument that is either weak, has false premises, or both. 75
Lecture Notes © 2008 McGraw Hill Higher Education Deductive argument evaluating  Deductive argument valid invalid Sound Unsound 37 lOMoARcPSD|359 747 69 10/14/2016 Inductive argument evaluating  Inductive argument strong weak Cogent Uncogent 38
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