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SCHEDULE – Spring ‘06
6 April
1.1-1.5
13
TEST 1 (Ch 1)
18
2.2, 2.3, & 8.7
TEST 2 (Ch 2.2, 2.3,8.7) 25
9.1-9.7
20
27
4 May
9.8, 9.9, &
practice
TEST 3 (Ch 9)
11 May
1 June
8
10.1 &
Practice
10.2 &
Practice
10.3 & 10.4
TEST 4 (Ch 10.1-.4)
10.5 & 10.6
11.1 – 11.5
MID-TERM
June 15, Test 5 (Ch 10.5-11.5) - FINAL
Are You Logical?
Why is it when
ducks fly in a
“v” shape that
one side of the
“v” is always
longer than
the other side?
There are more ducks on one side.
1.1 What is Logic?
Logic may be defined as the organized body of
knowledge, or science, that evaluates arguments.
All of us encounter arguments in our day-to-day
experience.
We read them in books and newspapers, hear them
on television, and formulate them when
communicating with friends and associates.
The aim of logic is to develop a system of methods and principles that we may
use as criteria for evaluating the arguments of others and as guides in
constructing arguments of our own.
Among the benefits to be expected from the study of logic is an increase in
confidence that we are making sense when we criticize the arguments of
others and when we advance arguments of our own.
1.2 Propositions
Proposition – An
assertion that
something is (or is not)
the case; all
propositions are either
True or False.
Statement – The
meaning of a
declarative sentence at
a particular time; in
Logic, the word
“statement” is basically
interchangeable with
the word “proposition.”
The following sentences are statements:
Aluminum is attacked by hydrochloric acid.
Broccoli is a good source of vitamin A.
Argentina is located in North America.
Napoleon prevailed at Waterloo.
Rembrandt was a painter, & Shelley was a
poet.
The first two simple statements are true,
the second two false. The last one, a
compound statement, expresses two
statements, both of which are true.
Truth and falsity are called the two
possible truth values of a statement.
Logic is the “hard-wiring” of our brains.
Both math and grammar are based on Logic (and not the other way
.
around).
You are logical (despite what other people tell you).
The fact that you made it to this class from work or home means
that you are capable of logical deduction.
But don’t get too excited yet. Even dogs and cats are capable of
doing some of the things we will be doing this
semester. But they cannot do the parts that are
uniquely human logic.
Some birds have the mental powers
of a 5 year-old, so being “bird-brained”
is not necessarily a bad thing.
Unlike statements, many sentences cannot be said to be either true
.
or false. Questions, proposals, suggestions, commands, and
exclamations usually cannot be determined to be true or false,
and so are not usually classified as statements.
The following sentences are not statements:
What is the atomic weight of carbon?
question
Let’s go to the park today.
proposal
We suggest that you travel by bus.
suggestion
Turn to the left at the next corner.
command
All right!
exclamation
In Logic, the only “meaningful” statements are declarative
statements, and they can have a truth value.
As noted above, declarative statements used in Logic can be either
simple or compound.
Simple proposition
- A statement making
only one assertion.
.
Compound proposition
- A statement containing two
or more simple statements
The most common compound statements in Logic are Disjunctive
Statements and Conditional Statements.
Conditional (or Hypothetical
Proposition – A type of compound
Disjunctive (or Alternative)
proposition - A type of compound
statement; if true, at least one of
the component statements is true
statement; it is false when the
antecedent is true and the
consequent is false.
IF (1) you make a 100 on the last
(1) You can have an apple,
test, THEN (2) I’ll give you an “A”
OR (2) you can have an orange.
for the course.
Disjunctive Statements
You can eat an apple OR you can eat an orange
Did you eat some
fruit? Yes (true)
Did you eat some
fruit? Yes (true)
Did you eat some
fruit? Yes (true)
Did you eat some
fruit? No (false)
Conditional Statements
If……………………..then
You make
I give
a 100
you an ‘A’
Did I tell you the
truth? Yes (true)
You make
a 100
I don’t give
you an ‘A’
Did I tell you the
truth? No (false)
You don’t
make a 100
I give
you an ‘A’
Did I tell you the
truth? Yes (true)
You don’t
make a 100
I don’t give
you an ‘A’
Did I tell you the
truth? Yes (true)
CONDITIONAL STATEMENTS (non-argumentative alone; no claim):
antecedent
consequent
consequent
antecedent
If ____________, then ____________. ____________, if ____________.
Regardless of the location of the “if,” the antecedent comes after the “if.”
.
sufficient condition: when the occurrence of A is ALL that is needed for the
occurrence of B
necessary condition: A cannot occur without the occurrence of B
A
B
If X is a drake, then X is a male. Sufficient condition; A can stand alone
If X is a drake, then X is a duck. Necessary condition; A needs B
Being a tiger is a sufficient condition for being an animal. true
Being an animal is a sufficient condition for being a tiger. false
Drinking a pint of gin is a necessary condition for being drunk. false
Having water present is a necessary condition for plant life. true
Getting into a fistfight is a sufficient condition for someone's being injured. true
Having one's eyes open is a sufficient condition for watching television. false
Fill in the blanks with ‘‘necessary’’ or ‘‘sufficient’’ to make the following
statements true. After the blanks have been filled in, express the
result in terms of conditional statements.
.
1. Being a tiger is a ___________ condition for being an animal.
2. Being an animal is a ___________condition for being a tiger.
3. Drinking water is a _____________ condition for quenching one’s
thirst.
4. Having a racquet is a _____________ condition for playing tennis.
5. Pulling the cork is a __________ condition for drinking an
expensive bottle of wine.
6. Stepping on a cat’s tail is a __________ condition for making the
cat yowl.
7. Burning leaves is a ___________ condition for producing smoke.
8. Paying attention is a ____________ condition for understanding a
lecture.
9. Taking a swim in the North Sea is a _________ condition for
cooling off.
10. Opening a door is a __________ condition for crossing the
threshold.
Propositional statements are the building blocks of which
.
arguments are made.
From propositional statements that are supposed to be providing
facts, we can make an inference (or draw a conclusion) from
those supposed “facts.”
Inference – A process
Argument – A structured
of linking statements
by affirming one
particular statement on
the basis of one or
more other supposedly
factual statements.
group of statements
reflecting an inference.
Nice definitions, huh?
1.3 – Arguments
.
But here is the next big question:
WHAT THE
HECK IS AN
ARGUMENT ?
An argument in Logic is NOT a disagreement with raised voices.
An argument, as it occurs in Logic, is a group of statements of which
one or more (the premises) claim to provide support for (or reasons
to believe) the one (the conclusion) that follows from them.
AN ARGUMENT:
1) at least one statement must claim to present evidence
.
2) there must be a claim that the evidence implies something
3) an argument is NOT just a contradiction (see movie )
In Chapter 2, we’ll look at some things that are NOT arguments,
and we’ll look at the confusing argument v. explanation problem.
ARGUMENTS prove THAT
EXPLANATIONS show WHY
Some other non-argumentative forms (lacking an inferential claim):
warnings
pieces of advice
statements of opinion
reports
loosely assorted statements
illustrations (can be argumentative)
expository passages (sometimes argumentative)
Premise – A statement used in an argument which provides the
supposed “evidence” needed in order to support some other
statement which we are to supposed believe follows from the
premise (or premises)
Conclusion – The statement in an argument that the other
“factual” statement (or statements) claim to support and
provide evidence
An Argument
PREMISE(S)
CONCLUSION
Claimed
evidence
What is claimed
to follow from
the premises
Premise indicator words:
since (not temporal)
because
in that
as
seeing that
inasmuch as
Conclusion indicator words:
therefore
accordingly
entails that
thus*
we may infer
for this reason
implies that
.
as indicated by
for
may be inferred from
given that
for the reason that
owing to
wherefore
we may conclude
hence
consequently
it must be that
it follows that
as a result
*Note: "Because" and "thus" can be used in both explanations and arguments.
Sometimes and argument has no indicator words:
The space program deserves increased expenditures in the
. national defense depend on it,
years ahead. Not only does the
but the program will more than pay for itself in terms of
technology. Furthermore, at current funding levels the program
cannot fulfill its anticipated potential.
Similar to the thesis statement in a paragraph in English, if there is
no conclusion indicator, odds are high that it’s the first sentence.
The conclusion is always listed after the premises:
P1: The national defense is dependent upon the space program.
P2: The space program will more than pay for itself with
technological spinoffs.
P3: At current funding levels the program cannot fulfill its
potential.
C: The space program deserves increased expenditures.
Dachshunds are ideal dogs for small children, as they are already
stretched and pulled to such a length that the child cannot do
.
much harm one way or the other.
(below) A not-so-smart cat
Cats can think circles around dogs! My cat regularly used to close
and lock the door to my neighbor’s doghouse, trapping their
sleeping Doberman inside. Try telling a cat what to do, or putting
a leash on him—he’ll glare at you and say, ‘‘I don’t think so. You
should have gotten a dog.’’
Identify the premise(s) and conclusion in the
following passages
A well regulated militia being necessary to the security of a free
state, the right of the people to keep and bear arms shall not be
infringed.
Premise:
A well regulated militia being necessary to the security

of a free state.
Conclusion: The right of the people to keep and bear arms shall
not be infringed.
Premise: The right of the people to keep and bear arms shall
not be infringed.
Conclusion: A well regulated militia being necessary to the
security of a free state.
Of all our passions and appetites, the love of power is the most
imperious and unsociable nature, since the pride of one man
requires the submission of the.multitude.
 Premise: Of all our passions and appetites, the love of power

is the most imperious and unsociable nature.
Conclusion: The pride of one man requires the submission of
the multitude.
 Premise: The pride of one man requires the submission of the
multitude.
Conclusion: Of all our passions and appetites, the love of power
is the most imperious and unsociable nature.

Unquestionably, no more important goal exists in medical
research today than the development
of an AIDS vaccine. Last
.
year (1998) AIDS, caused by HIV (the Human
Immunodeficiency Virus) was the infectious disease that killed
the most people around the world, and the epidemic is not
abating.
Premise:
In 1998, AIDS was the infectious disease that killed
the most people
around the world.
Premise: The epidemic is not abating.
Conclusion: No more important goal exists in medical research
today than the development of an AIDS vaccine.
 Premise: In 1998, AIDS was the infectious disease that killed
the most people around the world.
Premise: No more important goal exists in medical research
today than the development of an AIDS vaccine.
Conclusion: The epidemic is not abating.
1.4 – Deductive v. Inductive Arguments
Evaluating the strength of an inferential claim:
1) occurrence of indicator words
2) nature of the link between premise(s) and conclusion
3) form of argumentation by the arguer
Deductive: premises are claimed to provide NECESSARY support
Inductive: premises are claimed to prove only PROBABLE support
….IF the premises are assumed to be true
Inductive indicator words
probable/improbable
plausible/implausible
likely/unlikely
reasonable to conclude
Deductive indicator words
.
necessarily
certainly
definitely
absolutely
Note 1: "Must" can be used with either probability (induction) or
necessity (deduction).
Note 2: "It certainly follows that" can be used with either also, since
the phrase is often used rhetorically with induction without
asserting necessity.
In other words, both “must” and “it certainly follows” should be first
to considered as part of an inductive argument that the arguer is
trying to make sound more certain that it actually is. On the
other hand, it still could be a deductive argument.
.
INDUCTIVE (probably the case):
The vast majority of saleswomen are
extroverts.
Elizabeth is a saleswoman.
Therefore, Elizabeth is an extrovert.
DEDUCTIVE (necessarily the case):
All saleswomen are extroverts.
Elizabeth is a saleswoman.
Therefore, Elizabeth is an extrovert.
Without indicator words to determine induction or
deduction, it is necessary to take into account the FORM of
the argument.
DEDUCTIVE:
1) Argument based on mathematics
-- if the conclusion depends on some arithmetic or geometric
computation or measurement (but not statistics), it is
deductive (eg., 2 + 2 = 4)
-- if it is statistical, it is probably inductive
2) Argument from definition
-- conclusion is claimed to depend upon the definition of some
word or phrase used in the premise or conclusion
3) Categorical Syllogism: each. statement begins with one of the
words "all,“ "no," or "some"; almost always deductive
All lasers are optical devices.
Some lasers are surgical devices.
Therefore, some optical devices are surgical instruments.
4) Hypothetical Syllogism: has a conditional statement for one or
both of its premises; usually deductive but occasionally inductive
If X, then Y
A
B
If Y, then Z
B
C
Therefore, if X, then Z.
A
C
5) Disjunctive Syllogism: has "either/or" statements for one of its
premises; usually deductive .
Either breach of contract is a crime or it is not punishable
by the state.
Breach of contract is not a crime.
Therefore, it is not punishable by the state.
Generally, with DEDUCTIVE arguments, the premise(s) begins with
the familiar and conclusion moves to a subject that less is known
about.
Recap: These forms are generally Deductive arguments:
from mathematics
from definition
hypothetical syllogism
categorical syllogism
disjunctive syllogism
INDUCTIVE (probability & predictions) forms:
1) Argument from analogy (probablistic
at best)
.
--depends on the existence of a similarity of two things or states
of affair; a condition which affects a better-known thing is by
analogy demonstrated to affect similarly something less-known
Because Christina's Jaguar is a great handling car, it stands
to reason that Angela's new Jaguar will also handle well.
2) Inductive generalization (often statistics)
--knowledge concerning a selected sample is used to make a
claim about a larger group with similar characteristics
Because four out of five times that I go to Burger King they
get my order wrong, it stands to reason that BK generally
gets most orders wrong.
Even if it’s true, it’s still inductive.
3) Argument from Authority
--the conclusion rests upon a statement
made by some
.
presumed authority or witness
--A witness my testify to observing a murder, but because he
might be lying or simply mistaken, the argument is probablistic
4) Argument based on signs
--a certain sign is ascribed to symbolize the knowledge of a thing
or situation
--a road sign might indicate that there is
a steep hill ahead, leading one to argue
that there is indeed a steep hill within a
mile or so. But the sign could be in the
wrong location or in error about the slope
of the hill, so the conclusion is only
Dancing Cow Ahead
probable.
Is that probable?
5) Casual inference
--argument proceeds from knowledge of a cause to knowledge
.
of an effect, or visa-versa; lacking certainty to the conclusion, it is
inductive
--the knowledge that a bottle of wine had been left in the freezer
overnight might make someone conclude that it had frozen
(however, wine will NOT freeze overnight--usually--because of
the alcohol content, and, thus, the conclusion would be
incorrect)
inductive arguments:
predictions
arguments from analogy
inductive generalizations
arguments from authority
arguments based on signs
causal inferences
deductive arguments:
arguments based on mathematics
arguments from definition
categorical syllogisms
hypothetical syllogisms
disjunctive syllogisms
SCIENTIFIC AEGUMENTS: can be either deductive or inductive,
depending upon the circumstances
.
1) discovery--usually inductive and generalized based on
empirical evidence (premises); less known and unknown
conclusions
2) application--deductive with reservations; application of
previous laws and mathematical equations to something new
(but because sometimes a law works in one instance, this might
be inductive with the possibility that the same law might not work
in the future or in a different theory)
A PARTICULAR STATEMENT is one that makes a claim about one
or more particular members of a class
A GENERAL STATEMENT makes a claim about all the members of
a class
There are no hard and fast rules about particular and general when
determining induction and deduction, but we generally see……..
Deductive moving from particular to general:
. Three is a prime number.
One is a prime number.
Five is a prime number.
Seven is a prime number.
Therefore, all odd numbers between 0 and 8 are prime numbers.
Deductive moving from particular to particular:
Gabriel is a wolf.
Gabriel has a tail.
Therefore, Gabriel's tail is the tail of a wolf.
Inductive moving from the general to the particular:
All emeralds previously found have been green.
Therefore, the next emerald to be found will be green.
Recap in difference between induction and deduction:
1) differences in the occurrences of indicator words
2) differences in the nature of the link between premise and
conclusion
3) differences in the form of argumentation that the arguer uses
How “reasonable” is “Beyond a
Reasonable Doubt”?
You are on the jury for this court case.
It is a well-known fact that Bob hates Bill, and Bill has turned up
dead.
In court you learn that:
(1) there was a smoked Camel unfiltered cigarette lying next to
Bill’s body, and Bob smokes Camel unfiltered cigarettes
(2) there was an impression of a man’s size 11 Wilson tennis
shoe next to Bill’s body, and Bob wears Wilson tennis shoes –
size 11
(3) Bill was killed with a .38 revolver; Bob owns a .38 revolver,
but he says he can’t find, it so.it is missing
Now, add up the evidence. How reasonable would it be for you, as
a member of the jury, to conclude that Bob had killed Bill?
.Bob and cigs………Bob’s shoes…………..Bob’s missing gun
Sherlock Holmes always said that he “deduced” who the criminal
was, but he did not “deduce”.it, rather he “induced” it.
He added up the particular information and drew a general
conclusion.
Deductive
Inductive
PRACTICE: Determine whether the following arguments are best
interpreted as being inductive .or deductive. Also state the criteria
you use in reaching your decision (i.e., the presence of indicator
words, the nature of the inferential link between premises and
conclusion, or the character or form of argumentation).
1. Because triangle A is congruent with triangle B, and triangle A is
isosceles, it follows that triangle B is isosceles.
2. The plaque on the leaning tower
of Pisa says that Galileo performed
experiments there with falling
objects. It must be the case that
Galileo did indeed perform those
experiments there.
3.The rainfall in Seattle has been more than 15 inches every year
for the past thirty years. Therefore, the rainfall next year will
probably be more than 15 inches.
.
4. No e-mail messages are eloquent creations. Some love letters
are eloquent creations. Therefore, some love letters are not email messages.
5. Amoco, Exxon, and Texaco are all listed on the New York Stock
Exchange. It must be the case that all major American oil
companies are listed on the New York Stock Exchange.
6. The longer a pendulum is, the longer it takes to swing. Therefore,
when the pendulum of a clock is lengthened, the clock slows
down.
7. Paying off terrorists in exchange
. for hostages is not a wise
policy, since such action will only lead them to take more
hostages in the future.
8. The Matterhorn is higher than Mount Whitney, and Mount
Whitney is higher than Mount Rainier. The obvious conclusion is
that the Matterhorn is higher than Mount Rainier.
9. Although both front and rear doors were found open after the
burglary, there were pry marks around the lock on the rear door
and deposits of mud near the threshold. It must be the case that
the thief entered through the rear door and left through the front.
10. The Encylopaedia Britannica has an article on symbiosis. The
Encyclopedia Americana, like the Britannica, is an excellent
reference work. Therefore, the Americana probably also has an
article on symbiosis.
. humans. Therefore, it is
11. Cholesterol is endogenous with
manufactured inside the human body.
12. Either classical culture originated in Greece, or it originated in
Egypt. Classical culture did not originate in Egypt. Therefore,
classical culture originated in Greece.
13. World-renowned physicist Stephen Hawking says that the
condition of the universe at the instant of the Big Bang was more
highly ordered than it is today. In view of Hawking’s stature in the
scientific community, we should conclude that this description of
the universe is correct.
14. If Alexander the Great died from typhoid fever, then he became
infected in India. Alexander the Great did die from typhoid fever.
Therefore, he became infected in India.
25. The Simpson incident had shown me that a dog was kept in the
. had been in and had fetched
stables, and yet, though someone
out a horse, he had not barked enough to arouse the two lads in
the loft. Obviously the midnight visitor was someone whom the
dog knew well. (A. Conan Doyle, Memoirs of Sherlock Holmes)
D’oh!! Wrong “Simpson incident”!!!! Sorry!
15. It seems likely that young people will be at war with old people
in another 15 or 20 years. You.can see it coming in the numbers.
In 1900 only 1 percent of the population was older than 75.
Today 4 percent of all Americans are more than 75 years old,
and in a few years it’s going to be 5 percent . . . 13 million
people.
26. Eternity is simultaneously whole. But time has a before and an
after. Therefore time and eternity are not the same thing.
(Thomas Aquinas, Summa Theologica)
27. Ordinary things that we encounter every day are electrically
neutral. Therefore, since negatively charged electrons are a part
of everything, positively charged particles must also exist in all
matter. (James E. Brady and Gerard E. Humiston, General
Chemistry)
30. Because the moon moves relative to the earth so that it returns
to the same position overhead after about 25 hours, there are
two high and two low tides at any point every 25 hours.
Answer ‘‘true’’ or ‘‘false’’ to the following statements:
.
1. In an inductive argument, it is intended that the conclusion
contain more information than the premises.
2. In a deductive argument, the conclusion is not supposed to
contain more information than the premises.
3. The form of argumentation the arguer uses may allow one to
determine whether an argument is inductive or deductive.
4. The actual strength of the link between premises and conclusion
may allow one to determine whether an argument is inductive or
deductive.
5. A geometrical proof is an example of an inductive argument.
6. Most arguments based on statistical reasoning are deductive.
7. If the conclusion of an argument follows merely from the definition
of a word used in a premise, the argument is deductive.
8. An argument that draws a conclusion about a thing based on that
thing’s similarity to something else is a deductive argument.
.
9. An argument that draws a conclusion
that something is true
because someone has said that it is, is a deductive argument.
10. An argument that presents two alternatives and eliminates one,
leaving the other as the conclusion, is an inductive argument.
11. An argument that proceeds from knowledge of a cause to
knowledge of an effect is an inductive argument.
12. If an argument contains the phrase ‘‘it definitely follows that,’’
then we know for certain that the argument is deductive.
13. An argument that predicts what will happen in the future, based
upon what has happened in the past, is an inductive argument.
14. Inductive arguments always proceed from the particular to the
general.
15. Deductive arguments always proceed from the general to the
particular.
1.5 VALIDITY & TRUTH
Statements can be true or false, but only deductive arguments
(which are composed of statements) can be discussed in terms
of validity.
Definition of Validity:
If we assume the premises are true, it is impossible for the
conclusion not to follow from the premises.
A second Definition of Validity:
If the premises are true, it is impossible for the conclusion to
be false (because it cannot follow from the premises).
If I go to Publix, then I will Spend money.
I am going to Publix.
,
Therefore, I will Spend money. (valid)
All birds can sing.
Michael Jackson can sing.
Therefore, Michael Jackson is a bird. (invalid)
I’ve never seen a unicorn.
Therefore, unicorns are good at hide’n’seek.
Since Morgan is a Pisces, it necessarily
follows that she was born in March. (invalid)
An argument with true premises & a false conclusion is Invalid.
A BASIC ARGUMENT has two parts:
(1) evidence claim -- factual claim (the premise or premises)
.
(2) a claim that the alleged evidence supports something -inferential claim (the conclusion)
The most important is the inferential claim, because if the premises
fail to support the conclusion, an argument is worthless
Always test the inferential claim first, and only if the premises DO
support the conclusion will we test the factual claim (the claim
that the premises actually do present true evidence)
If you cannot get the (or a single) conclusion or a single highly
probable conclusion from the premises, the argument is
meaningless, and it no longer matters whether or not the
premises are true or false. The truth or falsity of the premises is
relevant ONLY in a VALID argument.; its soundness is second.
DEDUCTIVE
.
Deductive argument -- the premises are claimed to provide
necessary support for the conclusion
VALID DEDUCTIVE ARGUMENT -- of the premises are assumed
true, it is impossible for the claim to be false
INVALID DEDUCTIVE ARGUMENT -- the premises do NOT
provide support; therefore, it is possible for the conclusion to be
false
NO IN-BETWEENS – it’s either valid or invalid; if you can get more
than one possible conclusion based on the evidence, then the
argument is INVALID
Since Phyllis is the cousin of Denise,
and Denise is the cousin of Harriet,
it follows necessarily that Harriet is the cousin of Phyllis.
Since John loves Nancy,
and Nancy loves Peter,
it follows necessarily that John loves Peter.
Linda is older than her brother Frank,
and Frank is younger than his sister Evelyn.
Therefore, Linda is older than Evelyn.
There is only an indirect relationship between validity and truth.
For an argument to be valid, it is not necessary that either the
. true -- but merely that IF the
premises or the conclusion be
premises are ASSUMED to be true, it is impossible for the
conclusion to be false
Valid argument with false premises and false conclusion:
All auto makers are computer manufacturers.
Union Carbide is a an auto maker.
Therefore, Union Carbide is a computer manufacturer.
Invalid argument with true premises and false conclusion:
All banks are financial organizations.
Wells Fargo is a financial organization.
Therefore, Wells Fargo is a bank.
NOTE: to be VALID, the premises -- if assumed true (and even if
they are actually false) -- must support the conclusion
A sound argument is a deductive argument that is valid and has
all true premises.
.
Both conditions must be met for an argument to be sound, and if
either is missing the argument is unsound.
Thus, an unsound argument is a deductive argument that is
invalid, has one or more false premises, or both.
Because a valid argument is one such that it is impossible for the
premises to be true and the conclusion false, and because a
sound argument does in fact have true premises, it follows that
every sound argument, by definition, will have a true conclusion
as well.
A sound valid argument, therefore, is what is meant by a ‘‘good’’
deductive argument in the fullest sense of the term.
INDUCTIVE
.
STRONG INDUCTIVE ARGUMENT-- premises DO provide
probable support, and based on the assumption that the
premises are true, the conclusion is probably true
WEAK INDUCTIVE ARGUMENT-- premises do not provide
probable support, so it's not probable that the conclusion is true
NOTE: WEAK Inductive arguments (premises are claimed to
provide probable support for conclusion but don’t) or STRONG
Inductive arguments (premises DO provide support) is based on
degrees of believability (unlike the either/or validity of deductive)
. are Strong and have true
COGENT-- inductive argument that
premises; must reflect all of the important factors to the
argument and not ignore other major ones
UNCOGENT-- inductive argument which is either Weak or is Strong
but has false premises; an UNCOGENT example:
Swimming in the Caribbean is usually lots of fun. Today the
water is warm, the surf is gentle, and on this beach there are no
dangerous currents. Therefore, it would be fun to go swimming
here now.
If the premises reflect all the important factors but fail to mention
the several large dorsal fins presently cutting through the water,
then obviously the argument is Weak and therefore not cogent.
. and deductive arguments:
TWO QUESTIONS for both inductive
1) Do the premises support the conclusion?
--the support of the arguments inferential claim
--correctness of an argument's reasoning
--valid or invalid (deductive)
--strong or weak (inductive)
2) Are the premises true?
--sound or unsound (deductive)
--cogent or uncogent (inductive)
--concerns the truth of an argument's factual claim
stupid tables – if you simply learn to ask the two questions above in
.
the right order [(1) Does the conclusion
follow? (2) Are the
premises true?)], then you won’t have to even bother with the
somewhat confusing and hard to memorize charts in your book
– a better chart for determining validity/strength and
soundness/cogency is the one below
PRACTICE: The following arguments are deductive. Determine
whether each is valid or invalid,. and note the relationship
between your answer and the truth or falsity of the premises and
conclusion. Finally, determine whether the argument is sound or
unsound.
1. Since Moby Dick was written by Shakespeare, and Moby Dick is
a science fiction novel, it follows that Shakespeare wrote a
science fiction novel.
2. Since London is north of Paris and south of Edinburgh, it follows
that Paris is south of Edinburgh.
3. If George Washington was beheaded, then George Washington
died. George Washington died. Therefore, George Washington
was beheaded.
4. The longest river in South America is the Amazon, and the
Amazon flows through Brazil. Therefore, the longest river in
South America flows through Brazil.
5. Since the Spanish American War occurred before the American
Civil War, and the American Civil War occurred after the Korean
.
War, it follows that the Spanish American War occurred before
the Korean War.
6. The Empire State Building is taller than the Statue of Liberty, and
the Statue of Liberty is taller than the Eiffel Tower. Therefore, the
Empire State Building is taller than the Eiffel Tower.
7. All leopards with lungs are carnivores. Therefore, all leopards are
carnivores.
8. Chicago is a city in Michigan and Michigan is part of the United
States. Therefore, Chicago is a city in the United States.
9. If Senator Hillary Clinton represents California, then she
represents a western state. Hillary Clinton does not represent a
western state. Therefore, she does not represent California.
10. Every province in Canada has exactly one city as its capital.
Therefore, since there are thirty provinces in Canada, there are
.
thirty provincial capitals.
11. Since the Department of Defense Building in Washington, D.C.
has the shape of a hexagon, it follows that it has seven sides.
Department of Defense Building
12. Since Winston Churchill was.English, and Winston Churchill
was a famous statesman, we may conclude that at least one
Englishman was a famous statesman.
13. Since some fruits are green, and some fruits are apples, it
follows that some fruits are green apples.
14. All physicians are individuals who have earned degrees in
political science, and some lawyers are physicians. Therefore,
some lawyers are persons who have earned degrees in political
science.
15. The United States Congress has more members than there are
days in the year. Therefore, at least two members of Congress
have the same birthday.
The following arguments are inductive. Determine whether each is
strong or weak, and note the .relationship between your answer
and the truth or falsity of the premise(s) and conclusion. Then
determine whether each argument is cogent or uncogent.
1. The grave marker at Arlington National Cemetery says that John
F. Kennedy is buried there. It must be the case that Kennedy
really is buried in that cemetery.
2. The ebb and flow of the tides has been occurring every day for
millions of years. But nothing lasts forever. Therefore, probably
the motion of the tides will die out within a few years.
3. The vast majority of Rose Bowl games (in Pasadena, CA) have
been played in freezing cold weather. Therefore, probably the
next Rose Bowl game will be played in freezing cold weather.
4. Franklin Delano Roosevelt said that we have nothing to fear but
fear itself. Therefore, women have no reason to fear serial
.
rapists.
5. Most famous movie stars are millionaires. Leonardo Di Caprio is
a famous movie star. Therefore, probably Di Caprio is a
millionaire.
6. Constructing the great pyramid at Giza required lifting massive
stone blocks to great heights. .Probably the ancient Egyptians
had some antigravity device to accomplish this feat.
7. People have been listening to rock and roll music for over a
hundred years. Probably people will still be listening to it a year
from now.
8. Paleontologists have unearthed the fossilized bones of huge
reptiles, which we have named dinosaurs. Tests indicate that
these creatures roamed the earth more than 50 million years
ago. Therefore, probably dinosaurs really did roam the earth at
that time.
9. The Declaration of Independence says that all men are endowed
by their creator with certain unalienable rights. Therefore it
probably follows that a creator exists.
10. Coca-Cola is an extremely popular soft drink. Therefore,
probably someone, somewhere, is drinking a Coke right now.
. shows that Alabama is situated
11. Every map of the United States
on the Pacific coast. Therefore, Alabama must be a western
state.
12. When Neil Armstrong landed on the moon, he left behind a gold
plated Schwinn bicycle, which.he used to ride around on the
moon’s surface. Probably that bicycle is still up there on the
moon.
13. African American athlete Jerome Bettis is able to withstand
tremendous impacts on the football field. However, Venus
Williams, like Jerome Bettis, is a great African American athlete.
Therefore, Venus Williams should be able to withstand
tremendous impacts on the football field.
15. A random sample of twenty-five famous country and western
singers, including Garth Brooks and Dolly Parton, revealed that
every single one of them studied music in Afghanistan.
Therefore, probably the majority of famous country and western
singers studied in Afghanistan.
Determine whether the following arguments are inductive or
deductive. If an argument is inductive,
determine whether it is
.
strong or weak. If it is deductive, determine whether it is valid or
invalid.
1. Since Agatha is the mother of Raquel and the sister of Tom, it
follows that Tom is the uncle of Raquel.
2. When a cook can’t recall the ingredients in a recipe, it is
appropriate that she refresh her memory by consulting the recipe
book. Similarly, when a student can’t recall the answers during a
final exam, it is appropriate that she refresh her memory by
consulting the textbook.
3. The sign on the highway leading into Denver, Colorado says that
the city’s elevation is 5280 feet. It must be the case that Denver
is 1 mile high.
4. Since Christmas is always on a Thursday, it follows that the day
after Christmas is always a Friday.
5. This figure is a Euclidean triangle. Therefore, the sum of its
angles is equal to two right angles.
.
6. By accident Karen baked her brownies two hours longer than
she should have. Therefore, they have probably been ruined.
7. After taking LSD, Alice said she saw a flying saucer land in the
Greer Bi-Lo store parking lot. Since Alice has a reputation for
always telling the truth, we must conclude that a flying saucer
really did land there.
8. Since Phyllis is the cousin of Denise, and Denise is the cousin of
Harriet, it follows necessarily that Harriet is the cousin of Phyllis.
.
Remember – if it’s valid, there’s only one possible conclusion that can follow.
If there’s more than one, then the argument is invalid (but still deductive).
9. The picnic scheduled in the park for tomorrow will most likely be
cancelled. It’s been snowing for six days straight.
10. Circle A has exactly twice the diameter of circle B. From this we
may conclude that circle A has exactly twice the area of circle B.
11. Robert has lost consistently at blackjack every day for the past
several days. Therefore, it is very likely that he will win today.
12. Since John loves Nancy and Nancy loves Peter, it follows
necessarily that John loves Peter.
13. This cash register drawer contains over 100 coins. Three coins
selected at random were found to have dates earlier than 1945.
.
Therefore, probably all of the coins in the drawer have dates
earlier than 1945.
14. The Japanese attack on Pearl Harbor happened in either 1941
or 1951. But it didn’t happen in 1941. Therefore, it happened in
1951.
15. Since x + y equals 10, and x is 7, it follows that y is 4.
16. Harry will never be able to solve that difficult problem in
advanced calculus in the limited time allowed. He has never
. and in that he earned only a
studied anything beyond algebra,
‘C.’
17. If acupuncture is hocus pocus, then acupuncture cannot relieve
chronic pain. But acupuncture can relieve chronic pain.
Therefore, acupuncture is not hocus pocus.
18. If inflation heats up, then interest rates will rise. If interest rates
rise, then bond prices will decline. Therefore, if inflation heats up,
then bond prices will decline.
19. Statistics reveal that 86 percent of those who receive flu shots
do not get the flu. Jack received a flu shot one month ago.
Therefore, he should be immune, even though the flu is going
around now.
20. Since Michael is a Pisces, it necessarily follows that he was
born in March.
Answer ‘‘true’’ or ‘‘false’’ to the following statements:
.
1. Some arguments, while not completely valid, are almost valid.
2. Inductive arguments admit of varying degrees of strength and
weakness.
3. Invalid deductive arguments are basically the same as inductive
arguments.
4. If a deductive argument has true premises and a false
conclusion, it is necessarily invalid.
5. A valid argument may have a false premise and a false
conclusion.
6. A valid argument may have a false premise and a true
conclusion.
7. A sound argument may be invalid.
8. A sound argument may have a. false conclusion.
9. A strong argument may have false premises and a probably false
conclusion.
10. A strong argument may have true premises and a probably
false conclusion.
11. A cogent argument may have a probably false conclusion.
12. A cogent argument must be inductively strong.
13. If an argument has true premises and a true conclusion, we
know that it is a perfectly good argument.
14. A statement may legitimately be spoken of as ‘‘valid’’ or
‘‘invalid.’’
15. An argument may legitimately be spoken of as ‘‘true’’ or ‘‘false.’’
A
B
B
C
.
.
A
C
.
 MP VALID
VALID MT 
 AC – fallacy
Together, AC and DA have over the years
acquired the name of MODUS MORONS –
fallacy
– DA these two fallacies!!!
in other words,
avoid