Logic & Critical Thinking
@ Herman J. Suhendra
Produced by Herman J. Suhendra
A.B. Gadjah Mada University & M.A. University of Santo Tomas, Manila
MEETING 5
Argument Part 2
2. What is an Argument?
1. Distinguishing
Fact & Opinion
Arguments - Part
1 (of 3)
3. Identifying Premises
& Conclusions
4. What Is Not
an Argument?
8. Writing
Arguments
7. Evaluating
Arguments
6. Analyzing
Arguments
5. Deduction &
Induction
Remember!
Before we can effectively
analyze and evaluate an
argument, we need to
understand clearly what
kind of argument is being
offered.
Deduction & Induction
Arguments below
Argument 1
deductive or
inductive?
All Humans are Mortal.
SBY is human.
Therefore, SBY is Mortal.
Argument 2
All of Steven Spielberg‘s movies have been
good.
Therefore, Steven Spielberg‘s next movie will
probably be good.
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.
Key Differences:
Deductive arguments claim that…
Inductive arguments claim that…
 If the premises are true, then the
conclusion must be true.
 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.
 It is unlikely for the premises to be
true and the conclusion false.
 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:
1.
2.
3.
4.
The Indicator Word Test
The Strict Necessity Test
The Common Pattern Test
The Principle of Charity Test
1. The Indicator Word Test
Femina is a PU student.
Most PU students own laptops.
So, probably Femina 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.
deductive or
inductive? Why?
The Mona Lisa, by Da Vinci, is an excellent piece of art. The Last
Supper, by Da Vinci, is an excellent piece of art. The Madonna of
the Rocks, by Da Vinci, is an excellent piece of art. So probably,
all works done by Da Vinci are excellent pieces of art.
2. The Strict Necessity Test
Taxis are architects.
No architects are Democrats.
So, no Taxis 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.
deductive or
inductive? Why?
Our national heroes are Javanese.
Pangeran Diponegoro is a national hero.
Therefore, Pangeran Diponegoro is a Javanese.
3. The Common Pattern Test
Either Djoko voted in the last election, or he didn't.
Only citizens can vote. Djoko is not, and has never been, a citizen.
So, Djoko 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.
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.
4. The Principle of Charity Test
Ramlan: Karen told me her grandmother recently climbed
Gunung Merbabu.
Zeno : 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 Zeno'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 Zeno'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 Merbabu.) Thus, the principle of
charity test tells us to treat the argument as deductive.
deductive or
inductive? Why?
80% of the Indonesian lives below the poverty line.
Martono is an Indonesian. So probably, Martono
lives below the poverty line.
deductive or
inductive? Why?
If Munir was assassinated, then he died. He was
assassinated. Therefore, he died.
Exercise 1
Is Nasir’s argument
deductive or
inductive? Why?
Tony: Are there any good Italian restaurants in town?
Nasir: Yeah, Luigi's is pretty good. I've had their Neapolitan rigatoni,
their lasagne col pesto, and their mushroom ravioli. I don't think
you can go wrong with any of their pasta dishes.
Exercise 2
Is this argument
deductive or
inductive? Why?
I wonder if I have enough cash to buy my journalism textbook
as well as my public relations and communication textbooks. Let's see, I have
Rp200.000. My journalism textbook costs Rp65.000 and my communication
textbook costs Rp52.000. My public relations textbook costs Rp60.000.
With taxes, that should come to about Rp190.000 Yep, I have enough.
Exercise 3
deductive or inductive?
Why?
Mother: Don't give Jason that brownie. It contains walnuts, and I
think he is allergic to walnuts. Last week he ate some oatmeal
cookies with walnuts, and he broke out in a severe rash.
Father: Jason isn't allergic to walnuts. Don't you remember he ate
some walnut fudge ice cream at Ferrari's birthday party last
spring? He didn't have any allergic reaction then.
Exercise 4
deductive or inductive?
Why?
I went to Burger King last night and the service was horrible.
The same thing happened the last time I went there. The same thing
happened the time before that. Hence the service at Burger King is always horrible.
Exercise 5
deductive or inductive?
Why?
Susan is under 18. People under 18 in Indonesian cannot vote.
Therefore, Susan cannot vote
Exercise 6
deductive or inductive?
Why?
Imagine a friend gave you a guinea pig to look after but forgot to tell you
anything about what to feed it. You might say to yourself, 'I have a guinea
pig and do not know what to feed it; but I do know that my rabbit eats
carrots, and that rabbits and guinea pigs are similar. Hence, I can probably
feed my guinea pig carrots as well'.
Exercise 7
deductive or inductive?
Why?
Shaving cream is clearly similar in colour, texture, moistness, and body to
whipped cream, and I know that whipped cream is delicious on fruit salad.
Hence, shaving cream is delicious on fruit salad.
Deduction & Induction
Type
Description
Inductive
Reasoning





Making observations, and then drawing conclusions from those observations
Moves from specific evidence to general conclusion
Conclusion must be figured out and then evaluated for validity
Inductive = Evidence  Conclusion
Questions to ask:

What evidence is available? What has been observed?

What can be concluded from that evidence?

Is that conclusion logical?
Deductive
Reasoning





Moves from conclusion to evidence for the conclusion
Evaluate if the evidence is valid
Includes formal logic
Deductive = Conclusion  Evidence
Questions to ask:

What is the conclusion?

What evidence supports it?

Is that evidence logical?
Deductive Validity
Argument #1 :
Barbie is over 90 years old. So Barbie is over 20 years old.
Argument #2 :
Barbie is over 20 years old. So Barbie is over 90 years old.
Deduction Validity
•
•
Argument #1 :
Barbie is over 90 years old. So Barbie is over 20 years old.
Argument #2 :
Barbie is over 20 years old. So Barbie is over 90 years old.
Intuitively, the conclusion of the first argument follows from the premise,
whereas the conclusion of the second argument does not follow from its
premise. But how should we explain the difference between the two arguments
more precisely? Here is a thought :
In the first argument, if the premise is indeed true, then the conclusion cannot
be false. On the other hand, even if the premise in the second argument is true,
there is no guarantee that the conclusion must also be true.
For example, Barbie could be 30 years old.
Deduction Validity
•
•
Argument #1 :
Barbie is over 90 years old. So Barbie is over 20 years old.
Argument #2 :
Barbie is over 20 years old. So Barbie is over 90 years old.
Intuitively, the conclusion of the first argument follows from the premise,
whereas the conclusion of the second argument does not follow from its
premise. But how should we explain the difference between the two arguments
more precisely? Here is a thought :
In the first argument, if the premise is indeed true, then the conclusion cannot
be false. On the other hand, even if the premise in the second argument is true,
there is no guarantee that the conclusion must also be true.
For example, Barbie could be 30 years old.
Deductive
VALID (official definition)
Iff It is impossible the conclusion to be FALSE while all the premises are true.
That is : There is no logically possible situation where all the premises are true
and the conclusion is false at the same time.
VALID (intuitive idea)
Iff the truth of premises 100% logically guarantees the truth of conclusion.
It is logically NECESSARY that IF all the premises are true THEN
the conclusion is also true.
INVALID
Iff it is not logically NECESSARY that IF all the premises are true THEN
the conclusion is also true.
Iff it is logically POSSIBLE for the conclusion to be false WHILE all the
Premises are true.
What do we mean by “logically possible”?
Anything is logically possible so long as it is NOT self-contradictory.
IMPORTANT:
“VALIDITY” is a logical concept: it is defined in terms of “logical possibilty”.
(NOT any other kinds of possibility: Economy, political, technological,
psychological, physical, or legal possibilities)
POSSIBILITY: that which is ALLOWED (i.e. not ruled out)
IMPOSSIBILITY: that which is ruled out (i.e. not allowed).
SOMETHING is logically possible (or logically impossible): it is allowed
(or ruled out) by the laws of LOGIC.
LAW OF NON-CONTRADICTION:
SELF-CONTRADICTION (i.e. “P and not-P”) IS NOT ALLOWED
Deductive
The idea of validity provides a more precise explication of what it is
for a conclusion to follow from the premises. Applying this
definition, we can see that the FIRST argument above is VALID,
since there is no possible situation where Barbie can be over 90
but not over 20. The SECOND argument is INVALID because there
are plenty of possible situations where the premise is true but the
conclusion is false. Consider a situation where Barbie is 25, or one
where she is 85. The fact that these situations are possible is
enough to show the argument is not VALID, or INVALID.
Deductive
All pigs can fly. Anything that can fly can swim. So all pigs can swim.
Deductively
Although the two premises of this argument are false, this is actually a
VALID argument. To evaluate its validity, ask yourself whether it is possible
to come up with a situation where all the premises are true and the
conclusion is false. (We are not asking whether there is a situation where
the premises and the conclusion are all true.) Of course, the answer is 'no'.
If pigs can indeed fly, and if anything that can fly can also swim, then
it must be the case that all pigs can swim.
So this example tells us something:
(1) The premises and the conclusion of a valid argument can all be false.
Deductive
Hopefully you will now realize that validity is not about the actual
truth or falsity of the premises or the conclusion. Validity is about
the logical connection between the premises and the conclusion.
A valid argument is one where the truth of the premises
guarantees the truth of the conclusion, but validity does not
guarantee that the premises are in fact true. All that validity tells us
is that if the premises are true, the conclusion must also be true.
Deductive
Adam loves Beth. Beth loves Cathy. So Adam loves Cathy.
Deductive
Adam loves Beth. Beth loves Cathy. So Adam loves Cathy.
Deductive
Invalid for it is possible that the premises are true and yet the
conclusion is false. Perhaps Adam loves Beth but does not want
Beth to love anyone else. So Adam actually hates Cathy. The mere
possibility of such a situation is enough to show that the argument
is not valid.
Let us call these situations invalidating counterexamples to the
argument. Basically, we are defining a valid argument as an
argument with no possible invalidating counterexamples.
Note: to sharpen your skills in evaluating arguments, it is therefore
important that you are able to discover and construct such
examples.
Deductive
Notice that a counterexample need not be real in the sense of
being an actual situation. It might turn out that in fact that Adam,
Beth and Cathy are members of the same family and they love
each other. But the above argument is still invalid since the
counterexample constructed is a possible situation, even if it is not
actually real. All that is required of a counterexample is that the
situation is a coherent one in which all the premises of the
argument are true and the conclusion is false.
So we should remember this :
(2) An argument can be invalid even if the conclusion & the premises are all actually true.
Deductive
All pigs are purple in colour. Anything that is purple is an animal.
So all pig are animals .
Deductive
(3) It is possible for a VALID argument to have a true conclusion even.
when all its premises are false.
Deductive
The concept of validity provides a more precise explication of what
it is for a conclusion to follow from the premises. Since this is one
of the most important concepts, you should make sure you fully
understand the definition. In giving our definition we are making a
distinction between truth and validity. In ordinary usage "valid" is
often used interchangeably with "true" (similarly with "false" and
"not valid"). But here validity is restricted to only arguments and not
statements, and truth is a property of statements but not
arguments:
So never say things like
“this statement is valid”
or
“that argument is true”!
Exercise 2
Valid or
Invalid: Why?
Someone is sick. Someone is unhappy. So, Someone is unhappy and sick.
Exercise 2
Valid or
Invalid: Why?
If he loves me then he gives me some flowers. He gives me flowers.
So, he loves me.
Exercise 3
Valid or
Invalid: Why?
Beckham is famous. Beckham is a football player. Therefore, Beckham is
a famous football player.
Exercise 4
Valid or
Invalid: Why?
If it rains, the street will be wet. If the streets are wet, accidents will
happen. Therefore, accidents will happen if it rains.
Deductive Soundness
It should be obvious by now that validity is about the logical connection between
premises and the conclusion. When we are told that an argument is valid, this is
enough to tell us anything about the actual truth or falsity of the premises or
conclusion. All we know is that there is a logical connection between them, that
premises entail the conclusion.
the
not
the
the
So even if we are given a valid argument, we still need to be careful before
accepting the conclusion, since a valid argument might contain a false conclusion.
What we need to check further is of course whether the premises are true.
So never say things like
“this statement is sound”/
“invalid” or
“that argument is true”!
Deductive Soundness
If an argument is valid, and all the premises are true, then it is
called a sound argument. Of course, it follows from such a
definition that a sound argument must also have a true conclusion.
In a valid argument, if the premises are true, then the conclusion
cannot be false, since by definition it is impossible for a valid
argument to have true premises and a false conclusion in the same
situation. So given that a sound argument is valid and has true
premises, its conclusion must also be true. So if you have
determined that an argument is indeed sound, you can certainly
accept the conclusion.
An argument that is not sound is an unsound argument. If an
argument is unsound, it might be that it is invalid, or maybe it has at
least one false premise, or both.
So never say things like
“this statement is sound”/
“invalid” or
“that argument is true”!
Deductive Soundness
Sound:
Valid + All Premises are TRUE
Unsound:
Invalid + one of the premise is
FALSE
Comprehension:
1. All invalid arguments are unsound.
2. All true statements are valid.
3. To show that an argument is unsound, we must at
least show that some of its premises are actually false.
4. An invalid argument must have a false conclusion.
5. If all the premises of a valid argument are false, then
the conclusion must also be false.
6. If all the premises and the conclusion of an argument
are true, then the argument is valid.
7. All sound arguments are true.
8. Any valid argument with a true conclusion is sound.
Group Activity
20 min
Group discussion
5 min
Summarize discussion findings
15 min
Group presentation & discussion
The Group leader must submit their findings in hard or soft-copy format to the
lecturer and send to his email before or during the next class.
Summary
Deduction and
Induction
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.
Deductively Valid
and Sound
1. The premises and the conclusion of an invalid argument
can all be true.
2. A valid argument should not be defined as an argument
with true premises and a true conclusion.
3. The premises and the conclusion of a valid argument
can all be false.
4. A valid argument with false premises can still have a true
conclusion
5. A Sound argument is a valid argument with all the
premises are true.
Any Questions?
The End – Thank You!
Failed!
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