ARGUMENT AND CRITICALTHINKING
v
13/03/09
F Course outline
1. Nature
of Argument
2.
Fallacies
3.
Definitions.
F
Logic and its significance.
Logic
basically is concerned with reasoning and argument. Argument here takes on a
more technical structure. Logic is the method of distinguishing between good
and bad reasoning.
F Significance of
Reason.
1. Reason
is important in decision making
2.
Emotion is irrational (negative), illogical and dangerous.
3. Reason
helps an individual acknowledge bad reasoning.
4. The
human society have many illogical human beings, hence the need to be trained on
how to make rational rather than emotional decisions.
5. There
certain segment of people that delights in using false arguments to deceive
others – the advertisement industry, politicians, the 419ners, etc. Logical
reasoning helps us detect these fallacious arguments often hidden under the
mask of good argument or reasoning.
F
Argument.
Proposition
Argument
Statement
An
argument is a proposition. Usually a statement carries a proposition. A
proposition can be true or false – it affirms or denies that something is the
case, as such; it could be either true or false.
Examples:
1. It is
raining – affirmation. This is a statement, carrying a proposition.
If it is
actually raining, then the statement is said to be true. But if it is not
raining and the statement claims that it does, then it is said to be false.
2. It is
not raining – denial. This is also a statement, carrying a proposition.
If it is
actually not raining, then the statement is true. But if it is raining and the
statement states otherwise, then it is false.
F An
argument is a set of propositions in which one set of proposition makes a claim
and another set of proposition serves as the reason for making that claim.
Proposition(s)
1: a claim (Conclusion)
Proposition(s)
2: reason or justification (premise)
F
Structure of an argument.
First
structure of an argument – premise
Second
structure of an argument – conclusion
Third
structure of an argument – inference
An inference is the process of movement from
premise to a conclusion. Without the link between the premise and the
conclusion, there is no argument. It is this link or inference that established
or constitutes an argument.
- Since rationality is the distinguishing mark of
the human person from other animals, it follows that human beings are a special
type of animal.
v
20/03/09
F
Types of Argument
There are
two types of argument
1.
Deductive Argument
2.
Inductive Argument.
F
Deductive Argument
An
argument is deductive when you move from universal premise to a particular
conclusion. Also the premise of a deductive argument provides a conclusive
ground for its conclusion. Put differently, deductive argument is an argument
in which the premises give total support to the conclusion of the argument.
Example:
1. All Seminarians are wicked
Musa
is a Seminarian
Therefore
Musa is wicked.
2.
All birds fly
The
Ostrich is a bird
Therefore
the Ostrich fly.
Hence
if the premises are accepted the conclusion cannot be rejected. If the premises
are true, the conclusion must be true as well because the premise gives a
compulsory or necessary assurance for the conclusion.
F
Inductive Argument.
In
an Inductive argument, one moves from particular premises to universal
conclusion. Put differently, inductive argument is one in which the premises
give partial support to the conclusion
Example:
1.
Few of the emeralds that have been discovered so far contain arsenic.
Therefore
it is probable that some of the emeralds to be discovered will contain arsenic
– weak argument.
2.
All the emeralds discovered so far have been green
Therefore,
it is probable that those to be discovered will be green – strong argument in
the sense that all the emeralds so far discovered have actually been green.
From this fact, we now conclude that those to be discovered will also be green.
We
must note that the premises of an inductive argument do not give conclusive or
one hundred percent support to the conclusion, rather the premises in inductive
arguments only gives some support to the conclusion. This support may be
strong, weak or nil but certainly not total. In an inductive argument, it is
possible to accept the premises and deny the conclusion without contradicting
oneself when an inductive argument gives more that 50 percent support to the argument;
we say that it is a strong argument as in the second example above. But when it
gives less than 50 percent support to the argument, it is said to be weak
evident as in the first example above.
v 27/03/09
F Validity and Invalidity.
An
argument is valid if it is impossible for the premises to be true and the
conclusion false. In order words, if you assume that the premises are true,
then, the conclusion must also be true. It is only in an invalid argument that
the conclusion will not follow from the premise. In a valid argument therefore
we have true premise and true conclusion. Once we have true premise(s) and
false conclusion, the argument becomes invalid.
Example:
All
vice-chancellors are women
Afolayan
is a vice-Chancellor
Therefore
Afolayan is a woman
N.B. If
we assume the premise to be true, then the conclusion must be true also
otherwise the argument becomes invalid.
Example 2
If all
seminaries are for women who want to marry, then, SSPP is a seminary for women
who want to marry. This argument is valid because the conclusion follows from
the premise.
Another
point to note is that this is a valid form of an argument and that any argument
that is put in this form of argument is going to be valid.
All x are
y
P is x
Therefore
p is y.
As
earlier noted, in deductive argument, the conclusion follows necessarily from
the premise. This implies that all deductive arguments are valid arguments. It
is only in inductive argument that the conclusion does not follow necessarily
from the premises. The conclusion in inductive argument is based on
probability.
F
Soundness and Unsoundness of an argument.
An
argument is said to be sound when all the propositions in that argument are
sound. Put differently, this implies that both the premises and the conclusion
are actually true. If any of them is false, then the argument is unsound.
Sound argument:
All men
are mortal
Socrates
is a man
Therefore
Socrates is mortal.
Unsound argument:
All
Vice-Chancellors are men
Afolayan
is a Vice-Chancellor
Therefore
Afolayan is a man.
F
Propositional Constance .
Propositional
Constance A – Z
Propositional
Variables p – z
Propositional
Constance stands for upper case from A – Z and
it is used to represent specific proposition. On the other hand, propositional
variables stands for the lower case from p – z and is can be used to represent
any proposition.
Examples:
I am
going to school - specific proposition
J
T
If
John is a student then he is a truant, and if he is a truant then
he
F
is
going to fail his exams.
If J >
T
If T >
F
F
Logical Connectives.
There are
five logical connectives.
·
Conditional (‹)
if …then
·
Conjunction ( .) and
·
Disjunction ( v ) either …or
·
Negation ( ~
) not
·
Bicondition ( º
) if and only if.
Examples:
F Negation:
It is
going to rain – R
Negation:
It is not going to rain (~R)
F
Conditional
If it is
going to rain – R, then the Sun will not shine – S: (R‹S)
F
Conjunction
It is
going to rain – R and the sun will not shine – S: (R·S)
F
Disjunction.
Either it
is going to rain – R or the lecture will not hold – L: (R v L)
F
Biconditional
It will
rain – R if and only if the sky is dark – S: (R º
S)
§
Exercise: solve the following problem
If the
school is good then the teachers are graduates and if they are graduates then
the students’ population will be stupendous.
NB: In
handling question like this, ask yourself what form of argument that is set
before you. In the example above, it is clear that the argument is a condition
argument or statement with a conjunction. Here then is how it should be
tackled:
If the
school is good – S, then the teachers are graduates - G and if
they are
graduates - G then the students’ population will be stupendous.
- P
(S‹G)· (G‹P)
NB. Ask
yourself what is the basic form of the argument. The argument above is a
conditional argument.
v
03/04/09
F
Truth Value
1. Negation: (~)
P ~P
T F
F T
2. Conjunction – (and)
Conjunction can only be true when both conjuncts are true. If any of the
conjuncts are false, the conjunction is false.
p.q
p q p .q
T T T
Conjuncts T F F
F T F
F F F
p q
Example:
Segun is a lawyer and Tola is a teacher
3. Disjunction pvq
Disjunction
is false only if both disjuncts are false. Otherwise, it is true.
P q pvq
T T T
T F T
F T T
F F F
4. Conditional “‹” p‹q
Conditional
is false if the antecedent is true and the consequent false, otherwise it is
true.
p q
p ‹
q
T T T
T F F
F T T
F F T
5. Bio-condition
p º q
A
bio-condition is true if both components are true. It is also true when both
components are false otherwise; it is going to be false.
p q p º q
T T T
T F F
F T F
F F T
F
Basic Valid Argument Forms
v
Modus Ponens.
If p>q
p
.: q
If it has
rained then the grass will be wet. It has rained, therefore the grass is wet.
v
Modus Tollens
P ‹
q
~
p
.: ~ q
If it had
not rained then the grass will not be wet. It had not rained therefore the
grass is not wet.
v
Hypothetical Syllogisms
 |
p ‹ q
p ‹
q If Nigeria
p ‹
r q ‹
r government is good. If the
government is
.: p ‹
r .: p ‹
q good, then the masses will
enjoy. The gov.
Attains a great height, then the masses
enjoys
v
Disjunctive Syllogism
There are
two valid argument- forms that employ disjunction, namely, Addition and
Distinctive Syllogism.
·
Addition:
– the form of addition is:
p
.: p v q
This
means that if a proposition is true, then a disjunction of which it if a
disjunction is true.
Example:
·
Nigeria Nigeria
is going to collapse or I fly to America
·
Disjunctive Syllogism:
The two
forms of disjunctive syllogism are:
p v
q and p v q
~p ~q
.: q :. P
This
means that the falsity of one disjuncts of a true disjunction implies the truth
of the other disjunct.
Example:
Either Austin Austin Austin
v
Simplification.
 |
p.q p .q
:. p :. q
Example:
Segun is
a thief and Kola is a rubber. Therefore Kola is a thief.
v
Conjunction
p
q
:. p.q
Example:
Olu is a
robber and Segun is a seminarian. Therefore Olu is a robber and Segun is a
seminarian.
v 08/05/09
± Basic
fundamental decisions of life are not a decision one has to take based on
passion, sentiment or emotion.
± To
escape the bad influences around us, we need tutoring in logic.
± Our
society if filled with irrationality and we need to be trained in logical
thinking so as to be able to escape theses irrational tendencies.
F Fallacy.
A
fallacy is an argument or reasoning in which the conclusion does not follow
from the premises. A fallacy has two features:
·
First
it is an argument
·
Second
its premises provide no support to the conclusion though they appear to do so,
because the argument is psychologically persuasive. Fallacies
can be divided into three.
·
Fallacies of relevance
·
Fallacies of ambiguity
·
Fallacies of weak induction.
The
fallacies of relevance should actually be called fallacies of irrelevance
because the premise has no relevance to the conclusion.
± Argumentum ad
misericordiam (Appeal to pity)
Here, the
premise of fallacy appeals to certain sentimental or emotional rather than the
fact of the case or matter to justify a particular claim.
Example:
An
assignment was given to students. One fails to do his own and when the teachers
asks his reason, he say that his is the only son of his aged mother who is
presently hospitalized and he has to look after her and so he was not able to
do the assignment.
±
Argumentum ad populum (Appeal to the people)
Here one
appeals to a common practice that is general with the people in order to
justify a point – everybody is doing it.
Example:
You were
in your room studying because you have an important exam tomorrow. Because of
the importance of the exam to you, you have decided that you wouldn’t go out
today. Furthermore, you had failed that exam before. Now a fellow classmate
comes along and asks you to join him to watch the games at the field. To this
you replied in the negative. He now tells you everybody in the campus is at the
field and based on this information, you now abandon your previous decision and
goes out with him.
±
Argumentum ad baculum (Appeal to force)
The
person using this argument intends to force you to discard your own position
and accept his own. The force here could either be physical or psychological
but usually it is psychological. The person undermines your conclusion by
appealing to force – if you don’t do this, this will happen.
Example:
a child asks another, what are you eating, meat! Who gave you? I’ll not tell
you. Will you give me? I’ll not give you. I’ll tell mummy – I will give please
don’t tell her.
±
Argumentum ad verecundiam (Appeal to (unqualified)
authority).
If a
dentist tells me that chewing gum is not good for my teeth, I’ll be wise to
take that advice – he is an authority in the mechanization of the human body.
NB. This
does not imply that all advice form an authority in a particular field is
always right.
Argumentum
ad verecundiam is often used by advertising agents. Take for instance, Okocha
is shown on the television dribbling and eventually scores a goal. The next
thing you see is where he is shown drinking a Pepsi. At the end Okocha tells us
that he scored his goal because he drinks Pepsi therefore we should all drink
Pepsi. For one thing Okocha is an authority in football to be sure but he has
no knowledge whatever on the chemical components of drinks. So he has no
authority to tell us we should be drinking Pepsi – he is an unqualified
authority in that area.
±
Argumentum ad hominem (Appeal against the man)
This
fallacy has three components:
·
Abusive
·
Circumstantial
·
To quo que (you too!)
In
arguing with someone, instead of concentrating on the argument presented by
your opponent, you attach the person of your opponent.
±
15/05/09.
F Argumentum ad
ignorantiam
This
fallacy is committed when you argue that something is true simply because it
has not been proven false or that something is false simply because it has not
been proven to be true.
Example:
Because
God’s existence has not been proved to be false, therefore is true.
±
Argument of Accident.
This
fallacy consists in applying a general rule to a particular case whose
“accidental” circumstance renders the rule inapplicable.
±
Hasty Generalisation (Converse of
Accident)
Here, one reach a general rule from a specific
insufficient evident.
NB. Having observed 1000, 000, 000 swans as white, you
conclude that all swans are white.
± Fallacy of the
Complex Question
This fallacy is usually employed in the law court. It
is committed when you phrase two questions in form of one. So that when you
answer the question, you are answering an antecedent question which you did not
know.
Example:
Have you stopped beating your wife?
± Fallacy of
Begging the Question
This fallacy is committed when you assume in your
conclusion or premise what you are supposed to prove in the conclusion or
premise.
Example:
1. God is the almighty because anyone we call the
almighty is necessarily God.
2. Ronaldo is the best footballer in the world because
he scored thirty goals and anyone that scored thirty goals is the best
footballer in the world.
± Fallacy of
Equivocation
This is committed when you use ambiguous word or a
particular word in two senses.
Example:
1. The end of a thing is perfection – (Goal).
Death is the end of life – (Termination). Therefore death is the
perfection of life.
2. All solid things are dense. To be dense is to be a
dullard. Therefore, that block of stone is a dullard.
3. Every bank of a river is always wet. I kept my
money in the bank. Therefore money kept in the bank must be wet.
± Fallacy of
Division.
This is committed when the characteristic of a whole
is assumed to apply to the part.
Example:
± Fallacy of
Composition
This is committed when you attribute the qualities of
the part to the whole.
Example:
All the actors in this film performed excellently.
Therefore the film is moving excellently.
±
22/05/09
F Definition.
A proper definition has two parts
·
The Definiendom and
·
The definiens.
The definiendom is the group
of words that you want to define while the definient is the word or group of
words you use in defining.
± Purpose of
Definitions
The purpose of definition is to introduce a new word
into the language or to give a new meaning to what already holds.
F Types of
Definitions
±
Ostensive Definition.
This definition is achieved by pointing at something
or demonstrate something.
Example: This is a car.
± Stipulated
Definition.
This definition assigns a meaning to a word for the
first time and the meaning of that word is dependent on the definitor.
Example:
“Laugheep” means laughing and weeping at the same
time.
± Lexical
Definition.
This definition reports the meaning that a word has
for a group of people competent in a given language.
Example: English Language, Igbo Language, Yoruba
Language.
“Atheist” in English means someone who has no belief
in God.
“Miri” in Igbo language means water.
± Précising
Definition
This definition reduces the vagueness of any
particular word. it applies to all the vague words you can think of. Example:
average, rich, drunk etc.
Example:
Average in relation or in the context of PHILOSOPHY
101 means scoring a “C”
± Theoretical
Definition.
This definition gives a theoretical characterization
to certain entity that a term denotes.
Example:
“Gold” means an element having an atomic number of 79 and
an atomic weight of 197.
± Persuasive
Definition.
This definition expresses a favourable
or unfavourable attitude towards the thing or terms to be defined.
Example:
A terrorist is someone who fights for the cause of his
country – favourable.
A terrorist is someone who destroys lives and
properties – unfavourable.
F Function of a Language.
·
Language conveys information – cognitive meaning.
·
Language expresses or evokes feelings – emotive
meaning.
Language also contains certain defects. A language can
be ambiguous or vague. Language can lead to dispute and the commonest types of
disputes are verbal and factual disputes.
Factual disputes can easily be settled by
verification. For instance if someone argues that there are 300 students in
year one at SS Peter and Paul seminary and another argues that they are only
200, all you need do is to go to SS Peter and Paul and count the students in
year one class.
Verbal disputes on the other hand are not so easy to
resolved or settled. Usually it occurs due to vagueness or ambiguity of the
word used.
v
Vagueness has a long range of meanings or
interpretations
v
Ambiguity has about 2 to 3 meanings.
Extension
±
Cognitive meaning:
Cognitive meaning:
Intension
·
The extensional meaning refers to the class of things
or the individual that a particular thing could be truly applied to.
Example: Obasanjo would belong to the class of
Nigerian presidents
·
The intentional meaning of a term refers to the
connotation of that term. That is, the features, qualities that a thing must
possess for it to be that.
±
01/06/09
F Lexical Rules of
Definition.
For the definition, the lexical definition has about 5
rules.
1.
A definition should state the essential attributes of
the term to be defined.
2.
A definition must not be circular. In order words, the
definiendum must not appear in the definience.
Example:
A lecturer is someone that lectures.
3.
A definition must neither be too broad nor too narrow.
The definient must not state more things or less things in the definiendum
Examples:
·
Man is a featherless biped
·
A shoe is a leather covering for the leg.
4.
A definition must not be expressed in ambiguous,
obscure or figurative language.
Examples:
·
A net is anything reticulated or decussated at equal
distance with interstice between the intersections.
·
Oratory is a conspiracy between speech and action to
cheat the understanding.
5.
A definition should not be negative where it can be
affirmative. A definition should explain what a term or concept means rather
that what it is not.
Example:
·
A couch is a piece of furniture that is neither a bed
nor a chair
·
An orphan is a child who does not have parents.
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