MOI UNIVERSITY
SAS 202: INTRODUCTION TO CRITICAL THINKING
Introduction
Critical thinking is at the core of most intellectual activity that involves students in learning to
recognize or develop an argument, use evidence in support of that argument, draw
reasoned conclusions, and use information to solve problems. Examples of thinking skills
are interpreting, analyzing, evaluating, explaining, sequencing, reasoning, comparing,
questioning, inferring, hypothesizing, appraising, testing and generalizing.
Reflecting on thinking and processes
This element involves students thinking about thinking (metacognition), reflecting on actions
and processes, and transferring knowledge into new contexts to create alternatives or open
up possibilities. Students reflect on, adjust and explain their thinking and identify the thinking
behind choices, strategies and actions taken. They apply knowledge gained in one context
to clarify another. In summary, reflecting primarily consists of:
• think about thinking (meta-cognition)
• reflect on processes
• transfer knowledge into new contexts
Basic concepts
The process of drawing a conclusion from other propositions called premise(s). Hence the study of reasoning and
the principles of good reasoning is the study of arguments.
An argument
It is a set of propositions in which the truth of one of the propositions is claimed to be established on the basis of
the truth of the other propositions either necessarily or by probability. The one whose truth is asserted on the
basis of the truth of the other is called conclusion while the one whose truth provide the basis for the truth of the
conclusion is/ are called premise/ premises.
1. For example: since we are in the month of January, next month must be February.
2. Those who drink alcohol get drunk. Those who are drunk fall asleep. Those who are asleep commit no sin.
Those who commit no sins go to heaven. Therefore those who drink alcohol go to heaven.
Conclusion need not to be stated last. It can as well be stated first or within premises. EG. Next month must be
February since we are in the month of January.
A proposition
1
,It is a sentence that is either true or false. The condition of a sentence being either true or false is referred to as
truth value. Eg Kenyatta University is in Kenya. A proposition is a declarative sentence as opposed to interrogative
sentence, exclamation, imperative, suggestion and performative sentence.
Types of propositions
A proposition can be either simple or compound. A simple proposition is normally a categorical one while
compound are hypothetical (conditional), disjunctive, conjunctive or biconditional.
A hypothetical (conditional) proposition is of the form ‘if P then Q’, EG. If one is a Kenyan then one is an African. A
disjunctive proposition is in the form ‘Either P or Q” A conjunctive proposition is in the form “Both P and Q”, A Bi-
conditional is in the form “P if and only if Q” Eg. One is a wife if and only if one has a husband. Categorical
propositions are important in understanding elementary logic because they are the basic proposition through
which one often expresses one’s ideas.
A categorical proposition is one that asserts that the subject class is either wholly or partially included in or
excluded from the predicate class. A standard categorical proposition has four components:
i) A quantifier
ii) A subject term( a subject term represents a subject class)
iii) A copula ( a form of verb ‘to be’ e.g. is or are)
iv) A predicate term( a predicate term represents a predicate class)
Therefore a standard categorical proposition takes any of the following forms:
i) All S are P, e.g. all human beings are mortal
ii) No S are P, e.g. No human beings are mortal
iii) Some S are P, e.g. some human beings are mortal
iv) Some S are not P, e.g. some human beings are not mortal
When a proposition make reference to all the members of its subject class (whole class) then it is said to be
Universal as in (i) and (ii), But when a proposition make reference to only some members of its subject class (part
of the members), then it is said to be Particular as in (iii) and (iv). However when a proposition affirms the inclusion
of its subject class wholly or partially into its predicate class then it is said to be affirmative as in (i) and (iii). But
when a proposition denies the inclusion (assert the exclusion) of its subject class wholly or partially from its
predicate class, then it is said to be negative as in (ii) and (iv). Therefore any categorical proposition in the form of
‘All S are P’ is said to be Universal affirmative proposition, ‘No S are P’ is said to be Universal negative proposition,
‘some S are P’ is said to be Particular affirmative proposition, while ‘some S are not P’ is said to be particular
negative proposition.
Conventionally the four basic forms of categorical propositions are referred to by the letters A, E, I and O. The four
letters are derived from two latin words Affirmo (I affirm) and Nego (I deny). The first two vowels ( A and I ) from
the word Affirmo represent the two affirmative forms of the categorical propositions i.e the universal and
particular affirmative proposition and the two vowels (E and O) from the word Nego represent the two negative
forms of the categorical propositions.
Kinds of Arguments
2
, According to definition of an argument, two kinds of argument can be discerned. One of them is that there is a
claim that the truth of premises if granted implies the truth of its conclusion. That is if the premises are accepted
as truth, then the conclusion is also true as a matter of logical necessity. This kind of argument is called deductive
argument. Secondly, the claim that truth of its premises if granted offers only a probable support to the truth of its
conclusion. This kind of argument is called inductive argument.
For example: Deductive argument
A living thing must die
Human beings are living things
Therefore, human beings must die.
This argument can be expressed as one compound proposition as: ‘If any living thing must die and human beings
are living things, then human beings must die’.
But in a bad deductive argument, the truth of the conclusions does not follow necessarily from truth of its
premises. The argument is such that even if the truth of its premises is granted the truth of its conclusion must not
be inferred necessarily. For example:
All animals breathe
All human beings breathe.
Therefore, all human beings are animals.
The truth of the two premises taken together does not imply the truth of the conclusion. This means that the truth
of the conclusion cannot be accepted on the basis of the truth of premises, but the conclusion cannot be
independent of the truth of premises and if this were to be the case then it would be a matter of fact not logic.
Conclusion being true is not due to the truth of the premises.
For example: inductive argument
In inductive argument, the truth of premise if granted offers a partial or probable support to the truth of its
conclusion. If truth of premises of an inductive argument is granted then the truth of its conclusion is only probable
but not guaranteed.
Most luo like eating fish
Paul likes eating fish
Therefore, probably Paul is a luo
Therefore in an inductive argument, if the truth of its premises is granted, then the truth of its conclusion is only a
matter of probability.
Validity, strength and truth
Validity
3
SAS 202: INTRODUCTION TO CRITICAL THINKING
Introduction
Critical thinking is at the core of most intellectual activity that involves students in learning to
recognize or develop an argument, use evidence in support of that argument, draw
reasoned conclusions, and use information to solve problems. Examples of thinking skills
are interpreting, analyzing, evaluating, explaining, sequencing, reasoning, comparing,
questioning, inferring, hypothesizing, appraising, testing and generalizing.
Reflecting on thinking and processes
This element involves students thinking about thinking (metacognition), reflecting on actions
and processes, and transferring knowledge into new contexts to create alternatives or open
up possibilities. Students reflect on, adjust and explain their thinking and identify the thinking
behind choices, strategies and actions taken. They apply knowledge gained in one context
to clarify another. In summary, reflecting primarily consists of:
• think about thinking (meta-cognition)
• reflect on processes
• transfer knowledge into new contexts
Basic concepts
The process of drawing a conclusion from other propositions called premise(s). Hence the study of reasoning and
the principles of good reasoning is the study of arguments.
An argument
It is a set of propositions in which the truth of one of the propositions is claimed to be established on the basis of
the truth of the other propositions either necessarily or by probability. The one whose truth is asserted on the
basis of the truth of the other is called conclusion while the one whose truth provide the basis for the truth of the
conclusion is/ are called premise/ premises.
1. For example: since we are in the month of January, next month must be February.
2. Those who drink alcohol get drunk. Those who are drunk fall asleep. Those who are asleep commit no sin.
Those who commit no sins go to heaven. Therefore those who drink alcohol go to heaven.
Conclusion need not to be stated last. It can as well be stated first or within premises. EG. Next month must be
February since we are in the month of January.
A proposition
1
,It is a sentence that is either true or false. The condition of a sentence being either true or false is referred to as
truth value. Eg Kenyatta University is in Kenya. A proposition is a declarative sentence as opposed to interrogative
sentence, exclamation, imperative, suggestion and performative sentence.
Types of propositions
A proposition can be either simple or compound. A simple proposition is normally a categorical one while
compound are hypothetical (conditional), disjunctive, conjunctive or biconditional.
A hypothetical (conditional) proposition is of the form ‘if P then Q’, EG. If one is a Kenyan then one is an African. A
disjunctive proposition is in the form ‘Either P or Q” A conjunctive proposition is in the form “Both P and Q”, A Bi-
conditional is in the form “P if and only if Q” Eg. One is a wife if and only if one has a husband. Categorical
propositions are important in understanding elementary logic because they are the basic proposition through
which one often expresses one’s ideas.
A categorical proposition is one that asserts that the subject class is either wholly or partially included in or
excluded from the predicate class. A standard categorical proposition has four components:
i) A quantifier
ii) A subject term( a subject term represents a subject class)
iii) A copula ( a form of verb ‘to be’ e.g. is or are)
iv) A predicate term( a predicate term represents a predicate class)
Therefore a standard categorical proposition takes any of the following forms:
i) All S are P, e.g. all human beings are mortal
ii) No S are P, e.g. No human beings are mortal
iii) Some S are P, e.g. some human beings are mortal
iv) Some S are not P, e.g. some human beings are not mortal
When a proposition make reference to all the members of its subject class (whole class) then it is said to be
Universal as in (i) and (ii), But when a proposition make reference to only some members of its subject class (part
of the members), then it is said to be Particular as in (iii) and (iv). However when a proposition affirms the inclusion
of its subject class wholly or partially into its predicate class then it is said to be affirmative as in (i) and (iii). But
when a proposition denies the inclusion (assert the exclusion) of its subject class wholly or partially from its
predicate class, then it is said to be negative as in (ii) and (iv). Therefore any categorical proposition in the form of
‘All S are P’ is said to be Universal affirmative proposition, ‘No S are P’ is said to be Universal negative proposition,
‘some S are P’ is said to be Particular affirmative proposition, while ‘some S are not P’ is said to be particular
negative proposition.
Conventionally the four basic forms of categorical propositions are referred to by the letters A, E, I and O. The four
letters are derived from two latin words Affirmo (I affirm) and Nego (I deny). The first two vowels ( A and I ) from
the word Affirmo represent the two affirmative forms of the categorical propositions i.e the universal and
particular affirmative proposition and the two vowels (E and O) from the word Nego represent the two negative
forms of the categorical propositions.
Kinds of Arguments
2
, According to definition of an argument, two kinds of argument can be discerned. One of them is that there is a
claim that the truth of premises if granted implies the truth of its conclusion. That is if the premises are accepted
as truth, then the conclusion is also true as a matter of logical necessity. This kind of argument is called deductive
argument. Secondly, the claim that truth of its premises if granted offers only a probable support to the truth of its
conclusion. This kind of argument is called inductive argument.
For example: Deductive argument
A living thing must die
Human beings are living things
Therefore, human beings must die.
This argument can be expressed as one compound proposition as: ‘If any living thing must die and human beings
are living things, then human beings must die’.
But in a bad deductive argument, the truth of the conclusions does not follow necessarily from truth of its
premises. The argument is such that even if the truth of its premises is granted the truth of its conclusion must not
be inferred necessarily. For example:
All animals breathe
All human beings breathe.
Therefore, all human beings are animals.
The truth of the two premises taken together does not imply the truth of the conclusion. This means that the truth
of the conclusion cannot be accepted on the basis of the truth of premises, but the conclusion cannot be
independent of the truth of premises and if this were to be the case then it would be a matter of fact not logic.
Conclusion being true is not due to the truth of the premises.
For example: inductive argument
In inductive argument, the truth of premise if granted offers a partial or probable support to the truth of its
conclusion. If truth of premises of an inductive argument is granted then the truth of its conclusion is only probable
but not guaranteed.
Most luo like eating fish
Paul likes eating fish
Therefore, probably Paul is a luo
Therefore in an inductive argument, if the truth of its premises is granted, then the truth of its conclusion is only a
matter of probability.
Validity, strength and truth
Validity
3
