Arguments

3.2

Arguments

Definition

A process of making a conclusion based on statements is known as argumentations.
An argument can consist of several premises and one conclusion.
A premise is a statement that gives information before making a conlusion and conclusion is an outcome and decision.
The specific statements are statements that refer to a particular case, while the general statements that describe a concept.

Types of Arguments

Deductive argument
(A process of making a specific conclusion based on general premises)

Inductive argument
(A process of making a general conclusion based on specific premises)

Determine and Justify the Validity of Deductive Arguments

A valid deductive can be categorised into three forms.
A deductive arguments is said to be valid if all the premises and the conclusion are true.

	Form I	Form II	Form III
Premise 1	All \(P\) are \(Q\)	If \(a\) is \(b\)	If \(a\) is \(b\)
Premise 2	\(R\) is \(P\)	\(a\) is true	Not \(b\) is true
Conclusion	\(R\) is \(Q\)	\(b\) is ture	Not \(a\) is true

Form a Valid Deductive Argument for a Situation

Example

Question: All mammals are warm blooded. Cats are mammals. Cats are warm blooded.

Solution:

Premise \(1\)	All mammals are warm blooded.
Premise \(2\)	Cats are mammals.
Conclusion	Cats are warm blooded.

Question: If \(x\) is greater than \(0\), then \(x\) has a positive value. \(6\) is greater than \(0\). \(6\) has a positive value.

Solution:

Premise \(1\)	If \(x\) is greater than \(0\), then \(x\) has a positive value.
Premise \(2\)	\(6\) is greater than \(0\).
Conclusion	\(6\) has a positive value.

Determine and Justify the Strength of an Inductive Argument & Determine Whether the Strong Argument is Cogent

Deductive Argument	Inductive Argument
Emphasises the validity of the argument.	Emphasises the strength of the argument.

The Strength of an Inductive Argument

Determined based on the probability that the conclusion is tru, assuming all the premises are true.

Determine Whether the Strong Argument is Cogent or Not Cogent

It needs to be discussed based on the truth of the premises and its conclusion.

Example

Determine whether the given arguments are strong or weak. Hence, determine whether the strong argument is cogent or not cogent and justify your answer.

Question:

Premise \(1\)	The chairs in the living room are red.
Premise \(2\)	The chairs in the dining room are red.
Premise \(3\)	The chairs in the study room are red.
Premise \(4\)	The chairs in the bedroom are red.
Conclusion	All chairs in the house are red.

Solution:

This argument is weak and not cogent because although the premises are true, the conclusion is probably false.

Question:

Premise \(1\)	\(11\times5=55\)
Premise \(2\)	\(12\times5=60\)
Conclusion	All multiples of \(5\) end with digit \(0\) or \(5\).

Solution:

This argument is strong and cogent because all the premises and conclusion are true.

Arguments

3.2

Arguments

Definition

A process of making a conclusion based on statements is known as argumentations.
An argument can consist of several premises and one conclusion.
A premise is a statement that gives information before making a conlusion and conclusion is an outcome and decision.
The specific statements are statements that refer to a particular case, while the general statements that describe a concept.

Types of Arguments

Deductive argument
(A process of making a specific conclusion based on general premises)

Inductive argument
(A process of making a general conclusion based on specific premises)

Determine and Justify the Validity of Deductive Arguments

A valid deductive can be categorised into three forms.
A deductive arguments is said to be valid if all the premises and the conclusion are true.

	Form I	Form II	Form III
Premise 1	All \(P\) are \(Q\)	If \(a\) is \(b\)	If \(a\) is \(b\)
Premise 2	\(R\) is \(P\)	\(a\) is true	Not \(b\) is true
Conclusion	\(R\) is \(Q\)	\(b\) is ture	Not \(a\) is true

Form a Valid Deductive Argument for a Situation

Example

Question: All mammals are warm blooded. Cats are mammals. Cats are warm blooded.

Solution:

Premise \(1\)	All mammals are warm blooded.
Premise \(2\)	Cats are mammals.
Conclusion	Cats are warm blooded.

Question: If \(x\) is greater than \(0\), then \(x\) has a positive value. \(6\) is greater than \(0\). \(6\) has a positive value.

Solution:

Premise \(1\)	If \(x\) is greater than \(0\), then \(x\) has a positive value.
Premise \(2\)	\(6\) is greater than \(0\).
Conclusion	\(6\) has a positive value.

Determine and Justify the Strength of an Inductive Argument & Determine Whether the Strong Argument is Cogent

Deductive Argument	Inductive Argument
Emphasises the validity of the argument.	Emphasises the strength of the argument.

The Strength of an Inductive Argument

Determined based on the probability that the conclusion is tru, assuming all the premises are true.

Determine Whether the Strong Argument is Cogent or Not Cogent

It needs to be discussed based on the truth of the premises and its conclusion.

Example

Determine whether the given arguments are strong or weak. Hence, determine whether the strong argument is cogent or not cogent and justify your answer.

Question:

Premise \(1\)	The chairs in the living room are red.
Premise \(2\)	The chairs in the dining room are red.
Premise \(3\)	The chairs in the study room are red.
Premise \(4\)	The chairs in the bedroom are red.
Conclusion	All chairs in the house are red.

Solution:

This argument is weak and not cogent because although the premises are true, the conclusion is probably false.

Question:

Premise \(1\)	\(11\times5=55\)
Premise \(2\)	\(12\times5=60\)
Conclusion	All multiples of \(5\) end with digit \(0\) or \(5\).

Solution:

This argument is strong and cogent because all the premises and conclusion are true.

Arguments

Arguments

Chapter : Logic Reasoning

Topic : Argument

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