Chapter 2 Deductive Reasoning
Chapter 2
Deductive Reasoning
In chapter 1 we distinguished between deductive and inductive reasoning. As you have seen, in the former the conclusion follows necessarily from the premises, whereas in the latter the conclusion follows from the premises with a degree of probability. In this chapter we will examine some basic concepts of deductive logic.
Basics of Deductive Reasoning
Logical Form
All deductive arguments have argument forms. An argument form is a symbolic representation of an argument with all references to the world stripped away and replaced with variables (place holders). For example, look carefully at the following three arguments and their respective argument forms:
Argument
1
2
3
Argument Form
If Global warming continues to increase at the current rate then the earth is in imminent danger.
Global warming is continuing to increase at the current. rate Therefore, the earth is in imminent danger.
The Iraq war was based on shoddy intelligence or the Bush administration deliberately deceived the American people
The Iraq war was not based on shoddy intelligence.
Therefore, the Bush administration deliberately deceived the American people.
All deliberate killing of innocent persons is wrong
All mercy killing is the deliberate killing of innocent persons Therefore, all mercy killing is wrong
1
If p then q p Therefore q
p or q
Not p
Therefore q
All M is P
All S is M
Therefore, All S is P
The letters p and q in the above forms are called statement variables. That is, they are place holders for statements that they have replaced in their respective arguments.
All of these arguments are called syllogisms. A syllogism is a deductive argument with two premises. Each, however, is a different type of syllogism. Argument 1 is called a hypothetical (or conditional) syllogism because its first premise (referred to as the
“major premise”) is a conditional (if…then…) statement. A hypothetical syllogism is a syllogism with at least one conditional
Deductive Reasoning
In chapter 1 we distinguished between deductive and inductive reasoning. As you have seen, in the former the conclusion follows necessarily from the premises, whereas in the latter the conclusion follows from the premises with a degree of probability. In this chapter we will examine some basic concepts of deductive logic.
Basics of Deductive Reasoning
Logical Form
All deductive arguments have argument forms. An argument form is a symbolic representation of an argument with all references to the world stripped away and replaced with variables (place holders). For example, look carefully at the following three arguments and their respective argument forms:
Argument
1
2
3
Argument Form
If Global warming continues to increase at the current rate then the earth is in imminent danger.
Global warming is continuing to increase at the current. rate Therefore, the earth is in imminent danger.
The Iraq war was based on shoddy intelligence or the Bush administration deliberately deceived the American people
The Iraq war was not based on shoddy intelligence.
Therefore, the Bush administration deliberately deceived the American people.
All deliberate killing of innocent persons is wrong
All mercy killing is the deliberate killing of innocent persons Therefore, all mercy killing is wrong
1
If p then q p Therefore q
p or q
Not p
Therefore q
All M is P
All S is M
Therefore, All S is P
The letters p and q in the above forms are called statement variables. That is, they are place holders for statements that they have replaced in their respective arguments.
All of these arguments are called syllogisms. A syllogism is a deductive argument with two premises. Each, however, is a different type of syllogism. Argument 1 is called a hypothetical (or conditional) syllogism because its first premise (referred to as the
“major premise”) is a conditional (if…then…) statement. A hypothetical syllogism is a syllogism with at least one conditional