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
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:
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.
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
Therefore, all mercy killing is wrong
If p then q
p or 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 statement. Logicians refer to the if part of the major premise (“Global warming continues to increase at the current rate”) as the antecedent and the then part (“The earth is in imminent danger”) as the consequent. In these terms, the minor premise (second premise) of Argument 1 can be said to affirm the antecedent while its conclusion affirms the consequent.
Argument 2 is called a disjunctive syllogism because its major premise (first premise) is a disjunctive (“or”) statement. Logicians refer to each alternate in the major premise as a disjunct. In these terms, the minor premise can be said to be denying a disjunct while the conclusion is affirming the other.
Finally, Argument 3 is called a categorical syllogism because it consists of statements that relate classes or “categories” (the deliberate killing of innocent people, mercy killings, and wrong acts) and which uses quantifiers (“all” and “no”) to relate these classes.
We will look more carefully at each of these three types of syllogisms in the chapters that follow this one.
All three arguments are formally valid. A deductive argument is formally valid if and only if it has a valid form. A valid form is one such that any consistent substitution instances of the variables that make all of the premises true will also make the conclusion true. For example, consider the following substitutions for the statement variables in Argument 1:
p = July 4 is a Federal Holiday
q = The US Post Office is closed on July 4
When the above statements are consistently substituted for their respective statement variables in the argument form of Argument 1, we get the following argument: If July 4 is a Federal Holiday then The US Post Office is closed on July 4 July 4 is a Federal Holiday
Therefore, the Post Office is closed on July 4
Notice that these substitutions make the premises of the resulting argument true. But also notice that this automatically makes...
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