Spring 2004
Phl 204
Deductive Arguments
In the previous discussion, the subject of “statements” was introduced, and in class, assignments were given to write valid arguments using propositions and conclusions. It becomes clear that there is a difference between a “valid” argument and what would commonly be called “the truth”. In deduction, valid argument flows from its premises and is said to be valid if the conclusion logically follows when the propositions are true.
The result can often end in nothing more than word-play.
The
capital of the
I
live in
I
live in the
While this is in the form of a valid argument, the conclusion is not very compelling. Why play this game? There are at least two reasons for doing this: 1) it illustrates logical relationships between statements and conclusions and, 2) it illustrates that the form of an argument is not enough. There are two criteria for a sound deductive argument, the truth of the premises and the validity of the form.
The first reason should be significant for every student. In academic writing, for example, it is important to understand that the conclusions are supported by the premises (the research). Conclusions which are supported by sweeping generalizations or incomplete research may be in the form of a valid argument, but will seem more like word-play. A paper is not made stronger by concluding, “Every reasonable person would agree…” if what you really mean is “I think you should believe as I do” (which would mean that you have not demonstrated your thesis, but are expressing an opinion). Maybe you have not thought that a term paper is a sort of logical argument, but here’s another way of looking at the first example in an “argument” form:
Every
reasonable person will agree that blah is blah. (p)
I
(instructor) am not convinced by your presentation. (p)
The instructor is not a reasonable person. (c)
Is this the message you would want to convey in a term paper? Maybe you have never thought of an essay or presentation as a form of logical discourse?
Deductive arguments need to take a
valid form. To be a sound argument the premises must also be true. In a deductive argument if the premises are
true and the reasoning is correct, the conclusion must be true. The reason for this is that the conclusion of
a deductive argument doesn’t contain anything that is not in the premises. (This is as opposed to an inductive argument
in which the conclusion is only probably true… that is a later section.) Thus, one of the tests of validity is that a
valid argument (one with true premises) cannot have a false conclusion. Let me illustrate this by explaining a form
of deductive argument called a conditional
argument.
A conditional argument begins with an “if…then”, that is, a conditional statement. Here is an example of a conditional statement:
If today is Monday, then tomorrow is Tuesday.
“If today is Monday” is the antecedent (P) and “tomorrow is Tuesday” is the consequent (Q). In this case both the antecedent and the consequent can be affirmed or denied, so there are four possible forms of the conditional argument:
1. Affirming the Antecedent 2. Denying the Consequent
If P then Q If P then Q
P not-Q
>>Q >>not-P
3. Affirming the Consequent 4. Denying the Antecedent
If P then Q If P then Q
Q not-P
>>P >>not-Q
If you begin with the statement that “If today is Monday then tomorrow is Tuesday” all four of these forms for conditional arguments seem valid. That, however, breaks down when the P’s and Q’s are replaced by statements. In reality, only forms 1 & 2 are valid arguments. Affirming the Consequent and Denying the Antecedent are invalid. The explanation for this is involved, but consider this conditional statement:
If
Here are the conclusions (find them using P’s and Q’s):
1. Affirming the Antecedent: Fairborn is in the Midwest
2. Denying the Consequent:
3. Affirming the Consequent: Fairborn is in Indiana
4. Denying the Antecedent:
Remember, arguments are not valid simply because they are in the right form. They are also considered invalid if false conclusions proceed logically from true premises. Forms 1&2 above are considered valid forms of conditional arguments, but 3&4 are considered false.
These sample statements have been straight forward, but deciphering conditional arguments in the real world is not always easy. The application of this system of logic requires that statements can be placed in their logically correct form, that is, “If then”. For example:
I will go to the mall with you if you don’t
stay there too long.
This becomes:
If you don’t stay there too long, then I will go with you to the mall.
There is a step-by-step checklist for finding out whether a conditional argument is valid or not:
1. State the premises first, then the conclusion.
2. Insert any missing premise or conclusion.
3. Write the first statement as an “If…then”
4. Identify which form of the conditional argument follows,
and ask “Is it a valid form?”
EXAMPLE:
Fred said that he would go home if
we were not at the room by
1. Premise: If we were not at the room.
Conclusion: Fred would go home.
2. Possible missing premises: a) we were not at the room
b) Fred went home (Did not stay)
c) Fred did not go home (Stays)
d) we were at the room
3. The statement as an “If…then”:
If we were not at the room by
Or
(If we get to the room by
4. Of the possible premises a) and c) create valid arguments and
b) and d) do not. Why or why not? (Hint: What form of
argument do they represent?)