Deductive Reasoning: Testing the Soundness of Arguments

An argument is "sound" when it is true and valid.

An Introduction to Argument

How is deductive reasoning different from inductive reasoning?

According to Moore and Parker in their text, Critical Thinking (2012), when we “set forth reasons for accepting a claim,” we are creating an argument (pg. 8). In other words, arguments must include reasons, also called premises, and a conclusion.  This includes arguments we make as well as arguments we choose to accept.

The two types of reasoning we use to propose or come to conclusions are deductive reasoning and inductive reasoning.  We use both of these types of reasoning skills to create, or decide whether or not to accept, arguments.

Inductive reasoning is a form of reasoning we use to come to probable conclusions.  We can use narratives, testimony, personal experience, and a whole host of types of evidence to create and argue for probable conclusions.  In the end, however, they are merely probable, not certain.

Deductive reasoning, on the other hand,  is a form of reasoning we use to prove certain conclusions.
Before we can propose or come to certain conclusions, however, we must first test the soundness of a deductive argument.

Deductive Reasoning: Testing the Soundness of Arguments

In deductive reasoning, the “thinker” has two tasks to perform before accepting the certain conclusion of an argument: the test of truth, and the test of validity.  When an argument passes both tests, the argument is said to be sound.  If an argument fails one or both tests, the argument is said to be unsound.

The Test of Truth

When we test the truth of premises for a given conclusion, we ask ourselves if each statement asserts a reality.  We have to find or provide evidence of that reality, check to be sure the evidence itself has been gathered or tested in an ethical and logical manner, and ensure the evidence is reliable, relevant, accurate, and timely.  The test of truth is a matter of fact and meaning.

When we test premises for truth, or an assertion of reality, we must carefully consider the language and the semantic meaning of each premise.  We must consider denotative and connotative meanings of words, the clarity and specificity of words and phrases, or vagueness and ambiguity caused by improper grammar, mechanics, and usage. If we cannot understand the premises, or separate one premise from the next, we cannot test the truthfulness of those premises.

For example, I could make the argument that

Major Premise: All apples are good for me.
Minor Premise: All apple juice is made from apples.
Conclusion: Therefore, all apple juice is good for me.

In order to test the truthfulness of these statements, I must find and evaluate source content from experts that prove the true or false nature of each of the two premises, the first being called the "major premise," and the second being called the "minor premise." There is a lot of evidence to support the first statement, and there is no reason not to believe that all apples are good for me.  However, there is conflicting evidence about the minor premise, about all apple juice being made from apples.  In fact, according to several studies, there are many other man-made ingredients and artificial sweeteners found in several brands of apple juice that make it deceivingly "not" good for me.

So, although the first premise is true, the second premise is false, which means this argument fails the test of soundness, and we cannot accept the conclusion.  Does that mean we toss our argument?  In some cases, perhaps. However, in this case I can add specificity and clarity to my minor premise to make it a true statement.  I can make the argument that my homemade apple juice is good for me.

Take a look at the change:

Major Premise: Apples are good for me.
Minor Premise: My homemade apple juice is made only from apples.
Conclusion: Therefore, my homemade apple juice is good for me.

I have now proposed my conclusion based on two true premises.  If I wanted to be even more specific, I could define "good for me," using clearer language; however, for this example I will accept the colloquial understanding of "good for me."

The Test of Validity

After testing whether or not each premise within an argument asserts a reality, I can label each premise as either false or true to reality.  True or false premises, labeled “T” or “F,” can be placed in a truth table to test the validity of the argument, or the semantic meaning can be determined by rewriting the argument in the form of a valid syllogism.  Testing the validity of a premise is a matter of form.

Because this argument is stated as a syllogism, with two premises and a conclusion, I will test the validity of this particular argument by comparing its form to known valid forms of syllogisms.

Syllogisms

In order to test the validity of a syllogism, a "thinker" must compare the form of an argument to known valid forms of syllogisms.  There are 24 valid forms of syllogisms, and in order to be valid, the argument must match one of those 24 valid forms.  Labeling each piece of an argument by letter allows for closer examination of its form.

The three parts of my example argument's premises are

A. Apples, the subject of the major premise.
B. good for me, the predicate adjective of the major premise.
C. homemade apple juice, the subject of the minor premise.

That makes the form of the given syllogism

A. All apples B. are good for me.

C. My homemade apple juice A. is made only from apples.

C. My homemade apple juice B. is good for me.

When I compare my argument to the known valid forms of syllogisms, I can see that this is a valid form of a categorical syllogism, and my argument passes the test of validity.

My argument has passed both the test of truth and the test of validity, and I can therefore call it "sound."

Conclusion: If A, then B.  A.  Therefore, B.

If an argument's premises are true and stated in the proper form, then the argument is sound.

My argument's premises are true and stated in the proper form.

Therefore, _____________ .

Can you fill in the blank?

In conclusion, before making or accepting the certain truth of a deductive argument, a critical thinker must test the argument for the truth of its premises, and a critical thinker must test the argument for the validity of its form.  Only after the argument passes both of these tests can it be considered a sound argument.

Want to read more about critical thinking and argument?  Try

Paranormal Reality Television: A Lesson in Critical Thinking
Contemplative Education and the Cultivation of Diversity Skills
Introducing the Syllogism by Example, Example, Example
Monty PyTHon THursday: Diagramming Syllogisms

Copyright Amy Lynn Hess.  Please contact the author for permission to republish.