CAREFUL ARGUMENT ANALYSIS: Determining the Logical Structure of an Argument

 CLARIFICATION OF LOGICAL STRUCTURE

In addition to clarifying an argument by clarifying the explicit statements in the argument and by making unstated premises and unstated conclusions explicit, there is a third very important kind of clarification involved in careful argument analysis: determining and displaying the logical structure of the argument.

We have previously mentioned two useful tools for displaying the logical structure of an argument: (a) putting an argument into standard form, and (b) showing the logical structure of an argument in an argument diagram.  In order to be able to show the logical structure of an argument in either of those ways, one must be able to determine when one statement is being given as a reason or premise in support of another statement.  This post will provide some tips and hints about how to do this.

HOW TO DETERMINE LOGICAL STRUCTURE

The primary way to determine the logical structure of an argument is to use your own understanding of an argumentative text or speech.  Which statements are being given as reasons for other statements?  Which statement(s) are being given as the conclusion(s) of the argument?  Your experiences of reading and listening to arguments gives you some ability to answers these questions.

Here are some tips for determining and showing the logical structure of an argument:

1. IDENTIFY INFERENCE INDICATORS

Argumentative passages often include words that indicate that an inference is being made.  Some words are commonly used to indicate an inference:

X thus Y

X therefore Y

X so Y

X implies Y

Y because X

Y since X

The use of such words can help you determine which statements are reasons or premises, and which statements are conclusions.  Keep an eye out for these words when you analyze an argumentative passage in a text or speech.

2. IDENTIFY LOGICAL CONNECTIVES

Statements are often composed of two or more claims that are connected by a term or phrase indicating a logical relationship between those claims.  These words or phrases words indicate the logical structure contained within a statement:

IF P, THEN Q.

EITHER P OR Q.

BOTH P AND Q.

P IF AND ONLY IF Q.

The use of such logical connectives indicates that the reasoning in that argument or sub-argument involves propositional logic. 

3. IDENTIFY QUANTIFIERS

Similarly, the use of some quantifier terms in a statement indicates that the reasoning in the argument or sub-argument involves categorical logic:

ALL As ARE Bs.

NEARLY ALL As ARE Bs.

MOST As ARE Bs.

SOME As ARE Bs.

ALMOST NO As ARE Bs.

NO As ARE Bs.

More precise quantification often uses percentage:

X % OF As ARE Bs.

4. IDENTIFY COMMON LOGICAL FORMS

If you become familiar with some common forms of VALID logical inference, then you can more easily determine the logical structure of an argument:

5. DETERMINE WHEN PREMISES WORK TOGETHER

 The above valid argument forms that have two premises and a conclusion are examples of the kind of arguments where the premises work together to establish the conclusion.

For example, consider the following modus ponens argument:

1. IF Socrates is a human, THEN Socrates is mortal.

2. Socrates is a human.

THEREFORE:

3. Socrates is mortal.

Both premise (1) and premise (2) must be true in order for this argument to establish the conclusion.  If premise (1) were false, then this argument would fail even if premise (2) was true, because on this scenario Socrates being human would NOT imply that he was mortal.

Also, if premise (2) were false, then this argument would fail even if premise (1) was true, because on this scenario, premise (1) would not be relevant to Socrates.

Therefore, the above argument does not work unless both premises of the argument are true.  The premises must work together in order to establish the conclusion. That is how all valid deductive arguments (with more than one premise) work. 

 6. DETERMINE WHEN PREMISES ARE INDEPENDENT REASONS

Some non-deductive arguments provide a good or strong reason in support of the conclusion but the premises provide independent reasons for the conclusion.

1. It was sunny and did not rain on Monday.

2. It was sunny and did not rain on Tuesday.

3. It was sunny and did not rain on Wednesday.

4. It was sunny and did not rain on Thursday.

5. It was sunny and did not rain on Friday.

6. It was sunny and did not rain on Saturday. 

 THEREFORE:

7. It will be sunny and will not rain on Sunday.

This non-deductive argument gives us a good reason to believe the conclusion (7). However, it is not necessary that all six premises be true in order for this argument to give us a good reason to believe (7).

If we only knew that premises (2), (3), (4), (5), and (6) were true, and did not know whether premise (1) was true, that would still give us a good reason to believe the conclusion.

If we only knew that premises (1), (2), (3), (4), and (5) were true, and did not know whether premise (6) was true, that would still give us a good reason to believe the conclusion.

Each of the premises in the above argument provides an independent reason for the conclusion, so it is not necessary for all of the premises to be true for the argument to work. If we know that at least four or five of the premises are true, that would give us a good reason to believe the conclusion.