Taxonomy of Arguments

 

 

I. Deductive – Arguments that intend to provide necessary or indubitable support for the conclusion. They either provide the highest level of support or none at all (all or nothing).

 

A. Propositional Logic – The basic unit of these arguments is the proposition or statement, which are joined together with various logical operators or connectives, such as disjunction (‘or’) and the conditional (‘if … then …’).

 

Tests for Validity: Truth Tables, Natural Deduction

 

Examples:        Modus Tollens (Valid)                          Denying the Antecedent (Invalid)

1. If A then B                                                   1. If A then B

2. Not B                                                           2. Not A

3. Therefore, not A                                           3. Therefore, not B

 

B. Categorical Logic – The basic unit of these arguments is the category (e.g., dogs, books, vacations), which takes the form of a noun with qualifiers rather than a statement. Categories are connected together in categorical statements (e.g., ‘All dogs are mammals’).

 

Tests for Validity: Venn Diagrams, Rules for Categorical Syllogisms

 

Examples:       EIO-2 (Valid)                                                   (Argument Form)

                        1. No dogs are reptiles.                                    1. No P are M

                        2. Some animals are reptiles.                             2. Some S are M

                        3. Therefore, some animals are not dogs.           3. Therefore, some S are not P                        

                        AII-4 (Invalid)                                                  (Argument Form)

                        1. All dogs are mammals.                                  1. All P are M

                        2. Some mammals are birds.                             2. Some M are S

                        3. Therefore, some birds are dogs.                    3. Therefore, some S are P

 

 

II. Inductive – Arguments that intend to provide probable support for the conclusion. Since inductive arguments never prove the truth of the conclusion with certainty, doubt can never completely be eliminated. The degrees of possible support span the continuum from zero to 99.9% probability. These arguments are additive, i.e., it is always possible to further strengthen or weaken the argument through the discovery of additional evidence.

 

A. Inductive Generalization or Enumerative Induction – Argues from an observation about some members of a group (the sample) to a generalization about the entire group (the population).

 

Criteria for Strength – 1. How closely the sample represents the population; 2. The size of the sample.

 

Examples:        1. 73% of 1000 U.S. residents polled support increased spending on education.

                        2. Therefore, 73% of all U.S. residents support increased spending on education.

 

                        1. Most salespeople I have met are not trustworthy.

                        2. Therefore, the majority of salespeople are not trustworthy.

 

B. Argument from Analogy or Analogical Induction – This argument compares two things, and infers that because the second thing shares one or more features in common with the first thing that it is probably similar in some further respect.

 

Criteria for Strength – The greater the degree of similarity between the two things being compared, the more probable the conclusion is. This can be determined by examining their relevant similarities and differences.

 

Examples:        Strong Analogy

                        1. Me and Jane are both human beings.

                        2. Aspirin is a safe and effective pain medication for me.

                        3. Therefore, aspirin is a safe and effective pain medication for Jane.

 

                        Weak Analogy

                        1. Me and Fido are both mammals.

                        2. Aspirin is a safe and effective pain medication for me.

                        3. Therefore, aspirin is a safe and effective pain medication for Fido.

 

C. Inference to the Best Explanation – This type of argument attempts to identify the best explanation of a particular phenomenon by comparing the virtues and vices of all the available explanations. The Scientific Method is a version of this argument.

 

Criteria for Strength – The Criteria of Adequacy

 

Examples:        Strong

                        1. Bill was seen at the scene of the crime.

2. All of the other possible suspects have solid alibis.

                        3. Therefore, the best explanation is that Bill committed the crime.

 

                        Weak

                        1. Bill was seen at the scene of the crime.

                        2. We haven’t considered who the other possible suspects might be.

                        3. I have a hunch that Bill was the perpetrator.

                        4. Therefore, the best explanation is that Bill committed the crime.

 

D. Causal Arguments – Any inductive argument whose conclusion consists in a causal claim (e.g., “The accident was caused by icy roads”). These can include any of the other types of inductive arguments.

 

Tests for Strength – The revised version of Mill’s Methods, Causal Confusions

 

Examples:        Strong

                        1. My phone goes dead quite frequently.

2. It happens whenever I pull on the cord, and there is no other relevant factor that is common to all of these cases.

                        3. Therefore, a short in the cord is the cause of my phone going dead.

 

                        Weak

                        1. An hour after I drank the herbal elixir my headache went away.

                        2. Therefore, the herbal elixir cured my headache.