Taxonomy of Arguments
Arguments attempt to
provide good reasons why we should believe a particular claim. This claim is
the conclusion of the argument, and the reasons intended to support it are the
premises. ‘Inference’ and ‘reasoning’ are synonyms for ‘argument’.
A. Categorical Logic – The basic unit of these arguments is the category, which takes the form of a noun with qualifiers (e.g., dogs, used books, overseas vacations). Categories are related to one another 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
B. Propositional Logic – The basic unit of these arguments is the proposition or statement rather than categories; statements are modified or joined together with various logical operators, such as disjunction (‘or’) and the conditional (‘if … then …’).
Tests for Validity: Truth Tables, Natural Deduction
Examples: Modus Tollens (Valid) (Argument Form)
1. If I drop the glass then it will break. 1. If A then B
2. The glass didn’t break. 2. Not B
3. Therefore, I must not have dropped it. 3. Therefore, not A
Denying the Antecedent (Invalid) (Argument Form)
1. If I graduated then I passed Composition. 1. If A then B
2. I didn’t graduate. 2. Not A
3. Therefore, I didn’t pass Composition. 3. Therefore, not B
II. Inductive – Arguments that intend to provide probable support for the conclusion – i.e., to demonstrate that the conclusion has a greater than 50% likelihood of being true. Inductive arguments never prove the truth of the conclusion with certainty because the inference depends on empirical knowledge which may be fallible or incomplete. As a result, doubt can never be completely eliminated. The degrees of possible support span the continuum from zero to 99.9% probability. In contrast to deductive arguments, they are additive, i.e., it is always possible to further strengthen or weaken the argument through the discovery of additional evidence.
A. Inductive Generalization – 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
2.
Therefore, 73% of all
1. Most salespeople I have met are not trustworthy.
2. Therefore, the majority of salespeople are not trustworthy.
B. Argument from Analogy – This argument compares two things, and infers that because the first thing shares one or more features in common with the second thing, 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 – Consistency, the amount of confirming evidence, testability, fruitfulness, scope, simplicity, and conservatism.
Examples: 1. The loss of my application was either caused by a clerical oversight or by a massive conspiracy to ruin my life.
2. The first explanation – a clerical error – is simpler.
3. Therefore, the first explanation is the best explanation.
1. Crop circles are either caused by extraterrestrials or by pranksters.
2. The second explanation – pranksters – is easier to test and more conservative.
3. Therefore, the second explanation is the best explanation.
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. Causal arguments often use the process of elimination to identify the cause.
Criteria for Strength – The revised version of Mill’s Methods, avoiding 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 took the pill my headache went away.
2. Therefore, the pill cured my headache.
III. Informal Fallacies – Faulty arguments that provide no support or insufficient support for the conclusion, due to the type of reason given rather than the form of the argument. Informal fallacies are deceptive because they appear to be good arguments. They gain this appearance through sleight of hand, by exploiting our psychological insecurities, or by appealing to our emotions.
Examples: Appeal to Unjustified Authority
1. Jane Doe, the Nobel prize winner in chemistry, claims that our economic policies will eventually bankrupt the country.
2. Therefore, our economic policies will eventually bankrupt the country.
Equivocation
1.
Really exciting
novels are rare.
2. But rare books are
expensive.
3. Therefore, really
exciting novels are expensive.